CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Glass transition - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"c683645e-fd69-4378-b521-a08841f0b6dd","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Glass_transition","wgTitle":"Glass transition","wgCurRevisionId":1248575637,"wgRevisionId":1248575637,"wgArticleId":22122416,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 German-language sources (de)","Webarchive template wayback links","Articles with short description","Short description matches Wikidata","All articles with vague or ambiguous time","Vague or ambiguous time from October 2020","Wikipedia articles needing clarification from June 2016","Articles needing additional references from July 2009","All articles needing additional references","All articles with unsourced statements", "Articles with unsourced statements from September 2010","All accuracy disputes","Articles with disputed statements from July 2019","Commons category link is on Wikidata","Cryobiology","Glass engineering and science","Glass physics","Phase transitions","Polymer chemistry","Rubber properties","Threshold temperatures"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Glass_transition","wgRelevantArticleId":22122416,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true}, "wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":60000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q825643","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.tablesorter.styles":"ready","jquery.makeCollapsible.styles" :"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.tablesorter","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cjquery.tablesorter.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/1200px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="753"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/800px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="502"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/640px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="401"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Glass transition - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Glass_transition"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Glass_transition&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Glass_transition"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Glass_transition rootpage-Glass_transition skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Main menu </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z">Main page</a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia">Contents</a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events">Current events</a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x">Random article</a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works">About Wikipedia</a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia">Contact us</a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia">Help</a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia">Learn to edit</a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors">Community portal</a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r">Recent changes</a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia">Upload file</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"> Search </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Appearance </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class="">Donate</a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Glass+transition" title="You are encouraged to create an account and log in; however, it is not mandatory" class="">Create account</a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Glass+transition" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class="">Log in</a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Personal tools </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en">Donate</a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Glass+transition" title="You are encouraged to create an account and log in; however, it is not mandatory"> Create account</a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Glass+transition" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"> Log in</a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing">learn more</a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y">Contributions</a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n">Talk</a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Characteristics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristics"> <div class="vector-toc-text"> 1 Characteristics </div> </a> <ul id="toc-Characteristics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formal_definitions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formal_definitions"> <div class="vector-toc-text"> 2 Formal definitions </div> </a> <ul id="toc-Formal_definitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transition_temperature_Tg" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Transition_temperature_Tg"> <div class="vector-toc-text"> 3 Transition temperature Tg </div> </a> <button aria-controls="toc-Transition_temperature_Tg-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Transition temperature Tg subsection </button> <ul id="toc-Transition_temperature_Tg-sublist" class="vector-toc-list"> <li id="toc-Polymers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polymers"> <div class="vector-toc-text"> 3.1 Polymers </div> </a> <ul id="toc-Polymers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Silicates_and_other_covalent_network_glasses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Silicates_and_other_covalent_network_glasses"> <div class="vector-toc-text"> 3.2 Silicates and other covalent network glasses </div> </a> <ul id="toc-Silicates_and_other_covalent_network_glasses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Linear_heat_capacity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Linear_heat_capacity"> <div class="vector-toc-text"> 4 Linear heat capacity </div> </a> <button aria-controls="toc-Linear_heat_capacity-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Linear heat capacity subsection </button> <ul id="toc-Linear_heat_capacity-sublist" class="vector-toc-list"> <li id="toc-Experimental_data" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Experimental_data"> <div class="vector-toc-text"> 4.1 Experimental data </div> </a> <ul id="toc-Experimental_data-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kauzmann's_paradox" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kauzmann's_paradox"> <div class="vector-toc-text"> 5 Kauzmann's paradox </div> </a> <button aria-controls="toc-Kauzmann's_paradox-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Kauzmann's paradox subsection </button> <ul id="toc-Kauzmann's_paradox-sublist" class="vector-toc-list"> <li id="toc-Possible_resolutions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Possible_resolutions"> <div class="vector-toc-text"> 5.1 Possible resolutions </div> </a> <ul id="toc-Possible_resolutions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_specific_materials" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_specific_materials"> <div class="vector-toc-text"> 6 In specific materials </div> </a> <button aria-controls="toc-In_specific_materials-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle In specific materials subsection </button> <ul id="toc-In_specific_materials-sublist" class="vector-toc-list"> <li id="toc-Silica,_SiO2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Silica,_SiO2"> <div class="vector-toc-text"> 6.1 Silica, SiO2 </div> </a> <ul id="toc-Silica,_SiO2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polymers_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polymers_2"> <div class="vector-toc-text"> 6.2 Polymers </div> </a> <ul id="toc-Polymers_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mechanics_of_vitrification" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mechanics_of_vitrification"> <div class="vector-toc-text"> 7 Mechanics of vitrification </div> </a> <button aria-controls="toc-Mechanics_of_vitrification-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Mechanics of vitrification subsection </button> <ul id="toc-Mechanics_of_vitrification-sublist" class="vector-toc-list"> <li id="toc-Electronic_structure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electronic_structure"> <div class="vector-toc-text"> 7.1 Electronic structure </div> </a> <ul id="toc-Electronic_structure-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 8 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 9 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 10 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Glass transition</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 24 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-24" aria-hidden="true" > 24 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%B1%D8%AC%D8%A9_%D8%AD%D8%B1%D8%A7%D8%B1%D8%A9_%D8%A7%D9%84%D8%AA%D8%AD%D9%88%D9%84_%D8%A7%D9%84%D8%B2%D8%AC%D8%A7%D8%AC%D9%8A" title="درجة حرارة التحول الزجاجي – Arabic" lang="ar" hreflang="ar" data-title="درجة حرارة التحول الزجاجي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A6%BE%E0%A6%9A%E0%A7%80%E0%A6%AD%E0%A7%82%E0%A6%A4%E0%A6%95%E0%A6%B0%E0%A6%A3" title="কাচীভূতকরণ – Bangla" lang="bn" hreflang="bn" data-title="কাচীভূতকরণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Po-l%C3%AA_cho%C3%A1n-ho%C3%A0_un-t%C5%8D%CD%98" title="Po-lê choán-hoà un-tō͘ – Minnan" lang="nan" hreflang="nan" data-title="Po-lê choán-hoà un-tō͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Glas%C3%BCbergang" title="Glasübergang – German" lang="de" hreflang="de" data-title="Glasübergang" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CE%B1%CE%BB%CF%8E%CE%B4%CE%B7%CF%82_%CE%BC%CE%B5%CF%84%CE%AC%CF%80%CF%84%CF%89%CF%83%CE%B7" title="Υαλώδης μετάπτωση – Greek" lang="el" hreflang="el" data-title="Υαλώδης μετάπτωση" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Transici%C3%B3n_V%C3%ADtrea" title="Transición Vítrea – Spanish" lang="es" hreflang="es" data-title="Transición Vítrea" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%85%D8%A7%DB%8C_%D8%A7%D9%86%D8%AA%D9%82%D8%A7%D9%84_%D8%B4%DB%8C%D8%B4%D9%87" title="دمای انتقال شیشه – Persian" lang="fa" hreflang="fa" data-title="دمای انتقال شیشه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Transition_vitreuse" title="Transition vitreuse – French" lang="fr" hreflang="fr" data-title="Transition vitreuse" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A0%EB%A6%AC_%EC%A0%84%EC%9D%B4" title="유리 전이 – Korean" lang="ko" hreflang="ko" data-title="유리 전이" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A4%BE%E0%A4%9A_%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3" title="काच संक्रमण – Hindi" lang="hi" hreflang="hi" data-title="काच संक्रमण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%9E%D7%A4%D7%A8%D7%98%D7%95%D7%A8%D7%AA_%D7%9E%D7%A2%D7%91%D7%A8_%D7%96%D7%9B%D7%95%D7%9B%D7%99%D7%AA%D7%99" title="טמפרטורת מעבר זכוכיתי – Hebrew" lang="he" hreflang="he" data-title="טמפרטורת מעבר זכוכיתי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%8D%E0%B4%B2%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%B8%E0%B5%8D_%E0%B4%9F%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B5%BB%E0%B4%B8%E0%B5%80%E0%B4%B7%E0%B5%BB" title="ഗ്ലാസ്സ് ട്രാൻസീഷൻ – Malayalam" lang="ml" hreflang="ml" data-title="ഗ്ലാസ്സ് ട്രാൻസീഷൻ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Glasovergang" title="Glasovergang – Dutch" lang="nl" hreflang="nl" data-title="Glasovergang" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AC%E3%83%A9%E3%82%B9%E8%BB%A2%E7%A7%BB%E7%82%B9" title="ガラス転移点 – Japanese" lang="ja" hreflang="ja" data-title="ガラス転移点" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Transi%C3%A7%C3%A3o_v%C3%ADtrea" title="Transição vítrea – Portuguese" lang="pt" hreflang="pt" data-title="Transição vítrea" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B8%D1%82%D1%80%D0%B8%D1%84%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%8F" title="Витрификация – Russian" lang="ru" hreflang="ru" data-title="Витрификация" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Glass_transition" title="Glass transition – Simple English" lang="en-simple" hreflang="en-simple" data-title="Glass transition" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%86%DA%95%D8%A7%D9%86%DB%8C_%D8%B4%D9%88%D8%B4%DB%95%DB%8C%DB%8C" title="گۆڕانی شوشەیی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="گۆڕانی شوشەیی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Lasisiirtym%C3%A4" title="Lasisiirtymä – Finnish" lang="fi" hreflang="fi" data-title="Lasisiirtymä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Cams%C4%B1_ge%C3%A7i%C5%9F_s%C4%B1cakl%C4%B1%C4%9F%C4%B1" title="Camsı geçiş sıcaklığı – Turkish" lang="tr" hreflang="tr" data-title="Camsı geçiş sıcaklığı" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D1%82%D1%80%D0%B8%D1%84%D1%96%D0%BA%D0%B0%D1%86%D1%96%D1%8F" title="Вітрифікація – Ukrainian" lang="uk" hreflang="uk" data-title="Вітрифікація" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%83m_chuy%E1%BB%83n_d%E1%BB%8Bch_l%E1%BB%8Fng-r%E1%BA%AFn" title="Điểm chuyển dịch lỏng-rắn – Vietnamese" lang="vi" hreflang="vi" data-title="Điểm chuyển dịch lỏng-rắn" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%8E%BB%E7%92%83%E8%BD%89%E5%8C%96" title="玻璃轉化 – Cantonese" lang="yue" hreflang="yue" data-title="玻璃轉化" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%8E%BB%E7%92%83%E8%BD%AC%E5%8C%96" title="玻璃转化 – Chinese" lang="zh" hreflang="zh" data-title="玻璃转化" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q825643#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Glass_transition" title="View the content page [c]" accesskey="c">Article</a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Glass_transition" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t">Talk</a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" >English </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Glass_transition">Read</a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Glass_transition&action=edit" title="Edit this page [e]" accesskey="e">Edit</a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Glass_transition&action=history" title="Past revisions of this page [h]" accesskey="h">View history</a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" >Tools </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Glass_transition">Read</a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Glass_transition&action=edit" title="Edit this page [e]" accesskey="e">Edit</a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Glass_transition&action=history">View history</a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Glass_transition" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j">What links here</a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Glass_transition" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k">Related changes</a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u">Upload file</a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q">Special pages</a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Glass_transition&oldid=1248575637" title="Permanent link to this revision of this page">Permanent link</a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Glass_transition&action=info" title="More information about this page">Page information</a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Glass_transition&id=1248575637&wpFormIdentifier=titleform" title="Information on how to cite this page">Cite this page</a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FGlass_transition">Get shortened URL</a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FGlass_transition">Download QR code</a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Glass_transition&action=show-download-screen" title="Download this page as a PDF file">Download as PDF</a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Glass_transition&printable=yes" title="Printable version of this page [p]" accesskey="p">Printable version</a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Glass-liquid_transitions" hreflang="en">Wikimedia Commons</a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q825643" title="Structured data on this page hosted by Wikidata [g]" accesskey="g">Wikidata item</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Two-dimensional_schematic_diagram_of_quartz,_silica,_and_silica-based_glass.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/220px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/330px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png/440px-Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png 2x" data-file-width="2143" data-file-height="1344" /></a><figcaption>Two-dimensional, schematic, representation of the lattices of quartz (a), silica (b), and of silica based glasses (c).<a href="#cite_note-1">[1]</a></figcaption></figure> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Reversible transition in amorphous materials</div> The glass–liquid transition, or glass transition, is the gradual and <a href="/wiki/Reversible_reaction" title="Reversible reaction">reversible</a> transition in <a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous</a> materials (or in amorphous regions within <a href="/wiki/Crystallinity" title="Crystallinity">semicrystalline</a> materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased.<a href="#cite_note-iso11357-2-2">[2]</a> An amorphous solid that exhibits a glass transition is called a <a href="/wiki/Glass" title="Glass">glass</a>. The reverse transition, achieved by <a href="/wiki/Supercooling" title="Supercooling">supercooling</a> a <a href="/wiki/Viscous_liquid" title="Viscous liquid">viscous liquid</a> into the glass state, is called <a href="/wiki/Vitrification" title="Vitrification">vitrification</a>. The glass-transition temperature Tg of a material characterizes the range of temperatures over which this glass transition occurs (as an experimental definition, typically marked as 100 s of relaxation time). It is always lower than the <a href="/wiki/Melting_point" title="Melting point">melting temperature</a>, Tm, of the crystalline state of the material, if one exists, because the glass is a higher energy state (or enthalpy at constant pressure) than the corresponding crystal. Hard plastics like <a href="/wiki/Polystyrene" title="Polystyrene">polystyrene</a> and <a href="/wiki/Poly(methyl_methacrylate)" title="Poly(methyl methacrylate)">poly(methyl methacrylate)</a> are used well below their glass transition temperatures, i.e., when they are in their glassy state. Their Tg values are both at around 100 °C (212 °F). Rubber <a href="/wiki/Elastomer" title="Elastomer">elastomers</a> like <a href="/wiki/Synthetic_rubber" title="Synthetic rubber">polyisoprene</a> and <a href="/wiki/Butyl_rubber" title="Butyl rubber">polyisobutylene</a> are used above their Tg, that is, in the rubbery state, where they are soft and flexible; <a href="/wiki/Cross-link" title="Cross-link">crosslinking</a> prevents free flow of their molecules, thus endowing rubber with a set shape at room temperature (as opposed to a viscous liquid).