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id="toc-Rocks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rocks"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Rocks</span> </div> </a> <ul id="toc-Rocks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ice"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Ice</span> </div> </a> <ul id="toc-Ice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Organigenic_crystals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Organigenic_crystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Organigenic crystals</span> </div> </a> <ul id="toc-Organigenic_crystals-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Polymorphism_and_allotropy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Polymorphism_and_allotropy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Polymorphism and allotropy</span> </div> </a> <ul id="toc-Polymorphism_and_allotropy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crystallization" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Crystallization"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Crystallization</span> </div> </a> <ul id="toc-Crystallization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Defects,_impurities,_and_twinning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Defects,_impurities,_and_twinning"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Defects, impurities, and twinning</span> </div> </a> <ul id="toc-Defects,_impurities,_and_twinning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chemical_bonds" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Chemical_bonds"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Chemical bonds</span> </div> </a> <ul id="toc-Chemical_bonds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quasicrystals" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quasicrystals"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Quasicrystals</span> </div> </a> <ul id="toc-Quasicrystals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Special_properties_from_anisotropy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Special_properties_from_anisotropy"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Special properties from anisotropy</span> </div> </a> <ul id="toc-Special_properties_from_anisotropy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crystallography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Crystallography"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Crystallography</span> </div> </a> <ul id="toc-Crystallography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Image_gallery" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Image_gallery"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Image gallery</span> </div> </a> <ul id="toc-Image_gallery-sublist" class="vector-toc-list"> </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"> <span class="vector-toc-numb">12</span> <span>See also</span> </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"> <span class="vector-toc-numb">13</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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" title="Table of Contents" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </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"><span class="mw-page-title-main">Crystal</span></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 111 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-111" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">111 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Kristal" title="Kristal – Afrikaans" lang="af" hreflang="af" data-title="Kristal" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D8%B1%D8%A9" title="بلورة – Arabic" lang="ar" hreflang="ar" data-title="بلورة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Cristal" title="Cristal – Aragonese" lang="an" hreflang="an" data-title="Cristal" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B2%D5%AB%D6%82%D6%80%D5%A5%D5%B2" title="Բիւրեղ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Բիւրեղ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Crustalu" title="Crustalu – Aromanian" lang="rup" hreflang="rup" data-title="Crustalu" data-language-autonym="Armãneashti" data-language-local-name="Aromanian" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cristal" title="Cristal – Asturian" lang="ast" hreflang="ast" data-title="Cristal" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kristallar" title="Kristallar – Azerbaijani" lang="az" hreflang="az" data-title="Kristallar" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%AB%E0%A6%9F%E0%A6%BF%E0%A6%95" title="স্ফটিক – Bangla" lang="bn" hreflang="bn" data-title="স্ফটিক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Chi%E2%81%BF-th%C3%A9" title="Chiⁿ-thé – Minnan" lang="nan" hreflang="nan" data-title="Chiⁿ-thé" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D1%80%D1%8B%D1%88%D1%82%D0%B0%D0%BB%D1%96%D1%87%D0%BD%D1%8B%D1%8F_%D1%86%D0%B5%D0%BB%D1%8B" title="Крышталічныя целы – Belarusian" lang="be" hreflang="be" data-title="Крышталічныя целы" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D1%80%D1%8B%D1%88%D1%82%D0%B0%D0%BB%D1%8C" title="Крышталь – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Крышталь" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Кристал – Bulgarian" lang="bg" hreflang="bg" data-title="Кристал" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Kristall" title="Kristall – Bavarian" lang="bar" hreflang="bar" data-title="Kristall" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kristal" title="Kristal – Bosnian" lang="bs" hreflang="bs" data-title="Kristal" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cristall" title="Cristall – Catalan" lang="ca" hreflang="ca" data-title="Cristall" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB" title="Кристалл – Chuvash" lang="cv" hreflang="cv" data-title="Кристалл" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Krystal" title="Krystal – Czech" lang="cs" hreflang="cs" data-title="Krystal" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Grisial" title="Grisial – Welsh" lang="cy" hreflang="cy" data-title="Grisial" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Krystal" title="Krystal – Danish" lang="da" hreflang="da" data-title="Krystal" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%A8%D9%84%D8%A7%D8%B1" title="بلار – Moroccan Arabic" lang="ary" hreflang="ary" data-title="بلار" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kristall" title="Kristall – German" lang="de" hreflang="de" data-title="Kristall" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kristall" title="Kristall – Estonian" lang="et" hreflang="et" data-title="Kristall" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%81%CF%8D%CF%83%CF%84%CE%B1%CE%BB%CE%BB%CE%BF%CF%82" title="Κρύσταλλος – Greek" lang="el" hreflang="el" data-title="Κρύσταλλος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cristal" title="Cristal – Spanish" lang="es" hreflang="es" data-title="Cristal" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kristalo" title="Kristalo – Esperanto" lang="eo" hreflang="eo" data-title="Kristalo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kristal" title="Kristal – Basque" lang="eu" hreflang="eu" data-title="Kristal" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D8%B1" title="بلور – Persian" lang="fa" hreflang="fa" data-title="بلور" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cristal" title="Cristal – French" lang="fr" hreflang="fr" data-title="Cristal" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Criostal" title="Criostal – Irish" lang="ga" hreflang="ga" data-title="Criostal" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cristal" title="Cristal – Galician" lang="gl" hreflang="gl" data-title="Cristal" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B8%E0%AB%8D%E0%AA%AB%E0%AA%9F%E0%AA%BF%E0%AA%95" title="સ્ફટિક – Gujarati" lang="gu" hreflang="gu" data-title="સ્ફટિક" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B2%B0%EC%A0%95" title="결정 – Korean" lang="ko" hreflang="ko" data-title="결정" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Crystal" title="Crystal – Hausa" lang="ha" hreflang="ha" data-title="Crystal" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%B5%D5%B8%D6%82%D6%80%D5%A5%D5%B2" title="Բյուրեղ – Armenian" lang="hy" hreflang="hy" data-title="Բյուրեղ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%9F%E0%A4%B2" title="क्रिस्टल – Hindi" lang="hi" hreflang="hi" data-title="क्रिस्टल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kristal" title="Kristal – Croatian" lang="hr" hreflang="hr" data-title="Kristal" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kristalo" title="Kristalo – Ido" lang="io" hreflang="io" data-title="Kristalo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kristal" title="Kristal – Indonesian" lang="id" hreflang="id" data-title="Kristal" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Umncwebe" title="Umncwebe – Zulu" lang="zu" hreflang="zu" data-title="Umncwebe" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Kristall" title="Kristall – Icelandic" lang="is" hreflang="is" data-title="Kristall" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Cristallo" title="Cristallo – Italian" lang="it" hreflang="it" data-title="Cristallo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%91%D7%99%D7%A9" title="גביש – Hebrew" lang="he" hreflang="he" data-title="גביש" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kristal" title="Kristal – Javanese" lang="jv" hreflang="jv" data-title="Kristal" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B3%8D%E0%B2%AB%E0%B2%9F%E0%B2%BF%E0%B2%95" title="ಸ್ಫಟಿಕ – Kannada" lang="kn" hreflang="kn" data-title="ಸ್ಫಟಿಕ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A0%E1%83%98%E1%83%A1%E1%83%A2%E1%83%90%E1%83%9A%E1%83%98" title="კრისტალი – Georgian" lang="ka" hreflang="ka" data-title="კრისტალი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB" title="Кристалл – Kazakh" lang="kk" hreflang="kk" data-title="Кристалл" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Fuwele" title="Fuwele – Swahili" lang="sw" hreflang="sw" data-title="Fuwele" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kristal" title="Kristal – Haitian Creole" lang="ht" hreflang="ht" data-title="Kristal" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Kristal" title="Kristal – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Kristal" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB" title="Кристалл – Kyrgyz" lang="ky" hreflang="ky" data-title="Кристалл" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Crystallum" title="Crystallum – Latin" lang="la" hreflang="la" data-title="Crystallum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Krist%C4%81ls" title="Kristāls – Latvian" lang="lv" hreflang="lv" data-title="Kristāls" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kristalas" title="Kristalas – Lithuanian" lang="lt" hreflang="lt" data-title="Kristalas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Krist%C3%A1ly" title="Kristály – Hungarian" lang="hu" hreflang="hu" data-title="Kristály" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Кристал – Macedonian" lang="mk" hreflang="mk" data-title="Кристал" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kristaly" title="Kristaly – Malagasy" lang="mg" hreflang="mg" data-title="Kristaly" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B4%B0%E0%B5%BD_(%E0%B4%B0%E0%B4%B8%E0%B4%A4%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82)" title="പരൽ (രസതന്ത്രം) – Malayalam" lang="ml" hreflang="ml" data-title="പരൽ (രസതന്ത്രം)" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A5%8D%E0%A4%AB%E0%A4%9F%E0%A4%BF%E0%A4%95" title="स्फटिक – Marathi" lang="mr" hreflang="mr" data-title="स्फटिक" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hablur" title="Hablur – Malay" lang="ms" hreflang="ms" data-title="Hablur" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%80%EA%AF%AD%EA%AF%94%EA%AF%A4%EA%AF%81%EA%AF%87%EA%AF%A6%EA%AF%9C%EA%AF%82%EA%AF%A5%EA%AF%8F%EA%AF%9F" title="ꯀ꯭ꯔꯤꯁꯇꯦꯜꯂꯥꯏꯟ – Manipuri" lang="mni" hreflang="mni" data-title="ꯀ꯭ꯔꯤꯁꯇꯦꯜꯂꯥꯏꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="Manipuri" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BB%D1%81%D1%82" title="Талст – Mongolian" lang="mn" hreflang="mn" data-title="Талст" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%95%E1%80%AF%E1%80%B6%E1%80%86%E1%80%B1%E1%80%AC%E1%80%84%E1%80%BA%E1%80%81%E1%80%B2" title="ပုံဆောင်ခဲ – Burmese" lang="my" hreflang="my" data-title="ပုံဆောင်ခဲ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Tehuilotl" title="Tehuilotl – Nahuatl" lang="nah" hreflang="nah" data-title="Tehuilotl" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Karisitala" title="Karisitala – Fijian" lang="fj" hreflang="fj" data-title="Karisitala" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kristal_(natuurwetenschappen)" title="Kristal (natuurwetenschappen) – Dutch" lang="nl" hreflang="nl" data-title="Kristal (natuurwetenschappen)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AE%E0%A4%A3%E0%A4%BF%E0%A4%AD" title="मणिभ – Nepali" lang="ne" hreflang="ne" data-title="मणिभ" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%90%E6%99%B6" title="結晶 – Japanese" lang="ja" hreflang="ja" data-title="結晶" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Krystall" title="Krystall – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Krystall" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Krystall" title="Krystall – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Krystall" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Cristal" title="Cristal – Occitan" lang="oc" hreflang="oc" data-title="Cristal" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Baalcii" title="Baalcii – Oromo" lang="om" hreflang="om" data-title="Baalcii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kristallar" title="Kristallar – Uzbek" lang="uz" hreflang="uz" data-title="Kristallar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A8%B2%E0%A9%8C%E0%A8%B0" title="ਬਲੌਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਬਲੌਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D8%B1" title="بلور – Western Punjabi" lang="pnb" hreflang="pnb" data-title="بلور" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kristal" title="Kristal – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Kristal" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Cristal" title="Cristal – Piedmontese" lang="pms" hreflang="pms" data-title="Cristal" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Cia%C5%82o_krystaliczne" title="Ciało krystaliczne – Polish" lang="pl" hreflang="pl" data-title="Ciało krystaliczne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cristal" title="Cristal – Portuguese" lang="pt" hreflang="pt" data-title="Cristal" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cristal" title="Cristal – Romanian" lang="ro" hreflang="ro" data-title="Cristal" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pi%C3%B1i" title="Piñi – Quechua" lang="qu" hreflang="qu" data-title="Piñi" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB%D1%8B" title="Кристаллы – Russian" lang="ru" hreflang="ru" data-title="Кристаллы" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%B0%D0%BB%D0%BB%D0%B0%D1%80" title="Кристааллар – Yakut" lang="sah" hreflang="sah" data-title="Кристааллар" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Creestal" title="Creestal – Scots" lang="sco" hreflang="sco" data-title="Creestal" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kristali" title="Kristali – Albanian" lang="sq" hreflang="sq" data-title="Kristali" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B6%9A%E0%B7%90%E0%B6%A7" title="සකැට – Sinhala" lang="si" hreflang="si" data-title="සකැට" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Crystal" title="Crystal – Simple English" lang="en-simple" hreflang="en-simple" data-title="Crystal" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kry%C5%A1t%C3%A1l" title="Kryštál – Slovak" lang="sk" hreflang="sk" data-title="Kryštál" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kristal" title="Kristal – Slovenian" lang="sl" hreflang="sl" data-title="Kristal" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D9%88%D8%B1" title="بلوور – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بلوور" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Кристал – Serbian" lang="sr" hreflang="sr" data-title="Кристал" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kristal" title="Kristal – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Kristal" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kiteinen_aine" title="Kiteinen aine – Finnish" lang="fi" hreflang="fi" data-title="Kiteinen aine" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kristall" title="Kristall – Swedish" lang="sv" hreflang="sv" data-title="Kristall" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kristal" title="Kristal – Tagalog" lang="tl" hreflang="tl" data-title="Kristal" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%9F%E0%AE%BF%E0%AE%95%E0%AE%AE%E0%AF%8D" title="படிகம் – Tamil" lang="ta" hreflang="ta" data-title="படிகம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BB" title="Кристалл – Tatar" lang="tt" hreflang="tt" data-title="Кристалл" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B1%8D%E0%B0%AB%E0%B0%9F%E0%B0%BF%E0%B0%95%E0%B0%82" title="స్ఫటికం – Telugu" lang="te" hreflang="te" data-title="స్ఫటికం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9C%E0%B8%A5%E0%B8%B6%E0%B8%81" title="ผลึก – Thai" lang="th" hreflang="th" data-title="ผลึก" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kristal" title="Kristal – Turkish" lang="tr" hreflang="tr" data-title="Kristal" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB" title="Кристал – Ukrainian" lang="uk" hreflang="uk" data-title="Кристал" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D9%84%D9%88%D8%B1" title="بلور – Urdu" lang="ur" hreflang="ur" data-title="بلور" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D9%83%D9%89%D8%B1%D9%89%D8%B3%D8%AA%D8%A7%D9%84" title="كىرىستال – Uyghur" lang="ug" hreflang="ug" 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data-title="Kristal" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%99%B6%E4%BD%93" title="晶体 – Wu" lang="wuu" hreflang="wuu" data-title="晶体" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%A1%D7%98%D7%90%D7%9C" title="קריסטאל – Yiddish" lang="yi" hreflang="yi" data-title="קריסטאל" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%99%B6%E9%AB%94" title="晶體 – Cantonese" lang="yue" hreflang="yue" data-title="晶體" data-language-autonym="粵語" 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src="//upload.wikimedia.org/wikipedia/en/thumb/1/1b/Semi-protection-shackle.svg/20px-Semi-protection-shackle.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/1/1b/Semi-protection-shackle.svg/40px-Semi-protection-shackle.svg.png 1.5x" data-file-width="512" data-file-height="512" /></a></span></div></div> </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"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Solid material with highly ordered microscopic structure</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">"Crystalline" redirects here. For the Björk song, see <a href="/wiki/Crystalline_(song)" title="Crystalline (song)">Crystalline (song)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">"Xtal" redirects here. For other uses, see <a href="/wiki/Xtal_(disambiguation)" class="mw-disambig" title="Xtal (disambiguation)">Xtal (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">This article is about crystalline solids. For other uses, see <a href="/wiki/Crystal_(disambiguation)" class="mw-disambig" title="Crystal (disambiguation)">Crystal (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Quartz_28.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Quartz_28.jpg/280px-Quartz_28.jpg" decoding="async" width="280" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Quartz_28.jpg/420px-Quartz_28.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Quartz_28.jpg/560px-Quartz_28.jpg 2x" data-file-width="4288" data-file-height="2848" /></a><figcaption>Crystals of <a href="/wiki/Amethyst" title="Amethyst">amethyst</a> <a href="/wiki/Quartz" title="Quartz">quartz</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Crystalline_polycrystalline_amorphous2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Crystalline_polycrystalline_amorphous2.svg/280px-Crystalline_polycrystalline_amorphous2.svg.png" decoding="async" width="280" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Crystalline_polycrystalline_amorphous2.svg/420px-Crystalline_polycrystalline_amorphous2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Crystalline_polycrystalline_amorphous2.svg/560px-Crystalline_polycrystalline_amorphous2.svg.png 2x" data-file-width="511" data-file-height="188" /></a><figcaption>Microscopically, a <a href="/wiki/Single_crystal" title="Single crystal">single crystal</a> has atoms in a near-perfect <a href="/wiki/Periodic_function" title="Periodic function">periodic</a> arrangement; a polycrystal is composed of many microscopic crystals (called "<a href="/wiki/Crystallite" title="Crystallite">crystallites</a>" or "grains"); and an <a href="/wiki/Amorphous" class="mw-redirect" title="Amorphous">amorphous</a> solid (such as <a href="/wiki/Glass" title="Glass">glass</a>) has no periodic arrangement even microscopically.</figcaption></figure> <p>A <b>crystal</b> or <b>crystalline solid</b> is a <a href="/wiki/Solid" title="Solid">solid</a> material whose constituents (such as <a href="/wiki/Atom" title="Atom">atoms</a>, <a href="/wiki/Molecule" title="Molecule">molecules</a>, or <a href="/wiki/Ion" title="Ion">ions</a>) are arranged in a highly ordered microscopic structure, forming a <a href="/wiki/Crystal_lattice" class="mw-redirect" title="Crystal lattice">crystal lattice</a> that extends in all directions.