Strwythur crisial - Wicipedia

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class="vector-toc-list"> <li id="toc-Indecsau_Miller" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Indecsau_Miller"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Indecsau Miller</span> </div> </a> <ul id="toc-Indecsau_Miller-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Planau_a_chyfeiriadau" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Planau_a_chyfeiriadau"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Planau a chyfeiriadau</span> </div> </a> <ul id="toc-Planau_a_chyfeiriadau-sublist" class="vector-toc-list"> <li id="toc-Strwythurau_ciwbig" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Strwythurau_ciwbig"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Strwythurau ciwbig</span> </div> </a> <ul id="toc-Strwythurau_ciwbig-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gwahaniad_rhyng-blân" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gwahaniad_rhyng-blân"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Gwahaniad rhyng-blân</span> </div> </a> <ul id="toc-Gwahaniad_rhyng-blân-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Dosbarthiad_yn_ôl_cymesuredd" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dosbarthiad_yn_ôl_cymesuredd"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Dosbarthiad yn ôl cymesuredd</span> </div> </a> <button aria-controls="toc-Dosbarthiad_yn_ôl_cymesuredd-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toglo is-adran Dosbarthiad yn ôl cymesuredd</span> </button> <ul id="toc-Dosbarthiad_yn_ôl_cymesuredd-sublist" class="vector-toc-list"> <li id="toc-Systemau_dellt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Systemau_dellt"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Systemau dellt</span> </div> </a> <ul id="toc-Systemau_dellt-sublist" class="vector-toc-list"> <li id="toc-Dellt_Bravais" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Dellt_Bravais"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Dellt Bravais</span> </div> </a> <ul id="toc-Dellt_Bravais-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Systemau_crisial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Systemau_crisial"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Systemau crisial</span> </div> </a> <ul id="toc-Systemau_crisial-sublist" class="vector-toc-list"> <li id="toc-Grwpiau_pwynt" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Grwpiau_pwynt"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Grwpiau pwynt</span> </div> </a> <ul id="toc-Grwpiau_pwynt-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Grwpiau_gofod" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Grwpiau_gofod"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Grwpiau gofod</span> </div> </a> <ul id="toc-Grwpiau_gofod-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Cydlyniad_atomig" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cydlyniad_atomig"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Cydlyniad atomig</span> </div> </a> <button aria-controls="toc-Cydlyniad_atomig-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toglo is-adran Cydlyniad atomig</span> </button> <ul id="toc-Cydlyniad_atomig-sublist" class="vector-toc-list"> <li id="toc-Pacio_agos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pacio_agos"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Pacio agos</span> </div> </a> <ul id="toc-Pacio_agos-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ffiniau_graen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ffiniau_graen"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ffiniau graen</span> </div> </a> <ul id="toc-Ffiniau_graen-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diffygion_ac_amhureddau" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Diffygion_ac_amhureddau"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Diffygion ac amhureddau</span> </div> </a> <ul id="toc-Diffygion_ac_amhureddau-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rhagdybiaeth_strwythur" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rhagdybiaeth_strwythur"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Rhagdybiaeth strwythur</span> </div> </a> <ul id="toc-Rhagdybiaeth_strwythur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cyfeiriadau" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cyfeiriadau"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Cyfeiriadau</span> </div> </a> <ul id="toc-Cyfeiriadau-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="Cynnwys" 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="Toglo'r tabl cynnwys" > <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">Toglo'r tabl cynnwys</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">Strwythur crisial</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="Ewch i erthygl mewn iaith arall. Ar gael mewn 61 iaith" > <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 iaith</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 - Affricaneg" lang="af" hreflang="af" data-title="Kristalstruktuur" data-language-autonym="Afrikaans" data-language-local-name="Affricaneg" 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 - Aragoneg" lang="an" hreflang="an" data-title="Estructura cristalina" data-language-autonym="Aragonés" data-language-local-name="Aragoneg" 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 - Arabeg" lang="ar" hreflang="ar" data-title="بنية بلورية" data-language-autonym="العربية" data-language-local-name="Arabeg" 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 - Astwrianeg" lang="ast" hreflang="ast" data-title="Estructura cristalina" data-language-autonym="Asturianu" data-language-local-name="Astwrianeg" 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 - Bwlgareg" lang="bg" hreflang="bg" data-title="Кристална структура" data-language-autonym="Български" data-language-local-name="Bwlgareg" 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 - Bosnieg" lang="bs" hreflang="bs" data-title="Kristalna struktura" data-language-autonym="Bosanski" data-language-local-name="Bosnieg" 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 - Catalaneg" lang="ca" hreflang="ca" data-title="Estructura cristal·lina" data-language-autonym="Català" data-language-local-name="Catalaneg" 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 - Cwrdeg Sorani" lang="ckb" hreflang="ckb" data-title="پەیکەری بلووری" data-language-autonym="کوردی" data-language-local-name="Cwrdeg Sorani" 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 - Tsieceg" lang="cs" hreflang="cs" data-title="Krystalická struktura" data-language-autonym="Čeština" data-language-local-name="Tsieceg" 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 - Tshwfasheg" lang="cv" hreflang="cv" data-title="Кристалла тытăм" data-language-autonym="Чӑвашла" data-language-local-name="Tshwfasheg" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Krystalstruktur" title="Krystalstruktur - Daneg" lang="da" hreflang="da" data-title="Krystalstruktur" data-language-autonym="Dansk" data-language-local-name="Daneg" 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 - Almaeneg" lang="de" hreflang="de" data-title="Kristallstruktur" data-language-autonym="Deutsch" data-language-local-name="Almaeneg" 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 - Saesneg" lang="en" hreflang="en" data-title="Crystal structure" data-language-autonym="English" data-language-local-name="Saesneg" 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 - Sbaeneg" lang="es" hreflang="es" data-title="Estructura cristalina" data-language-autonym="Español" data-language-local-name="Sbaeneg" 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 - Estoneg" lang="et" hreflang="et" data-title="Kristallistruktuur" data-language-autonym="Eesti" data-language-local-name="Estoneg" 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 - Basgeg" lang="eu" hreflang="eu" data-title="Kristal-egitura" data-language-autonym="Euskara" data-language-local-name="Basgeg" 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 - Perseg" lang="fa" hreflang="fa" data-title="ساختار بلوری" data-language-autonym="فارسی" data-language-local-name="Perseg" 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 - Ffinneg" lang="fi" hreflang="fi" data-title="Kiderakenne" data-language-autonym="Suomi" data-language-local-name="Ffinneg" 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 - Ffrangeg" lang="fr" hreflang="fr" data-title="Structure cristalline" data-language-autonym="Français" data-language-local-name="Ffrangeg" 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 - Gwyddeleg" lang="ga" hreflang="ga" data-title="Criostalstruchtúr" data-language-autonym="Gaeilge" data-language-local-name="Gwyddeleg" 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 - Galisieg" lang="gl" hreflang="gl" data-title="Estrutura cristalina" data-language-autonym="Galego" data-language-local-name="Galisieg" 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 - Hebraeg" lang="he" hreflang="he" data-title="מבנה גבישי" data-language-autonym="עברית" data-language-local-name="Hebraeg" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kristalna_re%C5%A1etka" title="Kristalna rešetka - Croateg" lang="hr" hreflang="hr" data-title="Kristalna rešetka" data-language-autonym="Hrvatski" data-language-local-name="Croateg" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estrikti_kristalen" title="Estrikti kristalen - Creol Haiti" lang="ht" hreflang="ht" data-title="Estrikti kristalen" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Creol Haiti" 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 - Hwngareg" lang="hu" hreflang="hu" data-title="Kristályszerkezet" data-language-autonym="Magyar" data-language-local-name="Hwngareg" 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 - Armeneg" lang="hy" hreflang="hy" data-title="Բյուրեղային կառուցվածք" data-language-autonym="Հայերեն" data-language-local-name="Armeneg" 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 - Indoneseg" lang="id" hreflang="id" data-title="Struktur kristal" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indoneseg" 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 - Japaneeg" lang="ja" hreflang="ja" data-title="結晶構造" data-language-autonym="日本語" data-language-local-name="Japaneeg" 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 - Coreeg" lang="ko" hreflang="ko" data-title="결정 구조" data-language-autonym="한국어" data-language-local-name="Coreeg" 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 - Latfieg" lang="lv" hreflang="lv" data-title="Kristāliskā struktūra" data-language-autonym="Latviešu" data-language-local-name="Latfieg" 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 - Macedoneg" lang="mk" hreflang="mk" data-title="Кристална структура" data-language-autonym="Македонски" data-language-local-name="Macedoneg" 