<a href="#cite_note-3">[3]</a> Despite the change in the physical properties of a material through its glass transition, the transition is not considered a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a>; rather it is a phenomenon extending over a range of temperature and defined by one of several conventions.<a href="#cite_note-Debenedetti-4">[4]</a><a href="#cite_note-Angell-5">[5]</a> Such conventions include a constant cooling rate (20 kelvins per minute (36 °F/min))<a href="#cite_note-iso11357-2-2">[2]</a> and a viscosity threshold of 1012 <a href="/wiki/Pa%C2%B7s" class="mw-redirect" title="Pa·s">Pa·s</a>, among others. Upon cooling or heating through this glass-transition range, the material also exhibits a smooth step in the <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal-expansion coefficient</a> and in the <a href="/wiki/Specific_heat" class="mw-redirect" title="Specific heat">specific heat</a>, with the location of these effects again being dependent on the history of the material.<a href="#cite_note-z1-6">[6]</a> The question of whether some phase transition underlies the glass transition is a matter of ongoing research.<a href="#cite_note-Debenedetti-4">[4]</a><a href="#cite_note-Angell-5">[5]</a><a href="#cite_note-7">[7]</a>[<a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers">when?</a>] <style data-mw-deduplicate="TemplateStyles:r1224211176">.mw-parser-output .quotebox{background-color:#F9F9F9;border:1px solid #aaa;box-sizing:border-box;padding:10px;font-size:88%;max-width:100%}.mw-parser-output .quotebox.floatleft{margin:.5em 1.4em .8em 0}.mw-parser-output .quotebox.floatright{margin:.5em 0 .8em 1.4em}.mw-parser-output .quotebox.centered{overflow:hidden;position:relative;margin:.5em auto .8em auto}.mw-parser-output .quotebox.floatleft span,.mw-parser-output .quotebox.floatright span{font-style:inherit}.mw-parser-output .quotebox>blockquote{margin:0;padding:0;border-left:0;font-family:inherit;font-size:inherit}.mw-parser-output .quotebox-title{text-align:center;font-size:110%;font-weight:bold}.mw-parser-output .quotebox-quote>:first-child{margin-top:0}.mw-parser-output .quotebox-quote:last-child>:last-child{margin-bottom:0}.mw-parser-output .quotebox-quote.quoted:before{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" “ ";vertical-align:-45%;line-height:0}.mw-parser-output .quotebox-quote.quoted:after{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" ” ";line-height:0}.mw-parser-output .quotebox .left-aligned{text-align:left}.mw-parser-output .quotebox .right-aligned{text-align:right}.mw-parser-output .quotebox .center-aligned{text-align:center}.mw-parser-output .quotebox .quote-title,.mw-parser-output .quotebox .quotebox-quote{display:block}.mw-parser-output .quotebox cite{display:block;font-style:normal}@media screen and (max-width:640px){.mw-parser-output .quotebox{width:100%!important;margin:0 0 .8em!important;float:none!important}}</style><div class="quotebox pullquote floatright" style="width:30%; ;"> <div class="quotebox-title" style=""><a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a> definition</div> <blockquote class="quotebox-quote left-aligned" style=""> Glass transition (in polymer science): process in which a polymer melt changes on cooling to a polymer glass or a polymer glass changes on heating to a polymer melt.<a href="#cite_note-Stefano_et_al_2011-8">[8]</a> <ol><li>Phenomena occurring at the glass transition of polymers are still subject to ongoing scientific investigation and debate. The glass transition presents features of a second-order transition since thermal studies often indicate that the molar Gibbs energies, molar enthalpies, and the molar volumes of the two phases, i.e., the melt and the glass, are equal, while the heat capacity and the expansivity are discontinuous. However, the glass transition is generally not regarded as a thermodynamic transition in view of the inherent difficulty in reaching equilibrium in a polymer glass or in a polymer melt at temperatures close to the glass-transition temperature.</li> <li>In the case of polymers, conformational changes of segments, typically consisting of 10–20 main-chain atoms, become infinitely slow below the glass transition temperature.</li> <li>In a partially crystalline polymer the glass transition occurs only in the amorphous parts of the material.</li> <li>The definition is different from that in ref.<a href="#cite_note-9">[9]</a></li> <li>The commonly used term “glass-rubber transition” for glass transition is not recommended.<a href="#cite_note-Stefano_et_al_2011-8">[8]</a></li></ol> </blockquote> </div> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=1" title="Edit section: Characteristics">edit</a>]</div> The glass transition of a liquid to a solid-like state may occur with either cooling or compression.<a href="#cite_note-Hansen&McDonald-10">[10]</a> The transition comprises a smooth increase in the viscosity of a material by as much as 17 <a href="/wiki/Order_of_magnitude" title="Order of magnitude">orders of magnitude</a> within a temperature range of 500 K without any pronounced change in material structure.<a href="#cite_note-11">[11]</a> This transition is in contrast to the <a href="/wiki/Freezing" title="Freezing">freezing</a> or <a href="/wiki/Crystallization" title="Crystallization">crystallization</a> transition, which is a first-order <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> in the <a href="/wiki/Phase_transition#Ehrenfest_classification" title="Phase transition">Ehrenfest classification</a> and involves discontinuities in thermodynamic and dynamic properties such as volume, energy, and viscosity. In many materials that normally undergo a freezing transition, rapid cooling will avoid this phase transition and instead result in a glass transition at some lower temperature. Other materials, such as many <a href="/wiki/Polymers" class="mw-redirect" title="Polymers">polymers</a>, lack a well defined crystalline state and easily form glasses, even upon very slow cooling or compression. The tendency for a material to form a glass while quenched is called glass forming ability. This ability depends on the composition of the material and can be predicted by the <a href="/wiki/Rigidity_theory_(physics)" title="Rigidity theory (physics)">rigidity theory</a>.<a href="#cite_note-phillips1979-12">[12]</a> Below the transition temperature range, the glassy structure does not relax in accordance with the cooling rate used. The expansion coefficient for the glassy state is roughly equivalent to that of the crystalline solid. If slower cooling rates are used, the increased time for structural <a href="/wiki/Relaxation_(physics)" title="Relaxation (physics)">relaxation</a> (or intermolecular rearrangement) to occur may result in a higher density glass product. Similarly, by <a href="/wiki/Annealing_(glass)" title="Annealing (glass)">annealing</a> (and thus allowing for slow structural relaxation) the glass structure in time approaches an equilibrium density corresponding to the supercooled liquid at this same temperature. Tg is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid.<a href="#cite_note-CM-13">[13]</a><a href="#cite_note-14">[14]</a><a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a><a href="#cite_note-17">[17]</a> The configuration of the glass in this temperature range changes slowly with time towards the equilibrium structure. The principle of the minimization of the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> provides the thermodynamic driving force necessary for the eventual change. At somewhat higher temperatures than Tg, the structure corresponding to equilibrium at any temperature is achieved quite rapidly. In contrast, at considerably lower temperatures, the configuration of the glass remains sensibly stable over increasingly extended periods of time. Thus, the liquid-glass transition is not a transition between states of <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. It is widely believed that the true equilibrium state is always crystalline. Glass is believed to exist in a kinetically locked state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon. Time and temperature are interchangeable quantities (to some extent) when dealing with glasses, a fact often expressed in the <a href="/wiki/Time%E2%80%93temperature_superposition" title="Time–temperature superposition">time–temperature superposition</a> principle. On cooling a liquid, internal degrees of freedom successively fall out of equilibrium. However, there is a longstanding debate whether there is an underlying second-order phase transition in the hypothetical limit of infinitely long relaxation times.[<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>]<a href="#cite_note-z1-6">[6]</a><a href="#cite_note-18">[18]</a><a href="#cite_note-19">[19]</a><a href="#cite_note-20">[20]</a> In a more recent model of glass transition, the glass transition temperature corresponds to the temperature at which the largest openings between the vibrating elements in the liquid matrix become smaller than the smallest cross-sections of the elements or parts of them when the temperature is decreasing. As a result of the fluctuating input of thermal energy into the liquid matrix, the harmonics of the oscillations are constantly disturbed and temporary cavities ("free volume") are created between the elements, the number and size of which depend on the temperature. The glass transition temperature Tg0 defined in this way is a fixed material constant of the disordered (non-crystalline) state that is dependent only on the pressure. As a result of the increasing inertia of the molecular matrix when approaching Tg0, the setting of the thermal equilibrium is successively delayed, so that the usual measuring methods for determining the glass transition temperature in principle deliver Tg values that are too high. In principle, the slower the temperature change rate is set during the measurement, the closer the measured Tg value Tg0 approaches.<a href="#cite_note-21">[21]</a> Techniques such as <a href="/wiki/Dynamic_mechanical_analysis" title="Dynamic mechanical analysis">dynamic mechanical analysis</a> can be used to measure the glass transition temperature.<a href="#cite_note-22">[22]</a> <div class="mw-heading mw-heading2"><h2 id="Formal_definitions">Formal definitions</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=2" title="Edit section: Formal definitions">edit</a>]</div> The definition of the glass and the glass transition are not settled, and many definitions have been proposed over the past century.<a href="#cite_note-:1-23">[23]</a> <a href="/wiki/Francis_Simon" title="Francis Simon">Franz Simon</a>:<a href="#cite_note-24">[24]</a> Glass is a rigid material obtained from freezing-in a supercooled liquid in a narrow temperature range. <a href="/wiki/William_Houlder_Zachariasen" title="William Houlder Zachariasen">Zachariasen</a>:<a href="#cite_note-25">[25]</a> Glass is a topologically disordered network, with short range order equivalent to that in the corresponding crystal.<a href="#cite_note-26">[26]</a> Glass is a "frozen liquid” (i.e., liquids where ergodicity has been broken), which spontaneously relax towards the supercooled liquid state over a long enough time. Glasses are thermodynamically non-equilibrium kinetically stabilized amorphous solids, in which the molecular disorder and the thermodynamic properties corresponding to the state of the respective under-cooled melt at a temperature T* are frozen-in. Hereby T* differs from the actual temperature T.<a href="#cite_note-27">[27]</a> Glass is a nonequilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate is to solidify, i.e., crystallize.<a href="#cite_note-:1-23">[23]</a> <div class="mw-heading mw-heading2"><h2 id="Transition_temperature_Tg">Transition temperature Tg</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=3" title="Edit section: Transition temperature Tg">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></div></td><td class="mbox-text"><div class="mbox-text-span">This section needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a>. Please help <a href="/wiki/Special:EditPage/Glass_transition" title="Special:EditPage/Glass transition">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed. (July 2009) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tgdilatometric.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Tgdilatometric.gif/220px-Tgdilatometric.gif" decoding="async" width="220" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Tgdilatometric.gif/330px-Tgdilatometric.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Tgdilatometric.gif/440px-Tgdilatometric.gif 2x" data-file-width="2569" data-file-height="1752" /></a><figcaption>Determination of Tg by <a href="/wiki/Dilatometer" title="Dilatometer">dilatometry</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tgdscenglish.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Tgdscenglish.svg/220px-Tgdscenglish.svg.png" decoding="async" width="220" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Tgdscenglish.svg/330px-Tgdscenglish.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/Tgdscenglish.svg/440px-Tgdscenglish.svg.png 2x" data-file-width="420" data-file-height="348" /></a><figcaption>Measurement of Tg (the temperature at the point A) by differential scanning calorimetry</figcaption></figure> Refer to the figure on the bottom right plotting the heat capacity as a function of temperature. In this context, Tg is the temperature corresponding to point A on the curve.<a href="#cite_note-tgmeasurement-28">[28]</a> Different operational definitions of the glass transition temperature Tg are in use, and several of them are endorsed as accepted scientific standards. Nevertheless, all definitions are arbitrary, and all yield different numeric results: at best, values of Tg for a given substance agree within a few kelvins. One definition refers to the <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>, fixing Tg at a value of 1013 poise (or 1012 Pa·s). As evidenced experimentally, this value is close to the <a href="/wiki/Annealing_(glass)" title="Annealing (glass)">annealing point</a> of many glasses.<a href="#cite_note-29">[29]</a> In contrast to viscosity, the <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a>, <a href="/wiki/Heat_capacity" title="Heat capacity">heat capacity</a>, shear modulus, and many other properties of inorganic <a href="/wiki/Glass" title="Glass">glasses</a> show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define Tg. To make this definition reproducible, the cooling or heating rate must be specified. The most frequently used definition of Tg uses the energy release on heating in <a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">differential scanning calorimetry</a> (DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed. Yet another definition of Tg uses the kink in <a href="/wiki/Dilatometer" title="Dilatometer">dilatometry</a> (a.k.a. thermal expansion): refer to the figure on the top right. Here, heating rates of 3–5 K/min (5.4–9.0 °F/min) are common. The linear sections below and above Tg are colored green. Tg is the temperature at the intersection of the red regression lines.<a href="#cite_note-tgmeasurement-28">[28]</a> Summarized below are Tg values characteristic of certain classes of materials. <div class="mw-heading mw-heading3"><h3 id="Polymers">Polymers</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=4" title="Edit section: Polymers">edit</a>]</div> <table class="wikitable sortable"> <tbody><tr> <th>Material </th> <th>Tg (°C) </th> <th>Tg (°F) </th> <th>Commercial name </th></tr> <tr> <td><a href="/wiki/Tire" title="Tire">Tire</a> rubber </td> <td style="text-align:right;">−70 </td> <td style="text-align:right;">−94<a href="#cite_note-30">[30]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyvinylidene_fluoride" title="Polyvinylidene fluoride">Polyvinylidene fluoride</a> (PVDF) </td> <td style="text-align:right;">−35 </td> <td style="text-align:right;">−31<a href="#cite_note-Ibeh-31">[31]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polypropylene" title="Polypropylene">Polypropylene</a> (PP atactic) </td> <td style="text-align:right;">−20 </td> <td style="text-align:right;">−4<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyvinyl_fluoride" title="Polyvinyl fluoride">Polyvinyl fluoride</a> (PVF) </td> <td style="text-align:right;">−20 </td> <td style="text-align:right;">−4<a href="#cite_note-Ibeh-31">[31]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polypropylene" title="Polypropylene">Polypropylene</a> (PP isotactic) </td> <td style="text-align:right;">0 </td> <td style="text-align:right;">32<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Poly-3-hydroxybutyrate" class="mw-redirect" title="Poly-3-hydroxybutyrate">Poly-3-hydroxybutyrate</a> (PHB) </td> <td style="text-align:right;">15 </td> <td style="text-align:right;">59<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyvinyl_acetate" title="Polyvinyl acetate">Poly(vinyl acetate)</a> (PVAc) </td> <td style="text-align:right;">30 </td> <td style="text-align:right;">86<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polychlorotrifluoroethylene" title="Polychlorotrifluoroethylene">Polychlorotrifluoroethylene</a> (PCTFE) </td> <td style="text-align:right;">45 </td> <td style="text-align:right;">113<a href="#cite_note-Ibeh-31">[31]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyamide" title="Polyamide">Polyamide</a> (PA) </td> <td style="text-align:right;">47–60 </td> <td style="text-align:right;">117–140 </td> <td>Nylon-6,x </td></tr> <tr> <td><a href="/wiki/Polylactic_acid" title="Polylactic acid">Polylactic acid</a> (PLA) </td> <td style="text-align:right;">60–65 </td> <td style="text-align:right;">140–149 </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyethylene_terephthalate" title="Polyethylene terephthalate">Polyethylene terephthalate</a> (PET) </td> <td style="text-align:right;">70 </td> <td style="text-align:right;">158<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyvinyl_chloride" title="Polyvinyl chloride">Poly(vinyl chloride)</a> (PVC) </td> <td style="text-align:right;">80 </td> <td style="text-align:right;">176<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polyvinyl_alcohol" title="Polyvinyl alcohol">Poly(vinyl alcohol)</a> (PVA) </td> <td style="text-align:right;">85 </td> <td style="text-align:right;">185<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polystyrene" title="Polystyrene">Polystyrene</a> (PS) </td> <td style="text-align:right;">95 </td> <td style="text-align:right;">203<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Poly(methyl_methacrylate)" title="Poly(methyl methacrylate)">Poly(methyl methacrylate)</a> (PMMA atactic) </td> <td style="text-align:right;">105 </td> <td style="text-align:right;">221<a href="#cite_note-PVC-32">[32]</a> </td> <td>Plexiglas, Perspex </td></tr> <tr> <td><a href="/wiki/Acrylonitrile_butadiene_styrene" title="Acrylonitrile butadiene styrene">Acrylonitrile butadiene styrene</a> (ABS) </td> <td style="text-align:right;">105 </td> <td style="text-align:right;">221<a href="#cite_note-ABS-33">[33]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Polytetrafluoroethylene" title="Polytetrafluoroethylene">Polytetrafluoroethylene</a> (PTFE) </td> <td style="text-align:right;">115 </td> <td style="text-align:right;">239<a href="#cite_note-34">[34]</a> </td> <td>Teflon </td></tr> <tr> <td><a href="/wiki/Polycarbonate" title="Polycarbonate">Poly(carbonate)</a> (PC) </td> <td style="text-align:right;">145 </td> <td style="text-align:right;">293<a href="#cite_note-PVC-32">[32]</a> </td> <td>Lexan </td></tr> <tr> <td><a href="/wiki/Polysulfone" title="Polysulfone">Polysulfone</a> </td> <td style="text-align:right;">185 </td> <td style="text-align:right;">365 </td> <td> </td></tr> <tr> <td><a href="/wiki/Polynorbornene" class="mw-redirect" title="Polynorbornene">Polynorbornene</a> </td> <td style="text-align:right;">215 </td> <td style="text-align:right;">419<a href="#cite_note-PVC-32">[32]</a> </td> <td> </td></tr></tbody></table> Dry <a href="/wiki/Nylon" title="Nylon">nylon-6</a> has a glass transition temperature of 47 °C (117 °F).