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In addition, macroscopic <a href="/wiki/Single_crystal" title="Single crystal">single crystals</a> are usually identifiable by their <a href="/wiki/Geometry" title="Geometry">geometrical shape</a>, consisting of flat <a href="/wiki/Face_(geometry)" title="Face (geometry)">faces</a> with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as <a href="/wiki/Crystallography" title="Crystallography">crystallography</a>. The process of crystal formation via mechanisms of <a href="/wiki/Crystal_growth" title="Crystal growth">crystal growth</a> is called <a href="/wiki/Crystallization" title="Crystallization">crystallization</a> or <a href="/wiki/Solidification" class="mw-redirect" title="Solidification">solidification</a>. </p><p>The word <i>crystal</i> derives from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> word <span title="Ancient Greek (to 1453)-language text"><span lang="grc">κρύσταλλος</span></span> (<span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn"><i>krustallos</i></i></span>), meaning both "<a href="/wiki/Ice" title="Ice">ice</a>" and "<a href="/wiki/Quartz#Varieties_(according_to_color)" title="Quartz">rock crystal</a>",<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> from <span title="Ancient Greek (to 1453)-language text"><span lang="grc">κρύος</span></span> (<span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn"><i>kruos</i></i></span>), "icy cold, frost".<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Examples of large crystals include <a href="/wiki/Snowflake" title="Snowflake">snowflakes</a>, <a href="/wiki/Diamond" title="Diamond">diamonds</a>, and <a href="/wiki/Table_salt" class="mw-redirect" title="Table salt">table salt</a>. Most inorganic solids are not crystals but <a href="/wiki/Polycrystal" class="mw-redirect" title="Polycrystal">polycrystals</a>, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most <a href="/wiki/Metals" class="mw-redirect" title="Metals">metals</a>, rocks, <a href="/wiki/Ceramics" class="mw-redirect" title="Ceramics">ceramics</a>, and <a href="/wiki/Ice" title="Ice">ice</a>. A third category of solids is <a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous solids</a>, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include <a href="/wiki/Glass" title="Glass">glass</a>, <a href="/wiki/Wax" title="Wax">wax</a>, and many <a href="/wiki/Plastic" title="Plastic">plastics</a>. </p><p>Despite the name, <a href="/wiki/Lead_glass" title="Lead glass">lead crystal, crystal glass</a>, and related products are <i>not</i> crystals, but rather types of glass, i.e. amorphous solids. </p><p>Crystals, or crystalline solids, are often used in <a href="/wiki/Pseudoscientific" class="mw-redirect" title="Pseudoscientific">pseudoscientific</a> practices such as <a href="/wiki/Crystal_therapy" class="mw-redirect" title="Crystal therapy">crystal therapy</a>, and, along with <a href="/wiki/Gemstone" title="Gemstone">gemstones</a>, are sometimes associated with <a href="/wiki/Spell_(paranormal)" class="mw-redirect" title="Spell (paranormal)">spellwork</a> in <a href="/wiki/Wicca" title="Wicca">Wiccan</a> beliefs and related religious movements.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Crystal_structure_(microscopic)"><span id="Crystal_structure_.28microscopic.29"></span>Crystal structure (microscopic)</h2></div> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:408px;max-width:408px"><div class="trow"><div class="theader">Halite (table salt, NaCl): Microscopic and macroscopic</div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Sodium-chloride-3D-ionic.png" class="mw-file-description"><img alt="Halite crystal (microscopic)" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/200px-Sodium-chloride-3D-ionic.png" decoding="async" width="200" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/300px-Sodium-chloride-3D-ionic.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/400px-Sodium-chloride-3D-ionic.png 2x" data-file-width="1000" data-file-height="948" /></a></span></div><div class="thumbcaption">Microscopic structure of a <a href="/wiki/Halite" title="Halite">halite</a> crystal. (Purple is <a href="/wiki/Sodium" title="Sodium">sodium</a> ion, green is <a href="/wiki/Chlorine" title="Chlorine">chlorine</a> ion). There is <a href="/wiki/Cubic_crystal_system" title="Cubic crystal system">cubic symmetry</a> in the atoms' arrangement</div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Selpologne.jpg" class="mw-file-description"><img alt="Halite crystal (Macroscopic)" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/200px-Selpologne.jpg" decoding="async" width="200" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/300px-Selpologne.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/400px-Selpologne.jpg 2x" data-file-width="3780" data-file-height="3582" /></a></span></div><div class="thumbcaption">Macroscopic (~16 cm) halite crystal. The right-angles between crystal faces are due to the cubic symmetry of the atoms' arrangement</div></div></div></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Crystal_structure" title="Crystal structure">Crystal structure</a></div> <p>The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the <a href="/wiki/Crystal_structure" title="Crystal structure">crystal structure</a>. A crystal is a solid where the atoms form a periodic arrangement. (<a href="/wiki/Quasicrystal" title="Quasicrystal">Quasicrystals</a> are an exception, see <a href="#Quasicrystals">below</a>). </p><p>Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a <i><a href="/wiki/Polycrystalline" class="mw-redirect" title="Polycrystalline">polycrystalline</a></i> structure. In the final block of ice, each of the small crystals (called "<a href="/wiki/Crystallite" title="Crystallite">crystallites</a>" or "grains") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does <i>not</i> have a periodic arrangement of atoms, because the periodic pattern is broken at the <a href="/wiki/Grain_boundaries" class="mw-redirect" title="Grain boundaries">grain boundaries</a>. Most macroscopic <a href="/wiki/Inorganic" class="mw-redirect" title="Inorganic">inorganic</a> solids are polycrystalline, including almost all <a href="/wiki/Metal" title="Metal">metals</a>, <a href="/wiki/Ceramic" title="Ceramic">ceramics</a>, <a href="/wiki/Ice" title="Ice">ice</a>, <a href="/wiki/Rocks" class="mw-redirect" title="Rocks">rocks</a>, etc. Solids that are neither crystalline nor polycrystalline, such as <a href="/wiki/Glass" title="Glass">glass</a>, are called <i><a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous solids</a></i>, also called <a href="/wiki/Glass" title="Glass">glassy</a>, vitreous, or noncrystalline. These have no periodic order, even microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the <a href="/wiki/Latent_heat_of_fusion" class="mw-redirect" title="Latent heat of fusion">latent heat of fusion</a>, but forming a crystal does. </p><p>A crystal structure (an arrangement of atoms in a crystal) is characterized by its <i>unit cell</i>, a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are <a href="/wiki/Honeycomb_(geometry)" title="Honeycomb (geometry)">stacked</a> in three-dimensional space to form the crystal. </p><p>The <a href="/wiki/Crystal_structure" title="Crystal structure">symmetry of a crystal</a> is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries (230 is commonly cited, but this treats chiral equivalents as separate entities), called <a href="/wiki/Space_group" title="Space group">crystallographic space groups</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> These are grouped into 7 <a href="/wiki/Crystal_system" title="Crystal system">crystal systems</a>, such as <a href="/wiki/Cubic_crystal_system" title="Cubic crystal system">cubic crystal system</a> (where the crystals may form cubes or rectangular boxes, such as <a href="/wiki/Halite" title="Halite">halite</a> shown at right) or <a href="/wiki/Hexagonal_crystal_system" class="mw-redirect" title="Hexagonal crystal system">hexagonal crystal system</a> (where the crystals may form hexagons, such as <a href="/wiki/Ice_Ih" class="mw-redirect" title="Ice Ih">ordinary water ice</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Crystal_faces,_shapes_and_crystallographic_forms"><span id="Crystal_faces.2C_shapes_and_crystallographic_forms"></span>Crystal faces, shapes and crystallographic forms</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Crystal_facet_formation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Crystal_facet_formation.svg/350px-Crystal_facet_formation.svg.png" decoding="async" width="350" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Crystal_facet_formation.svg/525px-Crystal_facet_formation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Crystal_facet_formation.svg/700px-Crystal_facet_formation.svg.png 2x" data-file-width="1820" data-file-height="648" /></a><figcaption>As a <a href="/wiki/Halite" title="Halite">halite</a> crystal is growing, new atoms can very easily attach to the parts of the surface with rough atomic-scale structure and many <a href="/wiki/Dangling_bonds" class="mw-redirect" title="Dangling bonds">dangling bonds</a>. Therefore, these parts of the crystal grow out very quickly (yellow arrows). Eventually, the whole surface consists of smooth, <a href="/wiki/Surface_energy" title="Surface energy">stable</a> faces, where new atoms cannot as easily attach themselves.