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class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Sadržaj" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Elementi_simetrije_kristala" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elementi_simetrije_kristala"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Elementi simetrije kristala</span> </div> </a> <ul id="toc-Elementi_simetrije_kristala-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kristalografski_sustavi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kristalografski_sustavi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Kristalografski sustavi</span> </div> </a> <ul id="toc-Kristalografski_sustavi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kristalna_struktura_čvrstog_tijela" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kristalna_struktura_čvrstog_tijela"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Kristalna struktura čvrstog tijela</span> </div> </a> <ul id="toc-Kristalna_struktura_čvrstog_tijela-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_poveznice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_poveznice"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Vanjske poveznice</span> </div> </a> <ul id="toc-Vanjske_poveznice-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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaz sadržaja stranice" > <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">Prikaz sadržaja stranice</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">Kristal</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="Idi na druge jezične varijante članka. Dostupan je na 111 jezika" > <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 jezika</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-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Cristal" title="Cristal – aragonski" lang="an" hreflang="an" data-title="Cristal" data-language-autonym="Aragonés" data-language-local-name="aragonski" class="interlanguage-link-target"><span>Aragonés</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 – arapski" lang="ar" hreflang="ar" data-title="بلورة" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</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-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cristal" title="Cristal – asturijski" lang="ast" hreflang="ast" data-title="Cristal" data-language-autonym="Asturianu" data-language-local-name="asturijski" 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 – azerbajdžanski" lang="az" hreflang="az" data-title="Kristallar" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" class="interlanguage-link-target"><span>Azərbaycanca</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-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 – bjeloruski" lang="be" hreflang="be" data-title="Крышталічныя целы" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Balur" title="Balur – Betawi" lang="bew" hreflang="bew" data-title="Balur" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target"><span>Betawi</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 – bugarski" lang="bg" hreflang="bg" data-title="Кристал" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</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-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kristal" title="Kristal – bosanski" lang="bs" hreflang="bs" data-title="Kristal" data-language-autonym="Bosanski" data-language-local-name="bosanski" 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 – katalonski" lang="ca" hreflang="ca" data-title="Cristall" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</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 – soranski kurdski" lang="ckb" hreflang="ckb" data-title="بلوور" data-language-autonym="کوردی" data-language-local-name="soranski kurdski" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Krystal" title="Krystal – češki" lang="cs" hreflang="cs" data-title="Krystal" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</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 – čuvaški" lang="cv" hreflang="cv" data-title="Кристалл" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Grisial" title="Grisial – velški" lang="cy" hreflang="cy" data-title="Grisial" data-language-autonym="Cymraeg" data-language-local-name="velški" 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 – danski" lang="da" hreflang="da" data-title="Krystal" data-language-autonym="Dansk" data-language-local-name="danski" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kristall" title="Kristall – njemački" lang="de" hreflang="de" data-title="Kristall" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</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 – grčki" lang="el" hreflang="el" data-title="Κρύσταλλος" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Crystal" title="Crystal – engleski" lang="en" hreflang="en" data-title="Crystal" data-language-autonym="English" data-language-local-name="engleski" class="interlanguage-link-target"><span>English</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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cristal" title="Cristal – španjolski" lang="es" hreflang="es" data-title="Cristal" data-language-autonym="Español" data-language-local-name="španjolski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kristall" title="Kristall – estonski" lang="et" hreflang="et" data-title="Kristall" data-language-autonym="Eesti" data-language-local-name="estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kristal" title="Kristal – baskijski" lang="eu" hreflang="eu" data-title="Kristal" data-language-autonym="Euskara" data-language-local-name="baskijski" 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 – perzijski" lang="fa" hreflang="fa" data-title="بلور" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kiteinen_aine" title="Kiteinen aine – finski" lang="fi" hreflang="fi" data-title="Kiteinen aine" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Karisitala" title="Karisitala – fidžijski" lang="fj" hreflang="fj" data-title="Karisitala" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidžijski" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cristal" title="Cristal – francuski" lang="fr" hreflang="fr" data-title="Cristal" data-language-autonym="Français" data-language-local-name="francuski" 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 – irski" lang="ga" hreflang="ga" data-title="Criostal" data-language-autonym="Gaeilge" data-language-local-name="irski" class="interlanguage-link-target"><span>Gaeilge</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-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cristal" title="Cristal – galicijski" lang="gl" hreflang="gl" data-title="Cristal" data-language-autonym="Galego" data-language-local-name="galicijski" 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 – gudžaratski" lang="gu" hreflang="gu" data-title="સ્ફટિક" data-language-autonym="ગુજરાતી" data-language-local-name="gudžaratski" class="interlanguage-link-target"><span>ગુજરાતી</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-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%91%D7%99%D7%A9" title="גביש – hebrejski" lang="he" hreflang="he" data-title="גביש" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</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 – hindski" lang="hi" hreflang="hi" data-title="क्रिस्टल" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kristal" title="Kristal – haićanski kreolski" lang="ht" hreflang="ht" data-title="Kristal" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haićanski kreolski" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Krist%C3%A1ly" title="Kristály – mađarski" lang="hu" hreflang="hu" data-title="Kristály" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</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 – armenski" lang="hy" hreflang="hy" data-title="Բյուրեղ" data-language-autonym="Հայերեն" data-language-local-name="armenski" class="interlanguage-link-target"><span>Հայերեն</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-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kristal" title="Kristal – indonezijski" lang="id" hreflang="id" data-title="Kristal" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Kristall" title="Kristall – islandski" lang="is" hreflang="is" data-title="Kristall" data-language-autonym="Íslenska" data-language-local-name="islandski" 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 – talijanski" lang="it" hreflang="it" data-title="Cristallo" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</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 – japanski" lang="ja" hreflang="ja" data-title="結晶" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</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-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kristal" title="Kristal – javanski" lang="jv" hreflang="jv" data-title="Kristal" data-language-autonym="Jawa" data-language-local-name="javanski" class="interlanguage-link-target"><span>Jawa</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 – gruzijski" lang="ka" hreflang="ka" data-title="კრისტალი" data-language-autonym="ქართული" data-language-local-name="gruzijski" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/Kristal" title="Kristal – Komering" lang="kge" hreflang="kge" data-title="Kristal" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target"><span>Kumoring</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 – kazaški" lang="kk" hreflang="kk" data-title="Кристалл" data-language-autonym="Қазақша" data-language-local-name="kazaški" class="interlanguage-link-target"><span>Қазақша</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 – karnatački" lang="kn" hreflang="kn" data-title="ಸ್ಫಟಿಕ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="karnatački" class="interlanguage-link-target"><span>ಕನ್ನಡ</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 – korejski" lang="ko" hreflang="ko" data-title="결정" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</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 – kirgiski" lang="ky" hreflang="ky" data-title="Кристалл" data-language-autonym="Кыргызча" data-language-local-name="kirgiski" 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 – latinski" lang="la" hreflang="la" data-title="Crystallum" data-language-autonym="Latina" data-language-local-name="latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kristalas" title="Kristalas – litavski" lang="lt" hreflang="lt" data-title="Kristalas" data-language-autonym="Lietuvių" data-language-local-name="litavski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Krist%C4%81ls" title="Kristāls – latvijski" lang="lv" hreflang="lv" data-title="Kristāls" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kristaly" title="Kristaly – malgaški" lang="mg" hreflang="mg" data-title="Kristaly" data-language-autonym="Malagasy" data-language-local-name="malgaški" class="interlanguage-link-target"><span>Malagasy</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 – makedonski" lang="mk" hreflang="mk" data-title="Кристал" data-language-autonym="Македонски" data-language-local-name="makedonski" class="interlanguage-link-target"><span>Македонски</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) – malajalamski" lang="ml" hreflang="ml" data-title="പരൽ (രസതന്ത്രം)" data-language-autonym="മലയാളം" data-language-local-name="malajalamski" class="interlanguage-link-target"><span>മലയാളം</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 – mongolski" lang="mn" hreflang="mn" data-title="Талст" data-language-autonym="Монгол" data-language-local-name="mongolski" class="interlanguage-link-target"><span>Монгол</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 – manipurski" lang="mni" hreflang="mni" data-title="ꯀ꯭ꯔꯤꯁꯇꯦꯜꯂꯥꯏꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="manipurski" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</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 – marathski" lang="mr" hreflang="mr" data-title="स्फटिक" data-language-autonym="मराठी" data-language-local-name="marathski" 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 – malajski" lang="ms" hreflang="ms" data-title="Hablur" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</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 – burmanski" lang="my" hreflang="my" data-title="ပုံဆောင်ခဲ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmanski" 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-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 – nepalski" lang="ne" hreflang="ne" data-title="मणिभ" data-language-autonym="नेपाली" data-language-local-name="nepalski" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kristal_(natuurwetenschappen)" title="Kristal (natuurwetenschappen) – nizozemski" lang="nl" hreflang="nl" data-title="Kristal (natuurwetenschappen)" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Krystall" title="Krystall – norveški nynorsk" lang="nn" hreflang="nn" data-title="Krystall" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Krystall" title="Krystall – norveški bokmål" lang="nb" hreflang="nb" data-title="Krystall" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Cristal" title="Cristal – okcitanski" lang="oc" hreflang="oc" data-title="Cristal" data-language-autonym="Occitan" data-language-local-name="okcitanski" 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 – oromski" lang="om" hreflang="om" data-title="Baalcii" data-language-autonym="Oromoo" data-language-local-name="oromski" class="interlanguage-link-target"><span>Oromoo</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 – pandžapski" lang="pa" hreflang="pa" data-title="ਬਲੌਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</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 – poljski" lang="pl" hreflang="pl" data-title="Ciało krystaliczne" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</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-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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Cristal" title="Cristal – portugalski" lang="pt" hreflang="pt" data-title="Cristal" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pi%C3%B1i" title="Piñi – kečuanski" lang="qu" hreflang="qu" data-title="Piñi" data-language-autonym="Runa Simi" data-language-local-name="kečuanski" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cristal" title="Cristal – rumunjski" lang="ro" hreflang="ro" data-title="Cristal" data-language-autonym="Română" data-language-local-name="rumunjski" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Crustalu" title="Crustalu – aromunski" lang="rup" hreflang="rup" data-title="Crustalu" data-language-autonym="Armãneashti" data-language-local-name="aromunski" class="interlanguage-link-target"><span>Armãneashti</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 – ruski" lang="ru" hreflang="ru" data-title="Кристаллы" data-language-autonym="Русский" data-language-local-name="ruski" 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 – jakutski" lang="sah" hreflang="sah" data-title="Кристааллар" data-language-autonym="Саха тыла" data-language-local-name="jakutski" 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 – škotski" lang="sco" hreflang="sco" data-title="Creestal" data-language-autonym="Scots" data-language-local-name="škotski" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kristal" title="Kristal – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Kristal" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</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 – sinhaleški" lang="si" hreflang="si" data-title="සකැට" data-language-autonym="සිංහල" data-language-local-name="sinhaleški" 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 – slovački" lang="sk" hreflang="sk" data-title="Kryštál" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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 – slovenski" lang="sl" hreflang="sl" data-title="Kristal" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kristali" title="Kristali – albanski" lang="sq" hreflang="sq" data-title="Kristali" data-language-autonym="Shqip" data-language-local-name="albanski" class="interlanguage-link-target"><span>Shqip</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 – srpski" lang="sr" hreflang="sr" data-title="Кристал" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kristall" title="Kristall – švedski" lang="sv" hreflang="sv" data-title="Kristall" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Fuwele" title="Fuwele – svahili" lang="sw" hreflang="sw" data-title="Fuwele" data-language-autonym="Kiswahili" data-language-local-name="svahili" class="interlanguage-link-target"><span>Kiswahili</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 – tamilski" lang="ta" hreflang="ta" data-title="படிகம்" data-language-autonym="தமிழ்" data-language-local-name="tamilski" class="interlanguage-link-target"><span>தமிழ்</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 – teluški" lang="te" hreflang="te" data-title="స్ఫటికం" data-language-autonym="తెలుగు" data-language-local-name="teluški" 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 – tajlandski" lang="th" hreflang="th" data-title="ผลึก" data-language-autonym="ไทย" data-language-local-name="tajlandski" class="interlanguage-link-target"><span>ไทย</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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kristal" title="Kristal – turski" lang="tr" hreflang="tr" data-title="Kristal" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</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 – tatarski" lang="tt" hreflang="tt" data-title="Кристалл" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarski" class="interlanguage-link-target"><span>Татарча / tatarça</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 – ujgurski" lang="ug" hreflang="ug" data-title="كىرىستال" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="ujgurski" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</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 – ukrajinski" lang="uk" hreflang="uk" data-title="Кристал" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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 – urdski" lang="ur" hreflang="ur" data-title="بلور" data-language-autonym="اردو" data-language-local-name="urdski" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kristallar" title="Kristallar – uzbečki" lang="uz" hreflang="uz" data-title="Kristallar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tinh_th%E1%BB%83" title="Tinh thể – vijetnamski" lang="vi" hreflang="vi" data-title="Tinh thể" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kristal" title="Kristal – waray" lang="war" hreflang="war" 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 kineski" lang="wuu" hreflang="wuu" data-title="晶体" data-language-autonym="吴语" data-language-local-name="wu kineski" 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 – jidiš" lang="yi" hreflang="yi" data-title="קריסטאל" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%99%B6%E4%BD%93" title="晶体 – kineski" lang="zh" hreflang="zh" data-title="晶体" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%99%B6%E9%AB%94" title="晶體 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="晶體" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</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 – min nan kineski" lang="nan" hreflang="nan" data-title="Chiⁿ-thé" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kineski" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</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 – kantonski" lang="yue" hreflang="yue" data-title="晶體" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</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> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q43533#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kristal" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Kristal&action=edit&redlink=1" rel="discussion" class="new" title="Razgovorna stranica (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">hrvatski</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kristal"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kristal&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kristal&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kristal&action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Pomagala" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Pomagala</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Pomagala</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sakrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Više mogućnosti" > <div class="vector-menu-heading"> Radnje </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Kristal"><span>Čitaj</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kristal&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kristal&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kristal&action=history"><span>Vidi povijest</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Razno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovamo/Kristal" title="Popis svih stranica koje sadrže poveznice na ovu stranicu [j]" accesskey="j"><span>Što vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_promjene/Kristal" rel="nofollow" title="Nedavne promjene na stranicama koje su povezane s navedenom stranicom [k]" accesskey="k"><span>Povezane promjene</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedija:Upload" title="Postavi datoteke [u]" accesskey="u"><span>Postavi datoteku</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Popis svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Kristal&oldid=6411064" title="Trajna poveznica na ovu verziju stranice"><span>Trajna poveznica</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Kristal&action=info" title="Više informacija o ovoj stranici"><span>Podatci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&page=Kristal&id=6411064&wpFormIdentifier=titleform" title="Informacije o tome kako citirati ovu stranicu"><span>Citiraj ovu stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FKristal"><span>Skraćeni URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fhr.wikipedia.org%2Fwiki%2FKristal"><span>Preuzmi QR kôd</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Ispis/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Zbirka&bookcmd=book_creator&referer=Kristal"><span>Stvori knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Kristal&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Kristal&printable=yes" title="Inačica za ispis ove stranice [p]" accesskey="p"><span>Inačica za ispis</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Wikimedijini projekti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Crystal" hreflang="en"><span>Zajednički poslužitelj</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q43533" title="Poveznica na stavku na projektu Wikipodatci [g]" accesskey="g"><span>Stavka na Wikipodatcima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Preusmjereno s <a href="/w/index.php?title=Kristali&redirect=no" class="mw-redirect" title="Kristali">Kristali</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg/300px-Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg/450px-Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg/600px-Snow_crystallization_in_Akureyri_2005-02-26_19-03-37.jpeg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption><a href="/wiki/Kristalizacija" title="Kristalizacija">Kristalizacija</a> je nastajanje kristala u kojem se osnovne <a href="/wiki/%C4%8Cestica" class="mw-redirect" title="Čestica">čestice</a> (<a href="/wiki/Atom" title="Atom">atomi</a>, <a href="/wiki/Ion" title="Ion">ioni</a> ili <a href="/wiki/Molekule" class="mw-redirect" title="Molekule">molekule</a>) pravilno slažu u prostoru stvarajući <a href="/wiki/Kristalna_re%C5%A1etka" title="Kristalna rešetka">kristalnu rešetku</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Quartz_oisan.