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mw-first-heading"><span class="mw-page-title-main">Vacancy defect</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://de.wikipedia.org/wiki/Leerstelle" title="Leerstelle – German" lang="de" hreflang="de" data-title="Leerstelle" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Vakants_(materjaliteadus)" title="Vakants (materjaliteadus) – Estonian" lang="et" hreflang="et" data-title="Vakants (materjaliteadus)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D9%87%DB%8C%E2%80%8C%D8%AC%D8%A7%DB%8C%DB%8C" title="تهی‌جایی – Persian" lang="fa" hreflang="fa" data-title="تهی‌جایی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Lacune_(cristallographie)" title="Lacune (cristallographie) – French" lang="fr" hreflang="fr" data-title="Lacune (cristallographie)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Difetto_di_vacanza" title="Difetto di vacanza – Italian" lang="it" hreflang="it" data-title="Difetto di vacanza" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%92%D7%9D_%D7%94%D7%99%D7%A2%D7%93%D7%A8%D7%95%D7%AA" title="פגם היעדרות – Hebrew" lang="he" hreflang="he" data-title="פגם היעדרות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%BE%D1%81%D0%BE%D1%80%D1%8B%D0%BD" title="Босорын – Kazakh" lang="kk" hreflang="kk" data-title="Босорын" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%92%D0%B0%D0%BA%D0%B0%D0%BD%D1%81%D0%B8%D1%8F" title="Вакансия – Kyrgyz" lang="ky" hreflang="ky" data-title="Вакансия" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vacature-defect" title="Vacature-defect – Dutch" lang="nl" hreflang="nl" data-title="Vacature-defect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Vakansiyalar" title="Vakansiyalar – Uzbek" lang="uz" hreflang="uz" data-title="Vakansiyalar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wakans" title="Wakans – Polish" lang="pl" hreflang="pl" data-title="Wakans" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B0%D0%BA%D0%B0%D0%BD%D1%81%D0%B8%D1%8F_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Вакансия (физика) – Russian" lang="ru" hreflang="ru" data-title="Вакансия (физика)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vakanssi" title="Vakanssi – Finnish" lang="fi" hreflang="fi" data-title="Vakanssi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D0%B8%D2%B3%D0%B8%D2%B7%D0%BE%D0%B9%D3%A3" title="Тиҳиҷойӣ – Tajik" lang="tg" hreflang="tg" data-title="Тиҳиҷойӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B0%D0%BA%D0%B0%D0%BD%D1%81%D1%96%D1%8F_(%D0%BA%D1%80%D0%B8%D1%81%D1%82%D0%B0%D0%BB%D0%BE%D0%B3%D1%80%D0%B0%D1%84%D1%96%D1%8F)" title="Вакансія (кристалографія) – Ukrainian" lang="uk" hreflang="uk" data-title="Вакансія (кристалографія)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%99%B6%E6%A0%BC%E7%A9%BA%E4%BD%8D" title="晶格空位 – Chinese" lang="zh" hreflang="zh" data-title="晶格空位" data-language-autonym="中文" data-language-local-name="Chinese" 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/Q899743#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit 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searchaux" style="display:none">Crystallographic defect; an atom missing from a lattice site</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:MoS2_vacancies.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/MoS2_vacancies.jpg/220px-MoS2_vacancies.jpg" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/MoS2_vacancies.jpg/330px-MoS2_vacancies.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/MoS2_vacancies.jpg/440px-MoS2_vacancies.jpg 2x" data-file-width="806" data-file-height="764" /></a><figcaption><a href="/wiki/Electron_microscopy" class="mw-redirect" title="Electron microscopy">Electron microscopy</a> of sulfur vacancies in a <a href="/wiki/Monolayer" title="Monolayer">monolayer</a> of <a href="/wiki/Molybdenum_disulfide" title="Molybdenum disulfide">molybdenum disulfide</a>. Right circle points to a divacancy, i.e., sulfur atoms are missing both above and below the Mo layer. Other circles are single vacancies, i.e., sulfur atoms are missing only above or below the Mo layer. Scale bar: 1 nm.