</figcaption></figure> <p>Crystals are commonly recognized, macroscopically, by their shape, consisting of flat faces with sharp angles. These shape characteristics are not <i>necessary</i> for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is often present and easy to see. </p><p><a href="/wiki/Euhedral" class="mw-redirect" title="Euhedral">Euhedral</a> crystals are those that have obvious, well-formed flat faces. <a href="/wiki/Anhedral_(petrology)" class="mw-redirect" title="Anhedral (petrology)">Anhedral</a> crystals do not, usually because the crystal is one grain in a polycrystalline solid. </p><p>The flat faces (also called <a href="/wiki/Facet" title="Facet">facets</a>) of a <a href="/wiki/Euhedral" class="mw-redirect" title="Euhedral">euhedral</a> crystal are oriented in a specific way relative to the underlying <a href="/wiki/Crystal_structure" title="Crystal structure">atomic arrangement of the crystal</a>: they are <a href="/wiki/Plane_(mathematics)" title="Plane (mathematics)">planes</a> of relatively low <a href="/wiki/Miller_index" title="Miller index">Miller index</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This occurs because some surface orientations are more stable than others (lower <a href="/wiki/Surface_energy" title="Surface energy">surface energy</a>). As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.) </p><p>One of the oldest techniques in the science of <a href="/wiki/Crystallography" title="Crystallography">crystallography</a> consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer the underlying <a href="/wiki/Crystal_system" title="Crystal system">crystal symmetry</a>. </p><p><span class="anchor" id="Crystallographic_form"></span> A crystal's <b>crystallographic forms</b> are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of <a href="/wiki/Galena" title="Galena">galena</a> often take the shape of cubes, and the six faces of the cube belong to a crystallographic form that displays one of the symmetries of the <a href="/wiki/Isometric_crystal_system" class="mw-redirect" title="Isometric crystal system">isometric crystal system</a>. Galena also sometimes crystallizes as octahedrons, and the eight faces of the octahedron belong to another crystallographic form reflecting a different symmetry of the isometric system. A crystallographic form is described by placing the Miller indices of one of its faces within brackets. For example, the octahedral form is written as {111}, and the other faces in the form are implied by the symmetry of the crystal. </p><p>Forms may be closed, meaning that the form can completely enclose a volume of space, or open, meaning that it cannot. The cubic and octahedral forms are examples of closed forms. All the forms of the isometric system are closed, while all the forms of the monoclinic and triclinic crystal systems are open. A crystal's faces may all belong to the same closed form, or they may be a combination of multiple open or closed forms.<sup id="cite_ref-Sinkankas1964_11-0" class="reference"><a href="#cite_note-Sinkankas1964-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>A <a href="/wiki/Crystal_habit" title="Crystal habit">crystal's habit</a> is its visible external shape. This is determined by the <a href="/wiki/Crystal_structure" title="Crystal structure">crystal structure</a> (which restricts the possible facet orientations), the specific crystal chemistry and bonding (which may favor some facet types over others), and the conditions under which the crystal formed. </p> <div class="mw-heading mw-heading2"><h2 id="Occurrence_in_nature">Occurrence in nature</h2></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ice_crystals.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Ice_crystals.jpg/250px-Ice_crystals.jpg" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Ice_crystals.jpg/330px-Ice_crystals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Ice_crystals.jpg/500px-Ice_crystals.jpg 2x" data-file-width="1777" data-file-height="1338" /></a><figcaption><a href="/wiki/Ice" title="Ice">Ice</a> crystals</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CalciteEchinosphaerites.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/CalciteEchinosphaerites.jpg/220px-CalciteEchinosphaerites.jpg" decoding="async" width="220" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/CalciteEchinosphaerites.jpg/330px-CalciteEchinosphaerites.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/CalciteEchinosphaerites.jpg/440px-CalciteEchinosphaerites.jpg 2x" data-file-width="3456" data-file-height="2634" /></a><figcaption><a href="/wiki/Fossil" title="Fossil">Fossil</a> <a href="/wiki/Exoskeleton" title="Exoskeleton">shell</a> with <a href="/wiki/Calcite" title="Calcite">calcite</a> crystals</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Rocks">Rocks</h3></div> <p>By volume and weight, the largest concentrations of crystals in the Earth are part of its solid <a href="/wiki/Bedrock" title="Bedrock">bedrock</a>. Crystals found in rocks typically range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are occasionally found. As of 1999<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Crystal&action=edit">[update]</a></sup>, the world's largest known naturally occurring crystal is a crystal of <a href="/wiki/Beryl" title="Beryl">beryl</a> from Malakialina, <a href="/wiki/Madagascar" title="Madagascar">Madagascar</a>, 18 m (59 ft) long and 3.5 m (11 ft) in diameter, and weighing 380,000 kg (840,000 lb).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Some crystals have formed by <a href="/wiki/Magmatic" class="mw-redirect" title="Magmatic">magmatic</a> and <a href="/wiki/Metamorphic" class="mw-redirect" title="Metamorphic">metamorphic</a> processes, giving origin to large masses of crystalline <a href="/wiki/Rock_(geology)" title="Rock (geology)">rock</a>. The vast majority of <a href="/wiki/Igneous_rocks" class="mw-redirect" title="Igneous rocks">igneous rocks</a> are formed from molten magma and the degree of crystallization depends primarily on the conditions under which they solidified. Such rocks as <a href="/wiki/Granite" title="Granite">granite</a>, which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of <a href="/wiki/Lava" title="Lava">lava</a> were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or <a href="/wiki/Glass" title="Glass">glassy</a> matter is common. Other crystalline rocks, the metamorphic rocks such as <a href="/wiki/Marble" title="Marble">marbles</a>, <a href="/wiki/Mica-schist" class="mw-redirect" title="Mica-schist">mica-schists</a> and <a href="/wiki/Quartzite" title="Quartzite">quartzites</a>, are recrystallized. This means that they were at first fragmental rocks like <a href="/wiki/Limestone" title="Limestone">limestone</a>, <a href="/wiki/Shale" title="Shale">shale</a> and <a href="/wiki/Sandstone" title="Sandstone">sandstone</a> and have never been in a <a href="/wiki/Molten" class="mw-redirect" title="Molten">molten</a> condition nor entirely in solution, but the high temperature and pressure conditions of <a href="/wiki/Metamorphism" title="Metamorphism">metamorphism</a> have acted on them by erasing their original structures and inducing recrystallization in the solid state.<sup id="cite_ref-EB1911_13-0" class="reference"><a href="#cite_note-EB1911-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Other rock crystals have formed out of precipitation from fluids, commonly water, to form <a href="/wiki/Druse_(geology)" title="Druse (geology)">druses</a> or <a href="/wiki/Quartz" title="Quartz">quartz</a> veins. <a href="/wiki/Evaporite" title="Evaporite">Evaporites</a> such as <a href="/wiki/Halite" title="Halite">halite</a>, <a href="/wiki/Gypsum" title="Gypsum">gypsum</a> and some limestones have been deposited from aqueous solution, mostly owing to <a href="/wiki/Evaporation" title="Evaporation">evaporation</a> in arid climates. </p> <div class="mw-heading mw-heading3"><h3 id="Ice">Ice</h3></div> <p>Water-based <a href="/wiki/Ice" title="Ice">ice</a> in the form of <a href="/wiki/Snow" title="Snow">snow</a>, <a href="/wiki/Sea_ice" title="Sea ice">sea ice</a>, and <a href="/wiki/Glacier" title="Glacier">glaciers</a> are common crystalline/polycrystalline structures on Earth and other planets.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> A single <a href="/wiki/Snowflake" title="Snowflake">snowflake</a> is a single crystal or a collection of crystals,<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> while an <a href="/wiki/Ice_cube" title="Ice cube">ice cube</a> is a <a href="/wiki/Polycrystal" class="mw-redirect" title="Polycrystal">polycrystal</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Ice crystals may form from cooling liquid water below its freezing point, such as ice cubes or a frozen lake. <a href="/wiki/Frost" title="Frost">Frost</a>, snowflakes, or small ice crystals suspended in the air (<a href="/wiki/Ice_fog" class="mw-redirect" title="Ice fog">ice fog</a>) more often grow from a <a href="/wiki/Supersaturated" class="mw-redirect" title="Supersaturated">supersaturated</a> gaseous-solution of water vapor and air, when the temperature of the air drops below its <a href="/wiki/Dew_point" title="Dew point">dew point</a>, without passing through a liquid state. Another unusual property of water is that it expands rather than contracts when it crystallizes.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Organigenic_crystals">Organigenic crystals</h3></div> <p>Many living <a href="/wiki/Organisms" class="mw-redirect" title="Organisms">organisms</a> are able to produce crystals grown from an <a href="/wiki/Aqueous_solution" title="Aqueous solution">aqueous solution</a>, for example <a href="/wiki/Calcite" title="Calcite">calcite</a> and <a href="/wiki/Aragonite" title="Aragonite">aragonite</a> in the case of most <a href="/wiki/Mollusc" class="mw-redirect" title="Mollusc">molluscs</a> or <a href="/wiki/Hydroxylapatite" class="mw-redirect" title="Hydroxylapatite">hydroxylapatite</a> in the case of <a href="/wiki/Bone" title="Bone">bones</a> and <a href="/wiki/Teeth" class="mw-redirect" title="Teeth">teeth</a> in <a href="/wiki/Vertebrate" title="Vertebrate">vertebrates</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Polymorphism_and_allotropy">Polymorphism and allotropy</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">Polymorphism (materials science)</a> and <a href="/wiki/Allotropy" title="Allotropy">Allotropy</a></div> <p>The same group of atoms can often solidify in many different ways. <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">Polymorphism</a> is the ability of a solid to exist in more than one crystal form. For example, water <a href="/wiki/Ice" title="Ice">ice</a> is ordinarily found in the hexagonal form <a href="/wiki/Ice_Ih" class="mw-redirect" title="Ice Ih">Ice I<sub>h</sub></a>, but can also exist as the cubic <a href="/wiki/Ice_Ic" class="mw-redirect" title="Ice Ic">Ice I<sub>c</sub></a>, the <a href="/wiki/Rhombohedral" class="mw-redirect" title="Rhombohedral">rhombohedral</a> <a href="/wiki/Ice_II" class="mw-redirect" title="Ice II">ice II</a>, and many other forms. The different polymorphs are usually called different <i><a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a></i>. </p><p>In addition, the same atoms may be able to form noncrystalline <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>. For example, water can also form <a href="/wiki/Amorphous_ice" class="mw-redirect" title="Amorphous ice">amorphous ice</a>, while SiO<sub>2</sub> can form both <a href="/wiki/Fused_silica" class="mw-redirect" title="Fused silica">fused silica</a> (an amorphous glass) and <a href="/wiki/Quartz" title="Quartz">quartz</a> (a crystal). Likewise, if a substance can form crystals, it can also form polycrystals. </p><p>For pure chemical elements, polymorphism is referred to as <a href="/wiki/Allotropy" title="Allotropy">allotropy</a>. For example, <a href="/wiki/Diamond" title="Diamond">diamond</a> and <a href="/wiki/Graphite" title="Graphite">graphite</a> are two crystalline forms of <a href="/wiki/Carbon" title="Carbon">carbon</a>, while <a href="/wiki/Amorphous_carbon" title="Amorphous carbon">amorphous carbon</a> is a noncrystalline form. Polymorphs, despite having the same atoms, may have very different properties. For example, diamond is the hardest substance known, while graphite is so soft that it is used as a lubricant. <a href="/wiki/Chocolate" title="Chocolate">Chocolate</a> can form six different types of crystals, but only one has the suitable hardness and melting point for candy bars and confections. Polymorphism in <a href="/wiki/Steel" title="Steel">steel</a> is responsible for its ability to be <a href="/wiki/Heat_treating" title="Heat treating">heat treated</a>, giving it a wide range of properties. </p><p><a href="/wiki/Polyamorphism" title="Polyamorphism">Polyamorphism</a> is a similar phenomenon where the same atoms can exist in more than one <a href="/wiki/Amorphous_solid" title="Amorphous solid">amorphous solid</a> form. </p> <div class="mw-heading mw-heading2"><h2 id="Crystallization">Crystallization</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Crystallization" title="Crystallization">Crystallization</a> and <a href="/wiki/Crystal_growth" title="Crystal growth">Crystal growth</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:1-cooling-crystallizer-schladen.