<a href="#cite_note-35">[35]</a> Nylon-6,6 in the dry state has a glass transition temperature of about 70 °C (158 °F).<a href="#cite_note-36">[36]</a><a href="#cite_note-37">[37]</a> Whereas <a href="/wiki/Polyethene" class="mw-redirect" title="Polyethene">polyethene</a> has a glass transition range of −130 to −80 °C (−202 to −112 °F)<a href="#cite_note-38">[38]</a> The above are only mean values, as the glass transition temperature depends on the cooling rate and molecular weight distribution and could be influenced by additives. For a semi-crystalline material, such as <a href="/wiki/Polyethene" class="mw-redirect" title="Polyethene">polyethene</a> that is 60–80% crystalline at room temperature, the quoted glass transition refers to what happens to the amorphous part of the material upon cooling. <div class="mw-heading mw-heading3"><h3 id="Silicates_and_other_covalent_network_glasses">Silicates and other covalent network glasses</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=5" title="Edit section: Silicates and other covalent network glasses">edit</a>]</div> <table class="wikitable sortable"> <tbody><tr> <th>Material </th> <th>Tg (°C) </th> <th>Tg (°F) </th></tr> <tr> <td><a href="/wiki/Chalcogenide" title="Chalcogenide">Chalcogenide</a> GeSbTe </td> <td style="text-align:right;">150 </td> <td style="text-align:right;">302<a href="#cite_note-39">[39]</a> </td></tr> <tr> <td><a href="/wiki/Chalcogenide" title="Chalcogenide">Chalcogenide</a> AsGeSeTe </td> <td style="text-align:right;">245 </td> <td style="text-align:right;">473 </td></tr> <tr> <td><a href="/wiki/ZBLAN" title="ZBLAN">ZBLAN</a> fluoride glass </td> <td style="text-align:right;">235 </td> <td style="text-align:right;">455 </td></tr> <tr> <td><a href="/wiki/Tellurium_dioxide" title="Tellurium dioxide">Tellurium dioxide</a> </td> <td style="text-align:right;">280 </td> <td style="text-align:right;">536 </td></tr> <tr> <td>Fluoroaluminate </td> <td style="text-align:right;">400 </td> <td style="text-align:right;">752 </td></tr> <tr> <td><a href="/wiki/Soda-lime_glass" class="mw-redirect" title="Soda-lime glass">Soda-lime glass</a> </td> <td style="text-align:right;">520–600 </td> <td style="text-align:right;">968–1,112 </td></tr> <tr> <td><a href="/wiki/Fused_quartz" title="Fused quartz">Fused quartz</a> (approximate) </td> <td style="text-align:right;">1,200 </td> <td style="text-align:right;">2,200<a href="#cite_note-40">[40]</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Linear_heat_capacity">Linear heat capacity</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=6" title="Edit section: Linear heat capacity">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Specific_heat_of_several_glassy_solids.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Specific_heat_of_several_glassy_solids.png/220px-Specific_heat_of_several_glassy_solids.png" decoding="async" width="220" height="309" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Specific_heat_of_several_glassy_solids.png/330px-Specific_heat_of_several_glassy_solids.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Specific_heat_of_several_glassy_solids.png/440px-Specific_heat_of_several_glassy_solids.png 2x" data-file-width="1496" data-file-height="2098" /></a><figcaption>Specific heat of several noncrystalline solids, plotted as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (T^{2},c/T)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (T^{2},c/T)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f18627fc67751795348618cbf2a5366ffa7affbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.423ex; height:3.176ex;" alt="{\displaystyle (T^{2},c/T)}"> graph, showing linear dependence component in the low-temperature regime.<a href="#cite_note-:2-41">[41]</a></figcaption></figure> In 1971, Zeller and <a href="/wiki/Robert_Otto_Pohl" title="Robert Otto Pohl">Pohl</a> discovered that <a href="#cite_note-42">[42]</a> when glass is at a very low temperature ~1K, its specific heat has a linear component: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\approx c_{1}T+c_{3}T^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>≈</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>T</mi> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\approx c_{1}T+c_{3}T^{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64083590772dc2c49588709f6a5e77bc0a2fce78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.478ex; height:3.009ex;" alt="{\displaystyle c\approx c_{1}T+c_{3}T^{3}}">. This is an unusual effect, because crystal material typically has <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\propto T^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>∝</mo> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\propto T^{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c761a6c248cea53ecaceb0237d9e375a40868ff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.88ex; height:2.676ex;" alt="{\displaystyle c\propto T^{3}}">, as in the <a href="/wiki/Debye_model" title="Debye model">Debye model</a>. This was explained by the two-level system hypothesis,<a href="#cite_note-43">[43]</a> which states that a glass is populated by two-level systems, which look like a double potential well separated by a wall. The wall is high enough such that resonance tunneling does not occur, but thermal tunneling does occur. Namely, if the two wells have energy difference <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E\sim k_{B}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>∼</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E\sim k_{B}T}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae149ded1431380bde659659f029ba3c4b83fe11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.137ex; height:2.509ex;" alt="{\displaystyle \Delta E\sim k_{B}T}">, then a particle in one well can tunnel to the other well by thermal interaction with the environment. Now, imagine that there are many two-level systems in the glass, and their <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/345f0ed5ff6ec6eddc5f908d379f032c52f119c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.711ex; height:2.176ex;" alt="{\displaystyle \Delta E}"> is randomly distributed but fixed ("quenched disorder"), then as temperature drops, more and more of these two-level levels are frozen out (meaning that it takes such a long time for a tunneling to occur, that they cannot be experimentally observed). Consider a single two-level system that is not frozen-out, whose energy gap is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E=O(1/\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>=</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E=O(1/\beta )}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/475d6f8f56790b63c53df3e3658c3b42923d3eaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.049ex; height:2.843ex;" alt="{\displaystyle \Delta E=O(1/\beta )}">. It is in a Boltzmann distribution, so its average energy <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>β</mi> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mrow> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcfb1e0fe5a09ad841adad321b92a4531817118c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.844ex; height:5.843ex;" alt="{\displaystyle ={\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}}">. Now, assume that the two-level systems are all quenched, so that each <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/345f0ed5ff6ec6eddc5f908d379f032c52f119c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.711ex; height:2.176ex;" alt="{\displaystyle \Delta E}"> varies little with temperature. In that case, we can write <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(\Delta E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(\Delta E)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af877de3f2b5041e7f8c7d73f26e1386422b0412" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.916ex; height:2.843ex;" alt="{\displaystyle n(\Delta E)}"> as the density of states with energy gap <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/345f0ed5ff6ec6eddc5f908d379f032c52f119c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.711ex; height:2.176ex;" alt="{\displaystyle \Delta E}">. We also assume that <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(\Delta E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(\Delta E)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af877de3f2b5041e7f8c7d73f26e1386422b0412" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.916ex; height:2.843ex;" alt="{\displaystyle n(\Delta E)}"> is positive and smooth near <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E\approx 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>≈</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E\approx 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93a758108d847011c2dc63f497fc92a2a7f23df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.972ex; height:2.176ex;" alt="{\displaystyle \Delta E\approx 0}">. Then, the total energy contributed by those two-level systems is<math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {E}}\sim \int _{0}^{O(1/\beta )}{\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}\;n(\Delta E)d\Delta E=\beta ^{-2}\int _{0}^{O(1)}{\frac {a}{e^{a}-1}}n(a/\beta )da\propto \beta ^{-2}n(0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>∼</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>β</mi> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mrow> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> <mi mathvariant="normal">Δ</mi> <mi>E</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mi>n</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi mathvariant="normal">Δ</mi> <mi>E</mi> <mo>=</mo> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>β</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>a</mi> <mo>∝</mo> <msup> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {E}}\sim \int _{0}^{O(1/\beta )}{\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}\;n(\Delta E)d\Delta E=\beta ^{-2}\int _{0}^{O(1)}{\frac {a}{e^{a}-1}}n(a/\beta )da\propto \beta ^{-2}n(0)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8f2a04e5032d4a82f5fdd13ef8614d1bb83404" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:80.083ex; height:6.343ex;" alt="{\displaystyle {\bar {E}}\sim \int _{0}^{O(1/\beta )}{\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}\;n(\Delta E)d\Delta E=\beta ^{-2}\int _{0}^{O(1)}{\frac {a}{e^{a}-1}}n(a/\beta )da\propto \beta ^{-2}n(0)}"> The effect is that the average energy in these two-level systems is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {E}}\sim T^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>∼</mo> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {E}}\sim T^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f8ed654775664d394197b2fc2d8045fdc39ab76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.648ex; height:2.676ex;" alt="{\displaystyle {\bar {E}}\sim T^{2}}">, leading to a <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial _{T}{\bar {E}}\propto T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>∝</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{T}{\bar {E}}\propto T}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/245c788981e511dcfa9965f347af5bf66fe67ee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.134ex; height:2.843ex;" alt="{\displaystyle \partial _{T}{\bar {E}}\propto T}"> term. <div class="mw-heading mw-heading3"><h3 id="Experimental_data">Experimental data</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=7" title="Edit section: Experimental data">edit</a>]</div> In experimental measurements, the specific heat capacity of glass is measured at different temperatures, and a <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (T^{2},c/T)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (T^{2},c/T)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f18627fc67751795348618cbf2a5366ffa7affbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.423ex; height:3.176ex;" alt="{\displaystyle (T^{2},c/T)}"> graph is plotted. Assuming that <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\approx c_{1}T+c_{3}T^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>≈</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>T</mi> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\approx c_{1}T+c_{3}T^{3}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64083590772dc2c49588709f6a5e77bc0a2fce78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.478ex; height:3.009ex;" alt="{\displaystyle c\approx c_{1}T+c_{3}T^{3}}">, the graph should show <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c/T\approx c_{1}+c_{3}T^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo>≈</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c/T\approx c_{1}+c_{3}T^{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dab25795c40dc3c8e5e26ee262bcfd493d9c6e59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.641ex; height:3.176ex;" alt="{\displaystyle c/T\approx c_{1}+c_{3}T^{2}}">, that is, a straight line with slope showing the typical Debye-like heat capacity, and a vertical intercept showing the anomalous linear component.<a href="#cite_note-:2-41">[41]</a> <div class="mw-heading mw-heading2"><h2 id="Kauzmann's_paradox">Kauzmann's paradox</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=8" title="Edit section: Kauzmann's paradox">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:KauzmannParadox.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/KauzmannParadox.png/220px-KauzmannParadox.png" decoding="async" width="220" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/KauzmannParadox.png/330px-KauzmannParadox.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/KauzmannParadox.png/440px-KauzmannParadox.png 2x" data-file-width="485" data-file-height="417" /></a><figcaption>Entropy difference between crystal and undercooled melt</figcaption></figure> As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By <a href="/wiki/Extrapolating" class="mw-redirect" title="Extrapolating">extrapolating</a> the <a href="/wiki/Heat_capacity" title="Heat capacity">heat capacity</a> of the supercooled liquid below its <a href="/wiki/Glass_transition_temperature" class="mw-redirect" title="Glass transition temperature">glass transition temperature</a>, it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the <a href="/wiki/Walter_Kauzmann" title="Walter Kauzmann">Kauzmann</a> temperature. If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, this would be paradoxical, as the liquid phase should have the same vibrational entropy, but much higher positional entropy, as the crystal phase. This is the Kauzmann paradox, still not definitively resolved.<a href="#cite_note-44">[44]</a><a href="#cite_note-:0-45">[45]</a> <div class="mw-heading mw-heading3"><h3 id="Possible_resolutions">Possible resolutions</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=9" title="Edit section: Possible resolutions">edit</a>]</div> There are many possible resolutions to the Kauzmann paradox. Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached. Perhaps at the Kauzmann temperature, glass reaches an ideal glass phase, which is still amorphous, but has a long-range amorphous order which decreases its overall entropy to that of the crystal. The ideal glass would be a true phase of matter.<a href="#cite_note-:0-45">[45]</a><a href="#cite_note-46">[46]</a> The ideal glass is hypothesized, but cannot be observed naturally, as it would take too long to form. Something approaching an ideal glass has been observed as "ultrastable glass" formed by <a href="/wiki/Vacuum_deposition" title="Vacuum deposition">vapor deposition</a>,<a href="#cite_note-47">[47]</a> Perhaps there must be a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the calorimetric ideal glass transition temperature T0c. In this view, the glass transition is not merely a <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">kinetic</a> effect, i.e. merely the result of fast cooling of a melt, but there is an underlying <a href="/wiki/Thermodynamic" class="mw-redirect" title="Thermodynamic">thermodynamic</a> basis for glass formation. The glass transition temperature: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{g}\to T_{0c}{\text{ as }}{\frac {dT}{dt}}\to 0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>c</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> as </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>T</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">→</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{g}\to T_{0c}{\text{ as }}{\frac {dT}{dt}}\to 0.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0f258ca0caa5470e4103121a4050e0f2c62ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.468ex; height:5.509ex;" alt="{\displaystyle T_{g}\to T_{0c}{\text{ as }}{\frac {dT}{dt}}\to 0.}"></dd></dl> Perhaps the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value. Perhaps first order phase transition to another liquid state occurs before the Kauzmann temperature with the heat capacity of this new state being less than that obtained by extrapolation from higher temperature. <div class="mw-heading mw-heading2"><h2 id="In_specific_materials">In specific materials</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=10" title="Edit section: In specific materials">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Silica,_SiO2">Silica, SiO2</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=11" title="Edit section: Silica, SiO2">edit</a>]</div> <a href="/wiki/Silica" class="mw-redirect" title="Silica">Silica</a> (the chemical compound SiO2) has a number of distinct <a href="/wiki/Crystal" title="Crystal">crystalline</a> forms in addition to the quartz structure. Nearly all of the crystalline forms involve <a href="/wiki/Tetrahedral" class="mw-redirect" title="Tetrahedral">tetrahedral</a> SiO4 units linked together by shared vertices in different arrangements (<a href="/wiki/Stishovite" title="Stishovite">stishovite</a>, composed of linked SiO6 <a href="/wiki/Octahedron" title="Octahedron">octahedra</a>, is the main exception). Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is 161 picometres (6.3×10−9 in), whereas in α-tridymite it ranges from 154–171 pm (6.1×10−9–6.7×10−9 in). The Si-O-Si bond angle also varies from 140° in α-tridymite to 144° in α-quartz to 180° in β-tridymite. Any deviations from these standard parameters constitute microstructural differences or variations that represent an approach to an <a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous</a>, vitreous or <a href="/wiki/Amorphous_solid" title="Amorphous solid">glassy solid</a>. The transition temperature Tg in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bonds</a>. The Tg is clearly influenced by the chemistry of the glass. For example, addition of elements such as <a href="/wiki/Boron" title="Boron">B</a>, <a href="/wiki/Sodium" title="Sodium">Na</a>, <a href="/wiki/Potassium" title="Potassium">K</a> or <a href="/wiki/Calcium" title="Calcium">Ca</a> to a <a href="/wiki/Silica_glass" class="mw-redirect" title="Silica glass">silica glass</a>, which have a <a href="/wiki/Valency_(chemistry)" class="mw-redirect" title="Valency (chemistry)">valency</a> less than 4, helps in breaking up the network structure, thus reducing the Tg. Alternatively, <a href="/wiki/Phosphorus" title="Phosphorus">P</a>, which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the Tg.<a href="#cite_note-48">[48]</a> Tg is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy Hd and entropy Sd of configurons – broken bonds: Tg = Hd / [Sd + R ln[(1 − fc)/ fc] where R is the gas constant and fc is the percolation threshold. For strong melts such as SiO2 the percolation threshold in the above equation is the universal Scher–Zallen critical density in the 3-D space e.g. fc = 0.15, however for fragile materials the percolation thresholds are material-dependent and fc ≪ 1.<a href="#cite_note-49">[49]</a> The enthalpy Hd and the entropy Sd of configurons – broken bonds can be found from available experimental data on viscosity.<a href="#cite_note-50">[50]</a> On the surface of SiO2 films, scanning tunneling microscopy has resolved clusters of ca. 5 SiO2 in diameter that move in a two-state fashion on a time scale of minutes. This is much faster than dynamics in the bulk, but in agreement with models that compare bulk and surface dynamics.<a href="#cite_note-51">[51]</a><a href="#cite_note-52">[52]</a> <div class="mw-heading mw-heading3"><h3 id="Polymers_2">Polymers</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=12" title="Edit section: Polymers">edit</a>]</div> In <a href="/wiki/Polymer" title="Polymer">polymers</a> the glass transition temperature, Tg, is often expressed as the temperature at which the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> is such that the <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a> for the cooperative movement of 50 or so elements of the polymer is exceeded [<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]. This allows molecular chains to slide past each other when a force is applied. From this definition, we can see that the introduction of relatively stiff chemical groups (such as <a href="/wiki/Benzene" title="Benzene">benzene</a> rings) will interfere with the flowing process and hence increase Tg.<a href="#cite_note-53">[53]</a> The stiffness of thermoplastics decreases due to this effect (see figure.) When the glass temperature has been reached, the stiffness stays the same for a while, i.e., at or near E2, until the temperature exceeds Tm, and the material melts. This region is called the rubber plateau. <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ironing.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Ironing.jpg/220px-Ironing.jpg" decoding="async" width="220" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Ironing.jpg/330px-Ironing.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Ironing.jpg/440px-Ironing.jpg 2x" data-file-width="7513" data-file-height="6292" /></a><figcaption>In ironing, a fabric is heated through the glass-rubber transition.</figcaption></figure> In <a href="/wiki/Ironing" title="Ironing">ironing</a>, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation. Tg can be significantly decreased by addition of <a href="/wiki/Plasticizer" title="Plasticizer">plasticizers</a> into the polymer matrix. Smaller molecules of plasticizer embed themselves between the polymer chains, increasing the spacing and free volume, and allowing them to move past one another even at lower temperatures. Addition of plasticizer can effectively take control over polymer chain dynamics and dominate the amounts of the associated free volume so that the increased mobility of polymer ends is not apparent.<a href="#cite_note-54">[54]</a> The addition of nonreactive <a href="/wiki/Side_chain" title="Side chain">side groups</a> to a polymer can also make the chains stand off from one another, reducing Tg. If a plastic with some desirable properties has a Tg that is too high, it can sometimes be combined with another in a <a href="/wiki/Copolymer" title="Copolymer">copolymer</a> or <a href="/wiki/Composite_material" title="Composite material">composite material</a> with a Tg below the temperature of intended use. Note that some plastics are used at high temperatures, e.g., in automobile engines, and others at low temperatures.<a href="#cite_note-PVC-32">[32]</a> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Rubber_plateau.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Rubber_plateau.svg/220px-Rubber_plateau.svg.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Rubber_plateau.svg/330px-Rubber_plateau.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Rubber_plateau.svg/440px-Rubber_plateau.svg.png 2x" data-file-width="400" data-file-height="250" /></a><figcaption>Stiffness versus temperature</figcaption></figure>In <a href="/wiki/Viscoelasticity" title="Viscoelasticity">viscoelastic</a> materials, the presence of liquid-like behavior depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The <a href="/wiki/Silicone" title="Silicone">silicone</a> toy <a href="/wiki/Silly_Putty" title="Silly Putty">Silly Putty</a> behaves quite differently depending on the time rate of applying a force: pull slowly and it flows, acting as a heavily viscous liquid; hit it with a hammer and it shatters, acting as a glass. On cooling, <a href="/wiki/Rubber" class="mw-redirect" title="Rubber">rubber</a> undergoes a liquid-glass transition, which has also been called a rubber-glass transition. <div class="mw-heading mw-heading2"><h2 id="Mechanics_of_vitrification">Mechanics of vitrification</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=13" title="Edit section: Mechanics of vitrification">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></div> Molecular motion in condensed matter can be represented by a <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a> whose physical interpretation consists of a <a href="/wiki/Superposition_principle" title="Superposition principle">superposition</a> of <a href="/wiki/Longitudinal_wave" title="Longitudinal wave">longitudinal</a> and <a href="/wiki/Transverse_wave" title="Transverse wave">transverse</a> <a href="/wiki/Wave" title="Wave">waves</a> of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called <a href="/wiki/Density" title="Density">density</a> <a href="https://en.wiktionary.org/wiki/fluctuation" class="extiw" title="wikt:fluctuation">fluctuations</a>. (In polyatomic systems, they may also include <a href="https://en.wiktionary.org/wiki/composition" class="extiw" title="wikt:composition">compositional</a> fluctuations.)<a href="#cite_note-55">[55]</a> Thus, <a href="/wiki/Thermal_motion" class="mw-redirect" title="Thermal motion">thermal motion</a> in liquids can be decomposed into elementary <a href="/wiki/Longitudinal_wave" title="Longitudinal wave">longitudinal vibrations</a> (or acoustic <a href="/wiki/Phonon" title="Phonon">phonons</a>) while <a href="/wiki/Transverse_wave" title="Transverse wave">transverse vibrations</a> (or shear waves) were originally described only in <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elastic</a> solids exhibiting the highly ordered crystalline state of matter. In other words, simple liquids cannot support an applied force in the form of a <a href="/wiki/Shearing_stress" class="mw-redirect" title="Shearing stress">shearing stress</a>, and will yield mechanically via macroscopic <a href="/wiki/Plastic_deformation" class="mw-redirect" title="Plastic deformation">plastic deformation</a> (or viscous flow). Furthermore, the fact that a <a href="/wiki/Solid" title="Solid">solid</a> deforms locally while retaining its <a href="/wiki/Stiffness" title="Stiffness">rigidity</a> – while a <a href="/wiki/Liquid" title="Liquid">liquid</a> yields to macroscopic <a href="/wiki/Viscous_flow" class="mw-redirect" title="Viscous flow">viscous flow</a> in response to the application of an applied <a href="/wiki/Shearing_force" class="mw-redirect" title="Shearing force">shearing force</a> – is accepted by many as the mechanical distinction between the two.<a href="#cite_note-56">[56]</a><a href="#cite_note-57">[57]</a> The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the <a href="/wiki/Kinetic_theory_of_solids" class="mw-redirect" title="Kinetic theory of solids">kinetic theory of solids</a> and the <a href="/wiki/Theory_of_elasticity" class="mw-redirect" title="Theory of elasticity">theory of elasticity</a> in <a href="/wiki/Liquid" title="Liquid">liquids</a>. This revision follows directly from the continuous characteristic of the <a href="/wiki/Viscoelastic" class="mw-redirect" title="Viscoelastic">viscoelastic</a> crossover from the liquid state into the solid one when the transition is not accompanied by crystallization—ergo the supercooled <a href="/wiki/Viscous_liquid" title="Viscous liquid">viscous liquid</a>. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon <a href="/wiki/Vitrification" title="Vitrification">vitrification</a>, as described by Bartenev in his mechanical description of the vitrification process.<a href="#cite_note-D-58">[58]</a><a href="#cite_note-59">[59]</a> The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a> that levels out temperature differentials between <a href="/wiki/Compressibility" title="Compressibility">compressed</a> and <a href="/wiki/Thermal_expansion" title="Thermal expansion">expanded</a> volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "<a href="/wiki/Mean_free_path" title="Mean free path">mean free path</a>" for lattice phonons, and that the value of the mean free path is of the <a href="/wiki/Order_of_magnitude" title="Order of magnitude">order of magnitude</a> of the scale of disorder in the molecular structure of a liquid or solid. The thermal phonon mean free paths or relaxation lengths of a number of glass formers have been plotted versus the glass transition temperature, indicating a linear relationship between the two. This has suggested a new criterion for glass formation based on the value of the phonon mean free path.<a href="#cite_note-60">[60]</a> It has often been suggested that <a href="/wiki/Heat_conduction" class="mw-redirect" title="Heat conduction">heat transport</a> in <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic <a href="/wiki/Scattering" title="Scattering">scattering</a> of acoustic phonons by lattice defects (e.g. randomly spaced vacancies).<a href="#cite_note-61">[61]</a> These predictions were confirmed by experiments on commercial <a href="/wiki/Glasses" title="Glasses">glasses</a> and glass <a href="/wiki/Ceramic_engineering" title="Ceramic engineering">ceramics</a>, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10–100 micrometres (0.00039–0.00394 in).<a href="#cite_note-62">[62]</a><a href="#cite_note-63">[63]</a> The relationship between these transverse waves and the mechanism of vitrification has been described by several authors who proposed that the onset of correlations between such phonons results in an orientational ordering or "freezing" of local <a href="/wiki/Shear_stress" title="Shear stress">shear stresses</a> in glass-forming liquids, thus yielding the glass transition.<a href="#cite_note-64">[64]</a> <div class="mw-heading mw-heading3"><h3 id="Electronic_structure">Electronic structure</h3>[<a href="/w/index.php?title=Glass_transition&action=edit&section=14" title="Edit section: Electronic structure">edit</a>]</div> The influence of <a href="/wiki/Heat" title="Heat">thermal</a> <a href="/wiki/Phonon" title="Phonon">phonons</a> and their interaction with <a href="/wiki/Electron" title="Electron">electronic</a> structure is a topic that was appropriately introduced in a discussion of the <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> of liquid metals. Lindemann's theory of melting is referenced,<a href="#cite_note-65">[65]</a> and it is suggested that the drop in <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">conductivity</a> in going from the <a href="/wiki/Crystal" title="Crystal">crystalline</a> to the liquid state is due to the increased <a href="/wiki/Scattering" title="Scattering">scattering</a> of conduction electrons as a result of the increased <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of atomic <a href="/wiki/Vibration" title="Vibration">vibration</a>. Such theories of localization have been applied to transport in <a href="/wiki/Metallic_glass" class="mw-redirect" title="Metallic glass">metallic glasses</a>, where the <a href="/wiki/Mean_free_path" title="Mean free path">mean free path</a> of the electrons is very small (on the order of the interatomic spacing).<a href="#cite_note-66">[66]</a><a href="#cite_note-67">[67]</a> The formation of a non-crystalline form of a gold-silicon alloy by the method of <a href="/wiki/Splat_quenching" title="Splat quenching">splat quenching</a> from the melt led to further considerations of the influence of electronic structure on glass forming ability, based on the properties of the <a href="/wiki/Metallic_bond" class="mw-redirect" title="Metallic bond">metallic bond</a>.<a href="#cite_note-68">[68]</a><a href="#cite_note-69">[69]</a><a href="#cite_note-70">[70]</a><a href="#cite_note-71">[71]</a><a href="#cite_note-72">[72]</a> Other work indicates that the <a href="/wiki/Electron_mobility" title="Electron mobility">mobility</a> of localized <a href="/wiki/Electron" title="Electron">electrons</a> is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if <a href="/wiki/Chemical_bonds" class="mw-redirect" title="Chemical bonds">chemical bonds</a> are important, the <a href="/wiki/Nearly_free_electron_model" title="Nearly free electron model">nearly free electron models</a> should not be applicable. However, if the model includes the buildup of a <a href="/wiki/Charge_distribution" class="mw-redirect" title="Charge distribution">charge distribution</a> between all pairs of atoms just like a chemical bond (e.g., silicon, when a band is just filled with electrons) then it should apply to <a href="/wiki/Solid" title="Solid">solids</a>.<a href="#cite_note-73">[73]</a> Thus, if the <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a> is low, the <a href="/wiki/Mean_free_path" title="Mean free path">mean free path</a> of the electrons is very short. The electrons will only be sensitive to the <a href="/wiki/Short-range_order" class="mw-redirect" title="Short-range order">short-range order</a> in the glass since they do not get a chance to scatter from atoms spaced at large distances. Since the short-range order is similar in glasses and crystals, the electronic energies should be similar in these two states. For alloys with lower resistivity and longer electronic mean free paths, the electrons could begin to sense [<a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute">dubious</a> – <a href="/wiki/Talk:Glass_transition#Dubious" title="Talk:Glass transition">discuss</a>] that there is <a href="/wiki/Order_and_disorder_(physics)" class="mw-redirect" title="Order and disorder (physics)">disorder</a> in the glass, and this would raise their energies and destabilize the glass with respect to crystallization. Thus, the glass formation tendencies of certain alloys may therefore be due in part to the fact that the electron mean free paths are very short, so that only the short-range order is ever important for the energy of the electrons. It has also been argued that glass formation in metallic systems is related to the "softness" of the interaction potential between unlike atoms. Some authors, emphasizing the strong similarities between the local structure of the glass and the corresponding crystal, suggest that chemical bonding helps to stabilize the amorphous structure.<a href="#cite_note-74">[74]</a><a href="#cite_note-75">[75]</a> Other authors have suggested that the electronic structure yields its influence on glass formation through the directional properties of bonds. Non-crystallinity is thus favored in elements with a large number of <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">polymorphic</a> forms and a high degree of <a href="/wiki/Chemical_bond" title="Chemical bond">bonding</a> <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a>. Crystallization becomes more unlikely as bonding anisotropy is increased from <a href="/wiki/Isotropic" class="mw-redirect" title="Isotropic">isotropic</a> <a href="/wiki/Metal" title="Metal">metallic</a> to <a href="/wiki/Anisotropic" class="mw-redirect" title="Anisotropic">anisotropic</a> <a href="/wiki/Metal" title="Metal">metallic</a> to <a href="/wiki/Covalent" class="mw-redirect" title="Covalent">covalent</a> bonding, thus suggesting a relationship between the <a href="/wiki/Chemical_family" class="mw-redirect" title="Chemical family">group number</a> in the <a href="/wiki/Periodic_table" title="Periodic table">periodic table</a> and the glass forming ability in <a href="/wiki/Chemical_element" title="Chemical element">elemental</a> <a href="/wiki/Solid" title="Solid">solids</a>.<a href="#cite_note-76">[76]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=15" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/Gardner_transition" title="Gardner transition">Gardner transition</a></li> <li><a href="/wiki/Glass_formation" title="Glass formation">Glass formation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=16" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWarren1941" class="citation journal cs1">Warren, B. E. (August 1941). <a rel="nofollow" class="external text" href="https://ceramics.onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1941.tb14858.x">"SUMMARY OF WORK ON ATOMIC ARRANGEMENT IN GLASS*"</a>. Journal of the American Ceramic Society. 24 (8): 256–261. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1151-2916.1941.tb14858.x">10.1111/j.1151-2916.1941.tb14858.x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-7820">0002-7820</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Ceramic+Society&rft.atitle=SUMMARY+OF+WORK+ON+ATOMIC+ARRANGEMENT+IN+GLASS%2A&rft.volume=24&rft.issue=8&rft.pages=256-261&rft.date=1941-08&rft_id=info%3Adoi%2F10.1111%2Fj.1151-2916.1941.tb14858.x&rft.issn=0002-7820&rft.aulast=Warren&rft.aufirst=B.+E.&rft_id=https%3A%2F%2Fceramics.onlinelibrary.wiley.com%2Fdoi%2F10.1111%2Fj.1151-2916.1941.tb14858.