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<div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Mrežno mjesto"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="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-Podjela" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Podjela"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Podjela</span> </div> </a> <ul id="toc-Podjela-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Oblici_kristalnih_rešetki_i_pripadajuće_elementarne_ćelije" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Oblici_kristalnih_rešetki_i_pripadajuće_elementarne_ćelije"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Oblici kristalnih rešetki i pripadajuće elementarne ćelije</span> </div> </a> <ul id="toc-Oblici_kristalnih_rešetki_i_pripadajuće_elementarne_ćelije-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elastični_titraji_jednodimenzionalne_rešetke" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elastični_titraji_jednodimenzionalne_rešetke"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Elastični titraji jednodimenzionalne rešetke</span> </div> </a> <ul id="toc-Elastični_titraji_jednodimenzionalne_rešetke-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-Literatura" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Literatura</span> </div> </a> <ul id="toc-Literatura-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">Kristalna rešetka</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 61 jeziku" > <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-61" 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">61 jezik</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/Kristalstruktuur" title="Kristalstruktuur – afrikaans" lang="af" hreflang="af" data-title="Kristalstruktuur" 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/Estructura_cristalina" title="Estructura cristalina – aragonski" lang="an" hreflang="an" data-title="Estructura cristalina" 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%86%D9%8A%D8%A9_%D8%A8%D9%84%D9%88%D8%B1%D9%8A%D8%A9" title="بنية بلورية – arapski" lang="ar" hreflang="ar" data-title="بنية بلورية" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Estructura_cristalina" title="Estructura cristalina – asturijski" lang="ast" hreflang="ast" data-title="Estructura cristalina" data-language-autonym="Asturianu" data-language-local-name="asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D8%B1%DB%8C%D8%B3%D8%AA%D8%A7%D9%84_%D9%82%D9%88%D8%B1%D9%88%D9%84%D9%88%D8%B4%D9%88" title="کریستال قورولوشو – South Azerbaijani" lang="azb" hreflang="azb" data-title="کریستال قورولوشو" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</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%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0" title="Кристална структура – bugarski" lang="bg" hreflang="bg" data-title="Кристална структура" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kristalna_struktura" title="Kristalna struktura – bosanski" lang="bs" hreflang="bs" data-title="Kristalna struktura" 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/Estructura_cristal%C2%B7lina" title="Estructura cristal·lina – katalonski" lang="ca" hreflang="ca" data-title="Estructura cristal·lina" 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/%D9%BE%DB%95%DB%8C%DA%A9%DB%95%D8%B1%DB%8C_%D8%A8%D9%84%D9%88%D9%88%D8%B1%DB%8C" title="پەیکەری بلووری – soranski kurdski" lang="ckb" hreflang="ckb" data-title="پەیکەری بلووری" 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/Krystalick%C3%A1_struktura" title="Krystalická struktura – češki" lang="cs" hreflang="cs" data-title="Krystalická struktura" 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%D0%B0_%D1%82%D1%8B%D1%82%C4%83%D0%BC" title="Кристалла тытăм – čuvaški" lang="cv" hreflang="cv" data-title="Кристалла тытăм" 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/Strwythur_crisial" title="Strwythur crisial – velški" lang="cy" hreflang="cy" data-title="Strwythur crisial" 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/Krystalstruktur" title="Krystalstruktur – danski" lang="da" hreflang="da" data-title="Krystalstruktur" 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/Kristallstruktur" title="Kristallstruktur – njemački" lang="de" hreflang="de" data-title="Kristallstruktur" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Crystal_structure" title="Crystal structure – engleski" lang="en" hreflang="en" data-title="Crystal structure" 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/Kristala_strukturo" title="Kristala strukturo – esperanto" lang="eo" hreflang="eo" data-title="Kristala strukturo" 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/Estructura_cristalina" title="Estructura cristalina – španjolski" lang="es" hreflang="es" data-title="Estructura cristalina" 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/Kristallistruktuur" title="Kristallistruktuur – estonski" lang="et" hreflang="et" data-title="Kristallistruktuur" 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-egitura" title="Kristal-egitura – baskijski" lang="eu" hreflang="eu" data-title="Kristal-egitura" 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%B3%D8%A7%D8%AE%D8%AA%D8%A7%D8%B1_%D8%A8%D9%84%D9%88%D8%B1%DB%8C" title="ساختار بلوری – perzijski" lang="fa" hreflang="fa" data-title="ساختار بلوری" 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/Kiderakenne" title="Kiderakenne – finski" lang="fi" hreflang="fi" data-title="Kiderakenne" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Structure_cristalline" title="Structure cristalline – francuski" lang="fr" hreflang="fr" data-title="Structure cristalline" 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/Criostalstrucht%C3%BAr" title="Criostalstruchtúr – irski" lang="ga" hreflang="ga" data-title="Criostalstruchtúr" data-language-autonym="Gaeilge" data-language-local-name="irski" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Estrutura_cristalina" title="Estrutura cristalina – galicijski" lang="gl" hreflang="gl" data-title="Estrutura cristalina" data-language-autonym="Galego" data-language-local-name="galicijski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%91%D7%A0%D7%94_%D7%92%D7%91%D7%99%D7%A9%D7%99" title="מבנה גבישי – hebrejski" lang="he" hreflang="he" data-title="מבנה גבישי" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estrikti_kristalen" title="Estrikti kristalen – haićanski kreolski" lang="ht" hreflang="ht" data-title="Estrikti kristalen" 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%A1lyszerkezet" title="Kristályszerkezet – mađarski" lang="hu" hreflang="hu" data-title="Kristályszerkezet" 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%D5%A1%D5%B5%D5%AB%D5%B6_%D5%AF%D5%A1%D5%BC%D5%B8%D6%82%D6%81%D5%BE%D5%A1%D5%AE%D6%84" title="Բյուրեղային կառուցվածք – armenski" lang="hy" hreflang="hy" data-title="Բյուրեղային կառուցվածք" data-language-autonym="Հայերեն" data-language-local-name="armenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Struktur_kristal" title="Struktur kristal – indonezijski" lang="id" hreflang="id" data-title="Struktur 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-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%90%E6%99%B6%E6%A7%8B%E9%80%A0" title="結晶構造 – japanski" lang="ja" hreflang="ja" data-title="結晶構造" 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-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/krilysu%27a" title="krilysu'a – lojban" lang="jbo" hreflang="jbo" data-title="krilysu'a" data-language-autonym="La .lojban." data-language-local-name="lojban" class="interlanguage-link-target"><span>La .lojban.</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_%EA%B5%AC%EC%A1%B0" title="결정 구조 – korejski" lang="ko" hreflang="ko" data-title="결정 구조" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Krist%C4%81lisk%C4%81_strukt%C5%ABra" title="Kristāliskā struktūra – latvijski" lang="lv" hreflang="lv" data-title="Kristāliskā struktūra" data-language-autonym="Latviešu" data-language-local-name="latvijski" class="interlanguage-link-target"><span>Latviešu</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%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0" title="Кристална структура – makedonski" lang="mk" hreflang="mk" data-title="Кристална структура" 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%95%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%B8%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%BD_%E0%B4%98%E0%B4%9F%E0%B4%A8" title="ക്രിസ്റ്റൽ ഘടന – malajalamski" lang="ml" hreflang="ml" data-title="ക്രിസ്റ്റൽ ഘടന" 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%91%D0%BE%D0%BB%D1%80%D1%8B%D0%BD_%D0%B1%D2%AF%D1%82%D1%8D%D1%86" title="Болрын бүтэц – mongolski" lang="mn" hreflang="mn" data-title="Болрын бүтэц" data-language-autonym="Монгол" data-language-local-name="mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Struktur_hablur" title="Struktur hablur – malajski" lang="ms" hreflang="ms" data-title="Struktur 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kristalstructuur" title="Kristalstructuur – nizozemski" lang="nl" hreflang="nl" data-title="Kristalstructuur" 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/Krystallstruktur" title="Krystallstruktur – norveški nynorsk" lang="nn" hreflang="nn" data-title="Krystallstruktur" 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/Krystallstruktur" title="Krystallstruktur – norveški bokmål" lang="nb" hreflang="nb" data-title="Krystallstruktur" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B2%E0%A9%88%E0%A8%9F%E0%A8%BF%E0%A8%B8" title="ਲੈਟਿਸ – pandžapski" lang="pa" hreflang="pa" data-title="ਲੈਟਿਸ" 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/Sie%C4%87_krystaliczna" title="Sieć krystaliczna – poljski" lang="pl" hreflang="pl" data-title="Sieć krystaliczna" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Estrutura_cristalina" title="Estrutura cristalina – portugalski" lang="pt" hreflang="pt" data-title="Estrutura cristalina" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Structur%C4%83_cristalin%C4%83" title="Structură cristalină – rumunjski" lang="ro" hreflang="ro" data-title="Structură cristalină" data-language-autonym="Română" data-language-local-name="rumunjski" class="interlanguage-link-target"><span>Română</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%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0" title="Кристаллическая структура – ruski" lang="ru" hreflang="ru" data-title="Кристаллическая структура" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Creestal_structur" title="Creestal structur – škotski" lang="sco" hreflang="sco" data-title="Creestal structur" 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/Kristalna_struktura" title="Kristalna struktura – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Kristalna struktura" 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-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Crystal_structure" title="Crystal structure – Simple