<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></figcaption></figure> <p>In <a href="/wiki/Crystallography" title="Crystallography">crystallography</a>, a <b>vacancy</b> is a type of <a href="/wiki/Point_defect" class="mw-redirect" title="Point defect">point defect</a> in a <a href="/wiki/Crystal" title="Crystal">crystal</a> where an <a href="/wiki/Atom" title="Atom">atom</a> is missing from one of the <a href="/wiki/Bravais_lattice" title="Bravais lattice">lattice</a> sites.<sup id="cite_ref-Ehr91_2-0" class="reference"><a href="#cite_note-Ehr91-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Crystals inherently possess imperfections, sometimes referred to as <a href="/wiki/Crystallographic_defect" title="Crystallographic defect">crystallographic defects</a>. </p><p>Vacancies occur naturally in all crystalline materials. At any given temperature, up to the <a href="/wiki/Melting_point" title="Melting point">melting point</a> of the material, there is an equilibrium <a href="/wiki/Concentration" title="Concentration">concentration</a> (ratio of vacant lattice sites to those containing atoms).<sup id="cite_ref-Ehr91_2-1" class="reference"><a href="#cite_note-Ehr91-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> At the melting point of some metals the ratio can be approximately 1:1000.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> This temperature dependence can be modelled by </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 N_{\rm {v}}=N\exp \left({\frac {-Q_{\rm {v}}}{k_{\rm {B}}T}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>N</mi> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\rm {v}}=N\exp \left({\frac {-Q_{\rm {v}}}{k_{\rm {B}}T}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e3a66a30f5c83ce3f0cca2710bfbe85d12f2db9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.072ex; height:6.176ex;" alt="{\displaystyle N_{\rm {v}}=N\exp \left({\frac {-Q_{\rm {v}}}{k_{\rm {B}}T}}\right)}"></span></dd></dl> <p>where <span class="texhtml"><i>N</i><sub>v</sub></span> is the vacancy concentration, <span class="texhtml"><i>Q</i><sub>v</sub></span> is the energy required for vacancy formation, <span class="texhtml"><i>k</i><sub>B</sub></span> is the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a>, <span class="texhtml mvar" style="font-style:italic;">T</span> is the <a href="/wiki/Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a>, and <span class="texhtml mvar" style="font-style:italic;">N</span> is the concentration of atomic sites i.e. </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 N={\frac {\rho N_{\rm {A}}}{M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mrow> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N={\frac {\rho N_{\rm {A}}}{M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a94151485be158499c014799552ef51f13f03fa8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.531ex; height:5.343ex;" alt="{\displaystyle N={\frac {\rho N_{\rm {A}}}{M}}}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">ρ</span> is density, <span class="texhtml"><i>N</i><sub>A</sub></span> the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>, and <span class="texhtml mvar" style="font-style:italic;">M</span> the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a>. </p><p>It is the simplest point defect. In this system, an atom is missing from its regular atomic site. Vacancies are formed during <a href="/wiki/Solidification" class="mw-redirect" title="Solidification">solidification</a> due to vibration of atoms, local rearrangement of atoms, <a href="/wiki/Plastic_deformation" class="mw-redirect" title="Plastic deformation">plastic deformation</a> and ionic bombardments. </p><p>The creation of a vacancy can be simply modeled by considering the <a href="/wiki/Bond_energy" title="Bond energy">energy required to break the bonds</a> between an atom inside the crystal and its nearest neighbor atoms. Once that atom is removed from the lattice site, it is put back on the surface of the crystal and some energy is retrieved because new bonds are established with other atoms on the surface. However, there is a net input of energy because there are fewer bonds between surface atoms than between atoms in the interior of the crystal. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Material_physics">Material physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vacancy_defect&action=edit&section=1" title="Edit section: Material physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In most applications vacancy defects are irrelevant to the intended purpose of a material, as they are either too few or spaced throughout a multi-dimensional space in such a way that force or charge can move around the vacancy. In the case of more constrained structures like <a href="/wiki/Carbon_nanotube" title="Carbon nanotube">carbon nanotubes</a> however, vacancies and other crystalline defects can significantly weaken the material.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vacancy_defect&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Crystallographic_defect" title="Crystallographic defect">Crystallographic defect</a></li> <li><a href="/wiki/Schottky_defect" title="Schottky defect">Schottky defect</a></li> <li><a href="/wiki/Frenkel_defect" title="Frenkel defect">Frenkel defect</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vacancy_defect&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHongHuProbertLi2015" class="citation journal cs1">Hong, J.; Hu, Z.; Probert, M.; Li, K.; Lv, D.; Yang, X.; Gu, L.; Mao, N.; Feng, Q.; Xie, L.; Zhang, J.; Wu, D.; Zhang, Z.; Jin, C.; Ji, W.; Zhang, X.; Yuan, J.; Zhang, Z. (2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4346634">"Exploring atomic defects in molybdenum disulphide monolayers"</a>. <i>Nature Communications</i>. <b>6</b>: 6293. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015NatCo...6.6293H">2015NatCo...6.6293H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fncomms7293">10.1038/ncomms7293</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4346634">4346634</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25695374">25695374</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Communications&rft.atitle=Exploring+atomic+defects+in+molybdenum+disulphide+monolayers&rft.volume=6&rft.pages=6293&rft.date=2015&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4346634%23id-name%3DPMC&rft_id=info%3Apmid%2F25695374&rft_id=info%3Adoi%2F10.1038%2Fncomms7293&rft_id=info%3Abibcode%2F2015NatCo...6.6293H&rft.aulast=Hong&rft.aufirst=J.&rft.au=Hu%2C+Z.&rft.au=Probert%2C+M.&rft.au=Li%2C+K.&rft.au=Lv%2C+D.&rft.au=Yang%2C+X.&rft.au=Gu%2C+L.&rft.au=Mao%2C+N.&rft.au=Feng%2C+Q.&rft.au=Xie%2C+L.&rft.au=Zhang%2C+J.&rft.au=Wu%2C+D.&rft.au=Zhang%2C+Z.&rft.au=Jin%2C+C.&rft.au=Ji%2C+W.&rft.au=Zhang%2C+X.&rft.au=Yuan%2C+J.&rft.au=Zhang%2C+Z.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4346634&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVacancy+defect" class="Z3988"></span></span> </li> <li id="cite_note-Ehr91-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ehr91_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ehr91_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Ehrhart, P. (1991) "Properties and interactions of atomic defects in metals and alloys", chapter 2, p. 88 in <i>Landolt-Börnstein, New Series III</i>, Vol. 25, Springer, Berlin</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegel1978" class="citation journal cs1 cs1-prop-long-vol">Siegel, R. W. (1978). "Vacancy concentrations in metals". <i>Journal of Nuclear Materials</i>. 69–70: 117–146. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1978JNuM...69..117S">1978JNuM...69..117S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-3115%2878%2990240-4">10.1016/0022-3115(78)90240-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Nuclear+Materials&rft.atitle=Vacancy+concentrations+in+metals&rft.volume=69-70&rft.pages=117-146&rft.date=1978&rft_id=info%3Adoi%2F10.1016%2F0022-3115%2878%2990240-4&rft_id=info%3Abibcode%2F1978JNuM...69..117S&rft.aulast=Siegel&rft.aufirst=R.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVacancy+defect" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.physics.uci.edu/~collinsp/pubs/38.Collins.pdf">"Defects And Disorder In Carbon Nanotubes"</a> <span class="cs1-format">(PDF)</span>. Philip G. Collins<span class="reference-accessdate">. Retrieved <span class="nowrap">8 April</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Defects+And+Disorder+In+Carbon+Nanotubes&rft.pub=Philip+G.