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Quartz_oisan.jpg/300px-Quartz_oisan.jpg" decoding="async" width="300" height="302" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Quartz_oisan.jpg/450px-Quartz_oisan.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Quartz_oisan.jpg/600px-Quartz_oisan.jpg 2x" data-file-width="4004" data-file-height="4031" /></a><figcaption>Kristal <a href="/wiki/Kvarc" title="Kvarc">kvarca</a>.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r5770524/mw-parser-output/.tmulti">.mw-parser-output .tmulti .thumbinner{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{text-align:left;background-color:transparent}.mw-parser-output .tmulti .thumbcaption-center{text-align:center;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 .thumbcaption{text-align:center}}</style><div class="thumb tmulti tright"><div class="thumbinner" style="width:308px;max-width:308px"><div class="trow"><div class="theader" style="text-align:center;background-color:transparent"><a href="/wiki/Halit" title="Halit">Halit</a> (<a href="/wiki/Kuhinjska_sol" title="Kuhinjska sol">kuhinjska sol</a>, NaCl): mikroskopski i makroskopski</div></div><div class="trow"><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/Datoteka: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/150px-Sodium-chloride-3D-ionic.png" decoding="async" width="150" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/225px-Sodium-chloride-3D-ionic.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/300px-Sodium-chloride-3D-ionic.png 2x" data-file-width="1000" data-file-height="948" /></a></span></div><div class="thumbcaption">Mikroskopska struktura kristala <a href="/wiki/Halit" title="Halit">halita</a> (ljubičasti su ioni <a href="/wiki/Natrij" title="Natrij">natrija</a>, zeleni su ioni <a href="/wiki/Klor" title="Klor">klora</a>). To je <a href="/wiki/Kubi%C4%8Dni_kristalni_sustav" title="Kubični kristalni sustav">kubični kristalni sustav</a> u rasporedu <a href="/wiki/Atom" title="Atom">atoma</a>.</div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/Datoteka:Selpologne.jpg" class="mw-file-description"><img alt="Halite crystal (Macroscopic )" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/150px-Selpologne.jpg" decoding="async" width="150" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/225px-Selpologne.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Selpologne.jpg/300px-Selpologne.jpg 2x" data-file-width="3780" data-file-height="3582" /></a></span></div><div class="thumbcaption">Makroskopski kristal halita (~ 16 <a href="/wiki/Metar" title="Metar">cm</a>). Pravi kut (90˚) između kristalnih ploha nastaje zbog kubne simetrije rasporeda atoma.</div></div></div></div></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Crystal_on_graph_paper.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Crystal_on_graph_paper.jpg/300px-Crystal_on_graph_paper.jpg" decoding="async" width="300" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Crystal_on_graph_paper.jpg/450px-Crystal_on_graph_paper.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/Crystal_on_graph_paper.jpg/600px-Crystal_on_graph_paper.jpg 2x" data-file-width="1566" data-file-height="1092" /></a><figcaption>Kristal <a href="/wiki/Kalcit" title="Kalcit">kalcita</a> leži na milimetarskom papiru prikazujući <a href="/wiki/Dvolom" title="Dvolom">dvolom</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Kristallstruktur_Zementit.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Kristallstruktur_Zementit.png/300px-Kristallstruktur_Zementit.png" decoding="async" width="300" height="294" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Kristallstruktur_Zementit.png/450px-Kristallstruktur_Zementit.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Kristallstruktur_Zementit.png/600px-Kristallstruktur_Zementit.png 2x" data-file-width="1158" data-file-height="1134" /></a><figcaption>Prikaz <a href="/wiki/Kristalna_re%C5%A1etka" title="Kristalna rešetka">kristalne rešetke</a> <a href="/wiki/Cementit" title="Cementit">cementita</a> Fe<sub>3</sub>C. <a href="/wiki/Atom" title="Atom">Atomi</a> <a href="/wiki/%C5%BDeljezo" title="Željezo">željeza</a> su plave boje, a <a href="/wiki/Ugljik" title="Ugljik">ugljika</a> su crne boje i puno manji.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Diamonds_glitter.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Diamonds_glitter.png/300px-Diamonds_glitter.png" decoding="async" width="300" height="272" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/28/Diamonds_glitter.png 1.5x" data-file-width="359" data-file-height="326" /></a><figcaption>Dijamantna rešetka: struktura kubičnog <a href="/wiki/Dijamant" title="Dijamant">dijamanta</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Rough_diamond.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Rough_diamond.jpg/300px-Rough_diamond.jpg" decoding="async" width="300" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d7/Rough_diamond.jpg 1.5x" data-file-width="360" data-file-height="271" /></a><figcaption>Sirovi <a href="/wiki/Dijamant" title="Dijamant">dijamant</a>: kristal u obliku <a href="/wiki/Oktaedar" title="Oktaedar">oktaedra</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Platinum-unit_cell.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/d/de/Platinum-unit_cell.jpg/300px-Platinum-unit_cell.jpg" decoding="async" width="300" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/d/de/Platinum-unit_cell.jpg 1.5x" data-file-width="323" data-file-height="301" /></a><figcaption>Prikaz jedinične elementarne ćelije <a href="/wiki/Platina" title="Platina">platine</a>.