English" lang="en-simple" hreflang="en-simple" data-title="Crystal structure" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kristalna_struktura" title="Kristalna struktura – slovenski" lang="sl" hreflang="sl" data-title="Kristalna struktura" 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/Struktura_e_kristaleve_reale" title="Struktura e kristaleve reale – albanski" lang="sq" hreflang="sq" data-title="Struktura e kristaleve reale" 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%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0" title="Кристална структура – srpski" lang="sr" hreflang="sr" data-title="Кристална структура" 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/Kristallstruktur" title="Kristallstruktur – švedski" lang="sv" hreflang="sv" data-title="Kristallstruktur" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</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%85%E0%AE%AE%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="படிக அமைப்பு – tamilski" lang="ta" hreflang="ta" data-title="படிக அமைப்பு" data-language-autonym="தமிழ்" data-language-local-name="tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9C%E0%B8%A5%E0%B8%B6%E0%B8%81" title="โครงสร้างผลึก – tajlandski" lang="th" hreflang="th" data-title="โครงสร้างผลึก" data-language-autonym="ไทย" data-language-local-name="tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kristal_yap%C4%B1" title="Kristal yapı – turski" lang="tr" hreflang="tr" data-title="Kristal yapı" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D1%96%D1%87%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0" title="Кристалічна структура – ukrajinski" lang="uk" hreflang="uk" data-title="Кристалічна структура" 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/%D9%82%D9%84%D9%85%DB%8C_%D8%B3%D8%A7%D8%AE%D8%AA" title="قلمی ساخت – urdski" lang="ur" hreflang="ur" data-title="قلمی ساخت" 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/Kristall_panjara" title="Kristall panjara – uzbečki" lang="uz" hreflang="uz" data-title="Kristall panjara" 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/C%E1%BA%A5u_tr%C3%BAc_tinh_th%E1%BB%83" title="Cấu trúc tinh thể – vijetnamski" lang="vi" hreflang="vi" data-title="Cấu trúc 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%99%B6%E4%BD%93%E7%BB%93%E6%9E%84" title="晶体结构 – wu kineski" lang="wuu" hreflang="wuu" data-title="晶体结构" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%99%B6%E4%BD%93%E7%BB%93%E6%9E%84" title="晶体结构 – kineski" lang="zh" hreflang="zh" data-title="晶体结构" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</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/Q895901#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 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<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"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><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:NaCl_Formation_Lewis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/NaCl_Formation_Lewis.svg/300px-NaCl_Formation_Lewis.svg.png" decoding="async" width="300" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/NaCl_Formation_Lewis.svg/450px-NaCl_Formation_Lewis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/NaCl_Formation_Lewis.svg/600px-NaCl_Formation_Lewis.svg.png 2x" data-file-width="813" data-file-height="272" /></a><figcaption>Nastanak natrijeva klorida: <a href="/wiki/Elektron" title="Elektron">elektron</a> s <a href="/wiki/Atom" title="Atom">atoma</a> <a href="/wiki/Natrij" title="Natrij">natrija</a> potpuno prelazi na atom <a href="/wiki/Klor" title="Klor">klora</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:207_Ionic_Bonding-01.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/207_Ionic_Bonding-01.jpg/300px-207_Ionic_Bonding-01.jpg" decoding="async" width="300" height="454" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/207_Ionic_Bonding-01.jpg/450px-207_Ionic_Bonding-01.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/207_Ionic_Bonding-01.jpg/600px-207_Ionic_Bonding-01.jpg 2x" data-file-width="1533" data-file-height="2321" /></a><figcaption>Nastanak kristala natrijeva klorida.</figcaption></figure> <p><b>Kristalna rešetka</b> je pravilan trodimenzijski raspored periodički ponavljanih strukturnih jedinica (<a href="/wiki/Atom" title="Atom">atoma</a>, <a href="/wiki/Ion" title="Ion">iona</a>, <a href="/wiki/Molekula" title="Molekula">molekula</a>) kao građevnih čestica <a href="/wiki/Kristal" title="Kristal">kristala</a>, koji mu daje karakteristična svojstva i oblik. Prema vrsti čestica i njihovih veza razlikuju se atomske, ionske i molekularne kristalne rešetke. Tako na primjer rešetka je <a href="/wiki/Natrijev_klorid" title="Natrijev klorid">natrijeva klorida</a> (kuhinjska sol) <a href="/wiki/Ionska_veza" title="Ionska veza">ionska</a> (građena od <a href="/wiki/Natrij" title="Natrij">natrijevih</a> i <a href="/wiki/Klor" title="Klor">klorovih</a> iona), rešetka je <a href="/wiki/Dijamant" title="Dijamant">dijamanta</a> atomska s <a href="/wiki/Kovalentna_veza" title="Kovalentna veza">kovalentnom vezom</a> između <a href="/wiki/Ugljik" title="Ugljik">ugljikovih</a> atoma, rešetka <a href="/wiki/Benzen" title="Benzen">benzena</a> molekularna i tako dalje. Osnovne građevne čestice kristala nalaze se na točno određenim i stalnim položajima u jediničnoj ćeliji, osnovnom, najmanjem <a href="/wiki/Volumen" class="mw-redirect" title="Volumen">volumenu</a> prostorne rešetke,koji sadrži najmanji mogući broj strukturnih