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-iso11357-2-2">^ <a href="#cite_ref-iso11357-2_2-0">a</a> <a href="#cite_ref-iso11357-2_2-1">b</a> <a href="/wiki/International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a> 11357-2: Plastics – Differential scanning calorimetry – Part 2: Determination of glass transition temperature (1999). </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190115195943/http://pslc.ws/macrog/tg.htm">"The Glass Transition"</a>. Polymer Science Learning Center. Archived from <a rel="nofollow" class="external text" href="http://pslc.ws/macrog/tg.htm">the original</a> on 2019-01-15. Retrieved 2009-10-15.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Glass+Transition&rft.pub=Polymer+Science+Learning+Center&rft_id=http%3A%2F%2Fpslc.ws%2Fmacrog%2Ftg.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-Debenedetti-4">^ <a href="#cite_ref-Debenedetti_4-0">a</a> <a href="#cite_ref-Debenedetti_4-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDebenedettiStillinger2001" class="citation journal cs1">Debenedetti, P. G.; Stillinger (2001). "Supercooled liquids and the glass transition". Nature. 410 (6825): 259–267. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001Natur.410..259D">2001Natur.410..259D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35065704">10.1038/35065704</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11258381">11258381</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4404576">4404576</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Supercooled+liquids+and+the+glass+transition&rft.volume=410&rft.issue=6825&rft.pages=259-267&rft.date=2001&rft_id=info%3Adoi%2F10.1038%2F35065704&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4404576%23id-name%3DS2CID&rft_id=info%3Apmid%2F11258381&rft_id=info%3Abibcode%2F2001Natur.410..259D&rft.aulast=Debenedetti&rft.aufirst=P.+G.&rft.au=Stillinger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-Angell-5">^ <a href="#cite_ref-Angell_5-0">a</a> <a href="#cite_ref-Angell_5-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngellNgai,_K._L.McKenna,_G._B.McMillan,_P._F.2000" class="citation journal cs1">Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. (2000). <a rel="nofollow" class="external text" href="http://lib.dr.iastate.edu/mse_pubs/70">"Relaxation in glassforming liquids and amorphous solids"</a>. Appl. Phys. Rev. 88 (6): 3113–3157. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000JAP....88.3113A">2000JAP....88.3113A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1286035">10.1063/1.1286035</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200307171617/https://lib.dr.iastate.edu/mse_pubs/70/">Archived</a> from the original on 2020-03-07. Retrieved 2018-09-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Appl.+Phys.+Rev.&rft.atitle=Relaxation+in+glassforming+liquids+and+amorphous+solids&rft.volume=88&rft.issue=6&rft.pages=3113-3157&rft.date=2000&rft_id=info%3Adoi%2F10.1063%2F1.1286035&rft_id=info%3Abibcode%2F2000JAP....88.3113A&rft.aulast=Angell&rft.aufirst=C.+A.&rft.au=Ngai%2C+K.+L.&rft.au=McKenna%2C+G.+B.&rft.au=McMillan%2C+P.+F.&rft.au=Martin%2C+S.+W.&rft_id=http%3A%2F%2Flib.dr.iastate.edu%2Fmse_pubs%2F70&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-z1-6">^ <a href="#cite_ref-z1_6-0">a</a> <a href="#cite_ref-z1_6-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZarzycki,_J.1991" class="citation book cs1">Zarzycki, J. (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=D7Z8ywb3QggC">Glasses and the Vitreous State</a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521355827" title="Special:BookSources/978-0521355827"><bdi>978-0521355827</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200802204950/https://books.google.com/books?id=D7Z8ywb3QggC">Archived</a> from the original on 2020-08-02. Retrieved 2016-09-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Glasses+and+the+Vitreous+State&rft.pub=Cambridge+University+Press&rft.date=1991&rft.isbn=978-0521355827&rft.au=Zarzycki%2C+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DD7Z8ywb3QggC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOjovan2004" class="citation journal cs1">Ojovan, M. I. (2004). "Glass formation in amorphous SiO2 as a percolation phase transition in a system of network defects". Journal of Experimental and Theoretical Physics Letters. 79 (12): 632–634. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004JETPL..79..632O">2004JETPL..79..632O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1134%2F1.1790021">10.1134/1.1790021</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:124299526">124299526</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Experimental+and+Theoretical+Physics+Letters&rft.atitle=Glass+formation+in+amorphous+SiO%3Csub%3E2%3C%2Fsub%3E+as+a+percolation+phase+transition+in+a+system+of+network+defects&rft.volume=79&rft.issue=12&rft.pages=632-634&rft.date=2004&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A124299526%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1134%2F1.1790021&rft_id=info%3Abibcode%2F2004JETPL..79..632O&rft.aulast=Ojovan&rft.aufirst=M.+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-Stefano_et_al_2011-8">^ <a href="#cite_ref-Stefano_et_al_2011_8-0">a</a> <a href="#cite_ref-Stefano_et_al_2011_8-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeille_Stefano,_V.Allegra,_G.Geil_Phillip,_H.He,_J.2011" class="citation journal cs1">Meille Stefano, V.; Allegra, G.; Geil Phillip, H.; He, J.; Hess, M.; Jin, J.-I.; Kratochvíl, P.; Mormann, W.; Stepto, R. (2011). <a rel="nofollow" class="external text" href="https://www.degruyter.com/downloadpdf/j/pac.2011.83.issue-10/pac-rec-10-11-13/pac-rec-10-11-13.pdf">"Definitions of terms relating to crystalline polymers (IUPAC Recommendations 2011)"</a> (PDF). <a href="/wiki/Pure_and_Applied_Chemistry" title="Pure and Applied Chemistry">Pure and Applied Chemistry</a>. 83 (10): 1831. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2FPAC-REC-10-11-13">10.1351/PAC-REC-10-11-13</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:98823962">98823962</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180625161113/https://www.degruyter.com/downloadpdf/j/pac.2011.83.issue-10/pac-rec-10-11-13/pac-rec-10-11-13.pdf">Archived</a> (PDF) from the original on 2018-06-25. Retrieved 2018-06-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pure+and+Applied+Chemistry&rft.atitle=Definitions+of+terms+relating+to+crystalline+polymers+%28IUPAC+Recommendations+2011%29&rft.volume=83&rft.issue=10&rft.pages=1831&rft.date=2011&rft_id=info%3Adoi%2F10.1351%2FPAC-REC-10-11-13&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A98823962%23id-name%3DS2CID&rft.au=Meille+Stefano%2C+V.&rft.au=Allegra%2C+G.&rft.au=Geil+Phillip%2C+H.&rft.au=He%2C+J.&rft.au=Hess%2C+M.&rft.au=Jin%2C+J.-I.&rft.au=Kratochv%C3%ADl%2C+P.&rft.au=Mormann%2C+W.&rft.au=Stepto%2C+R.&rft_id=https%3A%2F%2Fwww.degruyter.com%2Fdownloadpdf%2Fj%2Fpac.2011.83.issue-10%2Fpac-rec-10-11-13%2Fpac-rec-10-11-13.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <a href="/wiki/IUPAC_books#Gold_Book" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a>, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/G02640.html">glass transition</a>". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.G02640">10.1351/goldbook.G02640</a> </li> <li id="cite_note-Hansen&McDonald-10"><a href="#cite_ref-Hansen&McDonald_10-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHansenMcDonald,_I._R.2007" class="citation book cs1">Hansen, J.-P.; McDonald, I. R. (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Uhm87WZBnxEC">Theory of Simple Liquids</a>. Elsevier. pp. 250–254. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0123705358" title="Special:BookSources/978-0123705358"><bdi>978-0123705358</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130921052911/http://books.google.com/books?id=Uhm87WZBnxEC">Archived</a> from the original on 2013-09-21. Retrieved 2016-09-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Simple+Liquids&rft.pages=250-254&rft.pub=Elsevier&rft.date=2007&rft.isbn=978-0123705358&rft.aulast=Hansen&rft.aufirst=J.-P.&rft.au=McDonald%2C+I.+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUhm87WZBnxEC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-11"><a href="#cite_ref-11">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdam,_J-LZhang,_X.2014" class="citation book cs1">Adam, J-L; Zhang, X. (14 February 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=IuNRAwAAQBAJ&pg=PA94">Chalcogenide Glasses: Preparation, Properties and Applications</a>. Elsevier Science. p. 94. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85709-356-1" title="Special:BookSources/978-0-85709-356-1"><bdi>978-0-85709-356-1</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170717080736/https://books.google.com/books?id=IuNRAwAAQBAJ&pg=PA94">Archived</a> from the original on 17 July 2017. Retrieved 2 May 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chalcogenide+Glasses%3A+Preparation%2C+Properties+and+Applications&rft.pages=94&rft.pub=Elsevier+Science&rft.date=2014-02-14&rft.isbn=978-0-85709-356-1&rft.au=Adam%2C+J-L&rft.au=Zhang%2C+X.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DIuNRAwAAQBAJ%26pg%3DPA94&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-phillips1979-12"><a href="#cite_ref-phillips1979_12-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPhillips1979" class="citation journal cs1">Phillips, J.C. (1979). "Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys". Journal of Non-Crystalline Solids. 34 (2): 153. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1979JNCS...34..153P">1979JNCS...34..153P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3093%2879%2990033-4">10.1016/0022-3093(79)90033-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Non-Crystalline+Solids&rft.atitle=Topology+of+covalent+non-crystalline+solids+I%3A+Short-range+order+in+chalcogenide+alloys&rft.volume=34&rft.issue=2&rft.pages=153&rft.date=1979&rft_id=info%3Adoi%2F10.1016%2F0022-3093%2879%2990033-4&rft_id=info%3Abibcode%2F1979JNCS...34..153P&rft.aulast=Phillips&rft.aufirst=J.C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-CM-13"><a href="#cite_ref-CM_13-0">^</a> Moynihan, C. et al. (1976) in The Glass Transition and the Nature of the Glassy State, M. Goldstein and R. Simha (Eds.), Ann. N.Y. Acad. Sci., Vol. 279. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0890720533" title="Special:BookSources/0890720533">0890720533</a>. </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngell1988" class="citation journal cs1">Angell, C. A. (1988). "Perspective on the glass transition". Journal of Physics and Chemistry of Solids. 49 (8): 863–871. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988JPCS...49..863A">1988JPCS...49..863A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3697%2888%2990002-9">10.1016/0022-3697(88)90002-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics+and+Chemistry+of+Solids&rft.atitle=Perspective+on+the+glass+transition&rft.volume=49&rft.issue=8&rft.pages=863-871&rft.date=1988&rft_id=info%3Adoi%2F10.1016%2F0022-3697%2888%2990002-9&rft_id=info%3Abibcode%2F1988JPCS...49..863A&rft.aulast=Angell&rft.aufirst=C.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdigerAngellNagel1996" class="citation journal cs1">Ediger, M. D.; Angell, C. A.; Nagel, Sidney R. (1996). "Supercooled Liquids and Glasses". The Journal of Physical Chemistry. 100 (31): 13200. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fjp953538d">10.1021/jp953538d</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Physical+Chemistry&rft.atitle=Supercooled+Liquids+and+Glasses&rft.volume=100&rft.issue=31&rft.pages=13200&rft.date=1996&rft_id=info%3Adoi%2F10.1021%2Fjp953538d&rft.aulast=Ediger&rft.aufirst=M.+D.&rft.au=Angell%2C+C.+A.&rft.au=Nagel%2C+Sidney+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-16"><a href="#cite_ref-16">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAngell1995" class="citation journal cs1">Angell, C. A. (1995). "Formation of Glasses from Liquids and Biopolymers". Science. 267 (5206): 1924–35. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995Sci...267.1924A">1995Sci...267.1924A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.267.5206.1924">10.1126/science.267.5206.1924</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17770101">17770101</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:927260">927260</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Formation+of+Glasses+from+Liquids+and+Biopolymers&rft.volume=267&rft.issue=5206&rft.pages=1924-35&rft.date=1995&rft_id=info%3Adoi%2F10.1126%2Fscience.267.5206.1924&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A927260%23id-name%3DS2CID&rft_id=info%3Apmid%2F17770101&rft_id=info%3Abibcode%2F1995Sci...267.1924A&rft.aulast=Angell&rft.aufirst=C.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStillinger1995" class="citation journal cs1">Stillinger, F. H. (1995). "A Topographic View of Supercooled Liquids and Glass Formation". Science. 267 (5206): 1935–9. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995Sci...267.1935S">1995Sci...267.1935S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.267.5206.1935">10.1126/science.267.5206.1935</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17770102">17770102</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:30407650">30407650</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=A+Topographic+View+of+Supercooled+Liquids+and+Glass+Formation&rft.volume=267&rft.issue=5206&rft.pages=1935-9&rft.date=1995&rft_id=info%3Adoi%2F10.1126%2Fscience.267.5206.1935&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A30407650%23id-name%3DS2CID&rft_id=info%3Apmid%2F17770102&rft_id=info%3Abibcode%2F1995Sci...267.1935S&rft.aulast=Stillinger&rft.aufirst=F.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-18"><a href="#cite_ref-18">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNemilov1994" class="citation book cs1">Nemilov SV (1994). Thermodynamic and Kinetic Aspects of the Vitreous State. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0849337826" title="Special:BookSources/978-0849337826"><bdi>978-0849337826</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamic+and+Kinetic+Aspects+of+the+Vitreous+State&rft.pub=CRC+Press&rft.date=1994&rft.isbn=978-0849337826&rft.aulast=Nemilov&rft.aufirst=SV&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-19"><a href="#cite_ref-19">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs,_J._H.1960" class="citation book cs1">Gibbs, J. H. (1960). MacKenzie, J. D. (ed.). Modern Aspects of the Vitreous State. Butterworth. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1690554">1690554</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Aspects+of+the+Vitreous+State&rft.pub=Butterworth&rft.date=1960&rft_id=info%3Aoclcnum%2F1690554&rft.au=Gibbs%2C+J.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-20"><a href="#cite_ref-20">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOjovanLee2010" class="citation journal cs1">Ojovan, Michael I; Lee, William (Bill) E (2010). "Connectivity and glass transition in disordered oxide systems". Journal of Non-Crystalline Solids. 356 (44–49): 2534. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010JNCS..356.2534O">2010JNCS..356.2534O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jnoncrysol.2010.05.012">10.1016/j.jnoncrysol.2010.05.012</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Non-Crystalline+Solids&rft.atitle=Connectivity+and+glass+transition+in+disordered+oxide+systems&rft.volume=356&rft.issue=44%E2%80%9349&rft.pages=2534&rft.date=2010&rft_id=info%3Adoi%2F10.1016%2Fj.jnoncrysol.2010.05.012&rft_id=info%3Abibcode%2F2010JNCS..356.2534O&rft.aulast=Ojovan&rft.aufirst=Michael+I&rft.au=Lee%2C+William+%28Bill%29+E&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-21"><a href="#cite_ref-21">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSturm2017" class="citation journal cs1">Sturm, Karl Günter (2017). <a rel="nofollow" class="external text" href="http://rgdoi.net/10.13140/RG.2.2.19831.73121">"Microscopic-Phenomenological Model of Glass Transition I. Foundations of the model (Revised and enhanced version) (Former title: Microscopic Model of Glass Transformation and Molecular Translations in Liquids I. Foundations of the Model-October 2015)"</a>. Ceramics. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.13140%2FRG.2.2.19831.73121">10.13140/RG.2.2.19831.73121</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ceramics&rft.atitle=Microscopic-Phenomenological+Model+of+Glass+Transition+I.+Foundations+of+the+model+%28Revised+and+enhanced+version%29+%28Former+title%3A+Microscopic+Model+of+Glass+Transformation+and+Molecular+Translations+in+Liquids+I.+Foundations+of+the+Model-October+2015%29&rft.date=2017&rft_id=info%3Adoi%2F10.13140%2FRG.2.2.19831.73121&rft.aulast=Sturm&rft.aufirst=Karl+G%C3%BCnter&rft_id=http%3A%2F%2Frgdoi.net%2F10.13140%2FRG.2.2.19831.73121&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-22"><a href="#cite_ref-22">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://coventivecomposites.com/explainers/dynamic-mechanical-analysis-dma/">"What is Dynamic Mechanical Testing (DMA)?"</a>. 2018. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201117144756/https://coventivecomposites.com/explainers/dynamic-mechanical-analysis-dma/">Archived</a> from the original on 2020-11-17. Retrieved 2020-12-09.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+Dynamic+Mechanical+Testing+%28DMA%29%3F&rft.date=2018&rft_id=https%3A%2F%2Fcoventivecomposites.com%2Fexplainers%2Fdynamic-mechanical-analysis-dma%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-:1-23">^ <a href="#cite_ref-:1_23-0">a</a> <a href="#cite_ref-:1_23-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZanottoMauro2017" class="citation journal cs1">Zanotto, Edgar D.; Mauro, John C. (September 2017). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0022309317302685">"The glassy state of matter: Its definition and ultimate fate"</a>. Journal of Non-Crystalline Solids. 471: 490–495. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017JNCS..471..490Z">2017JNCS..471..490Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jnoncrysol.2017.05.019">10.1016/j.jnoncrysol.2017.05.019</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Non-Crystalline+Solids&rft.atitle=The+glassy+state+of+matter%3A+Its+definition+and+ultimate+fate&rft.volume=471&rft.pages=490-495&rft.date=2017-09&rft_id=info%3Adoi%2F10.1016%2Fj.jnoncrysol.2017.05.019&rft_id=info%3Abibcode%2F2017JNCS..471..490Z&rft.aulast=Zanotto&rft.aufirst=Edgar+D.&rft.au=Mauro%2C+John+C.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0022309317302685&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-24"><a href="#cite_ref-24">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSimon1927" class="citation journal cs1 cs1-prop-foreign-lang-source">Simon, Franz (1927-04-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1007/BF01395487">"Zum Prinzip von der Unerreichbarkeit des absoluten Nullpunktes"</a>. Zeitschrift für Physik (in German). 41 (4): 806–809. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1927ZPhy...41..806S">1927ZPhy...41..806S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01395487">10.1007/BF01395487</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0044-3328">0044-3328</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+Physik&rft.atitle=Zum+Prinzip+von+der+Unerreichbarkeit+des+absoluten+Nullpunktes&rft.volume=41&rft.issue=4&rft.pages=806-809&rft.date=1927-04-01&rft.issn=0044-3328&rft_id=info%3Adoi%2F10.1007%2FBF01395487&rft_id=info%3Abibcode%2F1927ZPhy...41..806S&rft.aulast=Simon&rft.aufirst=Franz&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2FBF01395487&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-25"><a href="#cite_ref-25">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZachariasen1932" class="citation journal cs1">Zachariasen, W. H. (October 1932). <a rel="nofollow" class="external text" href="https://pubs.acs.org/doi/abs/10.1021/ja01349a006">"The Atomic Arrangement in Glass"</a>. Journal of the American Chemical Society. 54 (10): 3841–3851. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja01349a006">10.1021/ja01349a006</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-7863">0002-7863</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Chemical+Society&rft.atitle=The+Atomic+Arrangement+in+Glass&rft.volume=54&rft.issue=10&rft.pages=3841-3851&rft.date=1932-10&rft_id=info%3Adoi%2F10.1021%2Fja01349a006&rft.issn=0002-7863&rft.aulast=Zachariasen&rft.aufirst=W.+H.&rft_id=https%3A%2F%2Fpubs.acs.org%2Fdoi%2Fabs%2F10.1021%2Fja01349a006&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-26"><a href="#cite_ref-26">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGupta1996" class="citation journal cs1">Gupta, Prabhat K. (February 1996). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/0022309395005021">"Non-crystalline solids: glasses and amorphous solids"</a>. Journal of Non-Crystalline Solids. 195 (1–2): 158–164. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996JNCS..195..158G">1996JNCS..195..158G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3093%2895%2900502-1">10.1016/0022-3093(95)00502-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Non-Crystalline+Solids&rft.atitle=Non-crystalline+solids%3A+glasses+and+amorphous+solids&rft.volume=195&rft.issue=1%E2%80%932&rft.pages=158-164&rft.date=1996-02&rft_id=info%3Adoi%2F10.1016%2F0022-3093%2895%2900502-1&rft_id=info%3Abibcode%2F1996JNCS..195..158G&rft.aulast=Gupta&rft.aufirst=Prabhat+K.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2F0022309395005021&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGutzowSchmelzer2013" class="citation book cs1">Gutzow, Ivan S.; Schmelzer, Jürn W.P. (2013). <a rel="nofollow" class="external text" href="https://link.springer.com/10.1007/978-3-642-34633-0">The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization</a>. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 124. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-34633-0">10.1007/978-3-642-34633-0</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-34632-3" title="Special:BookSources/978-3-642-34632-3"><bdi>978-3-642-34632-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Vitreous+State%3A+Thermodynamics%2C+Structure%2C+Rheology%2C+and+Crystallization&rft.place=Berlin%2C+Heidelberg&rft.pages=124&rft.pub=Springer+Berlin+Heidelberg&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2F978-3-642-34633-0&rft.isbn=978-3-642-34632-3&rft.aulast=Gutzow&rft.aufirst=Ivan+S.&rft.au=Schmelzer%2C+J%C3%BCrn+W.P.&rft_id=https%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-642-34633-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-tgmeasurement-28">^ <a href="#cite_ref-tgmeasurement_28-0">a</a> <a href="#cite_ref-tgmeasurement_28-1">b</a> <a rel="nofollow" class="external text" href="http://www.glassproperties.com/tg/">Tg measurement of glasses</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090417092926/http://glassproperties.com/tg/">Archived</a> 2009-04-17 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Glassproperties.com. Retrieved on 2012-06-29. </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <a href="/wiki/IUPAC_books#Gold_Book" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a>, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/G02641.html">glass-transition temperature</a>". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.G02641">10.1351/goldbook.G02641</a> </li> <li id="cite_note-30"><a href="#cite_ref-30">^</a> <style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><a rel="nofollow" class="external text" href="http://patentscope.wipo.int/search/en/WO2003053721">EU WO03053721</a>, "TYRE COMPRISING A CYCLOOLEFIN POLYMER, TREAD BAND AND ELASTOMERIC COMPOSITION USED THEREIN", issued 2003-03-07<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=WO03053721&rft.cc=EU&rft.title=TYRE+COMPRISING+A+CYCLOOLEFIN+POLYMER%2C+TREAD+BAND+AND+ELASTOMERIC+COMPOSITION+USED+THEREIN&rft.date=2003-03-07">  </li> <li id="cite_note-Ibeh-31">^ <a href="#cite_ref-Ibeh_31-0">a</a> <a href="#cite_ref-Ibeh_31-1">b</a> <a href="#cite_ref-Ibeh_31-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIbeh,_Christopher_C.2011" class="citation book cs1">Ibeh, Christopher C. (2011). THERMOPLASTIC MATERIALS Properties, Manufacturing Methods, and Applications. CRC Press. pp. 491–497. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4200-9383-4" title="Special:BookSources/978-1-4200-9383-4"><bdi>978-1-4200-9383-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=THERMOPLASTIC+MATERIALS+Properties%2C+Manufacturing+Methods%2C+and+Applications&rft.pages=491-497&rft.pub=CRC+Press&rft.date=2011&rft.isbn=978-1-4200-9383-4&rft.au=Ibeh%2C+Christopher+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-PVC-32">^ <a href="#cite_ref-PVC_32-0">a</a> <a href="#cite_ref-PVC_32-1">b</a> <a href="#cite_ref-PVC_32-2">c</a> <a href="#cite_ref-PVC_32-3">d</a> <a href="#cite_ref-PVC_32-4">e</a> <a href="#cite_ref-PVC_32-5">f</a> <a href="#cite_ref-PVC_32-6">g</a> <a href="#cite_ref-PVC_32-7">h</a> <a href="#cite_ref-PVC_32-8">i</a> <a href="#cite_ref-PVC_32-9">j</a> <a href="#cite_ref-PVC_32-10">k</a> <a href="#cite_ref-PVC_32-11">l</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilkes,_C._E.2005" class="citation book cs1">Wilkes, C. E. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YUkJNI9QYsUC&pg=PT1">PVC Handbook</a>. Hanser Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56990-379-7" title="Special:BookSources/978-1-56990-379-7"><bdi>978-1-56990-379-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220403203715/https://books.google.com/books?id=YUkJNI9QYsUC&pg=PT1">Archived</a> from the original on 2022-04-03. Retrieved 2016-09-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=PVC+Handbook&rft.pub=Hanser+Verlag&rft.date=2005&rft.isbn=978-1-56990-379-7&rft.au=Wilkes%2C+C.+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYUkJNI9QYsUC%26pg%3DPT1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-ABS-33"><a href="#cite_ref-ABS_33-0">^</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120227150812/https://www.nrri.umn.edu/NLTC/ABS07.pdf">ABS</a>. nrri.umn.edu </li> <li id="cite_note-34"><a href="#cite_ref-34">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNicholson,_John_W.2011" class="citation book cs1">Nicholson, John W. (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=5XFsT69cX_YC&q=polymer+chemistry">The Chemistry of Polymers</a> (4, Revised ed.). Royal Society of Chemistry. p. 50. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781849733915" title="Special:BookSources/9781849733915"><bdi>9781849733915</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220410045651/https://books.google.com/books?id=5XFsT69cX_YC&q=polymer+chemistry">Archived</a> from the original on 10 April 2022. Retrieved 10 September 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Chemistry+of+Polymers&rft.pages=50&rft.edition=4%2C+Revised&rft.pub=Royal+Society+of+Chemistry&rft.date=2011&rft.isbn=9781849733915&rft.au=Nicholson%2C+John+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D5XFsT69cX_YC%26q%3Dpolymer%2Bchemistry&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-35"><a href="#cite_ref-35">^</a> <a rel="nofollow" class="external text" href="http://www.polymerprocessing.com/polymers/PA6.html">nylon-6 information and properties</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120110015535/http://www.polymerprocessing.com/polymers/PA6.html">Archived</a> 2012-01-10 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Polymerprocessing.com (2001-04-15). Retrieved on 2012-06-29. </li> <li id="cite_note-36"><a href="#cite_ref-36">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2014" class="citation journal cs1">Jones, A (2014). "Supplementary Materials for Artificial Muscles from Fishing Line and Sewing Thread". Science. 343 (6173): 868–72. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014Sci...343..868H">2014Sci...343..868H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1246906">10.1126/science.1246906</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24558156">24558156</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16577662">16577662</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Supplementary+Materials+for+Artificial+Muscles+from+Fishing+Line+and+Sewing+Thread&rft.volume=343&rft.issue=6173&rft.pages=868-72&rft.date=2014&rft_id=info%3Adoi%2F10.1126%2Fscience.1246906&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16577662%23id-name%3DS2CID&rft_id=info%3Apmid%2F24558156&rft_id=info%3Abibcode%2F2014Sci...343..868H&rft.aulast=Jones&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-37"><a href="#cite_ref-37">^</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150520110712/http://www.tainstruments.co.jp/application/pdf/Thermal_Library/Applications_Briefs/TA133.PDF">Measurement of Moisture Effects on the Mechanical Properties of 66 Nylon</a>. TA Instruments Thermal Analysis Application Brief TA-133 </li> <li id="cite_note-38"><a href="#cite_ref-38">^</a> <a rel="nofollow" class="external text" href="http://www.polyesterconverters.com/pcl_apps/stage1/stage2/applications_and_enduses/polyethene.htm">PCL | Applications and End Uses | Polythene</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130605113814/http://www.polyesterconverters.com/pcl_apps/stage1/stage2/applications_and_enduses/polyethene.htm">Archived</a> 2013-06-05 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Polyesterconverters.com. Retrieved on 2012-06-29. </li> <li id="cite_note-39"><a href="#cite_ref-39">^</a> <a rel="nofollow" class="external text" href="http://www.epcos.org/library/papers/pdf_2007/paper13_Salinga.pdf">EPCOS 2007: Glass Transition and Crystallization in Phase Change Materials</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110726033309/http://www.epcos.org/library/papers/pdf_2007/paper13_Salinga.pdf">Archived</a> 2011-07-26 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> . Retrieved on 2012-06-29. </li> <li id="cite_note-40"><a href="#cite_ref-40">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBucaro1974" class="citation journal cs1">Bucaro, J. A. (1974). "High-temperature Brillouin scattering in fused quartz". Journal of Applied Physics. 45 (12): 5324–5329. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1974JAP....45.5324B">1974JAP....45.5324B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1663238">10.1063/1.1663238</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=High-temperature+Brillouin+scattering+in+fused+quartz&rft.volume=45&rft.issue=12&rft.pages=5324-5329&rft.date=1974&rft_id=info%3Adoi%2F10.1063%2F1.1663238&rft_id=info%3Abibcode%2F1974JAP....45.5324B&rft.aulast=Bucaro&rft.aufirst=J.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-:2-41">^ <a href="#cite_ref-:2_41-0">a</a> <a href="#cite_ref-:2_41-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPohlLoveStephens1973" class="citation report cs1">Pohl, R. O.; Love, W. F.; Stephens, R. B. (1973-08-01). <a rel="nofollow" class="external text" href="https://www.osti.gov/biblio/4410557">Lattice vibrations in noncrystalline solids</a> (Report). Cornell Univ., Ithaca, N.Y. (USA). Lab. of Atomic and Solid State Physics. <a href="/wiki/OSTI_(identifier)" class="mw-redirect" title="OSTI (identifier)">OSTI</a> <a rel="nofollow" class="external text" href="https://www.osti.gov/biblio/4410557">4410557</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Lattice+vibrations+in+noncrystalline+solids&rft.pub=Cornell+Univ.%2C+Ithaca%2C+N.Y.+%28USA%29.+Lab.+of+Atomic+and+Solid+State+Physics&rft.date=1973-08-01&rft_id=https%3A%2F%2Fwww.osti.gov%2Fbiblio%2F4410557%23id-name%3DOSTI&rft.aulast=Pohl&rft.aufirst=R.+O.&rft.au=Love%2C+W.+F.&rft.au=Stephens%2C+R.+B.&rft_id=https%3A%2F%2Fwww.osti.gov%2Fbiblio%2F4410557&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-42"><a href="#cite_ref-42">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZellerPohl1971" class="citation journal cs1">Zeller, R. C.; Pohl, R. O. (1971-09-15). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRevB.4.2029">"Thermal Conductivity and Specific Heat of Noncrystalline Solids"</a>. Physical Review B. 4 (6): 2029–2041. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1971PhRvB...4.2029Z">1971PhRvB...4.2029Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevB.4.2029">10.1103/PhysRevB.4.2029</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+B&rft.atitle=Thermal+Conductivity+and+Specific+Heat+of+Noncrystalline+Solids&rft.volume=4&rft.issue=6&rft.pages=2029-2041&rft.date=1971-09-15&rft_id=info%3Adoi%2F10.1103%2FPhysRevB.4.2029&rft_id=info%3Abibcode%2F1971PhRvB...4.2029Z&rft.aulast=Zeller&rft.aufirst=R.+C.&rft.au=Pohl%2C+R.+O.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRevB.4.2029&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-43"><a href="#cite_ref-43">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAndersonHalperinVarma1972" class="citation journal cs1">Anderson, P. w.; Halperin, B. I.; Varma, c. M. (January 1972). <a rel="nofollow" class="external text" href="http://www.tandfonline.com/doi/abs/10.1080/14786437208229210">"Anomalous low-temperature thermal properties of glasses and spin glasses"</a>. Philosophical Magazine. 25 (1): 1–9. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1972PMag...25....1A">1972PMag...25....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786437208229210">10.1080/14786437208229210</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-8086">0031-8086</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=Anomalous+low-temperature+thermal+properties+of+glasses+and+spin+glasses&rft.volume=25&rft.issue=1&rft.pages=1-9&rft.date=1972-01&rft.issn=0031-8086&rft_id=info%3Adoi%2F10.1080%2F14786437208229210&rft_id=info%3Abibcode%2F1972PMag...25....1A&rft.aulast=Anderson&rft.aufirst=P.+w.&rft.au=Halperin%2C+B.+I.&rft.au=Varma%2C+c.+M.&rft_id=http%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Fabs%2F10.1080%2F14786437208229210&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-44"><a href="#cite_ref-44">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKauzmann1948" class="citation journal cs1">Kauzmann, Walter (1948). "The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures". Chemical Reviews. 43 (2): 219–256. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fcr60135a002">10.1021/cr60135a002</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chemical+Reviews&rft.atitle=The+Nature+of+the+Glassy+State+and+the+Behavior+of+Liquids+at+Low+Temperatures&rft.volume=43&rft.issue=2&rft.pages=219-256&rft.date=1948&rft_id=info%3Adoi%2F10.1021%2Fcr60135a002&rft.aulast=Kauzmann&rft.aufirst=Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-:0-45">^ <a href="#cite_ref-:0_45-0">a</a> <a href="#cite_ref-:0_45-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolchover2020" class="citation web cs1">Wolchover, Natalie (11 March 2020). <a rel="nofollow" class="external text" href="https://www.quantamagazine.org/ideal-glass-would-explain-why-glass-exists-at-all-20200311">"Ideal Glass Would Explain Why Glass Exists at All"</a>. Quanta Magazine. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200407071119/https://www.quantamagazine.org/ideal-glass-would-explain-why-glass-exists-at-all-20200311/">Archived</a> from the original on 7 April 2020. Retrieved 3 April 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Quanta+Magazine&rft.atitle=Ideal+Glass+Would+Explain+Why+Glass+Exists+at+All&rft.date=2020-03-11&rft.aulast=Wolchover&rft.aufirst=Natalie&rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fideal-glass-would-explain-why-glass-exists-at-all-20200311&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-46"><a href="#cite_ref-46">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbsDiMarzio1958" class="citation journal cs1">Gibbs, Julian H.; DiMarzio, Edmund A. (1958-03-01). <a rel="nofollow" class="external text" href="https://pubs.aip.org/jcp/article/28/3/373/75478/Nature-of-the-Glass-Transition-and-the-Glassy">"Nature of the Glass Transition and the Glassy State"</a>. The Journal of Chemical Physics. 28 (3): 373–383. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1958JChPh..28..373G">1958JChPh..28..373G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1744141">10.1063/1.1744141</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-9606">0021-9606</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Chemical+Physics&rft.atitle=Nature+of+the+Glass+Transition+and+the+Glassy+State&rft.volume=28&rft.issue=3&rft.pages=373-383&rft.date=1958-03-01&rft.issn=0021-9606&rft_id=info%3Adoi%2F10.1063%2F1.1744141&rft_id=info%3Abibcode%2F1958JChPh..28..373G&rft.aulast=Gibbs&rft.aufirst=Julian+H.&rft.au=DiMarzio%2C+Edmund+A.&rft_id=https%3A%2F%2Fpubs.aip.org%2Fjcp%2Farticle%2F28%2F3%2F373%2F75478%2FNature-of-the-Glass-Transition-and-the-Glassy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-47"><a href="#cite_ref-47">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwallenKearnsMapesKim2007" class="citation journal cs1">Swallen, Stephen F.; Kearns, Kenneth L.; Mapes, Marie K.; Kim, Yong Seol; McMahon, Robert J.; Ediger, M. D.; Wu, Tian; Yu, Lian; Satija, Sushil (2007-01-19). <a rel="nofollow" class="external text" href="https://www.science.org/doi/10.1126/science.1135795">"Organic Glasses with Exceptional Thermodynamic and Kinetic Stability"</a>. Science. 315 (5810): 353–356. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007Sci...315..353S">2007Sci...315..353S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1135795">10.1126/science.1135795</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0036-8075">0036-8075</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17158289">17158289</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Organic+Glasses+with+Exceptional+Thermodynamic+and+Kinetic+Stability&rft.volume=315&rft.issue=5810&rft.pages=353-356&rft.date=2007-01-19&rft_id=info%3Adoi%2F10.1126%2Fscience.1135795&rft.issn=0036-8075&rft_id=info%3Apmid%2F17158289&rft_id=info%3Abibcode%2F2007Sci...315..353S&rft.aulast=Swallen&rft.aufirst=Stephen+F.&rft.au=Kearns%2C+Kenneth+L.&rft.au=Mapes%2C+Marie+K.&rft.au=Kim%2C+Yong+Seol&rft.au=McMahon%2C+Robert+J.&rft.au=Ediger%2C+M.+D.&rft.au=Wu%2C+Tian&rft.au=Yu%2C+Lian&rft.au=Satija%2C+Sushil&rft_id=https%3A%2F%2Fwww.science.org%2Fdoi%2F10.1126%2Fscience.1135795&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-48"><a href="#cite_ref-48">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOjovan_M.I.2008" class="citation journal cs1">Ojovan M.I. (2008). <a rel="nofollow" class="external text" href="http://www.mdpi.org/entropy/papers/e10030334.pdf">"Configurons: thermodynamic parameters and symmetry changes at glass transition"</a> (PDF). Entropy. 