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 - Malayalam" lang="ml" hreflang="ml" data-title="ക്രിസ്റ്റൽ ഘടന" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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 - Mongoleg" lang="mn" hreflang="mn" data-title="Болрын бүтэц" data-language-autonym="Монгол" data-language-local-name="Mongoleg" 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 - Maleieg" lang="ms" hreflang="ms" data-title="Struktur hablur" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleieg" 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 - Iseldireg" lang="nl" hreflang="nl" data-title="Kristalstructuur" data-language-autonym="Nederlands" data-language-local-name="Iseldireg" 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 - Norwyeg Nynorsk" lang="nn" hreflang="nn" data-title="Krystallstruktur" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwyeg 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 - Norwyeg Bokmål" lang="nb" hreflang="nb" data-title="Krystallstruktur" data-language-autonym="Norsk bokmål" data-language-local-name="Norwyeg 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 - Pwnjabeg" lang="pa" hreflang="pa" data-title="ਲੈਟਿਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pwnjabeg" 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 - Pwyleg" lang="pl" hreflang="pl" data-title="Sieć krystaliczna" data-language-autonym="Polski" data-language-local-name="Pwyleg" 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 - Portiwgaleg" lang="pt" hreflang="pt" data-title="Estrutura cristalina" data-language-autonym="Português" data-language-local-name="Portiwgaleg" 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 - Rwmaneg" lang="ro" hreflang="ro" data-title="Structură cristalină" data-language-autonym="Română" data-language-local-name="Rwmaneg" 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 - Rwseg" lang="ru" hreflang="ru" data-title="Кристаллическая структура" data-language-autonym="Русский" data-language-local-name="Rwseg" 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 - Sgoteg" lang="sco" hreflang="sco" data-title="Creestal structur" data-language-autonym="Scots" data-language-local-name="Sgoteg" 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 - Serbo-Croateg" lang="sh" hreflang="sh" data-title="Kristalna struktura" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croateg" 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 - Slofeneg" lang="sl" hreflang="sl" data-title="Kristalna struktura" data-language-autonym="Slovenščina" data-language-local-name="Slofeneg" 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 - Albaneg" lang="sq" hreflang="sq" data-title="Struktura e kristaleve reale" data-language-autonym="Shqip" data-language-local-name="Albaneg" 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 - Serbeg" lang="sr" hreflang="sr" data-title="Кристална структура" data-language-autonym="Српски / srpski" data-language-local-name="Serbeg" 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 - Swedeg" lang="sv" hreflang="sv" data-title="Kristallstruktur" data-language-autonym="Svenska" data-language-local-name="Swedeg" 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 - Tamileg" lang="ta" hreflang="ta" data-title="படிக அமைப்பு" data-language-autonym="தமிழ்" data-language-local-name="Tamileg" 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 - Thai" lang="th" hreflang="th" data-title="โครงสร้างผลึก" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kristal_yap%C4%B1" title="Kristal yapı - Tyrceg" lang="tr" hreflang="tr" data-title="Kristal yapı" data-language-autonym="Türkçe" data-language-local-name="Tyrceg" 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 - Wcreineg" lang="uk" hreflang="uk" data-title="Кристалічна структура" data-language-autonym="Українська" data-language-local-name="Wcreineg" 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 - Wrdw" lang="ur" hreflang="ur" data-title="قلمی ساخت" data-language-autonym="اردو" data-language-local-name="Wrdw" 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 - Wsbeceg" lang="uz" hreflang="uz" data-title="Kristall panjara" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Wsbeceg" 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 - Fietnameg" lang="vi" hreflang="vi" data-title="Cấu trúc tinh thể" data-language-autonym="Tiếng Việt" data-language-local-name="Fietnameg" 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 Tsieineaidd" lang="wuu" hreflang="wuu" data-title="晶体结构" data-language-autonym="吴语" data-language-local-name="Wu Tsieineaidd" 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 - Tsieinëeg" lang="zh" hreflang="zh" data-title="晶体结构" data-language-autonym="中文" data-language-local-name="Tsieinëeg" 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="Golygu dolenni rhyngwici" class="wbc-editpage">Golygu dolenni</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="Parthau"> <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/Strwythur_crisial" title="Gweld y dudalen bwnc [c]" accesskey="c"><span>Erthygl</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Sgwrs:Strwythur_crisial&action=edit&redlink=1" rel="discussion" class="new" title="Sgwrsio am y dudalen (dim tudalen ar gael) [t]" accesskey="t"><span>Sgwrs</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="Newid amrywiad iaith" > <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">Cymraeg</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="Golygon"> <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/Strwythur_crisial"><span>Darllen</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Strwythur_crisial&veaction=edit" title="Golygu'r dudalen hon [v]" accesskey="v"><span>Golygu</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Strwythur_crisial&action=edit" title="Golygu cod ffynhonnell y dudalen hon [e]" accesskey="e"><span>Golygu cod</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Strwythur_crisial&action=history" title="Fersiynau cynt o'r dudalen hon. [h]" accesskey="h"><span>Gweld hanes</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Offer tudalen"> <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="Blwch offer" > <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">Blwch offer</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">Blwch offer</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">symud i'r bar ochr</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">cuddio</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Rhagor o opsiynau" > <div class="vector-menu-heading"> Gweithredoedd </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected 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class="infobox" style="width:22em"><caption>Strwythur crisial</caption><tbody><tr><td colspan="2" style="text-align:center"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Delwedd:NaCl-Ionengitter.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/NaCl-Ionengitter.svg/220px-NaCl-Ionengitter.svg.png" decoding="async" width="220" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/NaCl-Ionengitter.svg/330px-NaCl-Ionengitter.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/NaCl-Ionengitter.svg/440px-NaCl-Ionengitter.svg.png 2x" data-file-width="555" data-file-height="572" /></a></span></td></tr><tr><th scope="row">Math</th><td>strwythur <span class="penicon autoconfirmed-show"><span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q895901?uselang=cy#P279" title="Edit this on Wikidata"><img alt="Edit this on Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></td></tr><tr><td colspan="2" style="text-align:center"><span typeof="mw:File"><span title="Tudalen Comin"><img alt="Tudalen Comin" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Crystal_structures" class="extiw" title="commons:Category:Crystal structures">Ffeiliau perthnasol ar Gomin Wicimedia</a></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Sodium-chloride-3D-ionic.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/220px-Sodium-chloride-3D-ionic.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/330px-Sodium-chloride-3D-ionic.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Sodium-chloride-3D-ionic.png/440px-Sodium-chloride-3D-ionic.png 2x" data-file-width="1000" data-file-height="948" /></a><figcaption>Strwythur crisial <a href="/wiki/Sodiwm_clorid" title="Sodiwm clorid"> halen</a> (sodiwm mewn porffor, clorid mewn gwyrdd) </figcaption></figure> <p>Mewn <a href="/w/index.php?title=Crisialeg&action=edit&redlink=1" class="new" title="Crisialeg (dim tudalen ar gael)">crisialeg</a>, mae <b>strwythur crisial</b> yn ddisgrifiad o drefniant rheolaidd atomau, ïonau neu foleciwlau mewn defnydd crisialog. Gall strwythurau rheolaidd ddigwydd o natur gynhenid y gronynnau cyfansoddol i ffurfio patrymau cymesurol sy'n ailadrodd ar hyd prif gyfeiriadau gofod tri dimensiwn mewn mater. </p><p>Cell uned yw'r grŵp lleiaf o ronynnau mewn deunydd sy'n ffurfio'r patrwm ailadroddus hwn. Mae cell uned yn adlewyrchu cymesuredd ac adeiledd crisial cyfan yn llwyr, sy'n cael ei adeiladu trwy drosiad ailadroddus o gell uned ar hyd ei phrif echelinau. Mae'r fectorau trawsfudo yn diffinio nodau <a href="/w/index.php?title=Dellt_Bravais&action=edit&redlink=1" class="new" title="Dellt Bravais (dim tudalen ar gael)">dellt Bravais</a>. </p><p><a href="/w/index.php?title=Cysonion_dellt&action=edit&redlink=1" class="new" title="Cysonion dellt (dim tudalen ar gael)">Cysonion dellt</a> yw hydoedd y prif echelinau, neu ymylon, y gell uned a'r onglau rhyngddynt; fe'u gelwir hefyd yn <i>baramedrau dellt</i> neu <i>baramedrau cell</i>. Disgrifir priodweddau cymesuredd y grisial gan y cysyniad o <a href="/w/index.php?title=Grwpiau_gofod&action=edit&redlink=1" class="new" title="Grwpiau gofod (dim tudalen ar gael)">grwpiau gofod</a>. Gall pob trefniant cymesur posibl o ronynnau mewn gofod tri dimensiwn gael eu disgrifio gan y 230 o grwpiau gofod. </p><p>Mae'r strwythur crisial a chymesuredd yn chwarae rhan hanfodol wrth bennu llawer o briodweddau ffisegol, megis holltiad, strwythur band electronig, a thryloywder optegol. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Cell_uned">Cell uned</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=1" title="Golygu'r adran: Cell uned" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=1" title="Edit section's source code: Cell uned"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Disgrifir strwythur crisial yn nhermau geometreg trefniant gronynnau yn y gell uned. Diffinnir cell uned fel yr uned ailadrodd leiaf sydd â chymesuredd llawn y strwythur crisial. Diffinnir geometreg y gell unedol fel pibell paralel, gan ddarparu chwe pharamedr dellt a gymerir fel hyd ymylon y gell (<i>a</i>, <i>b</i>, <i>c</i>) a'r onglau rhyngddynt (α, β, γ). Disgrifir safleoedd y gronynnau y tu mewn i'r gell uned gan y cyfesurynnau ffracsiynol (<i>x<sub>i</sub></i>, <i>y<sub>i</sub></i>, <i>z<sub>i</sub></i>) ar hyd ymylon y gell, wedi'u mesur o bwynt cyfeirio. Dim ond adrodd am gyfesurynnau is-set anghymesur lleiaf o ronynnau sydd ei angen. Gellir dewis y grŵp hwn o ronynnau fel ei fod yn meddiannu'r gofod ffisegol lleiaf, sy'n golygu nad oes angen lleoli pob gronyn yn gorfforol y tu mewn i'r ffiniau a roddir gan y paramedrau dellt. Mae holl ronynnau eraill y gell uned yn cael eu cynhyrchu gan y gweithrediadau cymesuredd sy'n nodweddu cymesuredd y cell uned. Mynegir y casgliad o weithrediadau cymesuredd y gell uned yn ffurfiol fel <a href="/w/index.php?title=Gr%C5%B5p_gofod&action=edit&redlink=1" class="new" title="Grŵp gofod (dim tudalen ar gael)">grŵp gofod</a> y strwythur crisial. </p> <ul class="gallery mw-gallery-traditional center"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Delwedd:Lattic_simple_cubic.svg" class="mw-file-description" title="Ciwbig syml"><img alt="Ciwbig syml" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Lattic_simple_cubic.svg/120px-Lattic_simple_cubic.svg.png" decoding="async" width="120" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Lattic_simple_cubic.svg/180px-Lattic_simple_cubic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Lattic_simple_cubic.svg/240px-Lattic_simple_cubic.svg.png 2x" data-file-width="406" data-file-height="360" /></a></span></div> <div class="gallerytext">Ciwbig syml</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Delwedd:Lattice_body_centered_cubic.svg" class="mw-file-description" title="Ciwbig corff-ganolog"><img alt="Ciwbig corff-ganolog" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lattice_body_centered_cubic.svg/120px-Lattice_body_centered_cubic.svg.png" decoding="async" width="120" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lattice_body_centered_cubic.svg/180px-Lattice_body_centered_cubic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Lattice_body_centered_cubic.svg/240px-Lattice_body_centered_cubic.svg.png 2x" data-file-width="403" data-file-height="354" /></a></span></div> <div class="gallerytext">Ciwbig corff-ganolog</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Delwedd:Lattice_face_centered_cubic.svg" class="mw-file-description" title="Ciwbig wyneb-ganolog"><img alt="Ciwbig wyneb-ganolog" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Lattice_face_centered_cubic.svg/120px-Lattice_face_centered_cubic.svg.png" decoding="async" width="120" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Lattice_face_centered_cubic.svg/180px-Lattice_face_centered_cubic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Lattice_face_centered_cubic.svg/240px-Lattice_face_centered_cubic.svg.png 2x" data-file-width="399" data-file-height="359" /></a></span></div> <div class="gallerytext">Ciwbig wyneb-ganolog</div> </li> </ul> <p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Indecsau_Miller">Indecsau Miller</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=2" title="Golygu'r adran: Indecsau Miller" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=2" title="Edit section's source code: Indecsau Miller"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Miller_Indices_Cubes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Miller_Indices_Cubes.svg/220px-Miller_Indices_Cubes.svg.png" decoding="async" width="220" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Miller_Indices_Cubes.svg/330px-Miller_Indices_Cubes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Miller_Indices_Cubes.svg/440px-Miller_Indices_Cubes.svg.png 2x" data-file-width="570" data-file-height="600" /></a><figcaption>Planau gydag indecsau Miller gwahanol mewn crisialau ciwbig</figcaption></figure> <p>Disgrifir fectorau a phlanau mewn dellt crisial gan nodiant tri-gwerth indecs Miller. Mae'r gystrawen hon yn defnyddio'r indecsau ℓ, m, ac n fel paramedrau cyfeiriadol. </p><p>Trwy ddiffiniad, mae'r gystrawen (ℓmn) yn dynodi plân sy'n rhyngdorri'r tri phwynt <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 {a_{1}}{\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>ℓ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a_{1}}{\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8b59e2210d348ac0a497188d820cf53225f6802" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.12ex; height:4.843ex;" alt="{\displaystyle {\frac {a_{1}}{\ell }}}"></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 {\frac {a_{2}}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a_{2}}{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/634c148cdf8c149399f9d511e8f6a4759d294045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.12ex; height:4.676ex;" alt="{\displaystyle {\frac {a_{2}}{m}}}"></span>, a <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 {a_{3}}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a_{3}}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/914ee5990cb722015db887d2e28997bf27bf5da6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.12ex; height:4.676ex;" alt="{\displaystyle {\frac {a_{3}}{n}}}"></span>, neu ryw luosrif ohonynt. Hynny yw, mae indecsau Miller mewn cyfrannedd â gwrthdroadau rhyngdorriadau'r plân â'r gell uned (yn sail y fectorau dellt). Os yw un neu fwy o'r indecsau'n sero, mae'n golygu nad yw'r planau'n croestorri'r echelin honno (h.y., y rhyngdoriad yn "cyrraedd anfeidredd"). Mae plân sy'n cynnwys echelin gyfesurynnol yn cael ei drawsfudo fel nad yw'n cynnwys yr echelin honno mwyach cyn pennu ei indecsau Miller. Cyfanrifoedd heb ffactorau cyffredin yw indecsau Miller i blân. Nodir indecsau negyddol gyda barrau llorweddol, fel yn (1<a href="/w/index.php?title=Nodyn:Overbar&action=edit&redlink=1" class="new" title="Nodyn:Overbar (dim tudalen ar gael)">Nodyn:Overbar</a>3). Mewn system gyfesurynnol orthogonal ar gyfer cell giwbig, indecsau Miller plân yw cydrannau Cartesaidd fector sy'n normal i'r plân. </p><p>O ystyried dim ond planau (ℓmn) sy'n croestorri un neu fwy o bwyntiau dellt (y <i>planau dellt</i>), mae'r pellter <i>d</i> rhwng planau dellt cyfagos yn gysylltiedig â'r fector <a href="/w/index.php?title=Dellt_cilyddol&action=edit&redlink=1" class="new" title="Dellt cilyddol (dim tudalen ar gael)">dellt cilyddol</a> (byrraf) orthogonal i'r planau yn ôl y fformiwla: </p><p><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 d={\frac {2\pi }{|\mathbf {g} _{\ell mn}|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d={\frac {2\pi }{|\mathbf {g} _{\ell mn}|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8ca0c03b1448ac6ecdf25c4c6d6ba5cef56cdea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.128ex; height:6.009ex;" alt="{\displaystyle d={\frac {2\pi }{|\mathbf {g} _{\ell mn}|}}}"></span> </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Planau_a_chyfeiriadau">Planau a chyfeiriadau</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=3" title="Golygu'r adran: Planau a chyfeiriadau" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=3" title="Edit section's source code: Planau a chyfeiriadau"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Cristal_densite_surface.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cristal_densite_surface.svg/220px-Cristal_densite_surface.svg.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cristal_densite_surface.svg/330px-Cristal_densite_surface.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cristal_densite_surface.svg/440px-Cristal_densite_surface.svg.png 2x" data-file-width="212" data-file-height="201" /></a><figcaption>Planau crisialograffeg dwys</figcaption></figure> <p>Llinellau geometreg sy'n cysylltu nodau (atomau, ïonau neu foleciwlau) yw cyfeiriadau crisialogaidd. Yn yr un modd, mae planau crisialog yn blanau geometrig sy'n cysylltu nodau. Mae gan rai cyfeiriadau a blanau ddwysedd uwch o nodau. Mae'r planau dwysedd uchel hyn yn dylanwadu ar nodweddion y grisial fel a ganlyn: </p> <ul><li>Priodweddau optegol: Mae indecs plygiant yn gysylltiedig yn uniongyrchol â dwysedd (neu amrywiadau dwysedd cyfnodol).</li> <li>Arsugnedd ac adweithedd: Bydd arsugnedd ffisegol neu adweithiau cemegol yn digwydd ger neu ar arwyneb atomau neu folecylau. O ganlyniad, mae'r ffenomena hyn yn sensitif i ddwysedd y nodau.</li> <li>Tyniant arwyneb: Golyga cyddwysiad defnydd bod yr atomau, yr ïonau neu'r molecylau yn fwy sefydlog os ŷnt wedi eu hamgylchynnu gydag eraill o'r un fath. O ganlyniad, mae tyniant arwyneb yn amrywio yn ôl y dwysedd ar yr arwyneb.</li> <li>Diffygion microstrwythurol: Mae mandyllau a chrisialygon (crystallites) yn dueddol o fod â ffiniau graen syth, sy'n dilyn planau dwysedd uwch.</li> <li>Holltiad: Yn dueddol o ddigwydd yn baralel i blanau dwysedd uchel.</li> <li>Anffurfiad plastig: Mae llithriad dadleoli yn digwydd mewn paralel â phlanau dwysedd uwch. Mae'r aflonyddiad a gludir gan y dadleoliad (fector Burgers) ar hyd cyfeiriad dwys. Mae symudiad un nod i gyfeiriad mwy dwys angen llai o afluniad o'r dellt grisial.</li></ul> <p>Diffinnir rhai cyfeiriadau a phlanau gan gymesuredd y system crisial. Mewn systemau monoclinig, rhombohedrol, tetragonol, a thrionglog/hecsagonol mae un echel unigryw (a elwir weithiau y <b>brif echelin</b>) sydd â chymesuredd cylchdro uwch na'r ddwy echelin arall. Y <b>plân waelodol</b> yw'r plân sy'n berpendicwlar i'r brif echelin yn y systemau crisial hyn. Ar gyfer systemau triclinig, orthorhombig, a chrisial ciwbig, mae dynodiad yr echelin yn fympwyol ac nid oes prif echelin. </p><p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Strwythurau_ciwbig">Strwythurau ciwbig</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=4" title="Golygu'r adran: Strwythurau ciwbig" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=4" title="Edit section's source code: Strwythurau ciwbig"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I'r achos arbennig o grisialau ciwbig syml, mae'r fectorau dellt yn orthogonol ac o hyd cyfartal (dynodir fel arfer yn <i>a</i>); yr un modd i'r dellt cilyddol. Felly, yn yr achos cyffredin hwn, mae indecsau Miller (ℓmn) a [ℓmn] ill dau yn dynodi normalau/cyfeiriadau mewn cyfesurynnau Cartesaidd. Ar gyfer crisialau ciwbig gyda <a href="/w/index.php?title=Chysonyn_dellt&action=edit&redlink=1" class="new" title="Chysonyn dellt (dim tudalen ar gael)">chysonyn dellt</a> <i>a</i>, y gwahaniad <i>d</i> rhwng planau dellt cyfagos (ℓmn) yw: </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 d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+n^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <msqrt> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+n^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/650d7f5b9ff28c167bd34648d31c8ea1b9f41d8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:24.062ex; height:6.009ex;" alt="{\displaystyle d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+n^{2}}}}}"></span></dd></dl> <p>Oherwydd cymesuredd crisialau ciwbig, mae'n bosibl newid lle ac arwydd y cyfanrifau a chael cyfeiriadau a phlanau: </p> <ul><li>Mae cyfesurynnau mewn <i>cromfachau onglau</i> fel <100> yn dynodi teulu o gyfeiriadau sy'n gyfwerth oherwydd gweithrediadau cymesuredd, megis [100], [010], [001] neu'r negyddol o unrhyw un o'r cyfeiriadau hynny.