jedinica. Periodičkim ponavljanjem jedinične ćelije duž 3 nekoplanarna racionalna smjera izgrađena je cijela kristalna rešetka, to jest cijeli kristal. Svaka jedinična ćelija ima oblik <a href="/w/index.php?title=Paralelopiped&action=edit&redlink=1" class="new" title="Paralelopiped (stranica ne postoji)">paralelopipeda</a> i određena je s pomoću smjera i duljine triju bridova te s tri <a href="/wiki/Kut" title="Kut">kuta</a> među bridovima, a oblik ćelije mora imati najveću (maksimalnu) simetriju nekoga kristalnog sustava. </p><p>Osnovno je načelo (princip) prostorne rešetke: svaki čvor rešetke ima jednak broj susjednih čvorova na jednakoj udaljenosti i jednako raspoređenih, to jest čvorovi se ni po čemu međusobno ne razlikuju. S obzirom na moguće jedinične ćelije, postoji 14 međusobno različitih prostornih rešetki, koje nose naziv Bravaisove rešetke (prema <a href="/wiki/Auguste_Bravais" title="Auguste Bravais">A. Bravaisu</a>). Sedam od njih (triklinska, monoklinska, rompska, trigonska, tetragonska, heksagonska i kubična) nazivaju se primitivnima, jer imaju čvorove (mjesta u kristalu s identičnom okolinom u istom smjeru) samo u uglovima jedinične ćelije. Ostalih su sedam centrirane rešetke s dodatnim čvorovima u sredini ćelije, na suprotnim parovima ploha ili u sredini tih ploha. U Bravaisovim rešetkama postoji samo translacijska simetrija kristalne rešetke. Potpuna simetrija neke kristalne rešetke, to jest kristalne strukture, opisana je jednom od 230 prostornih, Fjodorovljevih skupina simetrije (prema <a href="/wiki/Jevgraf_Stepanovi%C4%8D_Fjodorov" title="Jevgraf Stepanovič Fjodorov">J. S. Fjodorovu</a>). Bravaisove rešetke i Fjodorovljeve skupine predstavljaju unutrašnju simetriju (mikrosimetriju) kristala.<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="Podjela">Podjela</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&veaction=edit&section=1" title="Uredi odlomak: Podjela" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&action=edit&section=1" title="Uredi kôd odjeljka Podjela"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Prema vrsti veze i rasporedu građevnih elemenata razlikuju se: </p> <ul><li>metalna kristalna rešetka</li> <li>atomska kristalna rešetka</li> <li>molekularna kristalna rešetka</li> <li>ionska kristalna rešetka</li></ul> <table class="wikitable"> <tbody><tr> <td>tip kristala </td> <td>Primjeri </td> <td>Energija veze kJ/mol </td> <td>Tip kemijske veze </td> <td>Strukturne jedinice </td> <td>Karakteristike kristala </td></tr> <tr> <td>ionski </td> <td>NaCl <p>LiF </p> </td> <td>753,624 <p>1004,832 </p> </td> <td>ionska (heteropolarna) </td> <td>pozitivni i negativni ioni </td> <td>Tvrdi i krti, visoko talište, jaka infracrvena apsorpcija, mala električna vodljivost na niskim temperaturama, dobra ionska vodljivost na visokim temperaturama. Topljivi u otapalima tipa vode. Otopine i taljevine su ionski vodiči. </td></tr> <tr> <td>kovalentni </td> <td>dijamant <p>SiC </p> </td> <td>~711,756 <p>1184,8644 </p> </td> <td>kovalentna (homopolarna) </td> <td>atomi </td> <td>Velika tvrdoća, visoko talište, niska električna vodljivost, praktički netopljivi u svim otapalima. </td></tr> <tr> <td>metalni </td> <td>Na <p>Fe </p> </td> <td>108,8568 <p>3935592 </p> </td> <td>metalna </td> <td>ioni metala </td> <td>Tvrdi i kovki, visoko talište, metalni sjaj, visoka električka i toplinska vodljivost, topljivi samo u tekućim metalima. </td></tr> <tr> <td>molekularni </td> <td>Ar <p>CH<sub>4</sub> </p> </td> <td>7,53624 <p>10,04832 </p> </td> <td>van der Waalsove sile </td> <td>atomi ili molekule </td> <td>Mekani, nisku talište, relativno velika kompresibilnost, niska električka vodljivost, topivi u organski tekućinama. </td></tr> <tr> <td>s vodikovim vezama </td> <td>H<sub>2</sub>O(led) <p>HF </p> </td> <td>50,2416 <p>29,3076 </p> </td> <td>vodikova </td> <td>atomi ili molekule </td> <td>U odnosu na molekularne kristale veća energija veze, više talište, pomak karakterističnih vrpci u infracrvenim spektrima prema nižim frekvencijama, veće dielektrične konstante; tendencija k polimerizaciji. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Oblici_kristalnih_rešetki_i_pripadajuće_elementarne_ćelije"><span id="Oblici_kristalnih_re.C5.A1etki_i_pripadaju.C4.87e_elementarne_.C4.87elije"></span>Oblici kristalnih rešetki i pripadajuće elementarne ćelije</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&veaction=edit&section=2" title="Uredi odlomak: Oblici kristalnih rešetki i pripadajuće elementarne ćelije" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&action=edit&section=2" title="Uredi kôd odjeljka Oblici kristalnih rešetki i pripadajuće elementarne ćelije"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div><p> U kristalografiji razlikujemo sedam kristalnih sustava i četrnaest elementarnih ćelija<sup>[<i><a href="/wiki/Wikipedija:Navo%C4%91enje_izvora" title="Wikipedija:Navođenje izvora">nedostaje izvor</a></i>]</sup>:</p><center> <table class="wikitable"> <tbody><tr> <td bgcolor="#B0E0E6" colspan="20">Kristalni sustavi </td></tr> <tr> <td rowspan="2">Redni broj </td> <td rowspan="2">Kristalni sustav </td> <td colspan="4">Tip rešetke </td> <td rowspan="2" colspan="4">Elementarna ćelija </td></tr> <tr> <td>Međusobni odnos bridova i kutova </td> <td>Bridovi i kutovi koji su specifični </td> <td>Broj rešetki </td> <td>Simetrija rešetke </td> <td>Primitivna </td> <td>Bazno centrirana </td> <td>Volumno centrirana </td> <td>Plošno centrirana </td></tr> <tr> <td>1 </td> <td>Triklinska </td> <td>a≠b≠c α≠β≠γ </td> <td>a,b,c, α,β,γ </td> <td>1 </td> <td><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 {\overline {1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mn>1</mn> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f50d1053ea4c96ed679d1deca6105c442b54bf11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.277ex; height:2.843ex;" alt="{\displaystyle {\overline {1}}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Triklinska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/b/b5/Triklinska.jpg/70px-Triklinska.jpg" decoding="async" width="70" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/b/b5/Triklinska.jpg/105px-Triklinska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/b/b5/Triklinska.jpg/140px-Triklinska.jpg 2x" data-file-width="482" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td>- </td> <td>- </td></tr> <tr> <td>2 </td> <td>Monoklinska </td> <td>a≠b≠c α=γ=90°≠β </td> <td>a,b,c, β </td> <td>2 </td> <td><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 {2}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2}{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d85b7a168c3fb2d64afaccd775987e0bc7c6584" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.877ex; height:5.176ex;" alt="{\displaystyle {\frac {2}{m}}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Monoklinska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/2/28/Monoklinska.jpg/70px-Monoklinska.jpg" decoding="async" width="70" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/2/28/Monoklinska.jpg/105px-Monoklinska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/2/28/Monoklinska.jpg/140px-Monoklinska.jpg 2x" data-file-width="482" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:MonoklinskaBC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/1/1e/MonoklinskaBC.jpg/70px-MonoklinskaBC.jpg" decoding="async" width="70" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/1/1e/MonoklinskaBC.jpg/105px-MonoklinskaBC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/1/1e/MonoklinskaBC.jpg/140px-MonoklinskaBC.jpg 2x" data-file-width="482" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td>- </td></tr> <tr> <td>3 </td> <td>Rompska </td> <td>a≠b≠c α=β=γ=90° </td> <td>a,b,c </td> <td>4 </td> <td><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 {mmm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>m</mi> <mi>m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {mmm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/836536afed5d7efaf311303b19efc3567afe8897" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.121ex; height:1.676ex;" alt="{\displaystyle {mmm}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Rompska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/3/3c/Rompska.jpg/70px-Rompska.jpg" decoding="async" width="70" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/3/3c/Rompska.jpg/105px-Rompska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/3/3c/Rompska.jpg/140px-Rompska.jpg 2x" data-file-width="483" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:RompskaBC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/f/fe/RompskaBC.jpg/70px-RompskaBC.jpg" decoding="async" width="70" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/f/fe/RompskaBC.jpg/105px-RompskaBC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/f/fe/RompskaBC.jpg/140px-RompskaBC.jpg 2x" data-file-width="483" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:RompskaVC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/0/0b/RompskaVC.jpg/70px-RompskaVC.jpg" decoding="async" width="70" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/0/0b/RompskaVC.jpg/105px-RompskaVC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/0/0b/RompskaVC.jpg/140px-RompskaVC.jpg 2x" data-file-width="483" data-file-height="816" /></a><figcaption></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:RompskaPC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/1/1e/RompskaPC.jpg/70px-RompskaPC.jpg" decoding="async" width="70" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/1/1e/RompskaPC.jpg/105px-RompskaPC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/1/1e/RompskaPC.jpg/140px-RompskaPC.jpg 2x" data-file-width="483" data-file-height="816" /></a><figcaption></figcaption></figure> </td></tr> <tr> <td>4 </td> <td>Trigonska </td> <td>a=b=c α=β=γ<120°≠90° </td> <td>a α </td> <td>1 </td> <td><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 {\overline {3m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mn>3</mn> <mi>m</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {3m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/749fc5bc865397cfb1f71ed27f693d02e6308964" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.318ex; height:2.843ex;" alt="{\displaystyle {\overline {3m}}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Trigonska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/f/f9/Trigonska.jpg/70px-Trigonska.jpg" decoding="async" width="70" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/f/f9/Trigonska.jpg/105px-Trigonska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/f/f9/Trigonska.jpg/140px-Trigonska.jpg 2x" data-file-width="814" data-file-height="1043" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td>- </td> <td>- </td></tr> <tr> <td>5 </td> <td>Tetragonska </td> <td>a=b≠c α=β=γ=90° </td> <td>a, c </td> <td>2 </td> <td><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 {4}{mmm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mrow> <mi>m</mi> <mi>m</mi> <mi>m</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4}{mmm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3581cfcc1454d6181706565947384a3086c44bc7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.957ex; height:5.176ex;" alt="{\displaystyle {\frac {4}{mmm}}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Tetragonska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/6/60/Tetragonska.jpg/70px-Tetragonska.jpg" decoding="async" width="70" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/6/60/Tetragonska.jpg/105px-Tetragonska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/6/60/Tetragonska.jpg/140px-Tetragonska.jpg 2x" data-file-width="659" data-file-height="815" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:TetragonskaVC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/b/b9/TetragonskaVC.jpg/70px-TetragonskaVC.jpg" decoding="async" width="70" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/b/b9/TetragonskaVC.jpg/105px-TetragonskaVC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/b/b9/TetragonskaVC.jpg/140px-TetragonskaVC.jpg 2x" data-file-width="659" data-file-height="815" /></a><figcaption></figcaption></figure> </td> <td>- </td></tr> <tr> <td>6 </td> <td>Heksagonska </td> <td>a=b≠c α=β=90° γ=120° </td> <td>a,c </td> <td>1 </td> <td><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 {6}{mmm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <mrow> <mi>m</mi> <mi>m</mi> <mi>m</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {6}{mmm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8da8c638dac571b86c7fd6f78f1799301e6f85b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.957ex; height:5.176ex;" alt="{\displaystyle {\frac {6}{mmm}}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Hegsagonska.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/d/da/Hegsagonska.jpg/70px-Hegsagonska.jpg" decoding="async" width="70" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/d/da/Hegsagonska.jpg/105px-Hegsagonska.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/d/da/Hegsagonska.jpg/140px-Hegsagonska.jpg 2x" data-file-width="678" data-file-height="786" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td>- </td> <td>- </td></tr> <tr> <td>7 </td> <td>Kubna </td> <td>a=b=c α=β=γ=90° </td> <td>a </td> <td>3 </td> <td><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 {m3m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mn>3</mn> <mi>m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {m3m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4843d72855ca1237c0fa7001ddc0998474cefab8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.243ex; height:2.176ex;" alt="{\displaystyle {m3m}}"></span> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Kubna.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/a/af/Kubna.jpg/70px-Kubna.jpg" decoding="async" width="70" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/a/af/Kubna.jpg/105px-Kubna.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/a/af/Kubna.jpg/140px-Kubna.jpg 2x" data-file-width="657" data-file-height="581" /></a><figcaption></figcaption></figure> </td> <td>- </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:KubnaVC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/a/a5/KubnaVC.jpg/70px-KubnaVC.jpg" decoding="async" width="70" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/a/a5/KubnaVC.jpg/105px-KubnaVC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/a/a5/KubnaVC.jpg/140px-KubnaVC.jpg 2x" data-file-width="657" data-file-height="581" /></a><figcaption></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:KubnaPC.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/3/30/KubnaPC.jpg/70px-KubnaPC.jpg" decoding="async" width="70" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/3/30/KubnaPC.jpg/105px-KubnaPC.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/3/30/KubnaPC.jpg/140px-KubnaPC.jpg 2x" data-file-width="657" data-file-height="581" /></a><figcaption></figcaption></figure> </td></tr></tbody></table> </center> <div class="mw-heading mw-heading2"><h2 id="Elastični_titraji_jednodimenzionalne_rešetke"><span id="Elasti.C4.8Dni_titraji_jednodimenzionalne_re.C5.A1etke"></span>Elastični titraji jednodimenzionalne rešetke</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&veaction=edit&section=3" title="Uredi odlomak: Elastični titraji jednodimenzionalne rešetke" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&action=edit&section=3" title="Uredi kôd odjeljka Elastični titraji jednodimenzionalne rešetke"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Onde_compression_impulsion_1d_30_petit.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Onde_compression_impulsion_1d_30_petit.gif/300px-Onde_compression_impulsion_1d_30_petit.gif" decoding="async" width="300" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/62/Onde_compression_impulsion_1d_30_petit.gif 1.5x" data-file-width="305" data-file-height="231" /></a><figcaption>Primjer <a href="/wiki/Longitudinalan_val" title="Longitudinalan val">longitudinalnog vala</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Onde_cisaillement_impulsion_1d_30_petit.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Onde_cisaillement_impulsion_1d_30_petit.gif/300px-Onde_cisaillement_impulsion_1d_30_petit.gif" decoding="async" width="300" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/6d/Onde_cisaillement_impulsion_1d_30_petit.gif 1.5x" data-file-width="305" data-file-height="231" /></a><figcaption>Primjer <a href="/wiki/Transverzalni_val" title="Transverzalni val">transverzalnog vala</a>.