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1-cooling-crystallizer-schladen.JPG/250px-1-cooling-crystallizer-schladen.JPG" decoding="async" width="170" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1-cooling-crystallizer-schladen.JPG/330px-1-cooling-crystallizer-schladen.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1-cooling-crystallizer-schladen.JPG/500px-1-cooling-crystallizer-schladen.JPG 2x" data-file-width="2096" data-file-height="3141" /></a><figcaption>Vertical <a href="/wiki/Crystallization" title="Crystallization">cooling crystallizer</a> in a beet sugar factory.</figcaption></figure> <p>Crystallization is the process of forming a crystalline structure from a fluid or from materials dissolved in a fluid. (More rarely, crystals may be <a href="/wiki/Deposition_(phase_transition)" title="Deposition (phase transition)">deposited</a> directly from gas; see: <a href="/wiki/Epitaxy" title="Epitaxy">epitaxy</a> and <a href="/wiki/Frost" title="Frost">frost</a>.) </p><p>Crystallization is a complex and extensively-studied field, because depending on the conditions, a single fluid can solidify into many different possible forms. It can form a <a href="/wiki/Single_crystal" title="Single crystal">single crystal</a>, perhaps with various possible <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>, <a href="/wiki/Stoichiometries" class="mw-redirect" title="Stoichiometries">stoichiometries</a>, impurities, <a href="/wiki/Crystallographic_defect" title="Crystallographic defect">defects</a>, and <a href="/wiki/Crystal_habit" title="Crystal habit">habits</a>. Or, it can form a <a href="/wiki/Polycrystal" class="mw-redirect" title="Polycrystal">polycrystal</a>, with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which the fluid is being solidified, such as the chemistry of the fluid, the <a href="/wiki/Ambient_pressure" title="Ambient pressure">ambient pressure</a>, the <a href="/wiki/Temperature" title="Temperature">temperature</a>, and the speed with which all these parameters are changing. </p><p>Specific industrial techniques to produce large single crystals (called <i><a href="/wiki/Boule_(crystal)" title="Boule (crystal)">boules</a></i>) include the <a href="/wiki/Czochralski_process" class="mw-redirect" title="Czochralski process">Czochralski process</a> and the <a href="/wiki/Bridgman_technique" class="mw-redirect" title="Bridgman technique">Bridgman technique</a>. Other less exotic methods of crystallization may be used, depending on the physical properties of the substance, including <a href="/wiki/Hydrothermal_synthesis" title="Hydrothermal synthesis">hydrothermal synthesis</a>, <a href="/wiki/Sublimation_(chemistry)" class="mw-redirect" title="Sublimation (chemistry)">sublimation</a>, or simply <a href="/wiki/Recrystallization_(chemistry)" title="Recrystallization (chemistry)">solvent-based crystallization</a>. </p><p>Large single crystals can be created by geological processes. For example, <a href="/wiki/Selenite_(mineral)" title="Selenite (mineral)">selenite</a> crystals in excess of 10 <a href="/wiki/Meter" class="mw-redirect" title="Meter">m</a> are found in the <a href="/wiki/Cave_of_the_Crystals" title="Cave of the Crystals">Cave of the Crystals</a> in Naica, Mexico.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> For more details on geological crystal formation, see <a href="#Rocks">above</a>. </p><p>Crystals can also be formed by biological processes, see <a href="#Organigenic_crystals">above</a>. Conversely, some organisms have special techniques to <i>prevent</i> crystallization from occurring, such as <a href="/wiki/Antifreeze_protein" title="Antifreeze protein">antifreeze proteins</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Defects,_impurities,_and_twinning"><span id="Defects.2C_impurities.2C_and_twinning"></span>Defects, impurities, and twinning</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Crystallographic_defect" title="Crystallographic defect">Crystallographic defect</a>, <a href="/wiki/Impurity" class="mw-redirect" title="Impurity">Impurity</a>, <a href="/wiki/Crystal_twinning" title="Crystal twinning">Crystal twinning</a>, and <a href="/wiki/Mosaicity" title="Mosaicity">Mosaicity</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Vector_de_Burgers.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Vector_de_Burgers.PNG/280px-Vector_de_Burgers.PNG" decoding="async" width="280" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Vector_de_Burgers.PNG/420px-Vector_de_Burgers.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Vector_de_Burgers.PNG/560px-Vector_de_Burgers.PNG 2x" data-file-width="758" data-file-height="505" /></a><figcaption>Two types of crystallographic defects. <u>Top right:</u> <a href="/wiki/Edge_dislocation" class="mw-redirect" title="Edge dislocation">edge dislocation</a>. <u>Bottom right:</u> <a href="/wiki/Screw_dislocation" class="mw-redirect" title="Screw dislocation">screw dislocation</a>.</figcaption></figure> <p>An <i>ideal</i> crystal has every atom in a perfect, exactly repeating pattern.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> However, in reality, most crystalline materials have a variety of <a href="/wiki/Crystallographic_defect" title="Crystallographic defect">crystallographic defects</a>: places where the crystal's pattern is interrupted. The types and structures of these defects may have a profound effect on the properties of the materials. </p><p>A few examples of crystallographic defects include <a href="/wiki/Vacancy_defect" title="Vacancy defect">vacancy defects</a> (an empty space where an atom should fit), <a href="/wiki/Interstitial_defect" title="Interstitial defect">interstitial defects</a> (an extra atom squeezed in where it does not fit), and <a href="/wiki/Dislocation" title="Dislocation">dislocations</a> (see figure at right). Dislocations are especially important in <a href="/wiki/Materials_science" title="Materials science">materials science</a>, because they help determine the <a href="/wiki/Strength_of_materials" title="Strength of materials">mechanical strength of materials</a>. </p><p>Another common type of crystallographic defect is an <a href="/wiki/Impurity" class="mw-redirect" title="Impurity">impurity</a>, meaning that the "wrong" type of atom is present in a crystal. For example, a perfect crystal of <a href="/wiki/Diamond" title="Diamond">diamond</a> would only contain <a href="/wiki/Carbon" title="Carbon">carbon</a> atoms, but a real crystal might perhaps contain a few <a href="/wiki/Boron" title="Boron">boron</a> atoms as well. These boron impurities change the <a href="/wiki/Diamond_color" title="Diamond color">diamond's color</a> to slightly blue. Likewise, the only difference between <a href="/wiki/Ruby" title="Ruby">ruby</a> and <a href="/wiki/Sapphire" title="Sapphire">sapphire</a> is the type of impurities present in a <a href="/wiki/Corundum" title="Corundum">corundum</a> crystal. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pyrite_60608.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pyrite_60608.jpg/250px-Pyrite_60608.jpg" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pyrite_60608.jpg/330px-Pyrite_60608.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Pyrite_60608.jpg/500px-Pyrite_60608.jpg 2x" data-file-width="1984" data-file-height="1768" /></a><figcaption>Twinned <a href="/wiki/Pyrite" title="Pyrite">pyrite</a> crystal group.</figcaption></figure> <p>In <a href="/wiki/Semiconductor" title="Semiconductor">semiconductors</a>, a special type of impurity, called a <a href="/wiki/Dopant" title="Dopant">dopant</a>, drastically changes the crystal's electrical properties. <a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductor devices</a>, such as <a href="/wiki/Transistor" title="Transistor">transistors</a>, are made possible largely by putting different semiconductor dopants into different places, in specific patterns. </p><p><a href="/wiki/Crystal_twinning" title="Crystal twinning">Twinning</a> is a phenomenon somewhere between a crystallographic defect and a <a href="/wiki/Grain_boundary" title="Grain boundary">grain boundary</a>. Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way. </p><p><a href="/wiki/Mosaicity" title="Mosaicity">Mosaicity</a> is a spread of crystal plane orientations. A <a href="/wiki/Mosaic_crystal" class="mw-redirect" title="Mosaic crystal">mosaic crystal</a> consists of smaller crystalline units that are somewhat misaligned with respect to each other. </p> <div class="mw-heading mw-heading2"><h2 id="Chemical_bonds">Chemical bonds</h2></div> <p>In general, solids can be held together by various types of <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bonds</a>, such as <a href="/wiki/Metallic_bond" class="mw-redirect" title="Metallic bond">metallic bonds</a>, <a href="/wiki/Ionic_bond" class="mw-redirect" title="Ionic bond">ionic bonds</a>, <a href="/wiki/Covalent_bond" title="Covalent bond">covalent bonds</a>, <a href="/wiki/Van_der_Waals_bond" class="mw-redirect" title="Van der Waals bond">van der Waals bonds</a>, and others. None of these are necessarily crystalline or non-crystalline. However, there are some general trends as follows: </p><p><a href="/wiki/Metal" title="Metal">Metals</a> crystallize rapidly and are almost always polycrystalline, though there are exceptions like <a href="/wiki/Amorphous_metal" title="Amorphous metal">amorphous metal</a> and single-crystal metals. The latter are grown synthetically, for example, fighter-jet turbines are typically made by first growing a single crystal of titanium alloy, increasing its strength and melting point over polycrystalline titanium. A small piece of metal may naturally form into a single crystal, such as Type 2 <a href="/wiki/Telluric_iron" title="Telluric iron">telluric iron</a>, but