</li> <li>Mae cyfesurynnau mewn <i>cromfachau cyrliog</i> megis {100} yn dynodi teulu o normalau plân sy'n gyfwerth oherwydd gweithrediadau cymesuredd, yn debyg iawn i sut mae cromfachau onglau yn dynodi teulu o gyfarwyddiadau.</li></ul> <p>Ar gyfer delltiau ciwbig wyneb-ganolog (<i>fcc - face-centered cubic</i>) a chorff-ganolog (<i>bcc - body-centered cubic</i>), nid yw'r fectorau dellt cysefin yn orthogonol. Fodd bynnag, yn yr achosion hyn mae indecsau Miller wedi'u diffinio'n gonfensiynol mewn perthynas â fectorau dellt yr <a href="/w/index.php?title=Uwchgell&action=edit&redlink=1" class="new" title="Uwchgell (dim tudalen ar gael)">uwchgell</a> ciwbig ac felly'n syml, y cyfeiriadau Cartesaidd ydynt eto. </p> <div class="mw-heading mw-heading3"><h3 id="Gwahaniad_rhyng-blân"><span id="Gwahaniad_rhyng-bl.C3.A2n"></span>Gwahaniad rhyng-blân</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=5" title="Golygu'r adran: Gwahaniad rhyng-blân" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=5" title="Edit section's source code: Gwahaniad rhyng-blân"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rhoddir y gwahaniad <i><b>d</b></i> rhwng planau dellt cyfagos (<i>hkℓ</i>) gan: </p> <ul><li>Ciwbig: <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 {1}{d^{2}}}={\frac {h^{2}+k^{2}+\ell ^{2}}{a^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}+k^{2}+\ell ^{2}}{a^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/573dc37321cce6a5b2c880f4147f4336529c2206" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.406ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}+k^{2}+\ell ^{2}}{a^{2}}}}"></span></dd></dl></li> <li>Tetragonol: <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 {1}{d^{2}}}={\frac {h^{2}+k^{2}}{a^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}+k^{2}}{a^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a31b25c0152c5d72b083abc5c85dd048187465b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.28ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}+k^{2}}{a^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}"></span></dd></dl></li> <li>Hecsagonol: <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 {1}{d^{2}}}={\frac {4}{3}}\left({\frac {h^{2}+hk+k^{2}}{a^{2}}}\right)+{\frac {\ell ^{2}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>h</mi> <mi>k</mi> <mo>+</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {4}{3}}\left({\frac {h^{2}+hk+k^{2}}{a^{2}}}\right)+{\frac {\ell ^{2}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edb1cd3eaa04c5b499ae6872f97388907110b8f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.477ex; height:6.343ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {4}{3}}\left({\frac {h^{2}+hk+k^{2}}{a^{2}}}\right)+{\frac {\ell ^{2}}{c^{2}}}}"></span></dd></dl></li> <li>Rhombohedrol: <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 {1}{d^{2}}}={\frac {(h^{2}+k^{2}+\ell ^{2})\sin ^{2}\alpha +2(hk+k\ell +h\ell )(\cos ^{2}\alpha -\cos \alpha )}{a^{2}(1-3\cos ^{2}\alpha +2\cos ^{3}\alpha )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mi>h</mi> <mi>k</mi> <mo>+</mo> <mi>k</mi> <mi>ℓ</mi> <mo>+</mo> <mi>h</mi> <mi>ℓ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mn>3</mn> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mn>2</mn> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {(h^{2}+k^{2}+\ell ^{2})\sin ^{2}\alpha +2(hk+k\ell +h\ell )(\cos ^{2}\alpha -\cos \alpha )}{a^{2}(1-3\cos ^{2}\alpha +2\cos ^{3}\alpha )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bb5afba19c68300efeb9413b0dbcf97dd438c6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:61.596ex; height:6.676ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {(h^{2}+k^{2}+\ell ^{2})\sin ^{2}\alpha +2(hk+k\ell +h\ell )(\cos ^{2}\alpha -\cos \alpha )}{a^{2}(1-3\cos ^{2}\alpha +2\cos ^{3}\alpha )}}}"></span></dd></dl></li> <li>Orthorhombig: <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 {1}{d^{2}}}={\frac {h^{2}}{a^{2}}}+{\frac {k^{2}}{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}}{a^{2}}}+{\frac {k^{2}}{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89308f758eac5104719f4ee73f9b9b2ef67760fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.116ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {h^{2}}{a^{2}}}+{\frac {k^{2}}{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}}"></span></dd></dl></li> <li>Monoclinig: <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 {1}{d^{2}}}=\left({\frac {h^{2}}{a^{2}}}+{\frac {k^{2}\sin ^{2}\beta }{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}-{\frac {2h\ell \cos \beta }{ac}}\right)\csc ^{2}\beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>β</mi> </mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>h</mi> <mi>ℓ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mrow> <mrow> <mi>a</mi> <mi>c</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>csc</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}=\left({\frac {h^{2}}{a^{2}}}+{\frac {k^{2}\sin ^{2}\beta }{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}-{\frac {2h\ell \cos \beta }{ac}}\right)\csc ^{2}\beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03865f4540d7e533becee58f18d857f54e84eb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:49.06ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{d^{2}}}=\left({\frac {h^{2}}{a^{2}}}+{\frac {k^{2}\sin ^{2}\beta }{b^{2}}}+{\frac {\ell ^{2}}{c^{2}}}-{\frac {2h\ell \cos \beta }{ac}}\right)\csc ^{2}\beta }"></span></dd></dl></li> <li>Triclinig: <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 {1}{d^{2}}}={\frac {{\frac {h^{2}}{a^{2}}}\sin ^{2}\alpha +{\frac {k^{2}}{b^{2}}}\sin ^{2}\beta +{\frac {\ell ^{2}}{c^{2}}}\sin ^{2}\gamma +{\frac {2k\ell }{bc}}(\cos \beta \cos \gamma -\cos \alpha )+{\frac {2h\ell }{ac}}(\cos \gamma \cos \alpha -\cos \beta )+{\frac {2hk}{ab}}(\cos \alpha \cos \beta -\cos \gamma )}{1-\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma +2\cos \alpha \cos \beta \cos \gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>β</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>γ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>k</mi> <mi>ℓ</mi> </mrow> <mrow> <mi>b</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>h</mi> <mi>ℓ</mi> </mrow> <mrow> <mi>a</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>h</mi> <mi>k</mi> </mrow> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>β</mi> <mo>−</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>γ</mi> <mo>+</mo> <mn>2</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{d^{2}}}={\frac {{\frac {h^{2}}{a^{2}}}\sin ^{2}\alpha +{\frac {k^{2}}{b^{2}}}\sin ^{2}\beta +{\frac {\ell ^{2}}{c^{2}}}\sin ^{2}\gamma +{\frac {2k\ell }{bc}}(\cos \beta \cos \gamma -\cos \alpha )+{\frac {2h\ell }{ac}}(\cos \gamma \cos \alpha -\cos \beta )+{\frac {2hk}{ab}}(\cos \alpha \cos \beta -\cos \gamma )}{1-\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma +2\cos \alpha \cos \beta \cos \gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/763f0644a0d9e770b754ffe79f8f9fc7a5bf6d28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:115.69ex; height:8.009ex;" alt="{\displaystyle {\frac {1}{d^{2}}}={\frac {{\frac {h^{2}}{a^{2}}}\sin ^{2}\alpha +{\frac {k^{2}}{b^{2}}}\sin ^{2}\beta +{\frac {\ell ^{2}}{c^{2}}}\sin ^{2}\gamma +{\frac {2k\ell }{bc}}(\cos \beta \cos \gamma -\cos \alpha )+{\frac {2h\ell }{ac}}(\cos \gamma \cos \alpha -\cos \beta )+{\frac {2hk}{ab}}(\cos \alpha \cos \beta -\cos \gamma )}{1-\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma +2\cos \alpha \cos \beta \cos \gamma }}}"></span></dd></dl></li></ul> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Dosbarthiad_yn_ôl_cymesuredd"><span id="Dosbarthiad_yn_.C3.B4l_cymesuredd"></span>Dosbarthiad yn ôl cymesuredd</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=6" title="Golygu'r adran: Dosbarthiad yn ôl cymesuredd" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=6" title="Edit section's source code: Dosbarthiad yn ôl cymesuredd"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Priodwedd diffiniol crisial yw ei gymesuredd cynhenid. Nid yw perfformio rhai gweithrediadau cymesuredd ar y dellt grisial yn ei newid. Mae gan pob crisial gymesuredd trosiadol mewn tri cyfeiriad, ond mae gan rai elfennau cymesuredd eraill hefyd. Er enghraifft, gall cylchdroi crisial 180° o amgylch echelin benodol arwain at gyfluniad atomig sy'n union yr un fath â'r cyfluniad gwreiddiol; mae gan y crisial gymesuredd cylchdro deublyg o amgylch yr echelin hon. Yn ogystal â chymesuredd cylchdro, gall crisial gael cymesuredd ar ffurf planau drych, a hefyd yr hyn a elwir yn gymesuredd cyfansawdd, sy'n gyfuniad o drawsfudiad a chymesuredd cylchdro neu ddrych. Cyflawnir dosbarthiad llawn o grisial pan nodir holl gymesuredd cynhenid y grisial. </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Systemau_dellt">Systemau dellt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=7" title="Golygu'r adran: Systemau dellt" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=7" title="Edit section's source code: Systemau dellt"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>System dellt yw grŵp o strwythurau crisial yn ôl y system echelinol a ddefnyddir i ddisgrifio eu dellt. Mae pob system dellt yn cynnwys set o dair echelin mewn trefniant geometrig penodol. Perthyn pob crisiau i un o'r saith system dellt. Maent yn debyg, ond nid yn union yr un fath â'r saith system grisial. </p> <table class="wikitable"> <tbody><tr> <th rowspan="2">Teulu crisial </th> <th rowspan="2">System dellt </th> <th rowspan="2">Grŵp pwynt <br />(Nodiant Schönflies) </th> <th colspan="4">14 dellt Bravais </th></tr> <tr> <th>Cysefin (P - <i>Primitive</i>) </th> <th>Sail-ganolog (S - <i>Base-centered</i>) </th> <th>Corff-ganolog (I - <i>Body-centered</i>) </th> <th>Wyneb-ganolog (F - <i>Face-centered</i>) </th></tr> <tr align="center"> <th colspan="2">Triclinig (a) </th> <td>C<sub>i</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Triclinic.svg" class="mw-file-description" title="Triclinic"><img alt="Triclinic" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Triclinic.svg/80px-Triclinic.svg.png" decoding="async" width="80" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Triclinic.svg/119px-Triclinic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Triclinic.svg/159px-Triclinic.svg.png 2x" data-file-width="129" data-file-height="149" /></a></span> <p>aP </p> </td> <td> </td> <td> </td> <td> </td></tr> <tr align="center"> <th colspan="2">Monoclinig (m) </th> <td>C<sub>2h</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Monoclinic.svg" class="mw-file-description" title="Monoclinic, simple"><img alt="Monoclinic, simple" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Monoclinic.svg/80px-Monoclinic.svg.png" decoding="async" width="80" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Monoclinic.svg/119px-Monoclinic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Monoclinic.svg/159px-Monoclinic.svg.png 2x" data-file-width="114" data-file-height="143" /></a></span> <p>mP </p> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Base-centered_monoclinic.svg" class="mw-file-description" title="Monoclinic, centered"><img alt="Monoclinic, centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Base-centered_monoclinic.svg/80px-Base-centered_monoclinic.svg.png" decoding="async" width="80" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Base-centered_monoclinic.svg/119px-Base-centered_monoclinic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Base-centered_monoclinic.svg/159px-Base-centered_monoclinic.svg.png 2x" data-file-width="114" data-file-height="143" /></a></span> <p>mS </p> </td> <td> </td> <td> </td></tr> <tr align="center"> <th colspan="2">Orthorhombig (o) </th> <td>D<sub>2h</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Orthorhombic.svg" class="mw-file-description" title="Orthorhombic, simple"><img alt="Orthorhombic, simple" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Orthorhombic.svg/80px-Orthorhombic.svg.png" decoding="async" width="80" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Orthorhombic.svg/120px-Orthorhombic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Orthorhombic.svg/160px-Orthorhombic.svg.png 2x" data-file-width="108" data-file-height="142" /></a></span> <p>oP </p> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Base-centered_orthorhombic.svg" class="mw-file-description" title="Orthorhombic, base-centered"><img alt="Orthorhombic, base-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Base-centered_orthorhombic.svg/80px-Base-centered_orthorhombic.svg.png" decoding="async" width="80" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Base-centered_orthorhombic.svg/120px-Base-centered_orthorhombic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Base-centered_orthorhombic.svg/160px-Base-centered_orthorhombic.svg.png 2x" data-file-width="108" data-file-height="142" /></a></span> <p>oS </p> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Body-centered_orthorhombic.svg" class="mw-file-description" title="Orthorhombic, body-centered"><img alt="Orthorhombic, body-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Body-centered_orthorhombic.svg/80px-Body-centered_orthorhombic.svg.png" decoding="async" width="80" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Body-centered_orthorhombic.svg/120px-Body-centered_orthorhombic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Body-centered_orthorhombic.svg/160px-Body-centered_orthorhombic.svg.png 2x" data-file-width="108" data-file-height="142" /></a></span> <p>oI </p> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Face-centered_orthorhombic.svg" class="mw-file-description" title="Orthorhombic, face-centered"><img alt="Orthorhombic, face-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Face-centered_orthorhombic.svg/80px-Face-centered_orthorhombic.svg.png" decoding="async" width="80" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Face-centered_orthorhombic.svg/120px-Face-centered_orthorhombic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Face-centered_orthorhombic.svg/160px-Face-centered_orthorhombic.svg.png 2x" data-file-width="108" data-file-height="142" /></a></span> <p>oF </p> </td></tr> <tr align="center"> <th colspan="2">Tetragonol (t) </th> <td>D<sub>4h</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Tetragonal.svg" class="mw-file-description" title="Tetragonal, simple"><img alt="Tetragonal, simple" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Tetragonal.svg/80px-Tetragonal.svg.png" decoding="async" width="80" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Tetragonal.svg/120px-Tetragonal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Tetragonal.svg/160px-Tetragonal.svg.png 2x" data-file-width="108" data-file-height="165" /></a></span> <p>tP </p> </td> <td> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Body-centered_tetragonal.svg" class="mw-file-description" title="Tetragonal, body-centered"><img alt="Tetragonal, body-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Body-centered_tetragonal.svg/80px-Body-centered_tetragonal.svg.png" decoding="async" width="80" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Body-centered_tetragonal.svg/120px-Body-centered_tetragonal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Body-centered_tetragonal.svg/160px-Body-centered_tetragonal.svg.png 2x" data-file-width="108" data-file-height="165" /></a></span> <p>tI </p> </td> <td> </td></tr> <tr align="center"> <th rowspan="2">Hecsagonol (h) </th> <th>Rhombohedrol </th> <td>D<sub>3d</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Rhombohedral.svg" class="mw-file-description" title="Rhombohedral"><img alt="Rhombohedral" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Rhombohedral.svg/80px-Rhombohedral.svg.png" decoding="async" width="80" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Rhombohedral.svg/120px-Rhombohedral.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Rhombohedral.svg/160px-Rhombohedral.svg.png 2x" data-file-width="139" data-file-height="141" /></a></span> <p>hR </p> </td> <td> </td> <td> </td> <td> </td></tr> <tr align="center"> <th>Hecsagonol </th> <td>D<sub>6h</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Hexagonal_latticeFRONT.svg" class="mw-file-description" title="Hexagonal"><img alt="Hexagonal" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Hexagonal_latticeFRONT.svg/80px-Hexagonal_latticeFRONT.svg.png" decoding="async" width="80" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Hexagonal_latticeFRONT.svg/120px-Hexagonal_latticeFRONT.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Hexagonal_latticeFRONT.svg/160px-Hexagonal_latticeFRONT.svg.png 2x" data-file-width="160" data-file-height="206" /></a></span> <p>hP </p> </td> <td> </td> <td> </td> <td> </td></tr> <tr align="center"> <th colspan="2">Ciwbig (c) </th> <td>O<sub>h</sub> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Cubic.svg" class="mw-file-description" title="Cubic, simple"><img alt="Cubic, simple" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Cubic.svg/80px-Cubic.svg.png" decoding="async" width="80" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Cubic.svg/120px-Cubic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Cubic.svg/160px-Cubic.svg.png 2x" data-file-width="109" data-file-height="127" /></a></span> <p>cP </p> </td> <td> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Cubic-body-centered.svg" class="mw-file-description" title="Cubic, body-centered"><img alt="Cubic, body-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cubic-body-centered.svg/80px-Cubic-body-centered.svg.png" decoding="async" width="80" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cubic-body-centered.svg/120px-Cubic-body-centered.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Cubic-body-centered.svg/160px-Cubic-body-centered.svg.png 2x" data-file-width="109" data-file-height="127" /></a></span> <p>cI </p> </td> <td><span typeof="mw:File"><a href="/wiki/Delwedd:Cubic-face-centered.svg" class="mw-file-description" title="Cubic, face-centered"><img alt="Cubic, face-centered" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Cubic-face-centered.svg/80px-Cubic-face-centered.svg.png" decoding="async" width="80" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Cubic-face-centered.svg/120px-Cubic-face-centered.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Cubic-face-centered.svg/160px-Cubic-face-centered.svg.png 2x" data-file-width="862" data-file-height="1002" /></a></span> <p>cF </p> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <p>Mae gan y system symlaf a mwyaf cymesur, y system giwbig neu isometrig, gymesuredd ciwb, sy'n arddangos pedair echelin cylchdro triphlyg wedi'i chyfeirio ar 109.5° (yr ongl tetrahedrol) mewn perthynas â'i gilydd. Gorwedd yr echelinau triphlyg hyn ar hyd croesliniau corff y ciwb. Y chwe system dellt arall, yw hecsagonol, tetragonol, rhombohedral (sy'n aml wedi'u drysu â'r system grisial drigonol), orthorhombig, monoclinig a thriclinig. </p> <div class="mw-heading mw-heading4"><h4 id="Dellt_Bravais">Dellt Bravais</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=8" title="Golygu'r adran: Dellt Bravais" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=8" title="Edit section's source code: Dellt Bravais"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Disgrifia delltau Bravais (cyfeirir atynt hefyd fel delltau gofod) trefniant geometrig y pwyntiau dellt, ac felly cymesuredd trosiadol crisial. Mae tri dimensiwn gofod yn rhoi 14 dellten Bravais unigryw sy'n disgrifio'r cymesuredd trosiadol. Mae'r holl ddefnyddiau crisialog a gydnabyddir heddiw, heb gynnwys lled-grisialau, yn ffitio yn un o'r trefniadau hyn. Mae'r pedwar ar ddeg dellten tri dimensiwn, wedi'u dosbarthu yn ôl system dellt, i'w gweld uchod. </p><p>Cynhwysa'r strwythur grisial yr un grŵp o atomau, y <i>sail</i>, wedi'i leoli o amgylch pob pwynt dellt. Mae'r grŵp hwn o atomau felly'n ailadrodd am gyfnod amhenodol mewn tri dimensiwn yn unol â threfniant un o ddelltau Bravais. Disgrifir cylchdro nodweddiadol a chymesuredd drych y gell uned gan ei <a href="/w/index.php?title=Gr%C5%B5p_pwyntiau_grisiallograffig&action=edit&redlink=1" class="new" title="Grŵp pwyntiau grisiallograffig (dim tudalen ar gael)">grŵp pwyntiau grisiallograffig</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Systemau_crisial">Systemau crisial</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=9" title="Golygu'r adran: Systemau crisial" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=9" title="Edit section's source code: Systemau crisial"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>System crisial yw set o grwpiau pwynt ble mae'r grwpiau pwynt eu hunain a'u grwpiau gofod cyfatebol yn cael eu neilttuo i system dellt. O'r 32 grŵp pwynt sy'n bodoli mewn tri dimensiwn, mae'r mwyafrif yn cael eu neilltuo i un system dellt yn unig, ac os felly mae gan y system grisial a'r system dellt yr un enw. Fodd bynnag, mae grwpiau pum pwynt yn cael eu neilltuo i ddwy system dellt, rhombohedral a hecsagonol, oherwydd bod y ddwy system dellt yn arddangos cymesuredd cylchdro triphlyg. Mae'r grwpiau pwynt hyn yn cael eu neilltuo i'r system grisial driongl. </p> <table class="wikitable"> <tbody><tr> <th>Teulu crisial </th> <th>System crisial </th> <th>Grŵp pwynt / Dosbarth crisial </th> <th>Nodiant Schönflies </th> <th>Cyfesurynnau pwynt </th> <th>Trefn </th> <th>Grŵp haniaethol </th></tr> <tr> <th colspan="2" rowspan="2">triclinig </th> <td>pediol </td> <td>C<sub>1</sub> </td> <td>pegynol enantiomorffig </td> <td>1 </td> <td>pitw <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 \mathbb {Z} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22e4eb51c96c79903d07a9536cdc8bca1c8368b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{1}}"></span> </td></tr> <tr> <td>pinacoidol </td> <td>C<sub>i</sub> (S<sub>2</sub>) </td> <td>canol-cymesurol </td> <td>2 </td> <td>cylchol <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 \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92aedfb5c02eff978ab963421ce930f46801657e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th colspan="2" rowspan="3">monoclinig </th> <td>sffenoidol </td> <td>C<sub>2</sub> </td> <td>pegynol enantiomorffig </td> <td>2 </td> <td>cylchol <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 \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92aedfb5c02eff978ab963421ce930f46801657e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>domatig </td> <td>C<sub>s</sub> (C<sub>1h</sub>) </td> <td>pegynol </td> <td>2 </td> <td>cylchol <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 \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92aedfb5c02eff978ab963421ce930f46801657e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>prismatig </td> <td>C<sub>2h</sub> </td> <td>canol-cymesurol </td> <td>4 </td> <td>pedwar Klein <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 \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">V</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fdd869d1a779597248750d08295bf5a29144515" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.826ex; height:2.509ex;" alt="{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th colspan="2" rowspan="3">orthorhombig </th> <td>rhombig-deusffenoidol </td> <td>D<sub>2</sub> (V) </td> <td>enantiomorffig </td> <td>4 </td> <td>pedwar Klein <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 \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">V</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fdd869d1a779597248750d08295bf5a29144515" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.826ex; height:2.509ex;" alt="{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>rhombig-pyramidol </td> <td>C<sub>2v</sub> </td> <td>pegynol </td> <td>4 </td> <td>pedwar Klein <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 \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">V</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fdd869d1a779597248750d08295bf5a29144515" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.826ex; height:2.509ex;" alt="{\displaystyle \mathbb {V} =\mathbb {Z} _{2}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>rhombig-deubyramidol </td> <td>D<sub>2h</sub> (V<sub>h</sub>) </td> <td>canol-cymesurol </td> <td>8 </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 \mathbb {V} \times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">V</mi> </mrow> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {V} \times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11d22542371d147128450f033b6d50a2784e68cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.123ex; height:2.509ex;" alt="{\displaystyle \mathbb {V} \times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th colspan="2" rowspan="7">tetragonol </th> <td>tetragonol-pyramidol </td> <td>C<sub>4</sub> </td> <td>pegynol enantiomorffig </td> <td>4 </td> <td>cylchol <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 \mathbb {Z} _{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ecbc000fbd9a59f44ec7502f5e4f4b24f9a8e06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{4}}"></span> </td></tr> <tr> <td>tetragonol-deusffenoidol </td> <td>S<sub>4</sub> </td> <td>di-ganol-cymesurol </td> <td>4 </td> <td>cylchol <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 \mathbb {Z} _{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ecbc000fbd9a59f44ec7502f5e4f4b24f9a8e06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{4}}"></span> </td></tr> <tr> <td>tetragonol-deubyramidol </td> <td>C<sub>4h</sub> </td> <td>canol-cymesurol </td> <td>8 </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 \mathbb {Z} _{4}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{4}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c214eeccdf84020b1a9b39b77d906cca7a68a63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.05ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{4}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>tetragonol-trapesohedrol </td> <td>D<sub>4</sub> </td> <td>enantiomorffig </td> <td>8 </td> <td>deuhedrol <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 \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43381980f390e931b1692bebaeb35cab24a95037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.88ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deudetragonol-pyramidol </td> <td>C<sub>4v</sub> </td> <td>pegynol </td> <td>8 </td> <td>deuhedrol <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 \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43381980f390e931b1692bebaeb35cab24a95037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.88ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>tetragonol-scalenohedrol </td> <td>D<sub>2d</sub> (V<sub>d</sub>) </td> <td>di-ganol-cymesurol </td> <td>8 </td> <td>deuhedrol <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 \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43381980f390e931b1692bebaeb35cab24a95037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.88ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{8}=\mathbb {Z} _{4}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deudetragonol-deubyramidol </td> <td>D<sub>4h</sub> </td> <td>canol-cymesurol </td> <td>16 </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 \mathbb {D} _{8}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{8}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3c660cbdd2611e1ec49640246ecb36faf44631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.177ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{8}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th rowspan="12">hecsagonol </th> <th rowspan="5">trigonol </th> <td>trigonol-pyramidol </td> <td>C<sub>3</sub> </td> <td>pegynol enantiomorffig </td> <td>3 </td> <td>cylchol <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 \mathbb {Z} _{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a5bb50b04d35fa08317c86cee60d88729c80ffa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{3}}"></span> </td></tr> <tr> <td>rhombohedrol </td> <td>C<sub>3i</sub> (S<sub>6</sub>) </td> <td>canol-cymesurol </td> <td>6 </td> <td>cylchol <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 \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c061461954d2f9b45de673119ec32aa863b9863" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.753ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>trigonol-trapesohedrol </td> <td>D<sub>3</sub> </td> <td>enantiomorffig </td> <td>6 </td> <td>deuhedrol <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 \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13a1fb4f7536f9856768ba8fcd8ee7c7f2f31328" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.88ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deudrigonol-pyramidol </td> <td>C<sub>3v</sub> </td> <td>pegynol </td> <td>6 </td> <td>deuhedrol <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 \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13a1fb4f7536f9856768ba8fcd8ee7c7f2f31328" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.88ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{6}=\mathbb {Z} _{3}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deudrigonol-scalenohedrol </td> <td>D<sub>3d</sub> </td> <td>canol-cymesurol </td> <td>12 </td> <td>deuhedrol <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 \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1045e40007d60804fd64cb01ed506615066b4c06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.702ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th rowspan="7">hecsagonol </th> <td>hecsagonol-pyramidol </td> <td>C<sub>6</sub> </td> <td>pegynol enantiomorffig </td> <td>6 </td> <td>cylchol <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 \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c061461954d2f9b45de673119ec32aa863b9863" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.753ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>trigonol-deubyramidol </td> <td>C<sub>3h</sub> </td> <td>di-ganol-cymesurol </td> <td>6 </td> <td>cylchol <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 \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c061461954d2f9b45de673119ec32aa863b9863" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.753ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{6}=\mathbb {Z} _{3}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>hecsagonol-deubyramidol </td> <td>C<sub>6h</sub> </td> <td>canol-cymesurol </td> <td>12 </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 \mathbb {Z} _{6}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{6}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abf2d6878d5dae53088e07db7e20b71bfcec16d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.05ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{6}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>hecsagonol-trapesohedrol </td> <td>D<sub>6</sub> </td> <td>enantiomorffig </td> <td>12 </td> <td>deuhedrol <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 \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1045e40007d60804fd64cb01ed506615066b4c06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.702ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deuhecsagonol-pyramidol </td> <td>C<sub>6v</sub> </td> <td>pegynol </td> <td>12 </td> <td>deuhedrol <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 \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1045e40007d60804fd64cb01ed506615066b4c06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.702ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deudrigonol-deubyramidol </td> <td>D<sub>3h</sub> </td> <td>di-ganol-cymesurol </td> <td>12 </td> <td>deuhedrol <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 \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mo>⋊</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1045e40007d60804fd64cb01ed506615066b4c06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.702ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{12}=\mathbb {Z} _{6}\rtimes \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>deuhexagonol-deubyramidol </td> <td>D<sub>6h</sub> </td> <td>canol-cymesurol </td> <td>24 </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 \mathbb {D} _{12}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">D</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {D} _{12}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbac7ec7a27880ab811591ab766d2fffa60295d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.999ex; height:2.509ex;" alt="{\displaystyle \mathbb {D} _{12}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <th colspan="2" rowspan="5">ciwbig </th> <td>tetartoidol </td> <td>T </td> <td>enantiomorffig </td> <td>12 </td> <td>eiledol <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 \mathbb {A} _{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {A} _{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e7acd8ad27cb4342f35187c9afa0ce9104d2d41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.732ex; height:2.509ex;" alt="{\displaystyle \mathbb {A} _{4}}"></span> </td></tr> <tr> <td>deubloidol </td> <td>T<sub>h</sub> </td> <td>canol-cymesurol </td> <td>24 </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 \mathbb {A} _{4}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {A} _{4}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2308f1d6f714a8482eea8b31da709ddad71f73b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.177ex; height:2.509ex;" alt="{\displaystyle \mathbb {A} _{4}\times \mathbb {Z} _{2}}"></span> </td></tr> <tr> <td>gyroidol </td> <td>O </td> <td>enantiomorffig </td> <td>24 </td> <td>cymesurol <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 \mathbb {S} _{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {S} _{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f807871dca6564e17b1f3b2ab98b485c6ddb66da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.347ex; height:2.509ex;" alt="{\displaystyle \mathbb {S} _{4}}"></span> </td></tr> <tr> <td>hecstetrahedrol </td> <td>T<sub>d</sub> </td> <td>di-ganol-cymesurol </td> <td>24 </td> <td>cymesurol <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 \mathbb {S} _{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {S} _{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f807871dca6564e17b1f3b2ab98b485c6ddb66da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.347ex; height:2.509ex;" alt="{\displaystyle \mathbb {S} _{4}}"></span> </td></tr> <tr> <td>hecsoctahedrol </td> <td>O<sub>h</sub> </td> <td>canol-cymesurol </td> <td>48 </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 \mathbb {S} _{4}\times \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {S} _{4}\times \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8a663102b36261cec5e8110ba2081fde432541f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.792ex; height:2.509ex;" alt="{\displaystyle \mathbb {S} _{4}\times \mathbb {Z} _{2}}"></span> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <p>Yn ei gyfanrwydd, mae saith system crisial: triclinig, monoclinig, orthorhombig, tetragonol, trigonol, hecsagonol, a ciwbig. </p><p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Grwpiau_pwynt">Grwpiau pwynt</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=10" title="Golygu'r adran: Grwpiau pwynt" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=10" title="Edit section's source code: Grwpiau pwynt"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Gr%C5%B5p_pwynt_crisialog&action=edit&redlink=1" class="new" title="Grŵp pwynt crisialog (dim tudalen ar gael)">Grŵp pwynt crisialog</a> neu <i>ddosbarth grisial</i> yw'r grŵp mathemategol sy'n cynnwys y gweithrediadau cymesuredd sy'n gadael ymddangosiad y strwythur grisial heb ei newid gydag o leiaf un pwynt heb ei symud. Mae'r gweithrediadau cymesuredd hyn yn cynnwys </p> <ul><li><i>Adlewyrchiad</i>, sy'n adlewyrchu'r strwythur ar draws <i>plân adlewyrchiad</i></li> <li>Cylchdroi, sy'n cylchdroi'r strwythur mewn mudiad cylch o amgylch <i>echelin cylchdro</i></li> <li>Gwrthdroad, sy'n newid arwydd cyfesuryn pob pwynt mewn perthynas â <i>chanolfan cymesuredd</i> neu <i>bwynt gwrthdroi</i></li> <li>Cylchdroi amhriodol, sy'n cynnwys cylchdro o amgylch echelin ac yna gwrthdroad.</li></ul> <p>Gelwir echelinau cylchdroi (priodol ac amhriodol), planau adlewyrchiad, a chanolfannau cymesuredd gyda'i gilydd yn <i>elfennau cymesuredd</i>. Mae yna 32 o ddosbarthiadau crisial posibl. Gellir dosbarthu pob un yn un o'r saith system grisial. </p> <div class="mw-heading mw-heading3"><h3 id="Grwpiau_gofod">Grwpiau gofod</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=11" title="Golygu'r adran: Grwpiau gofod" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=11" title="Edit section's source code: Grwpiau gofod"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Yn ogystal â gweithrediadau'r grŵp pwynt, mae grŵp gofod y strwythur grisial yn cynnwys gweithrediadau cymesuredd trosiadol. Mae'r rhain yn cynnwys: </p> <ul><li>Trawsfudiadau pur, sy'n symud pwynt ar hyd fector</li> <li>Echelinau sgriw, sy'n cylchdroi pwynt o amgylch echelin wrth drosi'n gyfochrog â'r echelin</li> <li>Planau llithro, sy'n adlewyrchu pwynt trwy blân wrth ei drosi'n baralel â phlân.</li></ul> <p>Mae yna 230 grŵp gofod gwahanol. </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Cydlyniad_atomig">Cydlyniad atomig</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=12" title="Golygu'r adran: Cydlyniad atomig" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=12" title="Edit section's source code: Cydlyniad atomig"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trwy ystyried trefniant atomau mewn perthynas â'i gilydd, eu niferoedd cydlynnu (neu nifer y cymdogion agosaf), pellteroedd rhyngatomig, mathau o fondio, ac ati, mae'n bosibl ffurfio barn gyffredinol o'r strwythurau a ffyrdd amgen o'u delweddu. </p> <div class="mw-heading mw-heading3"><h3 id="Pacio_agos">Pacio agos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=13" title="Golygu'r adran: Pacio agos" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=13" title="Edit section's source code: Pacio agos"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Close_packing.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Close_packing.svg/290px-Close_packing.svg.png" decoding="async" width="290" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Close_packing.svg/435px-Close_packing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Close_packing.svg/580px-Close_packing.svg.png 2x" data-file-width="1063" data-file-height="669" /></a><figcaption>Dellt pacio agos hecsagonol (hcp) ar y chwith a dellt ciwbig wyneb-ganolog (fcc) ar y dde.</figcaption></figure> <p>Gellir deall yr egwyddorion dan sylw trwy ystyried y ffordd fwyaf effeithlon o bacio sfferau maint cyfartal a phentyrru planau atomig wedi eu pacio'n agos mewn tri dimensiwn. Er enghraifft, os yw plân A yn gorwedd o dan plân B, mae dwy ffordd bosibl o osod atom ychwanegol ar ben haen B. Pe bai haen ychwanegol yn cael ei gosod yn union dros plân A, byddai hyn yn arwain at y gyfres ganlynol: </p> <dl><dd>...<b>ABABABAB</b>...</dd></dl> <p>Adnabyddir y trefniant hyn o atomau mewn crisial fel pacio agos hecsagonol <b>(hcp - <i>hexagonal close packing</i>)</b>. </p><p>Fodd bynnag, os yw'r tair plân wedi'u gwasgaru mewn perthynas â'i gilydd, ac nad yw'r dilyniant yn cael ei ailadrodd tan i'r bedwaredd haen gael ei gosod yn union dros plân A, yna mae'r dilyniant canlynol yn codi: </p> <dl><dd>...<b>ABCABCABC</b>...</dd></dl> <p>Adnabyddir y math hyn o drefniant strwythurol fel pacio agos ciwbig <b>(ccp - <i>cubic close packing</i>)</b>. </p><p>Cell uned trefniant pacio agos ciwbig (ccp) o atomau yw cell uned ciwbig wyneb-ganolog (fcc). Nid yw hyn yn amlwg ar unwaith gan fod yr haenau sydd wedi'u pacio'n agos yn baralel i blanau {111} cell uned ciwbig wyneb-ganolog (fcc). Mae pedwar cyfeiriadedd gwahanol i'r haenau sydd wedi eu pacio'n agos. </p><p>Gellir cyfrifo'r <b>effeithlonrwydd pacio</b> trwy rannu cyfanswm cyfaint y sfferau a'u rhannu dros cyfaint y gell, fel y ganlyn: </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 {4\times {\frac {4}{3}}\pi r^{3}}{16{\sqrt {2}}r^{3}}}={\frac {\pi }{3{\sqrt {2}}}}=0.7405...}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>16</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mrow> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.7405...</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4\times {\frac {4}{3}}\pi r^{3}}{16{\sqrt {2}}r^{3}}}={\frac {\pi }{3{\sqrt {2}}}}=0.7405...}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a19742185aa64f6df3b9c465e41626f5cb02d129" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:29.625ex; height:7.509ex;" alt="{\displaystyle {\frac {4\times {\frac {4}{3}}\pi r^{3}}{16{\sqrt {2}}r^{3}}}={\frac {\pi }{3{\sqrt {2}}}}=0.7405...}"></span></dd></dl> <p>Effeithlonrwydd pacio o 74% yw'r dwysedd mwyaf posib mewn cell uned wedi ei greu o sfferau o un maint yn unig. Mae'r mwyafrif o ffurfiau crisialog o elfenau metel yn pacio agos hecsagonol (hcp), ciwbig wyneb-ganolog (fcc) neu giwbig corff-ganolog (bcc). <a href="/w/index.php?title=Rhif_cydlyniad&action=edit&redlink=1" class="new" title="Rhif cydlyniad (dim tudalen ar gael)">Rhif cydlyniad</a> atomau mewn strwythurau hcp a fcc yw 12, a'i <a href="/w/index.php?title=Ffactor_pacio_atomig&action=edit&redlink=1" class="new" title="Ffactor pacio atomig (dim tudalen ar gael)">ffactor pacio atomig</a> (APF - <i>atomic packing factor</i>) yw'r rhif a gyflynwyd uchod, 0.74. Gellir cymharu hyn gyda APF strwythur bcc, sy'n 0.68. </p> <div class="mw-heading mw-heading2"><h2 id="Ffiniau_graen">Ffiniau graen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=14" title="Golygu'r adran: Ffiniau graen" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=14" title="Edit section's source code: Ffiniau graen"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ffiniau graen yw rhyngwynebau ble mae crisialau o gyfeiriadau gwahanol yn cwrdd. Mae <a href="/w/index.php?title=Ffin_graen&action=edit&redlink=1" class="new" title="Ffin graen (dim tudalen ar gael)">ffin graen</a> yn rhyngwyneb un-gwedd, gyda chrisialau y naill ochr i'r ffin yn union yr un fath ac eithrio mewn cyfeiriadedd. Er yn gywir, prin y defnyddir y term "ffin grisialaidd (<i>crystallite</i>)". Cynhwysa ffiniau graen ardaloedd ble mae atomau wedi'u haflonyddu o'u safleoedd dellt gwreiddiol, <a href="/w/index.php?title=Dadleoliadau&action=edit&redlink=1" class="new" title="Dadleoliadau (dim tudalen ar gael)">dadleoliadau</a>, ac amhureddau sydd wedi mudo i'r ffin graen egni is. </p><p>Trwy drin ffin graen yn geometrig fel rhyngwyneb o grisial sengl wedi'i dorri'n ddwy ran, gydag un ohonynt wedi'i gylchdroi, gwelwn fod angen pum newidyn i ddiffinio ffin graen. Daw'r ddau rif cyntaf o'r uned fector sy'n pennu echelin cylchdro. Mae'r trydydd rhif yn dynodi ongl cylchdroi'r graen. Mae'r ddau rif olaf yn nodi plân y ffin graen (neu uned fector sy'n normal i'r plân hwn). </p><p>Mae