</figcaption></figure> <p><b>Kristal</b> (<a href="/wiki/Latinski_jezik" title="Latinski jezik">lat</a>. <i>crystallus</i> od <a href="/wiki/Gr%C4%8Dki_jezik" title="Grčki jezik">grč</a>. <i>ϰρύσταλλος</i>: led, ledac, kremen prozirac) je <a href="/wiki/Fizikalno_tijelo" class="mw-redirect" title="Fizikalno tijelo">fizikalno tijelo</a> u <a href="/wiki/Krutine" title="Krutine">čvrstom</a> <a href="/wiki/Agregatna_stanja" class="mw-redirect" title="Agregatna stanja">agregatnom stanju</a> koje je građeno od pravilno <a href="/wiki/Prostor" title="Prostor">trodimenzijski</a> <a href="/wiki/Period" title="Period">periodički</a> raspoređenih <a href="/wiki/Atom" title="Atom">atoma</a>, <a href="/wiki/Ion" title="Ion">iona</a> ili <a href="/wiki/Molekula" title="Molekula">molekula</a>, to jest ima <a href="/wiki/Kristalna_re%C5%A1etka" title="Kristalna rešetka">kristalnu strukturu</a>. Pravilni je raspored <a href="/wiki/Termodinamika" title="Termodinamika">termodinamički</a> najstabilniji i većina <a href="/wiki/Krutine" title="Krutine">čvrstih tvari</a> kristalne je prirode. Kristali nastaju u procesu <a href="/wiki/Kristalizacija" title="Kristalizacija">kristalizacije</a> rastom iz pothlađene <a href="/wiki/Kapljevina" class="mw-redirect" title="Kapljevina">kapljevine</a>, pothlađene <a href="/wiki/Para" title="Para">pare</a>, <a href="/wiki/Plin" title="Plin">plina</a>, zasićene <a href="/wiki/Otopine" title="Otopine">otopine</a>, <a href="/wiki/Taljenje" title="Taljenje">taline</a>, <a href="/wiki/Amorfna_tvar" title="Amorfna tvar">nesređene (amorfne) čvrste faze</a> ili manje stabilne kristalne faze. Unutrašnji pravilni raspored daje kristalu određenu <a href="/wiki/Simetrija" title="Simetrija">simetriju</a> koja se iskazuje u svojstvima i u vanjskom obliku kristala. Kristal ima određen <a href="/wiki/Geometrija" title="Geometrija">geometrijski oblik</a>. <a href="/wiki/Kut" title="Kut">Kutovi</a> među <a href="/wiki/Ploha" class="mw-disambig" title="Ploha">plohama</a> kristala neke <a href="/wiki/Kemijska_tvar" title="Kemijska tvar">kemijske tvari</a> konstantni su i za tu tvar svojstveni (karakteristični). Dijelovi nastali kalanjem kristala imaju ravne površine, a njihovi su kutovi također konstantni i svojstveni za dotičnu tvar. Dijelovi nastali sitnjenjem kristala opet su kristalići istih svojstava. </p><p>Svojstva kristala kao što su <a href="/wiki/Gusto%C4%87a" title="Gustoća">gustoća</a>, <a href="/wiki/Tvrdo%C4%87a" title="Tvrdoća">tvrdoća</a>, kalavost, <a href="/wiki/Elasti%C4%8Dnost" title="Elastičnost">elastičnost</a>, <a href="/wiki/Plasti%C4%8Dnost" title="Plastičnost">plastičnost</a>, magnetska i električna <a href="/wiki/Polarizacija" class="mw-disambig" title="Polarizacija">polarizacija</a>, <a href="/wiki/Vodljivost" title="Vodljivost">vodljivost</a> topline i struje, <a href="/wiki/Boja" title="Boja">boja</a>, <a href="/wiki/Sjaj" title="Sjaj">sjaj</a>, <a href="/wiki/Refrakcija" title="Refrakcija">lom</a> i <a href="/wiki/Dvolom" title="Dvolom">dvolom</a> <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosti</a> ovise o kemijskom sastavu i kristalnoj strukturi pa su zbog toga stalna. Međutim, mnoga su svojstva različita u različitim <a href="/wiki/Smjer" class="mw-disambig" title="Smjer">smjerovima</a> u kristalu i to se svojstvo označuje kao <a href="/wiki/Anizotropija" title="Anizotropija">anizotropija</a>. Ako se rast kristala odvijao bez vanjskih zapreka, njihovi su vanjski oblici geometrijski pravilni (<a href="/wiki/Poliedar" title="Poliedar">poliedri</a>), što je odraz njihove pravilne strukture. Kristalni poliedri mogu biti sastavljeni od ploha jedne kristalne forme, to jest od ploha koje su međusobno simetrijski jednake, ili od kombinacije ploha više kristalnih formi. Iz stabilnosti strukture proizlaze i zakonitosti <a href="/wiki/Morfologija" class="mw-disambig" title="Morfologija">morfologije</a> poliedara, koje su sadržane u kristalnim zakonima: u zakonu stalnosti kutova između bilo kojeg para ploha prisutnog na svim kristalima iste tvari, te u zakonu racionalnog omjera parametara (odsječaka ploha po koordinatnim osima) prema kojemu su parametri po pojedinačnim osima bilo kojega para ploha na promatranom kristalu u omjeru malih <a href="/wiki/Racionalni_broj" title="Racionalni broj">racionalnih brojeva</a>. U tome je bitna razlika između kristalnih i proizvoljnih poliedara (mnogoplošnika). Kristalni oblik svojstven je za mnoge kemijske tvari pa često omogućuje njihovo otkrivanje (identifikaciju), što se osobito koristi u <a href="/wiki/Mineralogija" title="Mineralogija">mineralogiji</a>. Posve pravilni oblici susreću se samo kod monokristala; mnogo su češći kristalni agregati (polikristali) kod kojih svako zrno nema sve svoje svojstvene plohe ili je potpuno bez njih, a cijeli polikristal gledan kao cjelina nema jedinstvenu kristalnu strukturu.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Elementi_simetrije_kristala">Elementi simetrije kristala</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristal&veaction=edit&section=1" title="Uredi odlomak: Elementi simetrije kristala" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristal&action=edit&section=1" title="Uredi kôd odjeljka Elementi simetrije kristala"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kristali imaju tri vrste simetrijskih elemenata koje možemo zapaziti kako u njihovoj strukturi, tako i po vanjskom obliku. To su: </p> <ul><li>ravnina simetrije je ona <a href="/wiki/Ravnina" title="Ravnina">ravnina</a> koja dijeli kristal na dva zrcalno jednaka dijela;</li> <li>os simetrije ili gira je <a href="/wiki/Os" title="Os">os</a> (<a href="/wiki/Pravac" title="Pravac">pravac</a>) oko koje možemo okretati kristal da se pri tom pojavljuju istovrsni položaji kristala. Ti položaji se oko gire mogu pojavljivati dva, tri, četiri ili šest puta, pa prema tome postoje digire, trigire, tetragire i heksagire.</li> <li>centar simetrije je <a href="/wiki/To%C4%8Dka_(matematika)" class="mw-redirect" title="Točka (matematika)">točka</a> u geometrijskom središtu kristala, kroz koju prolaze pravci koji na oba kraja imaju istovrsne usporedne kristalografske elemente, i to plohe, bridove ili uglove.</li></ul> <p>Elemente simetrije opažamo već u <a href="/w/index.php?title=Jedini%C4%8Dna_elementarna_%C4%87elija_kristala&action=edit&redlink=1" class="new" title="Jedinična elementarna ćelija kristala (stranica ne postoji)">elementarnoj ćeliji</a> strukturne rešetke kristala. Broj elemenata simetrije je ograničen - postoje 32 kombinacije simetrijskih elemenata, po kojima razlikujemo i 32 <i>kristalne klase</i>. Mineralne forme jedne kristalne klase imaju iste elemente simetrije. </p> <div class="mw-heading mw-heading2"><h2 id="Kristalografski_sustavi">Kristalografski sustavi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristal&veaction=edit&section=2" title="Uredi odlomak: Kristalografski sustavi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristal&action=edit&section=2" title="Uredi kôd odjeljka Kristalografski sustavi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sve plohe koje se nalaze na kristalu fiksiramo na zamišljeni <a href="/wiki/Koordinatni_sustav" title="Koordinatni sustav">koordinatni sustav</a>, koji nazivamo kristalografskim osima. Plohe <a href="/wiki/Piramida_(geometrija)" title="Piramida (geometrija)">piramide</a> položene su tako da sijeku sve tri kristalografske osi, plohe <a href="/wiki/Prizma" title="Prizma">prizme</a> sijeku dvije osi, a s trećom su paralelne, dok plohe pinakoida sijeku samo jednu os, a s ostale dvije su paralelne. </p><p>S obzirom na kristalografske osi, nekoliko kristalnih klasa možemo spojiti u jedan kristalografski sustav. U jednom kristalnom sustavu nalaze se kristalne klase s različitim elementima simetrije, ali sve imaju isti položaj kristalografskih osi. </p><p>Postoji 6 kristalografskih sustava, a to su: </p> <ul><li><a href="/wiki/Kubi%C4%8Dni_kristalni_sustav" title="Kubični kristalni sustav">kubični kristalni sustav</a> obuhvaća kristalne forme (njih 15 ukupno) koje se mogu svesti na tri jednake i međusobno okomite kristalografske osi. Prostorna rešetka takvog sustava je jednostavna, plošnocentrirana ili volumnocentrirana <a href="/wiki/Kocka" title="Kocka">kocka</a>. Kubični sustav ima 5 kristalnih klasa.</li> <li><a href="/wiki/Heksagonski_kristalni_sustav" class="mw-redirect" title="Heksagonski kristalni sustav">heksagonski kristalni sustav</a> obuhvaća forme (njih 9) koje se mogu svesti na 4 kristalografske osi. Tri su jednake, leže u horizontalnoj ravnini i sijeku se međusobno pod kutom od 120°, a četvrta, duža ili kraća os na njih je okomita. Prostorna rešetka je heksagonska ili romboedrijska. Ovaj sustav ima 12 kristalnih klasa.