larger pieces generally do not unless extremely slow cooling occurs. For example, iron <a href="/wiki/Meteorite" title="Meteorite">meteorites</a> are often composed of single crystal, or many large crystals that may be several meters in size, due to very slow cooling in the vacuum of space. The slow cooling may allow the precipitation of a separate phase within the crystal lattice, which form at specific angles determined by the lattice, called <a href="/wiki/Widmanstatten_pattern" class="mw-redirect" title="Widmanstatten pattern">Widmanstatten patterns</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Ionic_compound" class="mw-redirect" title="Ionic compound">Ionic compounds</a> typically form when a metal reacts with a non-metal, such as sodium with chlorine. These often form substances called salts, such as sodium chloride (table salt) or potassium nitrate (<a href="/wiki/Saltpeter" class="mw-redirect" title="Saltpeter">saltpeter</a>), with crystals that are often brittle and cleave relatively easily. Ionic materials are usually crystalline or polycrystalline. In practice, large <a href="/wiki/Salt_(chemistry)" title="Salt (chemistry)">salt</a> crystals can be created by solidification of a <a href="/wiki/Molten" class="mw-redirect" title="Molten">molten</a> fluid, or by crystallization out of a solution. Some ionic compounds can be very hard, such as oxides like <a href="/wiki/Aluminium_oxide" title="Aluminium oxide">aluminium oxide</a> found in many gemstones such as <a href="/wiki/Ruby" title="Ruby">ruby</a> and <a href="/wiki/Synthetic_sapphire" class="mw-redirect" title="Synthetic sapphire">synthetic sapphire</a>. </p><p><a href="/wiki/Covalently_bonded" class="mw-redirect" title="Covalently bonded">Covalently bonded</a> solids (sometimes called <a href="/wiki/Covalent_network_solids" class="mw-redirect" title="Covalent network solids">covalent network solids</a>) are typically formed from one or more non-metals, such as carbon or silicon and oxygen, and are often very hard, rigid, and brittle. These are also very common, notable examples being <a href="/wiki/Diamond" title="Diamond">diamond</a> and <a href="/wiki/Quartz" title="Quartz">quartz</a> respectively.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Weak <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals forces</a> also help hold together certain crystals, such as crystalline <a href="/wiki/Molecular_solid" title="Molecular solid">molecular solids</a>, as well as the interlayer bonding in <a href="/wiki/Graphite" title="Graphite">graphite</a>. Substances such as <a href="/wiki/Fat" title="Fat">fats</a>, <a href="/wiki/Lipid" title="Lipid">lipids</a> and <a href="/wiki/Wax" title="Wax">wax</a> form molecular bonds because the large molecules do not pack as tightly as atomic bonds. This leads to crystals that are much softer and more easily pulled apart or broken. Common examples include chocolates, candles, or viruses. Water ice and <a href="/wiki/Dry_ice" title="Dry ice">dry ice</a> are examples of other materials with molecular bonding.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><a href="/wiki/Polymer" title="Polymer">Polymer</a> materials generally will form crystalline regions, but the lengths of the molecules usually prevent complete crystallization—and sometimes polymers are completely amorphous. </p> <div class="mw-heading mw-heading2"><h2 id="Quasicrystals">Quasicrystals</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ho-Mg-ZnQuasicrystal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Ho-Mg-ZnQuasicrystal.jpg/250px-Ho-Mg-ZnQuasicrystal.jpg" decoding="async" width="220" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Ho-Mg-ZnQuasicrystal.jpg/330px-Ho-Mg-ZnQuasicrystal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Ho-Mg-ZnQuasicrystal.jpg/500px-Ho-Mg-ZnQuasicrystal.jpg 2x" data-file-width="548" data-file-height="464" /></a><figcaption>The material <a href="/wiki/Holmium%E2%80%93magnesium%E2%80%93zinc_quasicrystal" title="Holmium–magnesium–zinc quasicrystal">holmium–magnesium–zinc</a> (Ho–Mg–Zn) forms <a href="/wiki/Quasicrystal" title="Quasicrystal">quasicrystals</a>, which can take on the macroscopic shape of a <a href="/wiki/Dodecahedron" title="Dodecahedron">pentagonal dodecahedron</a>. Only quasicrystals can take this 5-fold symmetry. The edges are 2 mm long.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quasicrystal" title="Quasicrystal">Quasicrystal</a></div> <p>A <a href="/wiki/Quasicrystal" title="Quasicrystal">quasicrystal</a> consists of arrays of atoms that are ordered but not strictly periodic. They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in <a href="/wiki/X-ray_diffraction" title="X-ray diffraction">x-ray diffraction</a>, and the ability to form shapes with smooth, flat faces. </p><p>Quasicrystals are most famous for their ability to show five-fold symmetry, which is impossible for an ordinary periodic crystal (see <a href="/wiki/Crystallographic_restriction_theorem" title="Crystallographic restriction theorem">crystallographic restriction theorem</a>). </p><p>The <a href="/wiki/International_Union_of_Crystallography" title="International Union of Crystallography">International Union of Crystallography</a> has redefined the term "crystal" to include both ordinary periodic crystals and quasicrystals ("any solid having an essentially discrete <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> diagram"<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>). </p><p>Quasicrystals, first discovered in 1982, are quite rare in practice. Only about 100 solids are known to form quasicrystals, compared to about 400,000 periodic crystals known in 2004.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The 2011 <a href="/wiki/Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a> was awarded to <a href="/wiki/Dan_Shechtman" title="Dan Shechtman">Dan Shechtman</a> for the discovery of quasicrystals.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Special_properties_from_anisotropy">Special properties from anisotropy</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Crystal_optics" title="Crystal optics">Crystal optics</a></div> <p>Crystals can have certain special electrical, optical, and mechanical properties that <a href="/wiki/Glass" title="Glass">glass</a> and <a href="/wiki/Polycrystal" class="mw-redirect" title="Polycrystal">polycrystals</a> normally cannot. These properties are related to the <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a> of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the <a href="/wiki/Piezoelectric_effect" class="mw-redirect" title="Piezoelectric effect">piezoelectric effect</a>, where a voltage across the crystal can shrink or stretch it. Another is <a href="/wiki/Birefringence" title="Birefringence">birefringence</a>, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a>, <a href="/wiki/Electrical_permittivity" class="mw-redirect" title="Electrical permittivity">electrical permittivity</a>, and <a href="/wiki/Young%27s_modulus" title="Young's modulus">Young's modulus</a>, may be different in different directions in a crystal. For example, <a href="/wiki/Graphite" title="Graphite">graphite</a> crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress. </p><p>Not all crystals have all of these properties. Conversely, these properties are not quite exclusive to crystals. They can appear in <a href="/wiki/Glass" title="Glass">glasses</a> or <a href="/wiki/Polycrystal" class="mw-redirect" title="Polycrystal">polycrystals</a> that have been made <a href="/wiki/Anisotropic" class="mw-redirect" title="Anisotropic">anisotropic</a> by <a href="/wiki/Work_hardening" title="Work hardening">working</a> or <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a>—for example, <a href="/wiki/Photoelasticity" title="Photoelasticity">stress-induced birefringence</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Crystallography">Crystallography</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></div> <p><i><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></i> is the science of measuring the <a href="/wiki/Crystal_structure" title="Crystal structure">crystal structure</a> (in other words, the atomic arrangement) of a crystal. One widely used crystallography technique is <a href="/wiki/X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a>. Large numbers of known crystal structures are stored in <a href="/wiki/Crystallographic_database" title="Crystallographic database">crystallographic databases</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Image_gallery">Image gallery</h2></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Insulincrystals.jpg" class="mw-file-description" title="Insulin crystals grown in earth orbit. The low gravity allows crystals to be grown with minimal defects."><img alt="Insulin crystals grown in earth orbit. The low gravity allows crystals to be grown with minimal defects." src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Insulincrystals.jpg/250px-Insulincrystals.jpg" decoding="async" width="200" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Insulincrystals.jpg/330px-Insulincrystals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Insulincrystals.jpg/500px-Insulincrystals.jpg 2x" data-file-width="1024" data-file-height="717" /></a></span></div> <div class="gallerytext"><a href="/wiki/Insulin" title="Insulin">Insulin</a> crystals <a href="/wiki/Space_manufacturing" title="Space manufacturing">grown in earth orbit</a>. The low gravity allows crystals to be grown with minimal defects.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Hoar_frost_macro2.jpg" class="mw-file-description" title="Hoar frost: A type of ice crystal (picture taken from a distance of about 5 cm)."><img alt="Hoar frost: A type of ice crystal (picture taken from a distance of about 5 cm)." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Hoar_frost_macro2.jpg/200px-Hoar_frost_macro2.jpg" decoding="async" width="200" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Hoar_frost_macro2.jpg/300px-Hoar_frost_macro2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Hoar_frost_macro2.jpg/400px-Hoar_frost_macro2.jpg 2x" data-file-width="1117" data-file-height="947" /></a></span></div> <div class="gallerytext"><a href="/wiki/Hoar_frost" class="mw-redirect" title="Hoar frost">Hoar frost</a>: A type of ice crystal (picture taken from a distance of about 5 cm).</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Gallium_crystals.jpg" class="mw-file-description" title="Gallium, a metal that easily forms large crystals."><img alt="Gallium, a metal that easily forms large crystals." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Gallium_crystals.jpg/250px-Gallium_crystals.jpg" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Gallium_crystals.jpg/330px-Gallium_crystals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Gallium_crystals.jpg/500px-Gallium_crystals.jpg 2x" data-file-width="1024" data-file-height="768" /></a></span></div> <div class="gallerytext"><a href="/wiki/Gallium" title="Gallium">Gallium</a>, a metal that easily forms large crystals.