</figcaption></figure> <p>Bitna fizička svojstva kristala možemo studirati na jednostavnom jednodimenzionalnom modelu. Takav jednodimenzionalni <a href="/wiki/Kristal" title="Kristal">kristal</a> sastoji se od niza <a href="/wiki/%C4%8Cestica" class="mw-redirect" title="Čestica">čestica</a> koje su međusobno poredane u jednakim razmacima. Kristalni vez možemo u modelu prikazati elastičnim <a href="/wiki/Opruga" title="Opruga">oprugama</a>, kojima su među sobom čestice povezane. Mi ćemo sada studirati <a href="/wiki/Titranje" title="Titranje">titranje</a> te jednodimenzionalne rešetke, i to najprije ćemo stvoriti neke očigledne predstave, a zatim ćemo i to isto gibanje proračunati na osnovu <a href="/wiki/Newtonovi_zakoni_gibanja" title="Newtonovi zakoni gibanja">Newtonova zakona gibanja</a>. U stanju ravnoteže imaju sve kuglice među sobom jednaki razmak. Pomaknemo li neku kuglicu nalijevo ili nadesno, odmah se ravnoteža naruši. Pomak nadesno stavlja kuglicu na veću udaljenost od lijeve susjedne kuglice, a u manju udaljenost od desne nego što odgovara tim kuglicama u <a href="/wiki/Ravnote%C5%BEa_(mehanika)" title="Ravnoteža (mehanika)">ravnoteži</a>. Posljedica je toga da se javljaju elestične sile. Na pomaknutu kuglicu djeluje dalja kuglica privlačnom silom, a bliža kuglica odbojnom silom, jer je elastična opruga u prvom slučaju rastegnuta, a u drugom stisnuta. Pomaknutu kuglicu tjeraju dakle elastične sile natrag u položaj ravnoteže. Ovamo se kuglica vraća s ubrzanim <a href="/wiki/Gibanje" title="Gibanje">gibanjem</a>. Kada kuglica dođe u položaj ravnoteže, ona ima veliku brzinu, i ta je osposobljuje da preleti položaj ravnoteže i dosegne isti pomak na suprotnoj strani. Sada se ponavlja ista slika, samo s druge strane. Jedanput pomaknuta kuglica iz položaja ravnoteže titra neprekidno lijevo-desno. </p><p>U našem nizu kuglica, povezanih međusobno elastičnim silama, ne ostaje titranje izolirano na pojedinu kuglicu. Udaljavanjem od ravnoteže vrši kuglica, po <a href="/wiki/Newtonovi_zakoni_gibanja" title="Newtonovi zakoni gibanja">zakonu akcije i reakcije</a>, jednake sile suprotnog smjera na svoje susjedne kuglice. Bliža susjedna kuglica biva dakle odgurnuta, a dalja privučena. Obje susjedne kuglice, bliža i dalja, dobivaju pomak u smjeru pomaka srednje kuglice. Čim smo počeli vući srednju kuglicu nadesno, i obje susjedne kuglice počele su se pomicati u istom smjeru. Te kuglice opet sa svoje strane povuku svoje susjedne kuglice, i tako se postepeno prenosi pomak od jedne kuglice na drugu. Sve kuglice u nizu zatitraju poslije nekog vremena. </p><p>Od kuglice do kuglice prenosi se pomak s izvjesnim zakašnjenjem. Treba da prođe izvjesno vrijeme dok se pomakne kuglica koja je na primjer dvanaesta po redu iza prvotno pomaknute kuglice. Ovo zakašnjenje prouzrokuje da u isti čas sve kuglice ne pokazuju isto stanje titranja. Dok je prva kuglica postigla svoj najveći pomak, možda se četvrta po redu tek pokrenula iz položaja ravnoteže. Ako je to slučaj, tada će se trinaesta kuglica tek tada pokrenuti kad se prva kuglica vrati u svoj položaj ravnoteže izvršivši jedan puni titraj. Prva i trinaesta kuglica miču se tada u istom smjeru istovremeno iz položaja ravnoteže, prva kuglica, naravno, po drugi put. Poslije dužeg vremena titra već čitav niz elastično povezanih kuglica. U tom nizu uvijek se vide kuglice koje istovremeno dosežu svoj najveći pomak u istom smjeru. Udaljenost između dviju najbližih kuglica s istim pomakom jest <a href="/wiki/Valna_duljina" title="Valna duljina">valna duljina</a>. U našem primjeru valna duljina iznosi dvanaest razmaka između kuglica. </p><p>Može se vrlo lako proračunati <a href="/wiki/Brzina" title="Brzina">brzina</a> kojom se val, to jest isto stanje titranja, širi nizom. Za vrijeme jednog punog titraja proširi se val za jednu valnu duljinu. Put od jedne valne duljine prevaljen je za vrijeme jednog titraja. Valna brzina je prema tome jednaka omjeru između valne duljine <i>λ</i> i vrijeme titraja <i>T</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 {\text{valna brzina}}={{\text{valna duljina}} \over {\text{vrijeme titraja}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>valna brzina</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mtext>valna duljina</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>vrijeme titraja</mtext> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{valna brzina}}={{\text{valna duljina}} \over {\text{vrijeme titraja}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c32e6a93f92787818642925874310381a7c3f44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:30.829ex; height:5.843ex;" alt="{\displaystyle {\text{valna brzina}}={{\text{valna duljina}} \over {\text{vrijeme titraja}}}}"></span></dd></dl> <p>Brzinu rasprostiranja vala označit ćemo slovom <i>v</i>, valnu duljinu slovom <i>λ</i>, a vrijeme jednog punog titraja slovom <i>T</i>. Prethodni odnos možemo tada izraziti simbolički: </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 {\lambda }{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {\lambda }{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e7c044c1c04db44d9524765663cdec6c087336" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.698ex; height:5.343ex;" alt="{\displaystyle v={\frac {\lambda }{T}}}"></span></dd></dl> <p>Ovaj odnos može se u preglednom obliku pisati i pomoću frekvencije. <a