+Collins&rft_id=https%3A%2F%2Fwww.physics.uci.edu%2F~collinsp%2Fpubs%2F38.Collins.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVacancy+defect" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vacancy_defect&action=edit&section=4" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.siliconfareast.com/crystaldefects.htm">Crystalline Defects in Silicon</a></li></ul> <div class="navbox-styles"><style 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style="width:1%;background:#e5e5ff;">Key concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Timeline_of_crystallography" title="Timeline of crystallography">Timeline of crystallography</a> <ul><li><a href="/wiki/Category:Crystallographers" title="Category:Crystallographers">Crystallographers</a></li></ul></li> <li><a href="/wiki/Metallurgy" title="Metallurgy">Metallurgy</a></li> <li><a href="/w/index.php?title=Biocrystallography&action=edit&redlink=1" class="new" title="Biocrystallography (page does not exist)">Biocrystallography</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Crystal_structure" title="Crystal structure">Structure</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Unit_cell" title="Unit cell">Unit cell</a> <ul><li><a href="/wiki/Bravais_lattice" title="Bravais lattice">Bravais lattice</a></li> <li><a href="/wiki/Miller_index" title="Miller index">Miller index</a></li> <li><a href="/wiki/Crystallographic_point_group" title="Crystallographic point group">Point group</a></li> <li><a href="/wiki/Reciprocal_lattice" title="Reciprocal lattice">Reciprocal lattice</a></li> <li><a href="/wiki/Crystallographic_restriction_theorem" title="Crystallographic restriction theorem">Restriction theorem</a></li></ul></li> <li><a href="/wiki/Periodic_table_(crystal_structure)" title="Periodic table (crystal structure)">Periodic table</a></li> <li><a href="/wiki/Crystal_structure_prediction" title="Crystal structure prediction">Structure prediction</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Systems" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Crystal_system" title="Crystal system">Systems</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cubic_crystal_system" title="Cubic crystal system">Cubic</a></li> <li><a href="/wiki/Hexagonal_crystal_family" title="Hexagonal crystal family">Hexagonal</a></li> <li><a href="/wiki/Monoclinic_crystal_system" title="Monoclinic crystal system">Monoclinic</a></li> <li><a href="/wiki/Orthorhombic_crystal_system" title="Orthorhombic crystal system">Orthorhombic</a></li> <li><a href="/wiki/Tetragonal_crystal_system" title="Tetragonal crystal system">Tetragonal</a></li> <li><a href="/wiki/Triclinic_crystal_system" title="Triclinic crystal system">Triclinic</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Crystal_growth" title="Crystal growth">Growth</a> <ul><li><a href="/wiki/Crystallite" title="Crystallite">Crystallite</a></li> <li><a href="/wiki/Equiaxed_crystal" title="Equiaxed crystal">Equiaxed</a></li></ul></li> <li><a href="/wiki/Crystal_twinning" title="Crystal twinning">Twinning</a> <ul><li><a href="/wiki/Fiveling" title="Fiveling">Fiveling</a></li></ul></li> <li><a href="/wiki/Aperiodic_crystal" title="Aperiodic crystal">Aperiodic crystal</a> <ul><li><a href="/wiki/Quasicrystal" title="Quasicrystal">Quasicrystal</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Phase_transition" title="Phase transition">Phase<br />transition</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Phase_diagram" title="Phase diagram">Phase diagram</a> <ul><li><a href="/wiki/Eutectic_system" title="Eutectic system">Eutectic</a></li> <li><a href="/wiki/Miscibility_gap" title="Miscibility gap">Miscibility gap</a></li> <li><a href="/wiki/Crystal_polymorphism" title="Crystal polymorphism">Polymorphism</a></li> <li><a href="/wiki/Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li></ul></li> <li><a href="/wiki/Phase_transformation_crystallography" title="Phase transformation crystallography">Phase transformation crystallography</a></li> <li><a href="/wiki/Precipitation_hardening" title="Precipitation