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Apatite-Rhodochrosite-Fluorite-169799.jpg" class="mw-file-description" title="An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes."><img alt="An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Apatite-Rhodochrosite-Fluorite-169799.jpg/198px-Apatite-Rhodochrosite-Fluorite-169799.jpg" decoding="async" width="198" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Apatite-Rhodochrosite-Fluorite-169799.jpg/297px-Apatite-Rhodochrosite-Fluorite-169799.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Apatite-Rhodochrosite-Fluorite-169799.jpg/397px-Apatite-Rhodochrosite-Fluorite-169799.jpg 2x" data-file-width="595" data-file-height="600" /></a></span></div> <div class="gallerytext">An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg" class="mw-file-description" title="Boules of silicon, like this one, are an important type of industrially-produced single crystal."><img alt="Boules of silicon, like this one, are an important type of industrially-produced single crystal." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg/120px-Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg" decoding="async" width="75" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg/149px-Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg 2x" data-file-width="220" data-file-height="588" /></a></span></div> <div class="gallerytext"><a href="/wiki/Boule_(crystal)" title="Boule (crystal)">Boules</a> of <a href="/wiki/Silicon" title="Silicon">silicon</a>, like this one, are an important type of industrially-produced <a href="/wiki/Single_crystal" title="Single crystal">single crystal</a>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Bornite-Chalcopyrite-Pyrite-180794.jpg" class="mw-file-description" title="A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across."><img alt="A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Bornite-Chalcopyrite-Pyrite-180794.jpg/250px-Bornite-Chalcopyrite-Pyrite-180794.jpg" decoding="async" width="200" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Bornite-Chalcopyrite-Pyrite-180794.jpg/330px-Bornite-Chalcopyrite-Pyrite-180794.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Bornite-Chalcopyrite-Pyrite-180794.jpg/500px-Bornite-Chalcopyrite-Pyrite-180794.jpg 2x" data-file-width="500" data-file-height="454" /></a></span></div> <div class="gallerytext">A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Calcite-millerite_association.jpg" class="mw-file-description" title="Needle-like millerite crystals partially encased in calcite crystal and oxidized on their surfaces to zaratite; from the Devonian Milwaukee Formation of Wisconsin"><img alt="Needle-like millerite crystals partially encased in calcite crystal and oxidized on their surfaces to zaratite; from the Devonian Milwaukee Formation of Wisconsin" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Calcite-millerite_association.jpg/200px-Calcite-millerite_association.jpg" decoding="async" width="200" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Calcite-millerite_association.jpg/300px-Calcite-millerite_association.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Calcite-millerite_association.jpg/400px-Calcite-millerite_association.jpg 2x" data-file-width="2744" data-file-height="1914" /></a></span></div> <div class="gallerytext">Needle-like <a href="/wiki/Millerite" title="Millerite">millerite</a> crystals partially encased in <a href="/wiki/Calcite" title="Calcite">calcite</a> crystal and oxidized on their surfaces to <a href="/wiki/Zaratite" title="Zaratite">zaratite</a>; from the <a href="/wiki/Devonian" title="Devonian">Devonian</a> <a href="/wiki/Milwaukee_Formation" title="Milwaukee Formation">Milwaukee Formation</a> of <a href="/wiki/Wisconsin" title="Wisconsin">Wisconsin</a></div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 230px;"><span typeof="mw:File"><a href="/wiki/File:Crystallized_sugar,_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg" class="mw-file-description" title="Crystallized sugar. Crystals on the right were grown from a sugar cube, while the left from a single seed crystal taken from the right. Red dye was added to the solution when growing the larger crystal, but, insoluble with the solid sugar, all but small traces were forced to precipitate out as it grew."><img alt="Crystallized sugar. Crystals on the right were grown from a sugar cube, while the left from a single seed crystal taken from the right. Red dye was added to the solution when growing the larger crystal, but, insoluble with the solid sugar, all but small traces were forced to precipitate out as it grew." src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg/250px-Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg" decoding="async" width="200" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg/330px-Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg/500px-Crystallized_sugar%2C_multiple_crystals_and_a_single_crystal_grown_from_seed.jpg 2x" data-file-width="2297" data-file-height="1586" /></a></span></div> <div class="gallerytext">Crystallized sugar. Crystals on the right were grown from a sugar cube, while the left from a single seed crystal taken from the right. Red dye was added to the solution when growing the larger crystal, but, insoluble with the solid sugar, all but small traces were forced to precipitate out as it grew. </div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 15em;"> <ul><li><a href="/wiki/Atomic_packing_factor" title="Atomic packing factor">Atomic packing factor</a></li> <li><a href="/wiki/Anticrystal" class="mw-redirect" title="Anticrystal">Anticrystal</a></li> <li><a href="/wiki/Cocrystal" title="Cocrystal">Cocrystal</a></li> <li><a href="/wiki/Colloidal_crystal" title="Colloidal crystal">Colloidal crystal</a></li> <li><a href="/wiki/Crystal_growth" title="Crystal growth">Crystal growth</a></li> <li><a href="/wiki/Crystal_oscillator" title="Crystal oscillator">Crystal oscillator</a></li> <li><a href="/wiki/Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></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"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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 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Retrieved <span class="nowrap">14 November</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=About.com&rft.atitle=Using+Crystals+and+Gemstones+in+Magic&rft.date=2016-08-31&rft.au=Patti+Wigington&rft_id=http%3A%2F%2Fpaganwiccan.about.com%2Fod%2Fspellworkfolkmagic%2Fss%2FMagical-Crystals-And-Gemstones.htm%23showall&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://witcheslore.com/bookofshadows/healing/the-magic-of-crystals-and-gemstones/4765/">"The Magic of Crystals and Gemstones"</a>. <i>WitchesLore</i>. 14 December 2011<span class="reference-accessdate">. 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Mercer, (1999) <i>Crystals</i>, London, Natural History Museum, page 58</span> </li> <li id="cite_note-EB1911-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-EB1911_13-0">^</a></b></span> <span class="reference-text"><span class="noprint"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/20px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/40px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> </span>One or more of the preceding sentences incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFlett1911" class="citation encyclopaedia cs1">Flett, John Smith (1911). 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Dobhal, "Glacier"; and other articles in Vijay P. Singh, Pratap Singh, and Umesh K. 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A</i>. <b>48</b> (6): <span class="nowrap">922–</span>946. <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/1992AcCrA..48..922.">1992AcCrA..48..922.</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1107%2FS0108767392008328">10.1107/S0108767392008328</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1826680">1826680</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Crystallogr.+A&rft.atitle=Report+of+the+Executive+Committee+for+1991&rft.volume=48&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E922-%3C%2Fspan%3E946&rft.date=1992&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1826680%23id-name%3DPMC&rft_id=info%3Adoi%2F10.1107%2FS0108767392008328&rft_id=info%3Abibcode%2F1992AcCrA..48..922.&rft.au=International+Union+of+Crystallography&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1826680&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSteurer_W.2004" class="citation journal cs1">Steurer W. (2004). <a rel="nofollow" class="external text" href="https://doi.org/10.1524%2Fzkri.219.7.391.35643">"Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals"</a>. <i>Z. Kristallogr</i>. <b>219</b> (<span class="nowrap">7–</span>2004): <span class="nowrap">391–</span>446. <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/2004ZK....219..391S">2004ZK....219..391S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1524%2Fzkri.219.7.391.35643">10.1524/zkri.219.7.391.35643</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Z.+Kristallogr.&rft.atitle=Twenty+years+of+structure+research+on+quasicrystals.+Part+I.+Pentagonal%2C+octagonal%2C+decagonal+and+dodecagonal+quasicrystals&rft.volume=219&rft.issue=%3Cspan+class%3D%22nowrap%22%3E7%E2%80%93%3C%2Fspan%3E2004&rft.pages=%3Cspan+class%3D%22nowrap%22%3E391-%3C%2Fspan%3E446&rft.date=2004&rft_id=info%3Adoi%2F10.1524%2Fzkri.219.7.391.35643&rft_id=info%3Abibcode%2F2004ZK....219..391S&rft.au=Steurer+W.&rft_id=https%3A%2F%2Fdoi.org%2F10.1524%252Fzkri.219.7.391.35643&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/">"The Nobel Prize in Chemistry 2011"</a>. Nobelprize.org<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-12-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Nobel+Prize+in+Chemistry+2011&rft.pub=Nobelprize.org&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fnobel_prizes%2Fchemistry%2Flaureates%2F2011%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></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:r1250146164">.mw-parser-output .sister-box .side-box-abovebelow{padding:0.75em 0;text-align:center}.mw-parser-output .sister-box .side-box-abovebelow>b{display:block}.mw-parser-output .sister-box .side-box-text>ul{border-top:1px solid #aaa;padding:0.75em 0;width:217px;margin:0 auto}.mw-parser-output .sister-box .side-box-text>ul>li{min-height:31px}.mw-parser-output .sister-logo{display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center}.mw-parser-output .sister-link{display:inline-block;margin-left:4px;width:182px;vertical-align:middle}@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-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-v2.svg"]{background-color:white}}</style><div role="navigation" aria-labelledby="sister-projects" class="side-box metadata side-box-right sister-box sistersitebox plainlinks"><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-abovebelow"> <b>Crystal</b> at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects"><span id="sister-projects">sister projects</span></a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/40px-Wiktionary-logo-v2.