</li> <li><a href="/wiki/Tetragonski_kristalni_sustav" title="Tetragonski kristalni sustav">tetragonski kristalni sustav</a> - obuhvaća forme (njih 5) s tri međusobno okomite kristalografske, od kojih su dvije jednake i leže u vodoravnoj ravnini, a treća kraća ili duža leži okomito na njih. Prostorna rešetka je jednostavna ili volumnocentrirana tetragonska prizma. Tetragonski sustav ima 7 kristalnih klasa.</li> <li><a href="/wiki/Ortorompski_kristalni_sustav" title="Ortorompski kristalni sustav">ortorompski kristalni sustav</a> obuhvaća forme (njih 3) koje se mogu svesti na 3 nejednake i međusobno okomite osi. Prostorna rešetka je jednostavna ili volumnocentrirana rompska prizma. Sustav ima 3 kristalne klase.</li> <li><a href="/wiki/Monoklinski_kristalni_sustav" title="Monoklinski kristalni sustav">monoklinski kristalni sustav</a> obuhvaća forme (njih 3) koje se svode na 3 nejednake kristalografske osi, od kojih su samo dvije međusobno okomite, a treća je kosa. Prostorna rešetka je jednostavna ili baznocentrirana monoklinska prizma, a sustav ima 3 kristalne klase.</li> <li><a href="/wiki/Triklinski_kristalni_sustav" title="Triklinski kristalni sustav">triklinski kristalni sustav</a> obuhvaća forme (njih 3) koje se mogu svesti na tri kristalografske osi nejednake dužine i koje se međusobno sijeku pod kosim kutom. Prostorna rešetka ima samo centar simetrije.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Kristalna_struktura_čvrstog_tijela"><span id="Kristalna_struktura_.C4.8Dvrstog_tijela"></span>Kristalna struktura čvrstog tijela</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristal&veaction=edit&section=3" title="Uredi odlomak: Kristalna struktura čvrstog tijela" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristal&action=edit&section=3" title="Uredi kôd odjeljka Kristalna struktura čvrstog tijela"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>U prirodi se često nalaze komadići <a href="/wiki/Materija" title="Materija">materije</a>, koji su omeđeni ravnim plohama i predstavljaju pravilna geometrijska tijela kao <a href="/wiki/Kocka" title="Kocka">kocke</a>, <a href="/wiki/Piramida_(geometrija)" title="Piramida (geometrija)">piramide</a>, <a href="/wiki/Oktaedar" title="Oktaedar">oktaedre</a> i tako dalje. Proučavanje takvih pravilnih kristala već je odavno jedan od osnovnih zadataka <a href="/wiki/Mineralogija" title="Mineralogija">mineraloga</a>, a <a href="/wiki/Matemati%C4%8Dar" title="Matematičar">matematičari</a> su našli poticaja u kristalima da nauku o <a href="/wiki/Simetrija" title="Simetrija">simetrijama</a> razviju do vrlo visokog stupnja. Duboko fizičko značenje dobilo je ispitivanje kristala tek modernom <a href="/wiki/Atomska_fizika" title="Atomska fizika">atomnom teorijom</a>. Činjenice o kristalima nesumljivo govore da je to prototip sastava <a href="/wiki/Krutine" title="Krutine">čvrstog tijela</a>. Čvrsti oblik materije osniva se na kristalnoj strukturi. Ako je komadić čvrste materije jedan kristal, tad se pravilni oblik razabire na prvi pogled. No ako se čvrsto tijelo sastoji od mnogo sitnih kristala, koji su poredani u svim mogućim smjerovima, tad je simetrija strukture izbrisana za naše oko. </p><p>Već u 18. stoljeću je naslutio <a href="/wiki/Ren%C3%A9_Just_Ha%C3%BCy" title="René Just Haüy">R. J. Haüy</a>, da je pojava kristala uzrokovana pravilnim rasporedom osnovnih djelića. Zamislimo li te djeliće kao kocke, možemo njima izgraditi razna <a href="/wiki/Geometrijsko_tijelo" title="Geometrijsko tijelo">geometrijska tijela</a>. Haüyev model kristala usavršio je <a href="/wiki/Auguste_Bravais" title="Auguste Bravais">A. Bravais</a> 1848. On se oslobodio naivnih predodžbi o kompaktnim djelićima i uzeo, da su <a href="/wiki/Te%C5%BEi%C5%A1te" title="Težište">težišta</a> molekula poredana u pravilnim geometrijskim razmacima. Ona čine <a href="/wiki/Kristalna_re%C5%A1etka" title="Kristalna rešetka">kristalnu rešetku</a>. Opću sistematiku kristalnih rešetaka razvili su 1891. <a href="/wiki/Jevgraf_Stepanovi%C4%8D_Fjodorov" title="Jevgraf Stepanovič Fjodorov">J. S. Fjodorov</a> i Arthur Moritz Schoenflies (1853. – 1928.). </p><p>Za kristal je svojstveno da se određeni raspored molekula periodički ponavlja u prostoru. Promatrat ćemo najprije jednostavnu kristalnu rešetku koja je građena od samih jednakih <a href="/wiki/Atom" title="Atom">atoma</a> ili <a href="/wiki/Molekula" title="Molekula">molekula</a>. Onaj određeni raspored molekula koji se ponavlja u prostoru obuhvatimo u jednu elementarnu ćeliju. Paralelnim pomakom ćelije u sva tri prostorna smjera možemo izgraditi čitavu rešetku. Tip rešetke možemo prema tome jednoznačno utvrditi elementarnom ćelijom. </p><p>Najjednostavniju elementarnu ćeliju predstavlja <a href="/wiki/Kocka" title="Kocka">kocka</a> koja u svakom kutu sadrži jedan atom ili molekulu. Takva ćelija zove se još prosta kubna. Nešto složenija je ćelija koja u centru kocke sadrži još jedan atom ili molekulu. Takvu kubičnu rešetku s prostornim centrima imaju kristali <a href="/wiki/Alkalijski_metali" title="Alkalijski metali">alkalijskih metala</a> (Li, Na, K, Rb, Cs), zatim <a href="/wiki/Vanadij" title="Vanadij">vanadij</a> V, <a href="/wiki/Krom" title="Krom">krom</a> Cr, <a href="/wiki/Molibden" title="Molibden">molibden</a> Mo, <a href="/wiki/Tantal" class="mw-disambig" title="Tantal">tantal</a> Ta i neki drugi. Mjesto u prostornom centru kocke može po jedan atom stajati u centru svake stranice. Kubne rešetke s takvim plošnim centrima također su česte u prirodi. Tako se kristaliziraju kemijski elementi <a href="/wiki/Srebro" title="Srebro">srebro</a> Ag, <a href="/wiki/Zlato" title="Zlato">zlato</a> Au, <a href="/wiki/Platina" title="Platina">platina</a> Pt, <a href="/wiki/Bakar_(element)" class="mw-redirect" title="Bakar (element)">bakar</a> Cu, <a href="/wiki/Olovo_(element)" title="Olovo (element)">olovo</a> Pb i drugi. </p><p>Svakom kristalu pripadaju 3 glavne osi smjera ili osi. Ako je elementarna ćelija kocka, tada su osi među sobom okomite. Općenito mogu osi kristala zatvarati kutove različite od 90°. Elementarnu ćeliju možemo općenito opisati s 3 vektora <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202889033b10f6d3545f44d2531a75857267f816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{1}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b05552ea48f46fed2e6cd299fe48c752832f058c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{2}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34668ac05c4c81f4662714bf4cf8973d3563fcca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{3}}"></span>, koji određuju bridove ćelije. Čvor ove jednostavne rešetke dobijemo tako da vektore <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202889033b10f6d3545f44d2531a75857267f816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{1}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b05552ea48f46fed2e6cd299fe48c752832f058c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{2}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34668ac05c4c81f4662714bf4cf8973d3563fcca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{3}}"></span> nanesemo cijeli broj puta. Točke rešetke su dane sa: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {n}}=n_{1}\cdot {\vec {a}}_{1}+n_{2}\cdot {\vec {a}}_{2}+n_{3}\cdot {\vec {a}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {n}}=n_{1}\cdot {\vec {a}}_{1}+n_{2}\cdot {\vec {a}}_{2}+n_{3}\cdot {\vec {a}}_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70995f1f10655eab32812fdbcc46c0d5f7e7d139" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.41ex; height:2.676ex;" alt="{\displaystyle {\vec {n}}=n_{1}\cdot {\vec {a}}_{1}+n_{2}\cdot {\vec {a}}_{2}+n_{3}\cdot {\vec {a}}_{3}}"></span></dd></dl> <p>gdje <i>n<sub>1</sub></i>, <i>n<sub>2</sub></i> i <i>n<sub>3</sub></i> mogu poprimiti sve cijele