hardening">Precipitation</a></li> <li><a href="/wiki/Segregation_(materials_science)" title="Segregation (materials science)">Segregation</a></li> <li><a href="/wiki/Spinodal_decomposition" title="Spinodal decomposition">Spinodal decomposition</a></li> <li><a href="/wiki/Supersaturation" title="Supersaturation">Supersaturation</a></li> <li><a href="/wiki/Guinier%E2%80%93Preston_zone" title="Guinier–Preston zone">GP-zone</a></li> <li><a href="/wiki/Ostwald_ripening" title="Ostwald ripening">Ostwald ripening</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Crystallographic_defect" title="Crystallographic defect">Defects</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Grain_boundary" title="Grain boundary">Grain boundary</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Disclination" title="Disclination">Disclination</a></li> <li><a href="/w/index.php?title=Coincidence_site_lattice&action=edit&redlink=1" class="new" title="Coincidence site lattice (page does not exist)">CSL</a></li> <li><a href="/wiki/Grain_growth" title="Grain growth">Growth</a></li> <li><a href="/wiki/Abnormal_grain_growth" title="Abnormal grain growth">Abnormal growth</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Perfect_crystal" title="Perfect crystal">Perfect crystal</a></li> <li><a href="/wiki/Stacking_fault" title="Stacking fault">Stacking fault</a></li> <li><a href="/wiki/Dislocation" title="Dislocation">Dislocation</a> <ul><li><a href="/wiki/Burgers_vector" title="Burgers vector">Burgers vector</a></li> <li><a href="/wiki/Partial_dislocation" title="Partial dislocation">Partial dislocation</a></li> <li><a href="/wiki/Kink_(materials_science)" title="Kink (materials science)">Kink</a></li> <li><a href="/wiki/Cross_slip" title="Cross slip">Cross slip</a></li> <li><a href="/wiki/Frank%E2%80%93Read_source" title="Frank–Read source">Frank–Read source</a></li> <li><a href="/wiki/Cottrell_atmosphere" title="Cottrell atmosphere">Cottrell atmosphere</a></li> <li><a href="/wiki/Peierls_stress" title="Peierls stress">Peierls stress</a></li> <li><a href="/wiki/Geometrically_necessary_dislocations" title="Geometrically necessary dislocations">GND</a></li> <li><a href="/wiki/Lomer%E2%80%93Cottrell_junction" title="Lomer–Cottrell junction">Lomer–Cottrell junction</a></li></ul></li> <li><a href="/wiki/Slip_(materials_science)" title="Slip (materials science)">Slip</a> <ul><li><a href="/wiki/Slip_bands_in_metals" title="Slip bands in metals">Slip bands</a></li></ul></li> <li><a href="/wiki/Interstitial_defect" title="Interstitial defect">Interstitials</a> <ul><li><a href="/wiki/Bjerrum_defect" title="Bjerrum defect">Bjerrum defect</a></li> <li><a href="/wiki/Frenkel_defect" title="Frenkel defect">Frenkel defect</a></li> <li><a href="/wiki/Wigner_effect" title="Wigner effect">Wigner effect</a></li></ul></li> <li><a class="mw-selflink selflink">Vacancy</a> <ul><li><a href="/wiki/Schottky_defect" title="Schottky defect">Schottky defect</a></li> <li><a href="/wiki/F-center" title="F-center">F-center</a></li></ul></li> <li><a href="/wiki/Stone%E2%80%93Wales_defect" title="Stone–Wales defect">Stone–Wales defect</a></li> <li><a href="/wiki/Crystallographic_defects_in_diamond" title="Crystallographic defects in diamond">Defects in diamond</a></li></ul></div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Bragg%27s_law" title="Bragg's law">Bragg's law</a></li> <li><a href="/wiki/Bragg_plane" title="Bragg plane">Bragg plane</a></li> <li><a href="/wiki/Ewald%27s_sphere" title="Ewald's sphere">Ewald's sphere</a></li> <li><a href="/wiki/Friedel%27s_law" title="Friedel's law">Friedel's law</a></li> <li><a href="/wiki/Hermann%E2%80%93Mauguin_notation" title="Hermann–Mauguin notation">Hermann–Mauguin notation</a></li> <li><a href="/wiki/Structure_factor" title="Structure factor">Structure factor</a></li> <li><a href="/wiki/Thermal_ellipsoid" title="Thermal ellipsoid">Thermal ellipsoid</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Sites_interstitiels_cubique_a_faces_centrees.