10 (3): 334–364. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008Entrp..10..334O">2008Entrp..10..334O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe10030334">10.3390/e10030334</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090711015530/http://www.mdpi.org/entropy/papers/e10030334.pdf">Archived</a> (PDF) from the original on 2009-07-11. Retrieved 2009-09-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=Configurons%3A+thermodynamic+parameters+and+symmetry+changes+at+glass+transition&rft.volume=10&rft.issue=3&rft.pages=334-364&rft.date=2008&rft_id=info%3Adoi%2F10.3390%2Fe10030334&rft_id=info%3Abibcode%2F2008Entrp..10..334O&rft.au=Ojovan+M.I.&rft_id=http%3A%2F%2Fwww.mdpi.org%2Fentropy%2Fpapers%2Fe10030334.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-49"><a href="#cite_ref-49">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOjovan,_M.I.2008" class="citation journal cs1">Ojovan, M.I. (2008). <a rel="nofollow" class="external text" href="http://www.mdpi.org/entropy/papers/e10030334.pdf">"Configurons: thermodynamic parameters and symmetry changes at glass transition"</a> (PDF). Entropy. 10 (3): 334–364. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008Entrp..10..334O">2008Entrp..10..334O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe10030334">10.3390/e10030334</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090711015530/http://www.mdpi.org/entropy/papers/e10030334.pdf">Archived</a> (PDF) from the original on 2009-07-11. Retrieved 2009-09-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=Configurons%3A+thermodynamic+parameters+and+symmetry+changes+at+glass+transition&rft.volume=10&rft.issue=3&rft.pages=334-364&rft.date=2008&rft_id=info%3Adoi%2F10.3390%2Fe10030334&rft_id=info%3Abibcode%2F2008Entrp..10..334O&rft.au=Ojovan%2C+M.I.&rft_id=http%3A%2F%2Fwww.mdpi.org%2Fentropy%2Fpapers%2Fe10030334.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-50"><a href="#cite_ref-50">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOjovanTravisHand2007" class="citation journal cs1">Ojovan, Michael I; Travis, Karl P; Hand, Russell J (2007). <a rel="nofollow" class="external text" href="http://eprints.whiterose.ac.uk/4058/1/ojovanm1.pdf">"Thermodynamic parameters of bonds in glassy materials from viscosity–temperature relationships"</a> (PDF). Journal of Physics: Condensed Matter. 19 (41): 415107. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007JPCM...19O5107O">2007JPCM...19O5107O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0953-8984%2F19%2F41%2F415107">10.1088/0953-8984/19/41/415107</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28192319">28192319</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:24724512">24724512</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180725094232/http://eprints.whiterose.ac.uk/4058/1/ojovanm1.pdf">Archived</a> (PDF) from the original on 2018-07-25. Retrieved 2019-07-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics%3A+Condensed+Matter&rft.atitle=Thermodynamic+parameters+of+bonds+in+glassy+materials+from+viscosity%E2%80%93temperature+relationships&rft.volume=19&rft.issue=41&rft.pages=415107&rft.date=2007&rft_id=info%3Adoi%2F10.1088%2F0953-8984%2F19%2F41%2F415107&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A24724512%23id-name%3DS2CID&rft_id=info%3Apmid%2F28192319&rft_id=info%3Abibcode%2F2007JPCM...19O5107O&rft.aulast=Ojovan&rft.aufirst=Michael+I&rft.au=Travis%2C+Karl+P&rft.au=Hand%2C+Russell+J&rft_id=http%3A%2F%2Feprints.whiterose.ac.uk%2F4058%2F1%2Fojovanm1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-51"><a href="#cite_ref-51">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNguyenLiaWallumLyding2019" class="citation journal cs1">Nguyen, Huy; Lia, Can; Wallum, Alison; Lyding, Joseph; Gruebele, Martin (2019). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844102">"Multi-scale dynamics at the glassy silica surface"</a>. J. Chem. Phys. 151 (1): 62–68. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnphys1432">10.1038/nphys1432</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844102">2844102</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20336168">20336168</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Chem.+Phys.&rft.atitle=Multi-scale+dynamics+at+the+glassy+silica+surface&rft.volume=151&rft.issue=1&rft.pages=62-68&rft.date=2019&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2844102%23id-name%3DPMC&rft_id=info%3Apmid%2F20336168&rft_id=info%3Adoi%2F10.1038%2Fnphys1432&rft.aulast=Nguyen&rft.aufirst=Huy&rft.au=Lia%2C+Can&rft.au=Wallum%2C+Alison&rft.au=Lyding%2C+Joseph&rft.au=Gruebele%2C+Martin&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2844102&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-52"><a href="#cite_ref-52">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolynesStevenson2009" class="citation journal cs1">Wolynes, PG; Stevenson, JD (2009). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844102">"A universal origin for secondary relaxations in supercooled liquids and structural glasses"</a>. Nature Physics. 6 (1): 62–68. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.5123228">10.1063/1.5123228</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844102">2844102</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20336168">20336168</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Physics&rft.atitle=A+universal+origin+for+secondary+relaxations+in+supercooled+liquids+and+structural+glasses&rft.volume=6&rft.issue=1&rft.pages=62-68&rft.date=2009&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2844102%23id-name%3DPMC&rft_id=info%3Apmid%2F20336168&rft_id=info%3Adoi%2F10.1063%2F1.5123228&rft.aulast=Wolynes&rft.aufirst=PG&rft.au=Stevenson%2C+JD&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2844102&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-53"><a href="#cite_ref-53">^</a> Cowie, J. M. G. and Arrighi, V., Polymers: Chemistry and Physics of Modern Materials, 3rd Edn. (CRC Press, 2007) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0748740732" title="Special:BookSources/0748740732">0748740732</a> </li> <li id="cite_note-54"><a href="#cite_ref-54">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCapponiAlvarezRacko2020" class="citation cs2">Capponi, S.; Alvarez, F.; Racko, D. (2020), "Free Volume in a PVME Polymer–Water Solution", Macromolecules, 53 (12): 4770–4782, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020MaMol..53.4770C">2020MaMol..53.4770C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Facs.macromol.0c00472">10.1021/acs.macromol.0c00472</a>, <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10261%2F218380">10261/218380</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:219911779">219911779</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Macromolecules&rft.atitle=Free+Volume+in+a+PVME+Polymer%E2%80%93Water+Solution&rft.volume=53&rft.issue=12&rft.pages=4770-4782&rft.date=2020&rft_id=info%3Ahdl%2F10261%2F218380&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A219911779%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1021%2Facs.macromol.0c00472&rft_id=info%3Abibcode%2F2020MaMol..53.4770C&rft.aulast=Capponi&rft.aufirst=S.&rft.au=Alvarez%2C+F.&rft.au=Racko%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-55"><a href="#cite_ref-55">^</a> Slater, J.C., Introduction to Chemical Physics (3rd Ed., Martindell Press, 2007) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1178626598" title="Special:BookSources/1178626598">1178626598</a> </li> <li id="cite_note-56"><a href="#cite_ref-56">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn2008" class="citation journal cs1">Born, Max (2008). "On the stability of crystal lattices. I". Mathematical Proceedings of the Cambridge Philosophical Society. 36 (2): 160–172. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1940PCPS...36..160B">1940PCPS...36..160B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0305004100017138">10.1017/S0305004100017138</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:104272002">104272002</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Proceedings+of+the+Cambridge+Philosophical+Society&rft.atitle=On+the+stability+of+crystal+lattices.+I&rft.volume=36&rft.issue=2&rft.pages=160-172&rft.date=2008&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A104272002%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1017%2FS0305004100017138&rft_id=info%3Abibcode%2F1940PCPS...36..160B&rft.aulast=Born&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-57"><a href="#cite_ref-57">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn1939" class="citation journal cs1">Born, Max (1939). "Thermodynamics of Crystals and Melting". The Journal of Chemical Physics. 7 (8): 591–603. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1939JChPh...7..591B">1939JChPh...7..591B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1750497">10.1063/1.1750497</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Chemical+Physics&rft.atitle=Thermodynamics+of+Crystals+and+Melting&rft.volume=7&rft.issue=8&rft.pages=591-603&rft.date=1939&rft_id=info%3Adoi%2F10.1063%2F1.1750497&rft_id=info%3Abibcode%2F1939JChPh...7..591B&rft.aulast=Born&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-D-58"><a href="#cite_ref-D_58-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrenkel,_J.1946" class="citation book cs1">Frenkel, J. (1946). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.53485">Kinetic Theory of Liquids</a>. Clarendon Press, Oxford.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kinetic+Theory+of+Liquids&rft.pub=Clarendon+Press%2C+Oxford&rft.date=1946&rft.au=Frenkel%2C+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.53485&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-59"><a href="#cite_ref-59">^</a> Bartenev, G. M., Structure and Mechanical Properties of Inorganic Glasses (Wolters – Noordhoof, 1970) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9001054501" title="Special:BookSources/9001054501">9001054501</a> </li> <li id="cite_note-60"><a href="#cite_ref-60">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReynolds,_C._L._Jr.1979" class="citation journal cs1">Reynolds, C. L. Jr. (1979). "Correlation between the low temperature phonon mean free path and glass transition temperature in amorphous solids". J. Non-Cryst. Solids. 30 (3): 371. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1979JNCS...30..371R">1979JNCS...30..371R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3093%2879%2990174-1">10.1016/0022-3093(79)90174-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Non-Cryst.+Solids&rft.atitle=Correlation+between+the+low+temperature+phonon+mean+free+path+and+glass+transition+temperature+in+amorphous+solids&rft.volume=30&rft.issue=3&rft.pages=371&rft.date=1979&rft_id=info%3Adoi%2F10.1016%2F0022-3093%2879%2990174-1&rft_id=info%3Abibcode%2F1979JNCS...30..371R&rft.au=Reynolds%2C+C.+L.+Jr.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-61"><a href="#cite_ref-61">^</a> Rosenburg, H. M. (1963) Low Temperature Solid State Physics. Clarendon Press, Oxford. </li> <li id="cite_note-62"><a href="#cite_ref-62">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKittel,_C.1946" class="citation journal cs1">Kittel, C. (1946). "Ultrasonic Propagation in Liquids". J. Chem. Phys. 14 (10): 614. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1946JChPh..14..614K">1946JChPh..14..614K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1724073">10.1063/1.1724073</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F5041">1721.1/5041</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Chem.+Phys.&rft.atitle=Ultrasonic+Propagation+in+Liquids&rft.volume=14&rft.issue=10&rft.pages=614&rft.date=1946&rft_id=info%3Ahdl%2F1721.1%2F5041&rft_id=info%3Adoi%2F10.1063%2F1.1724073&rft_id=info%3Abibcode%2F1946JChPh..14..614K&rft.au=Kittel%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKittel,_C.1949" class="citation journal cs1">Kittel, C. (1949). "Interpretation of the Thermal Conductivity of Glasses". Phys. Rev. 75 (6): 972. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1949PhRv...75..972K">1949PhRv...75..972K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.75.972">10.1103/PhysRev.75.972</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.&rft.atitle=Interpretation+of+the+Thermal+Conductivity+of+Glasses&rft.volume=75&rft.issue=6&rft.pages=972&rft.date=1949&rft_id=info%3Adoi%2F10.1103%2FPhysRev.75.972&rft_id=info%3Abibcode%2F1949PhRv...75..972K&rft.au=Kittel%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-64"><a href="#cite_ref-64">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChenEgamiVitek1985" class="citation journal cs1">Chen, Shao-Ping; Egami, T.; Vitek, V. (1985). "Orientational ordering of local shear stresses in liquids: A phase transition?". Journal of Non-Crystalline Solids. 75 (1–3): 449. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1985JNCS...75..449C">1985JNCS...75..449C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3093%2885%2990256-X">10.1016/0022-3093(85)90256-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Non-Crystalline+Solids&rft.atitle=Orientational+ordering+of+local+shear+stresses+in+liquids%3A+A+phase+transition%3F&rft.volume=75&rft.issue=1%E2%80%933&rft.pages=449&rft.date=1985&rft_id=info%3Adoi%2F10.1016%2F0022-3093%2885%2990256-X&rft_id=info%3Abibcode%2F1985JNCS...75..449C&rft.aulast=Chen&rft.aufirst=Shao-Ping&rft.au=Egami%2C+T.&rft.au=Vitek%2C+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-65"><a href="#cite_ref-65">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSorkin2005" class="citation thesis cs1">Sorkin, Viacheslav (2005). <a rel="nofollow" class="external text" href="http://phycomp.technion.ac.il/~phsorkin/thesis/thesis.pdf">"Lindemann criterion"</a> (PDF). Point Defects, Lattice Structure and Melting (MSc). Israel Institute of Technology. pp. 5–8. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190819095312/http://phycomp.technion.ac.il/~phsorkin/thesis/thesis.pdf">Archived</a> (PDF) from the original on 19 August 2019. Retrieved 6 January 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Point+Defects%2C+Lattice+Structure+and+Melting&rft.inst=Israel+Institute+of+Technology&rft.date=2005&rft.aulast=Sorkin&rft.aufirst=Viacheslav&rft_id=http%3A%2F%2Fphycomp.technion.ac.il%2F~phsorkin%2Fthesis%2Fthesis.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-66"><a href="#cite_ref-66">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMott,_N._F.1934" class="citation journal cs1">Mott, N. F. (1934). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1934.0166">"The Resistance of Liquid Metals"</a>. <a href="/wiki/Proceedings_of_the_Royal_Society_A" class="mw-redirect" title="Proceedings of the Royal Society A">Proceedings of the Royal Society A</a>. 146 (857): 465. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1934RSPSA.146..465M">1934RSPSA.146..465M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1934.0166">10.1098/rspa.1934.0166</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.atitle=The+Resistance+of+Liquid+Metals&rft.volume=146&rft.issue=857&rft.pages=465&rft.date=1934&rft_id=info%3Adoi%2F10.1098%2Frspa.1934.0166&rft_id=info%3Abibcode%2F1934RSPSA.146..465M&rft.au=Mott%2C+N.+F.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frspa.1934.0166&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-67"><a href="#cite_ref-67">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindemann,_C.1911" class="citation journal cs1">Lindemann, C. (1911). "On the calculation of molecular natural frequencies". Phys. Z. 11: 609.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Z.&rft.atitle=On+the+calculation+of+molecular+natural+frequencies&rft.volume=11&rft.pages=609&rft.date=1911&rft.au=Lindemann%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-68"><a href="#cite_ref-68">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlementWillensDuwez1960" class="citation journal cs1">Klement, W.; Willens, R. H.; Duwez, POL (1960). "Non-crystalline Structure in Solidified Gold–Silicon Alloys". Nature. 187 (4740): 869. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960Natur.187..869K">1960Natur.187..869K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F187869b0">10.1038/187869b0</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4203025">4203025</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Non-crystalline+Structure+in+Solidified+Gold%E2%80%93Silicon+Alloys&rft.volume=187&rft.issue=4740&rft.pages=869&rft.date=1960&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4203025%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F187869b0&rft_id=info%3Abibcode%2F1960Natur.187..869K&rft.aulast=Klement&rft.aufirst=W.&rft.au=Willens%2C+R.+H.&rft.au=Duwez%2C+POL&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-69"><a href="#cite_ref-69">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuwezWillensKlement1960" class="citation journal cs1">Duwez, Pol; Willens, R. H.; Klement, W. (1960). <a rel="nofollow" class="external text" href="http://authors.library.caltech.edu/3755/1/DUWjap60.pdf">"Continuous Series of Metastable Solid Solutions in Silver-Copper Alloys"</a> (PDF). Journal of Applied Physics. 31 (6): 1136. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960JAP....31.1136D">1960JAP....31.1136D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1735777">10.1063/1.1735777</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171202104916/https://authors.library.caltech.edu/3755/1/DUWjap60.pdf">Archived</a> (PDF) from the original on 2017-12-02. Retrieved 2018-05-16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=Continuous+Series+of+Metastable+Solid+Solutions+in+Silver-Copper+Alloys&rft.volume=31&rft.issue=6&rft.pages=1136&rft.date=1960&rft_id=info%3Adoi%2F10.1063%2F1.1735777&rft_id=info%3Abibcode%2F1960JAP....31.1136D&rft.aulast=Duwez&rft.aufirst=Pol&rft.au=Willens%2C+R.+H.&rft.au=Klement%2C+W.&rft_id=http%3A%2F%2Fauthors.library.caltech.edu%2F3755%2F1%2FDUWjap60.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuwezWillensKlement1960" class="citation journal cs1">Duwez, Pol; Willens, R. H.; Klement, W. (1960). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/33559/1/DUWjap60b.pdf">"Metastable Electron Compound in Ag-Ge Alloys"</a> (PDF). Journal of Applied Physics. 31 (6): 1137. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960JAP....31.1137D">1960JAP....31.1137D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1735778">10.1063/1.1735778</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200418184208/https://authors.library.caltech.edu/33559/1/DUWjap60b.pdf">Archived</a> (PDF) from the original on 2020-04-18. Retrieved 2019-07-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=Metastable+Electron+Compound+in+Ag-Ge+Alloys&rft.volume=31&rft.issue=6&rft.pages=1137&rft.date=1960&rft_id=info%3Adoi%2F10.1063%2F1.1735778&rft_id=info%3Abibcode%2F1960JAP....31.1137D&rft.aulast=Duwez&rft.aufirst=Pol&rft.au=Willens%2C+R.+H.&rft.au=Klement%2C+W.&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F33559%2F1%2FDUWjap60b.