href="/wiki/Frekvencija" title="Frekvencija">Frekvencija</a> <i>f</i> je po definiciji jednaka recipročnoj vrijednosti vremena titraja. Tada možemo prethodnu jednadžbu pisati u obliku: </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=f\cdot \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>f</mi> <mo>⋅</mo> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=f\cdot \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b2e6b860fb4e5fe6770ed2334e85924649480a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.539ex; height:2.509ex;" alt="{\displaystyle v=f\cdot \lambda }"></span></dd></dl> <p>Za vrijeme jedne sekunde pomakne se <a href="/wiki/Val" title="Val">val</a> za toliko valnih duljina kolika je frekvencija titraja. </p><p>Promatramo li u neki čas raspored kuglica u nizu, opažamo da su one uzastopno gušće i rjeđe poredane. Titranja kuglica oko položaja ravnoteže imaju za posljedicu da se nizom šire zgušćaji i razrjeđaji. Takvi valovi kod kojih kuglice titraju u smjeru svojih spojnica, to jest u smjeru širenja vala, zovu se <a href="/wiki/Longitudinalan_val" title="Longitudinalan val">longitudinalni</a>. Longitudinalni valovi prenose zgušćaje i razrjeđaje. </p><p>Osim longitudinalnih titraja elastično povezane kuglice mogu izvoditi i okomite titraje na svoje spojnice. U našem modelu nastaje takvo titranje ako jednu kuglicu iz položaja ravnoteže pomaknemo okomito na niz. Elastične sile napetih opruga tjeraju pomaknutu kuglicu prema pravcu niza, i ona zatitra gore-dolje. <a href="/w/index.php?title=Harmoni%C4%8Dno_titranje&action=edit&redlink=1" class="new" title="Harmonično titranje (stranica ne postoji)">Harmonično titranje</a> te kuglice prenosi se i na ostale kuglice, naravno s izvjesnim zakašnjenjem. Poslije izvesnog vremena titraju sve kuglice niza. Zakašnjavanje pomaka ima za posljedicu da istodobno ne postignu svoj najveći pomak sve kuglice, već neke su u jedan čas gore, druge dolje, a treće na pravcu niza. U svaki trenutak prikazuju kuglice pravilnu valnu krivulju s izmjeničnim brijegom i dolom. Budući da pojedini brijeg ili dol postepeno izgrađuju uvijek sljedeće kuglice, takvi se bregovi i dolovi s jednakom brzinom rasprostiru nizom. Okomiti titraji ne očituju se dakle u zgušćivanju ili razrjeđivanju kuglica, nego u postepenom pomicanju valne krivulje u jednom smjeru. Ovakvi valovi, kod kojih kuglice titraju okomito na smjer širenja vala nazvani su <a href="/wiki/Transverzalni_val" title="Transverzalni val">transverzalnim</a>. </p><p>Transverzalni i longitudinalni valovi su najjednostavniji tipovi titranja kuglica u nizu. Općenito kuglice mogu istodobno titrati i longitudinalno i transverzalno. Pomaknemo li istodobno kuglicu nalijevo i prema gore, dakle u kosom smjeru prema nizu, tad kuglica titra stalno koso prema nizu. Ovakvo koso titranje prenese se i na ostale kuglice. Kuglice u ovakvom titranju prikazuju pravilnu valnu krivulju, u kojoj se kuglice izmjenično zgušćuju i razrjeđuju. Pri takvom općenitom titranju opažamo svojstva i longitudinalnih i transverzalnih valova. </p><p>Međutim, moguća su i titranja kod kojih pojedine kuglice kruže oko svojih položaja ravnoteže. Takva kružna gibanja nastaju također slaganjem iz longitudinalnih i transverzalnih titraja. Zamislimo da neku kuglicu pobudimo najprije udarcem da transverzalno titra. Kad dosegne svoj najveći transverzalni pomak, zadajmo joj jednako jak longitudinalni udarac. Pod djelovanjem tog longitudinalnog udarca kuglica bi započela longitudinalno titranje. Budući da već transverzalno titra iz najvećeg pomaka, kuglica opisuje kružnicu. U nizu svaka po redu kuglica zakašnjava s vrtnjom, i mi opet imamo pravilnu valnu krivulju, u kojoj su kuglice gušće i rjeđe poredane.<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=Kristalna_re%C5%A1etka&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=Kristalna_re%C5%A1etka&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>kristalna rešetka</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=34007">[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="Literatura">Literatura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&veaction=edit&section=5" title="Uredi odlomak: Literatura" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kristalna_re%C5%A1etka&action=edit&section=5" title="Uredi kôd odjeljka Literatura"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>C. W. Bunn: <i>Chemical Crystallography an introduction to optical and x-ray methods</i>, Oxford at the Clarendon press, 1952.</li> <li><i>Tehnička enciklopedija</i>, tom 7., Ke-Međ, Zagreb, 1980.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Dobavljeno iz "<a dir="ltr" href="https://hr.wikipedia.org/w/index.php?title=Kristalna_rešetka&oldid=7051918">https://hr.wikipedia.org/w/index.php?title=Kristalna_rešetka&oldid=7051918</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:%C4%8Clanci_kojima_nedostaje_izvor" title="Kategorija:Članci kojima nedostaje izvor">Članci kojima nedostaje izvor</a></li><li><a href="/wiki/Kategorija:Kemija" title="Kategorija:Kemija">Kemija</a></li><li><a href="/wiki/Kategorija:Kristalografija" title="Kategorija:Kristalografija">Kristalografija</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica posljednji je put uređivana 3. studenoga 2024. u 09:27.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencijom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hr">Creative Commons: Imenuj autora/Dijeli pod istim uvjetima</a>; mogu se primjenjivati i dodatni uvjeti. 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