brojeve. Pomakom rešetke u glavnim smjerovima za veličinu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1}\cdot {\vec {a}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{1}\cdot {\vec {a}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/476f74c5be6be4d3eeaa66d05c655b98af8bc8c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.412ex; height:2.676ex;" alt="{\displaystyle n_{1}\cdot {\vec {a}}_{1}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{2}\cdot {\vec {a}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{2}\cdot {\vec {a}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9863e163d6d24bd56aa16c84f93873f355ff7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.412ex; height:2.676ex;" alt="{\displaystyle n_{2}\cdot {\vec {a}}_{2}}"></span> ili <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{3}\cdot {\vec {a}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{3}\cdot {\vec {a}}_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3dfc00b82fd465e6edfd4ed1f3f21f14daa244f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.412ex; height:2.676ex;" alt="{\displaystyle n_{3}\cdot {\vec {a}}_{3}}"></span> ne mijenja se raspored molekula u prostoru. Ta invarijantnost prema prostornim pravocrtnim pomacima (translacijama) osnovna je simetrija kristala. </p><p>Jednostavna rešetka izgrađena je od jednakih atoma ili jednakih atomskih grupa. Svaki atom ili svaka atomska grupa na isti su način opkoljeni od drugih atoma ili atomskih grupa. Nijedan atom ne ističe se ničim ispred drugog. Ako se kristal sastoji od različitih atoma ili više vrsta atomskih grupa, tad svaka čini za sebe jednu jednostavnu rešetku. Kristal je složena rešetka. U takvom kristalu opet svaki atom ili svaka ista atomna grupa ima istu okolinu, ali različiti atomi opkoljeni su različitim rasporedom atoma. </p><p>Najjednostavniju složenu rešetku čine kristali <a href="/wiki/Kuhinjska_sol" title="Kuhinjska sol">kuhinjske soli</a>. Atomi <a href="/wiki/Natrij" title="Natrij">natrija</a> i <a href="/wiki/Klor" title="Klor">klora</a> poredani su u 3 okomita smjera u jednakim razmacima. Da su atomi jednaki, imali bismo prostu kubnu rešetku. Budući da nisu jednaki, moramo kristal NaCl sastaviti od dvije jednostavne kubne rešetke s plošnim centrima. Vidi se da je svaki natrijev atom opkoljen sa 6 klorovih atoma, i obratno, svaki klorov sa 6 natrijevih atoma. Kod kristala od mnogo različitih elemenata simetrije su mnogo složenije. Tek odabranim geometrijskim rasporedom može se postići da jednaki atomi budu opkoljeni istovrsnom skupinom drugih atoma. Po osnovnom načelu simetrije moraju jednaki atomi imati jednaku okolinu; ničim ne smije biti jedan isti atom istaknut pred drugim istim atomom. </p><p>Matematičari su općenito ispitivali koji su kristalni oblici mogući po zakonu simetrije. Matematička disciplina, teorija grupa, pruža općenito pregled nad svim mogućim kristalnim oblicima. Najveći broj matematičkih simetrija je zaista nađen kod stvarnih kristala u prirodi. Svaka kristalna mreža u prirodi odgovara jednoj matematički mogućoj simetriji. Nikada se još nije naišlo na kristale koji bi se protivili zakonu simetrije. Simetrija kristalnih oblika jedan je od najdubljih prirodnih zakona. Simetrija proniče čitavu prirodu, savršeno u njenim najsitnijim dijelovima, a djelomično u njenim makroskopskim oblicima. Stvarajući pravilne geometrijske likove, čovjek je samo oponašao prirodu, koja je upravo neiscrpna u stvaranju raznih simetričnih oblika. Simetrije, koje je narod dugogodišnjim radom razvio u <a href="/wiki/Ornament" title="Ornament">ornamentici</a>, one lijepe oblike na vezovima, nalazimo i u prirodi. Atomni sistemi poprimaju nužno izvjesne simetrije, oni iz samih sebe proizvode uvijek nove i uvijek ljepše oblike. Simetrija je najljepši izraz duboke harmonije i zakonitosti koje vladaju u atomnim procesima. </p><p>Sva svojstva čvrstog tijela određena su kristalnom rešetkom. Ako se jedan element javlja u dvije različite modifikacije, tad se njegovi atomi na dva različita načina raspoređuju u rešetke. Premda su na primjer <a href="/wiki/Dijamant" title="Dijamant">dijamant</a> i <a href="/wiki/Grafit" title="Grafit">grafit</a> građeni od jednakih <a href="/wiki/Ugljik" title="Ugljik">ugljikovih</a> atoma, oni se ipak u osnovi razlikuju čemu je uzrok različita struktura kristalne rešetke. </p><p>Ispitivanje <a href="/wiki/Rendgenske_zrake" title="Rendgenske zrake">rendgenskim zrakama</a> dalo je uvid u strukturu kristala. Iz rendgenskih slika utvrđene su elementarne ćelije pojedinih kristala. Zasad ćemo samo iznijeti, da hipoteza o rešetki objašnjava sva svojstva čvrstog stanja materije. Poznato je, da postoji izvjesna <a href="/wiki/Anizotropija" title="Anizotropija">anizotropija</a> u elastičnim i optičkim svojstvima kristala. Postojanje triju glavnih osi obzirom na prolaz svjetlosti ili deformaciju čvrstog tijela objašnjava se s tri glavna smjera kristalne rešetke. Samo kod apsolutne nule miruju atomi u čvorovima rešetke. <a href="/wiki/Titranje" title="Titranje">Titranjem</a> molekula ili atoma oko položaja mogu se objasniti sva <a href="/wiki/Akustika" title="Akustika">akustična</a> i <a href="/wiki/Toplinska_vodljivost" title="Toplinska vodljivost">toplinska svojstva</a> čvrstih tijela. </p><p>Na kraju nameće se pitanje: koliki su razmaci između atoma ili molekula u kristalnoj rešetki? Razmake možemo proračunati kad znamo vrstu elementarne ćelije i broj atoma u <a href="/wiki/Kubi%C4%8Dni_metar" title="Kubični metar">m<sup>3</sup></a>. Uzmimo da se <a href="/wiki/Kemijski_element" title="Kemijski element">kemijski element</a>, što je često slučaj, kristalizira u kubnoj rešetki s prostornim centrom. <a href="/wiki/Volumen" class="mw-redirect" title="Volumen">Volumen</a> ćelije jednak je <i>a<sup>3</sup></i>, gdje je <i>a</i> stranica kocke. Svakoj elementarnoj ćeliji pripadaju dva atoma. Jedan daje prvi ugao kocke, a drugi je centar kocke. Na svaki atom, otpada polovina volumena ćelije: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{2}}\cdot a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{2}}\cdot a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/153debf5b39a453db1a8a78c45cb6a65b0fb37cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.847ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{2}}\cdot a^{3}}"></span></dd></dl> <p>gdje je: <i>V</i> - <a href="/wiki/Volumen" class="mw-redirect" title="Volumen">volumen</a> koji otpada na jedan <a href="/wiki/Atom" title="Atom">atom</a>, pomnožen s <i>N</i>, brojem atoma u 1 m<sup>3</sup>, daje 1: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28d003a73c6e5bb9fa0d3ce3476b1494fa4b3e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.785ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{N}}}"></span></dd></dl> <p>Broj atoma u 1 m<sup>3</sup> odnosi se prema broju atoma u jednom <a href="/wiki/Mol_(mjerna_jedinica)" title="Mol (mjerna jedinica)">molu</a> <i>L</i> kao <a href="/wiki/Gusto%C4%87a" title="Gustoća">gustoća</a> <i>ρ</i> prema <a href="/wiki/Molna_masa" title="Molna masa">masi mola</a> <i>M</i>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {N}{L}}={\frac {\rho }{M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <mi>L</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {N}{L}}={\frac {\rho }{M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e9c8a47ff7709115c83ce429bc11fcb9cd4757f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.277ex; height:5.176ex;" alt="{\displaystyle {\frac {N}{L}}={\frac {\rho }{M}}}"></span></dd></dl> <p>Uzmemo li u obzir sva tri odnosa, dobivamo da je razmak između atoma u kubnoj rešetki s prostornim centrima jednak: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\sqrt[{3}]{2\cdot