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-71"><a href="#cite_ref-71">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChaudhariTurnbull1978" class="citation journal cs1">Chaudhari, P; Turnbull, D (1978). "Structure and properties of metallic glasses". Science. 199 (4324): 11–21. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1978Sci...199...11C">1978Sci...199...11C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.199.4324.11">10.1126/science.199.4324.11</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17841932">17841932</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7786426">7786426</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Structure+and+properties+of+metallic+glasses&rft.volume=199&rft.issue=4324&rft.pages=11-21&rft.date=1978&rft_id=info%3Adoi%2F10.1126%2Fscience.199.4324.11&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7786426%23id-name%3DS2CID&rft_id=info%3Apmid%2F17841932&rft_id=info%3Abibcode%2F1978Sci...199...11C&rft.aulast=Chaudhari&rft.aufirst=P&rft.au=Turnbull%2C+D&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-72"><a href="#cite_ref-72">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChen,_J._S.1980" class="citation journal cs1">Chen, J. S. (1980). "Glassy metals". Reports on Progress in Physics. 43 (4): 353. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1980RPPh...43..353C">1980RPPh...43..353C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F43%2F4%2F001">10.1088/0034-4885/43/4/001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:250804009">250804009</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reports+on+Progress+in+Physics&rft.atitle=Glassy+metals&rft.volume=43&rft.issue=4&rft.pages=353&rft.date=1980&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250804009%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F43%2F4%2F001&rft_id=info%3Abibcode%2F1980RPPh...43..353C&rft.au=Chen%2C+J.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJonson,_M.Girvin,_S._M.1979" class="citation journal cs1">Jonson, M.; Girvin, S. M. (1979). "Electron-Phonon Dynamics and Transport Anomalies in Random Metal Alloys". Phys. Rev. Lett. 43 (19): 1447. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1979PhRvL..43.1447J">1979PhRvL..43.1447J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.43.1447">10.1103/PhysRevLett.43.1447</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+Lett.&rft.atitle=Electron-Phonon+Dynamics+and+Transport+Anomalies+in+Random+Metal+Alloys&rft.volume=43&rft.issue=19&rft.pages=1447&rft.date=1979&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.43.1447&rft_id=info%3Abibcode%2F1979PhRvL..43.1447J&rft.au=Jonson%2C+M.&rft.au=Girvin%2C+S.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-74"><a href="#cite_ref-74">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTurnbull,_D.1974" class="citation journal cs1">Turnbull, D. (1974). "Amorphous Solid Formation and Interstitial Solution Behavior in Metallic Alloy System". J. Phys. C. 35 (C4): C4–1. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.596.7462">10.1.1.596.7462</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1051%2Fjphyscol%3A1974401">10.1051/jphyscol:1974401</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:52102270">52102270</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Phys.+C&rft.atitle=Amorphous+Solid+Formation+and+Interstitial+Solution+Behavior+in+Metallic+Alloy+System&rft.volume=35&rft.issue=C4&rft.pages=C4-1&rft.date=1974&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.596.7462%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A52102270%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1051%2Fjphyscol%3A1974401&rft.au=Turnbull%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChen,_H._S.Park,_B._K.1973" class="citation journal cs1">Chen, H. S.; Park, B. K. (1973). "Role of chemical bonding in metallic glasses". Acta Metall. 21 (4): 395. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0001-6160%2873%2990196-X">10.1016/0001-6160(73)90196-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Metall.&rft.atitle=Role+of+chemical+bonding+in+metallic+glasses&rft.volume=21&rft.issue=4&rft.pages=395&rft.date=1973&rft_id=info%3Adoi%2F10.1016%2F0001-6160%2873%2990196-X&rft.au=Chen%2C+H.+S.&rft.au=Park%2C+B.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> <li id="cite_note-76"><a href="#cite_ref-76">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWang,_R.Merz,_D.1977" class="citation journal cs1">Wang, R.; Merz, D. (1977). "Polymorphic bonding and thermal stability of elemental noncrystalline solids". Physica Status Solidi A. 39 (2): 697. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977PSSAR..39..697W">1977PSSAR..39..697W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fpssa.2210390240">10.1002/pssa.2210390240</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physica+Status+Solidi+A&rft.atitle=Polymorphic+bonding+and+thermal+stability+of+elemental+noncrystalline+solids&rft.volume=39&rft.issue=2&rft.pages=697&rft.date=1977&rft_id=info%3Adoi%2F10.1002%2Fpssa.2210390240&rft_id=info%3Abibcode%2F1977PSSAR..39..697W&rft.au=Wang%2C+R.&rft.au=Merz%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGlass+transition" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Glass_transition&action=edit&section=17" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Category:Glass-liquid_transitions" class="extiw" title="commons:Category:Glass-liquid transitions">Glass-liquid transitions</a>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://eprints.iisc.ernet.in/archive/00000257/01/kjrao.pdf">Fragility</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070628185015/http://eprints.iisc.ernet.in/archive/00000257/01/kjrao.pdf">Archived</a> 2007-06-28 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.iop.org/EJ/abstract/0953-8984/12/46/305">VFT Eqn.</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190115195943/http://pslc.ws/macrog/tg.htm">Polymers I</a></li> <li><a rel="nofollow" class="external text" href="http://www.lasalle.edu/academ/chem/ms/polymersRus/Resources/GlassTrans.htm">Polymers II</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100111055937/http://www.lasalle.edu/academ/chem/ms/polymersRus/Resources/GlassTrans.htm">Archived</a> 2010-01-11 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.public.asu.edu/~caangell/Abstracts/395.pdf">Angell: Aqueous media</a></li> <li><a rel="nofollow" class="external text" href="http://www.doitpoms.ac.uk/tlplib/glass-transition/index.php">DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"</a></li> <li><a rel="nofollow" class="external text" href="https://coatings.specialchem.com/coatings-properties/glass-transition-temperature">Glass Transition Temperature short overview</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Glass_science_topics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Glass_science" title="Template:Glass science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Glass_science" title="Template talk:Glass science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Glass_science" title="Special:EditPage/Template:Glass science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Glass_science_topics" style="font-size:114%;margin:0 4em"><a href="/wiki/Glass" title="Glass">Glass</a> science topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glass" title="Glass">Glass</a></li> <li><a class="mw-selflink selflink">Glass transition</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AgInSbTe" title="AgInSbTe">AgInSbTe</a></li> <li><a href="/wiki/Bioglass" class="mw-redirect" title="Bioglass">Bioglass</a></li> <li><a href="/wiki/Borophosphosilicate_glass" title="Borophosphosilicate glass">Borophosphosilicate glass</a></li> <li><a href="/wiki/Borosilicate_glass" title="Borosilicate glass">Borosilicate glass</a></li> <li><a href="/wiki/Ceramic_glaze" title="Ceramic glaze">Ceramic glaze</a></li> <li><a href="/wiki/Chalcogenide_glass" title="Chalcogenide glass">Chalcogenide glass</a></li> <li><a href="/wiki/Cobalt_glass" title="Cobalt glass">Cobalt glass</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Cranberry glass</a></li> <li><a href="/wiki/Crown_glass_(optics)" title="Crown glass (optics)">Crown glass</a></li> <li><a href="/wiki/Flint_glass" title="Flint glass">Flint glass</a></li> <li><a href="/wiki/Fluorosilicate_glass" title="Fluorosilicate glass">Fluorosilicate glass</a></li> <li><a href="/wiki/Fused_quartz" title="Fused quartz">Fused quartz</a></li> <li><a href="/wiki/GeSbTe" title="GeSbTe">GeSbTe</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Gold ruby glass</a></li> <li><a href="/wiki/Lead_glass" title="Lead glass">Lead glass</a></li> <li><a href="/wiki/Milk_glass" title="Milk glass">Milk glass</a></li> <li><a href="/wiki/Phosphosilicate_glass" title="Phosphosilicate glass">Phosphosilicate glass</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens glass</a></li> <li><a href="/wiki/Glass#Silicate_glass" title="Glass">Silicate glass</a></li> <li><a href="/wiki/Soda%E2%80%93lime_glass" title="Soda–lime glass">Soda–lime glass</a></li> <li><a href="/wiki/Sodium_hexametaphosphate" title="Sodium hexametaphosphate">Sodium hexametaphosphate</a></li> <li><a href="/wiki/Sodium_silicate" title="Sodium silicate">Soluble glass</a></li> <li><a href="/wiki/Tellurite_glass" title="Tellurite glass">Tellurite glass</a></li> <li><a href="/wiki/Thoriated_glass" title="Thoriated glass">Thoriated glass</a></li> <li><a href="/wiki/Ultra_low_expansion_glass" title="Ultra low expansion glass">Ultra low expansion glass</a></li> <li><a href="/wiki/Uranium_glass" title="Uranium glass">Uranium glass</a></li> <li><a href="/wiki/Vitreous_enamel" title="Vitreous enamel">Vitreous enamel</a></li> <li><a href="/wiki/Wood%27s_glass" title="Wood's glass">Wood's glass</a></li> <li><a href="/wiki/ZBLAN" title="ZBLAN">ZBLAN</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glass-ceramic" title="Glass-ceramic">Glass-ceramics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bioactive_glass" title="Bioactive glass">Bioactive glass</a></li> <li><a href="/wiki/CorningWare" title="CorningWare">CorningWare</a></li> <li><a href="/wiki/Glass-ceramic-to-metal_seals" title="Glass-ceramic-to-metal seals">Glass-ceramic-to-metal seals</a></li> <li><a href="/wiki/Macor" title="Macor">Macor</a></li> <li><a href="/wiki/Zerodur" title="Zerodur">Zerodur</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Preparation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Annealing_(glass)" title="Annealing (glass)">Annealing</a></li> <li><a href="/wiki/Chemical_vapor_deposition" title="Chemical vapor deposition">Chemical vapor deposition</a></li> <li><a href="/wiki/Glass_batch_calculation" title="Glass batch calculation">Glass batch calculation</a></li> <li><a href="/wiki/Glass_production" title="Glass production">Glass forming</a></li> <li><a href="/wiki/Glass_production#Hot_end" title="Glass production">Glass melting</a></li> <li><a href="/wiki/Calculation_of_glass_properties" title="Calculation of glass properties">Glass modeling</a></li> <li><a href="/wiki/Ion_implantation" title="Ion implantation">Ion implantation</a></li> <li><a href="/wiki/Liquidus" class="mw-redirect" title="Liquidus">Liquidus temperature</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Viscosity#Viscosity_of_amorphous_materials" title="Viscosity">Viscosity</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Optics" title="Optics">Optics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Achromatic_lens" title="Achromatic lens">Achromat</a></li> <li><a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">Dispersion</a></li> <li><a href="/wiki/Gradient-index_optics" title="Gradient-index optics">Gradient-index optics</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Optical_amplifier" title="Optical amplifier">Optical amplifier</a></li> <li><a href="/wiki/Optical_fiber" title="Optical fiber">Optical fiber</a></li> <li><a href="/wiki/Optical_lens_design" title="Optical lens design">Optical lens design</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens</a></li> <li><a href="/wiki/Photosensitive_glass" title="Photosensitive glass">Photosensitive glass</a></li> <li><a href="/wiki/Refraction" title="Refraction">Refraction</a></li> <li><a href="/wiki/Transparency_and_translucency" title="Transparency and translucency">Transparent materials</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Surface modification</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anti-reflective_coating" title="Anti-reflective coating">Anti-reflective coating</a></li> <li><a href="/wiki/Chemically_strengthened_glass" title="Chemically strengthened glass">Chemically strengthened glass</a></li> <li><a href="/wiki/Corrosion#Corrosion_of_glasses" title="Corrosion">Corrosion</a></li> <li><a href="/wiki/Dealkalization" title="Dealkalization">Dealkalization</a></li> <li><a href="/wiki/DNA_microarray" title="DNA microarray">DNA microarray</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Insulated_glazing" title="Insulated glazing">Insulated glazing</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Self-cleaning_glass" title="Self-cleaning glass">Self-cleaning glass</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Tempered_glass" title="Tempered glass">Tempered glass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diverse topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Conservation_and_restoration_of_glass_objects" title="Conservation and restoration of glass objects">Conservation and restoration of glass objects</a></li> <li><a href="/wiki/Glass-coated_wire" title="Glass-coated wire">Glass-coated wire</a></li> <li><a href="/wiki/Safety_glass" title="Safety glass">Safety glass</a></li> <li><a href="/wiki/Glass_databases" title="Glass databases">Glass databases</a></li> <li><a href="/wiki/Glass_electrode" title="Glass electrode">Glass electrode</a></li> <li><a href="/wiki/Glass_fiber_reinforced_concrete" title="Glass fiber reinforced concrete">Glass fiber reinforced concrete</a></li> <li><a href="/wiki/Glass_ionomer_cement" title="Glass ionomer cement">Glass ionomer cement</a></li> <li><a href="/wiki/Glass_microsphere" title="Glass microsphere">Glass microspheres</a></li> <li><a href="/wiki/Fiberglass" title="Fiberglass">Glass-reinforced plastic</a></li> <li><a href="/wiki/Glass_cloth" title="Glass cloth">Glass cloth</a></li> <li><a href="/wiki/Glass-to-metal_seal" title="Glass-to-metal seal">Glass-to-metal seal</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Pre-preg" title="Pre-preg">Pre-preg</a></li> <li><a href="/wiki/Prince_Rupert%27s_drop" title="Prince Rupert's drop">Prince Rupert's drops</a></li> <li><a href="/wiki/Radioactive_waste#Vitrification" title="Radioactive waste">Radioactive waste vitrification</a></li> <li><a href="/wiki/Windshield" title="Windshield">Windshield</a></li> <li><a href="/wiki/Glass_fiber" title="Glass fiber">Glass fiber</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <a href="https://www.wikidata.org/wiki/Q825643#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh94004665">United States</a></li><li><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007542055805171">Israel</a></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Glass_transition&oldid=1248575637">https://en.wikipedia.org/w/index.php?title=Glass_transition&oldid=1248575637</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Cryobiology" title="Category:Cryobiology">Cryobiology</a></li><li><a href="/wiki/Category:Glass_engineering_and_science" title="Category:Glass engineering and science">Glass engineering and science</a></li><li><a href="/wiki/Category:Glass_physics" title="Category:Glass physics">Glass physics</a></li><li><a href="/wiki/Category:Phase_transitions" title="Category:Phase transitions">Phase transitions</a></li><li><a href="/wiki/Category:Polymer_chemistry" title="Category:Polymer chemistry">Polymer chemistry</a></li><li><a href="/wiki/Category:Rubber_properties" title="Category:Rubber properties">Rubber properties</a></li><li><a href="/wiki/Category:Threshold_temperatures" title="Category:Threshold temperatures">Threshold temperatures</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_German-language_sources_(de)" title="Category:CS1 German-language sources (de)">CS1 German-language sources (de)</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_vague_or_ambiguous_time" title="Category:All articles with vague or ambiguous time">All articles with vague or ambiguous time</a></li><li><a href="/wiki/Category:Vague_or_ambiguous_time_from_October_2020" title="Category:Vague or ambiguous time from October 2020">Vague or ambiguous time from October 2020</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_June_2016" title="Category:Wikipedia articles needing clarification from June 2016">Wikipedia articles needing clarification from June 2016</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_July_2009" title="Category:Articles needing additional references from July 2009">Articles needing additional references from July 2009</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_September_2010" title="Category:Articles with unsourced statements from September 2010">Articles with unsourced statements from September 2010</a></li><li><a href="/wiki/Category:All_accuracy_disputes" title="Category:All accuracy disputes">All accuracy disputes</a></li><li><a href="/wiki/Category:Articles_with_disputed_statements_from_July_2019" title="Category:Articles with disputed statements from July 2019">Articles with disputed statements from July 2019</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 30 September 2024, at 08:56 (UTC).</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Glass_transition&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-7c4dcdbb87-zdnzl","wgBackendResponseTime":175,"wgPageParseReport":{"limitreport":{"cputime":"0.973","walltime":"1.231","ppvisitednodes":{"value":6777,"limit":1000000},"postexpandincludesize":{"value":184941,"limit":2097152},"templateargumentsize":{"value":6131,"limit":2097152},"expansiondepth":{"value":16,"limit":100},"expensivefunctioncount":{"value":7,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":278069,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 960.013 1 -total"," 51.53% 494.732 1 Template:Reflist"," 30.19% 289.806 45 Template:Cite_journal"," 9.05% 86.891 1 Template:Short_description"," 7.00% 67.158 1 Template:Glass_science"," 6.70% 64.297 1 Template:Navbox"," 6.29% 60.403 36 Template:Convert"," 4.32% 41.427 10 Template:Cite_book"," 4.15% 39.823 3 Template:Fix"," 4.15% 39.802 2 Template:Pagetype"]},"scribunto":{"limitreport-timeusage":{"value":"0.543","limit":"10.000"},"limitreport-memusage":{"value":9890026,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-5857dfdcd6-jqph2","timestamp":"20241203072611","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Glass transition","url":"https:\/\/en.wikipedia.org\/wiki\/Glass_transition","sameAs":"http:\/\/www.wikidata.org\/entity\/Q825643","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q825643","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2009-03-24T22:12:51Z","dateModified":"2024-09-30T08:56:43Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/53\/Two-dimensional_schematic_diagram_of_quartz%2C_silica%2C_and_silica-based_glass.png","headline":"reversible transition in amorphous materials"}</script> </body> </html>