ffiniau graen yn tarfu ar symudiad dadleoliadau trwy ddefnydd, felly mae lleihau maint grisialaidd yn ffordd gyffredin o wella cryfder, fel y disgrifir gan y berthynas <a href="/w/index.php?title=Hall-Petch&action=edit&redlink=1" class="new" title="Hall-Petch (dim tudalen ar gael)">Hall-Petch</a>. Gan fod ffiniau graen yn ddiffygion yn y strwythur crisial, maent yn tueddu i leihau dargludedd trydanol a thermol y defnydd. Mae'r egni rhyngwynebol uchel a'r bondio cymharol wan yn y rhan fwyaf o ffiniau graen, yn aml, yn eu gwneud yn safleoedd a ffafrir ar gyfer dechrau cyrydiad ac ar gyfer dyddodiad gweddau newydd o'r solid. Maent hefyd yn bwysig i lawer o fecanweithiau <a href="/w/index.php?title=Ymgripiad&action=edit&redlink=1" class="new" title="Ymgripiad (dim tudalen ar gael)">ymgripiad</a>. </p><p>Yn gyffredinol, dim ond ychydig o nanometrau o led yw ffiniau graen. Mewn defnyddiau cyffredin, mae grisialaidd (<i>crystallite</i>) yn ddigon mawr fel bod ffiniau graen yn ffracsiwn bach o'r defnydd. Fodd bynnag, mae meintiau graen bach iawn yn bosib. Mewn solidau nanogrisialog, mae ffiniau graen yn dod yn ffracsiwn sylweddol o gyfaint defnydd, gydag effeithiau dwys ar nodweddion megis <a href="/w/index.php?title=Trylediad&action=edit&redlink=1" class="new" title="Trylediad (dim tudalen ar gael)">trylediad</a> a <a href="/w/index.php?title=Phlastigrwydd&action=edit&redlink=1" class="new" title="Phlastigrwydd (dim tudalen ar gael)">phlastigrwydd</a>. Mewn crisialaidd (crystallite) bach, wrth i ffracsiwn cyfaint y ffiniau graen agosáu at 100%, mae'r deunydd yn peidio â chael unrhyw gymeriad crisialog, ac felly'n dod yn solet amorffaidd. </p> <div class="mw-heading mw-heading2"><h2 id="Diffygion_ac_amhureddau">Diffygion ac amhureddau</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=15" title="Golygu'r adran: Diffygion ac amhureddau" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=15" title="Edit section's source code: Diffygion ac amhureddau"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bydd crisialau go iawn yn cynnwys diffygion neu afreoleidd-dra a ddisgrifir uchod. Y namau hyn sy'n pennu llawer o briodweddau trydanol a mecanyddol deunyddiau go iawn. Pan fydd un atom yn cymryd lle un o'r prif gydrannau atomig o fewn y strwythur crisial, gall newid briodweddau trydanol a thermol y deunydd. Gall amhureddau hefyd ddod i'r amlwg fel amhureddau sbin electronau mewn rhai deunyddiau. Mae ymchwil ar amhureddau magnetig yn dangos y gall grynodiadau bach o amhuredd arwain at newidiadau sylweddol, megis gwres penodol. Er enghraifft, gall amhureddau mewn aloiau fferromagnetig lled-ddargludol arwain at newidiadau sylweddol, fel y rhagwelwyd gyntaf ddiwedd y 1960au. Mae dadleoliadau yn y dellt grisial yn golygu bod angen llai o groesrym i'w hollti, o'i gymharu â'r hyn sydd ei angen ar gyfer strwythur crisial perffaith. </p> <div class="mw-heading mw-heading2"><h2 id="Rhagdybiaeth_strwythur">Rhagdybiaeth strwythur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=16" title="Golygu'r adran: Rhagdybiaeth strwythur" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=16" title="Edit section's source code: Rhagdybiaeth strwythur"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ers erioed, mae hi wedi bod yn anodd dylunio a modelu strwythurau crisial yn gyfrifiadurol, yn seiliedig ar wybodaeth am gyfansoddiadau cemegol. Bellach mae'n bosib rhagdybio strwythurau gyda chymhlethdod canolig, gan ddefnyddio dulliau megis samplu ar hap, metadynameg neu algorithmau esblygiadol; hyn oll yn bosib wrth gyfrifiaduron perfformiad uchel ac algorithmau mwy pwerus. </p><p>Fel arfer, bydd strwythurau crisial o solidau ionig syml, megis NaCl (halen cyffredin), yn cael eu rhesymoli yn nhermau rheolau Pauling, a osodwyd yn gyntaf yn 1929 gan <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a>. Ystyriwyd Pauling yn "tad y bond cemegol" a bu'n ystyried natur grymoedd rhyngatomig mewn metelau. Daeth i gasgliad bod hanner o'r pum orbital-d metelau trosiannol yn rhan o fondio, gyda'r orbitalau-d difondio sy'n weddill yn gyfrifol am y priodweddau magnetig. Yr oedd felly'n gallu cydberthyn y nifer o orbitalau-d wrth ffurfio bond gyda hyd y bond, yn ogystal â llawer o briodweddau ffisegol y sylwedd. Wedi hynny, cyflwynodd yr orbital metelaidd, orbital ychwanegol sy'n angenrheidiol i ganiatáu cyseiniant di-rwystr bondiau falens, ymhlith strwythurau electronig amrywiol. </p><p>Yn <a href="/w/index.php?title=Namcaniaeth_bond_falens_cyseiniol&action=edit&redlink=1" class="new" title="Namcaniaeth bond falens cyseiniol (dim tudalen ar gael)">namcaniaeth bond falens cyseiniol</a>, bydd egni cyseiniad ymhlith safloedd rhyngatomig yn dylanwadu ar ddetholiad un o blith strwythurau crisial o gyfansoddiad metelaidd neu ryngfetelaidd. Mae'n amlwg y byddai rhai moddau cyseiniant yn gwneud mwy o gyfraniadau (yn fwy sefydlog yn fecanyddol nag eraill), ac y byddai cymhareb syml o nifer bondiau i nifer safleoedd yn arbennig. Yr egwyddor sy'n deillio o hyn yw bod sefydlogrwydd arbennig yn gysylltiedig â'r cymarebau neu'r "rhifau bond" symlaf: 1⁄2, 1⁄3, 2⁄3, 1⁄4, 3⁄4, ac ati. Mae'r dewis o strwythur a gwerth y gymhareb echelinol (sy'n pennu hyd y bondiau cymharol) yn ganlyniad i ymdrech atom i ddefnyddio ei falens wrth ffurfio bondiau sefydlog, gyda rhifau bond ffracsiynol syml. </p><p>Wedi myfyrio ar gydberthynas uniongyrchol rhwng crynodiad electronau a strwythur grisial mewn aloion beta-wedd, dadansoddodd <a href="/w/index.php?title=Hume-Rothery&action=edit&redlink=1" class="new" title="Hume-Rothery (dim tudalen ar gael)">Hume-Rothery</a> y tueddiadau mewn ymdoddbwyntiau, cywasgedd a hyd bondiau fel ffwythiant rhif grŵp yn y tabl cyfnodol, er mwyn sefydlu system o falensau o'r elfennau trosiannol yn y cyflwr metelaidd.<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> Yr oedd y driniaeth hon felly'n pwysleisio cryfder bondiau cynyddol fel ffwythiant rhif grŵp. Pwysleisiwyd gweithrediad grymoedd cyfeiriadol mewn un erthygl ar y berthynas rhwng hybridau bondiau a'r strwythurau metelaidd. Mae'r gydberthynas canlyniadol rhwng strwythurau electronig a grisialaidd yn cael ei grynhoi gan un paramedr, sef pwysau electronau-d fesul orbital metelaidd hybrid. Mae'r "pwysau-d" yn cyfrifo 0.5, 0.7 a 0.9 ar gyfer y strwythurau fcc, hcp a bcc yn y drefn honno. Felly, mae'r berthynas rhwng electronau-d a strwythur crisial yn dod i'r amlwg. </p><p>Mewn rhagfynegiadau/efelychiadau strwythur crisial cymwysir cyfnodoldeb fel arfer, gan fod y system yn cael ei ddychmygu fel un diderfyn ym mhob cyfeiriad. Gan ddechrau gyda strwythur triclinig heb unrhyw briodwedd cymesuredd pellach yn cael ei dybio, gellir gyrru'r system i ddangos rhai priodweddau cymesuredd ychwanegol trwy gymhwyso <a href="/w/index.php?title=Ail_Ddeddf_Newton&action=edit&redlink=1" class="new" title="Ail Ddeddf Newton (dim tudalen ar gael)">Ail Ddeddf Newton</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> Caiff hyn ei wneud ar ronynnau yn y gell uned a hafaliad dynamig a ddatblygwyd yn ddiweddar ar gyfer fectorau cyfnod y system (paramedrau dellt gan gynnwys onglau), hyd yn oed os yw'r system yn destun straen allanol. </p> <div class="mw-heading mw-heading2"><h2 id="Cyfeiriadau">Cyfeiriadau</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Strwythur_crisial&veaction=edit&section=17" title="Golygu'r adran: Cyfeiriadau" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Strwythur_crisial&action=edit&section=17" title="Edit section's source code: Cyfeiriadau"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <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"><span class="citation Journal">Hume-rothery, W.; Irving, H. M.; Williams, R. J. P. (1951). "The Valencies of the Transition Elements in the Metallic State" (yn en). <i><a href="/w/index.php?title=Proceedings_of_the_Royal_Society_A&action=edit&redlink=1" class="new" title="Proceedings of the Royal Society A (dim tudalen ar gael)">Proceedings of the Royal Society A</a></i> <b>208</b> (1095): 431. <a href="/w/index.php?title=Bibcode&action=edit&redlink=1" class="new" title="Bibcode (dim tudalen ar gael)">Bibcode</a> <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1951RSPSA.208..431H">1951RSPSA.208..431H</a>. <a href="/wiki/Digital_object_identifier" class="mw-redirect" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098%2Frspa.1951.0172">10.1098/rspa.1951.0172</a>.</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="citation Journal">Liu, Gang (2015). "Dynamical equations for the period vectors in a periodic system under constant external stress" (yn en). <i><a href="/w/index.php?title=Can._J._Phys.&action=edit&redlink=1" class="new" title="Can. J. Phys. (dim tudalen ar gael)">Can. J. Phys.</a></i> <b>93</b> (9): 974–978. <a href="/w/index.php?title=ArXiv&action=edit&redlink=1" class="new" title="ArXiv (dim tudalen ar gael)">arXiv</a>:<a rel="nofollow" class="external text" href="http://arxiv.org/abs/cond-mat/0209372">cond-mat/0209372</a>. <a href="/w/index.php?title=Bibcode&action=edit&redlink=1" class="new" title="Bibcode (dim tudalen ar gael)">Bibcode</a> <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/2015CaJPh..93..974L">2015CaJPh..93..974L</a>. <a href="/wiki/Digital_object_identifier" class="mw-redirect" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1139%2Fcjp-2014-0518">10.1139/cjp-2014-0518</a>.</span></span> </li> </ol></div></div>    </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="">Wedi dod o "<a dir="ltr" href="https://cy.wikipedia.org/w/index.php?title=Strwythur_crisial&oldid=11817595">https://cy.wikipedia.org/w/index.php?title=Strwythur_crisial&oldid=11817595</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Arbennig:Categories" title="Arbennig:Categories">Categorïau</a>: <ul><li><a href="/wiki/Categori:Grisialau" title="Categori:Grisialau">Grisialau</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Chategori cudd: <ul><li><a href="/wiki/Categori:Tudalennau_gyda_meysydd_deublyg_yn_y_Nodion" title="Categori:Tudalennau gyda meysydd deublyg yn y Nodion">Tudalennau gyda meysydd deublyg yn y Nodion</a></li><li><a href="/wiki/Categori:Erthyglau_gyda_gwybodlen_yn_gyfan_gwbl_o_Wicidata" title="Categori:Erthyglau gyda gwybodlen yn gyfan gwbl o Wicidata">Erthyglau gyda gwybodlen yn gyfan gwbl o Wicidata</a></li><li><a href="/wiki/Categori:Erthyglau_sy%27n_defnyddio_Nodyn_Gwybodlen_pethau_Wicidata" title="Categori:Erthyglau sy'n defnyddio Nodyn Gwybodlen pethau Wicidata">Erthyglau sy'n defnyddio Nodyn Gwybodlen pethau Wicidata</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"> Golygwyd y dudalen hon ddiwethaf ar 19 Mehefin 2023, am 10:49.</li> <li id="footer-info-copyright">Mae'r testun ar gael o dan <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike License</a>; gall telerau ychwanegol fod yn berthnasol. 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