V}}={\sqrt[{3}]{\frac {2\cdot M}{L\cdot \rho }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>M</mi> </mrow> <mrow> <mi>L</mi> <mo>⋅</mo> <mi>ρ</mi> </mrow> </mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\sqrt[{3}]{2\cdot V}}={\sqrt[{3}]{\frac {2\cdot M}{L\cdot \rho }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eba3f5495c866c9803229f5ed6147d322115c7a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:22.435ex; height:7.676ex;" alt="{\displaystyle a={\sqrt[{3}]{2\cdot V}}={\sqrt[{3}]{\frac {2\cdot M}{L\cdot \rho }}}}"></span></dd></dl> <p><a href="/wiki/Molna_masa" title="Molna masa">Težinu mola</a>, kao i <a href="/wiki/Relativna_gusto%C4%87a" title="Relativna gustoća">specifičnu težinu</a>, poznajemo za svaki <a href="/wiki/Kemijski_element" title="Kemijski element">kemijski element</a>, pa odatle možemo proračunati razmak između atoma rešetke. U donjoj tablici su dane vrijednosti za neke elemente koji se kristaliziraju u kubičnoj rešetki s prostornim centrima. Te vrijednosti su provjerene rendgenskim snimkama: </p> <dl><dd><table class="wikitable"> <tbody><tr> <th></th> <th><a href="/wiki/Litij" title="Litij">Litij</a></th> <th><a href="/wiki/Natrij" title="Natrij">Natrij</a></th> <th><a href="/wiki/Kalij" title="Kalij">Kalij</a></th> <th><a href="/wiki/Volfram" title="Volfram">Volfram</a></th> <th><a href="/wiki/Ferit" title="Ferit">Alfa-željezo</a> </th></tr> <tr> <td><a href="/wiki/Molna_masa" title="Molna masa">Molna masa</a> <i>M</i></td> <td>6,94</td> <td>22,997</td> <td>39,096</td> <td>184</td> <td>55,84 </td></tr> <tr> <td><a href="/wiki/Gusto%C4%87a" title="Gustoća">Gustoća</a> <i>ρ</i></td> <td>0,534</td> <td>0,97</td> <td>0,86</td> <td>19,3</td> <td>7,86 </td></tr> <tr> <td>Razmak između atoma <i>a</i> (<a href="/wiki/Metar" title="Metar">nm</a>)</td> <td>35,1</td> <td>43,0</td> <td>53,3</td> <td>31,59</td> <td>28,61 </td></tr></tbody></table></dd></dl> <p>Vidi se odmah da kubična rešetka s prostornim centrima ne predstavlja najgušći oblik rešetke. Gušća je kubična rešetka s plošnim centrima. Tu otpadaju četiri čestice na svaku elementarnu ćeliju. Jedna čestica određuje početni čvor ćelije, a tri čestice leže u centrima stranica koje polaze od te točke. Prema tome, između volumena ćelije <i>a<sup>3</sup></i> i volumena <i>V</i> koji otpada na česticu postoji kod kubične rešetke s plošnim centrima relacija: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{4}}\cdot a^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>⋅</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{4}}\cdot a^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/597615157ff86095bfd0ba282cf1d50a166e334b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.847ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{4}}\cdot a^{3}}"></span></dd></dl> <p>Brid ćelije dan je sada izrazom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\sqrt[{3}]{4\cdot V}}={\sqrt[{3}]{\frac {4\cdot M}{L\cdot \rho }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mn>4</mn> <mo>⋅</mo> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mfrac> <mrow> <mn>4</mn> <mo>⋅</mo> <mi>M</mi> </mrow> <mrow> <mi>L</mi> <mo>⋅</mo> <mi>ρ</mi> </mrow> </mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\sqrt[{3}]{4\cdot V}}={\sqrt[{3}]{\frac {4\cdot M}{L\cdot \rho }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5b8729e182d7afad292083e111e985196dfdc3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:22.435ex; height:7.676ex;" alt="{\displaystyle a={\sqrt[{3}]{4\cdot V}}={\sqrt[{3}]{\frac {4\cdot M}{L\cdot \rho }}}}"></span></dd></dl> <p>Prema toj jednadžbi izračunati su razmaci između atoma za neke elemente i korigirani rendgenskim zrakama: </p> <dl><dd><table class="wikitable"> <tbody><tr> <th></th> <th><a href="/wiki/Aluminij" title="Aluminij">Aluminij</a></th> <th><a href="/wiki/Bakar_(element)" class="mw-redirect" title="Bakar (element)">Bakar</a></th> <th><a href="/wiki/Srebro" title="Srebro">Srebro</a></th> <th><a href="/wiki/Platina" title="Platina">Platina</a></th> <th><a href="/wiki/Olovo_(element)" title="Olovo (element)">Olovo</a> </th></tr> <tr> <td><a href="/wiki/Molna_masa" title="Molna masa">Molna masa</a> <i>M</i></td> <td>26,97</td> <td>63,57</td> <td>107,88</td> <td>195,23</td> <td>207,22 </td></tr> <tr> <td><a href="/wiki/Gusto%C4%87a" title="Gustoća">Gustoća</a> <i>ρ</i></td> <td>2,72</td> <td>8,93</td> <td>10,5</td> <td>21,4</td> <td>11,34 </td></tr> <tr> <td>Razmak između atoma <i>a</i> (<a href="/wiki/Metar" title="Metar">nm</a>)</td> <td>40,41</td> <td>36,08</td> <td>40,78</td> <td>39,16</td> <td>49,39 </td></tr></tbody></table></dd></dl> <p>Razmaci između čestica kristala veličine su istog reda kao i molekularni promjeri. Približnu sliku kristala možemo dobiti ako atome ili molekule predočimo kao kugle koje su naslagane jedna do druge. Već prema tome kako slažemo kugle jednu do druge dobivamo različite tipove elementarnih ćelija. </p><p>Kristalna rešetka vrlo je čvrsta tvorevina. Ona se teško razara mehaničkim silama. Oko svojih položaja ravnoteže koji se podudaraju s čvorovima rešetke mogu se atomi samo malo pomicati. Kristalnu rešetku možemo razoriti tako da čvrsto tijelo ugrijemo do temperature <a href="/wiki/Tali%C5%A1te" title="Talište">tališta</a>. Tada temperaturna titranja atoma prevladavaju <a href="/wiki/Kohezija" title="Kohezija">kohezione sile</a>, i kristalna struktura iščezava. Teorija sila koje drže rešetku izlazi iz okvira <a href="/wiki/Klasi%C4%8Dna_fizika" title="Klasična fizika">klasične fizike</a> i pripada modernoj <a href="/wiki/Valna_teorija" title="Valna teorija">valnoj mehanici</a> (<a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">L. de Broglie</a>, <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a>, <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">E. Schrödinger</a>).<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> </p> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristal&veaction=edit&section=4" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristal&action=edit&section=4" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <b>kristali</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=34004">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2019.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> <a href="/wiki/Ivan_Supek" title="Ivan Supek">Ivan Supek</a>: "Nova fizika", Školska knjiga Zagreb, 1966.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Vanjske_poveznice">Vanjske poveznice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristal&veaction=edit&section=5" title="Uredi odlomak: Vanjske poveznice" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristal&action=edit&section=5" title="Uredi kôd odjeljka Vanjske poveznice"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <table border="0" class="noprint" style="clear: right; border: solid var(--border-color-base, #a2a9b1) 1px; margin: 0 0 1em 1em; font-size: 90%; background: var(--background-color-neutral-subtle, #f8f9fa); color: inherit; width: 250px; padding: 4px; spacing: 0px; text-align: left; float: right;"> <tbody><tr> <td><figure class="mw-halign-none" typeof="mw:File"><span title="Logotip Zajedničkog poslužitelja"><img alt="Logotip Zajedničkog poslužitelja" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span><figcaption>Logotip Zajedničkog poslužitelja</figcaption></figure> </td> <td><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Glavna_stranica?uselang=hr">Zajednički poslužitelj</a> ima stranicu o temi <i><b><a class="external text" href="https://commons.wikimedia.org/wiki/Crystal_structure?uselang=hr">Kristal</a></b></i></span> </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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