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/60px-Wiktionary-logo-v2.svg.png 1.5x" data-file-width="391" data-file-height="391" /></span></span></span><span class="sister-link"><a href="https://en.wiktionary.org/wiki/Special:Search/Crystal" class="extiw" title="wikt:Special:Search/Crystal">Definitions</a> from Wiktionary</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" 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title="n:Special:Search/Crystal">News</a> from Wikinews</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></span><span class="sister-link"><a href="https://en.wikiquote.org/wiki/Crystal" class="extiw" title="q:Crystal">Quotations</a> from Wikiquote</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/40px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/60px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span></span><span class="sister-link"><a href="https://en.wikisource.org/wiki/Special:Search/Crystal" class="extiw" title="s:Special:Search/Crystal">Texts</a> from Wikisource</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/27px-Wikibooks-logo.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/41px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/54px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span></span><span class="sister-link"><a href="https://en.wikibooks.org/wiki/Introduction_to_Mathematical_Physics/N_body_problem_and_matter_description/Crystalline_solids" class="extiw" title="b:Introduction to Mathematical Physics/N body problem and matter description/Crystalline solids">Textbooks</a> from Wikibooks</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></span></span></span><span class="sister-link"><a href="https://en.wikiversity.org/wiki/Special:Search/Crystal" class="extiw" title="v:Special:Search/Crystal">Resources</a> from Wikiversity</span></li></ul></div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHowardDarcy_Howard_(Illustrator)1998" class="citation web cs1">Howard, J. Michael; Darcy Howard (Illustrator) (1998). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060826015700/http://www.rockhounds.com/rockshop/xtal/index.html">"Introduction to Crystallography and Mineral Crystal Systems"</a>. Bob's Rock Shop. Archived from <a rel="nofollow" class="external text" href="http://www.rockhounds.com/rockshop/xtal/index.html">the original</a> on 2006-08-26<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-04-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Introduction+to+Crystallography+and+Mineral+Crystal+Systems&rft.pub=Bob%27s+Rock+Shop&rft.date=1998&rft.aulast=Howard&rft.aufirst=J.+Michael&rft.au=Darcy+Howard+%28Illustrator%29&rft_id=http%3A%2F%2Fwww.rockhounds.com%2Frockshop%2Fxtal%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKrassmann2005–2008" class="citation web cs1">Krassmann, Thomas (2005–2008). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080426185221/http://giantcrystals.strahlen.org/">"The Giant Crystal Project"</a>. Krassmann. Archived from <a rel="nofollow" class="external text" href="http://giantcrystals.strahlen.org">the original</a> on 2008-04-26<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-04-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Giant+Crystal+Project&rft.pub=Krassmann&rft.date=2005%2F2008&rft.aulast=Krassmann&rft.aufirst=Thomas&rft_id=http%3A%2F%2Fgiantcrystals.strahlen.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></li> <li><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/20080417001743/http://www.iucr.ac.uk/iucr-top/comm/cteach/pamphlets.html">"Teaching Pamphlets"</a>. Commission on Crystallographic Teaching. 2007. Archived from <a rel="nofollow" class="external text" href="http://www.iucr.ac.uk/iucr-top/comm/cteach/pamphlets.html">the original</a> on 2008-04-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-04-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Teaching+Pamphlets&rft.pub=Commission+on+Crystallographic+Teaching&rft.date=2007&rft_id=http%3A%2F%2Fwww.iucr.ac.uk%2Fiucr-top%2Fcomm%2Fcteach%2Fpamphlets.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.atomic-scale-physics.de/lattice/spcgrp/index.html">"Crystal Lattice Structures:Index by Space Group"</a>. 2004<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-12-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Crystal+Lattice+Structures%3AIndex+by+Space+Group&rft.date=2004&rft_id=https%3A%2F%2Fwww.atomic-scale-physics.de%2Flattice%2Fspcgrp%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACrystal" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.xtal.iqfr.csic.es/Cristalografia/index-en.html">"Crystallography"</a>. <a href="/wiki/Spanish_National_Research_Council" title="Spanish National Research Council">Spanish National Research Council</a>, Department of Crystallography. 2010<span class="reference-accessdate">. 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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:Patterns_in_nature" title="Template:Patterns in nature"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Patterns_in_nature" title="Template talk:Patterns in nature"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a 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href="/wiki/Symmetry" title="Symmetry">Symmetry</a> <ul><li><a href="/wiki/Crystal_structure" title="Crystal structure">in crystals</a></li> <li><a href="/wiki/Quasicrystal" title="Quasicrystal">Quasicrystals</a></li> <li><a href="/wiki/Floral_symmetry" title="Floral symmetry">in flowers</a></li> <li><a href="/wiki/Symmetry_in_biology" title="Symmetry in biology">in biology</a></li></ul></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tessellation</a></li> <li><a href="/wiki/K%C3%A1rm%C3%A1n_vortex_street" title="Kármán vortex street">Vortex street</a></li> <li><a href="/wiki/Wave" title="Wave">Wave</a></li> <li><a href="/wiki/Widmanst%C3%A4tten_pattern" title="Widmanstätten pattern">Widmanstätten pattern</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Yemen_Chameleon_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Yemen_Chameleon_%28cropped%29.jpg/80px-Yemen_Chameleon_%28cropped%29.jpg" decoding="async" width="80" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Yemen_Chameleon_%28cropped%29.jpg/120px-Yemen_Chameleon_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Yemen_Chameleon_%28cropped%29.jpg/160px-Yemen_Chameleon_%28cropped%29.jpg 2x" data-file-width="2086" data-file-height="1411" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Causes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a></li> <li><a href="/wiki/Biology" title="Biology">Biology</a> <ul><li><a href="/wiki/Natural_selection" title="Natural selection">Natural selection</a></li> <li><a href="/wiki/Camouflage" title="Camouflage">Camouflage</a></li> <li><a href="/wiki/Mimicry" title="Mimicry">Mimicry</a></li> <li><a href="/wiki/Sexual_selection" title="Sexual selection">Sexual selection</a></li></ul></li> <li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a> <ul><li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Logarithmic_spiral" title="Logarithmic spiral">Logarithmic spiral</a></li></ul></li> <li><a href="/wiki/Physics" title="Physics">Physics</a> <ul><li><a class="mw-selflink selflink">Crystal</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Plateau%27s_laws" title="Plateau's laws">Plateau's laws</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</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 href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Empedocles" title="Empedocles">Empedocles</a></li> <li><a href="/wiki/Fibonacci" title="Fibonacci">Fibonacci</a> <ul><li><i><a href="/wiki/Liber_Abaci" title="Liber Abaci">Liber Abaci</a></i></li></ul></li> <li><a href="/wiki/Adolf_Zeising" title="Adolf Zeising">Adolf Zeising</a></li> <li><a href="/wiki/Ernst_Haeckel" title="Ernst Haeckel">Ernst Haeckel</a></li> <li><a href="/wiki/Joseph_Plateau" title="Joseph Plateau">Joseph Plateau</a></li> <li><a href="/wiki/Wilson_Bentley" title="Wilson Bentley">Wilson Bentley</a></li> <li><a href="/wiki/D%27Arcy_Wentworth_Thompson" title="D'Arcy Wentworth Thompson">D'Arcy Wentworth Thompson</a> <ul><li><i><a href="/wiki/On_Growth_and_Form" title="On Growth and Form">On Growth and Form</a></i></li></ul></li> <li><a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a> <ul><li><i><a href="/wiki/The_Chemical_Basis_of_Morphogenesis" title="The Chemical Basis of Morphogenesis">The Chemical Basis of Morphogenesis</a></i></li></ul></li> <li><a href="/wiki/Aristid_Lindenmayer" title="Aristid Lindenmayer">Aristid Lindenmayer</a></li> <li><a href="/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot">Benoît Mandelbrot</a> <ul><li><i><a href="/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension" class="mw-redirect" title="How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension">How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pattern_recognition_(psychology)" title="Pattern recognition (psychology)">Pattern recognition</a></li> <li><a href="/wiki/Emergence" title="Emergence">Emergence</a></li> <li><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</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" /><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319" /></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q43533#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1447" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q43533#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1447" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q43533#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></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/884667/">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Kristall"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4033209-3">Germany</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85034503">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11941210s">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11941210s">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00565650">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="krystaly"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph121980&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://datos.bne.es/resource/XX526709">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007536082305171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>111 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> 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