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Sites_interstitiels_cubique_a_faces_centrees.svg/50px-Sites_interstitiels_cubique_a_faces_centrees.svg.png" decoding="async" width="50" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Sites_interstitiels_cubique_a_faces_centrees.svg/75px-Sites_interstitiels_cubique_a_faces_centrees.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Sites_interstitiels_cubique_a_faces_centrees.svg/100px-Sites_interstitiels_cubique_a_faces_centrees.svg.png 2x" data-file-width="120" data-file-height="125" /></a></span><br /></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/w/index.php?title=Crystallographic_characterization&action=edit&redlink=1" class="new" title="Crystallographic characterization (page does not exist)">Characterisation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electron_crystallography" title="Electron crystallography">Electron</a> <ul><li><a href="/wiki/Electron_diffraction" title="Electron diffraction">Diffraction</a></li> <li><a href="/wiki/Electron_scattering" title="Electron scattering">Scattering</a></li></ul></li> <li><a href="/wiki/Neutron_crystallography" class="mw-redirect" title="Neutron crystallography">Neutron</a> <ul><li><a href="/wiki/Neutron_diffraction" title="Neutron diffraction">Diffraction</a></li> <li><a href="/wiki/Neutron_scattering" title="Neutron scattering">Scattering</a></li></ul></li> <li><a href="/wiki/Nuclear_magnetic_resonance_crystallography" title="Nuclear magnetic resonance crystallography">Nuclear magnetic resonance</a></li> <li><a href="/wiki/X-ray_crystallography" title="X-ray crystallography">X-ray</a> <ul><li><a href="/wiki/X-ray_diffraction" title="X-ray diffraction">Diffraction</a></li> <li><a href="/wiki/X-ray_scattering" class="mw-redirect" title="X-ray scattering">Scattering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;">Algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Direct_methods_(crystallography)" title="Direct methods (crystallography)">Direct methods</a></li> <li><a href="/wiki/Isomorphous_replacement" title="Isomorphous replacement">Isomorphous replacement</a></li> <li><a href="/wiki/Molecular_replacement" title="Molecular replacement">Molecular replacement</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li> <li><a href="/wiki/Patterson_map" class="mw-redirect" title="Patterson map">Patterson map</a></li> <li><a href="/wiki/Phase_retrieval" title="Phase retrieval">Phase retrieval</a> <ul><li><a href="/wiki/Gerchberg%E2%80%93Saxton_algorithm" title="Gerchberg–Saxton algorithm">Gerchberg–Saxton</a></li></ul></li> <li><a href="/wiki/Single_particle_analysis" title="Single particle analysis">Single particle analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/wiki/Category:Crystallography_software" title="Category:Crystallography software">Software</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Collaborative_Computational_Project_Number_4" title="Collaborative Computational Project Number 4">CCP4</a></li> <li><a href="/wiki/Coot_(software)" title="Coot (software)">Coot</a></li> <li><a href="/wiki/CrystalExplorer" title="CrystalExplorer">CrystalExplorer</a></li> <li><a href="/wiki/Disordered_Structure_Refinement" title="Disordered Structure Refinement">DSR</a></li> <li><a rel="nofollow" class="external text" href="http://jana.fzu.cz/">JANA2020</a></li> <li><a href="/wiki/MTEX" title="MTEX">MTEX</a></li> <li><a href="/wiki/OctaDist" title="OctaDist">OctaDist</a></li> <li><a href="/wiki/Olex2" title="Olex2">Olex2</a></li> <li><a href="/wiki/ShelXle" title="ShelXle">SHELX</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/wiki/Crystallographic_database" title="Crystallographic database">Databases</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bilbao_Crystallographic_Server" title="Bilbao Crystallographic Server">Bilbao Crystallographic Server</a></li> <li><a href="/wiki/Cambridge_Structural_Database" title="Cambridge Structural Database">CCDC</a></li> <li><a href="/wiki/Crystallographic_Information_File" title="Crystallographic Information File">CIF</a></li> <li><a href="/wiki/Crystallography_Open_Database" title="Crystallography Open Database">COD</a></li> <li><a href="/wiki/Inorganic_Crystal_Structure_Database" title="Inorganic Crystal Structure Database">ICSD</a></li> <li><a href="/wiki/International_Centre_for_Diffraction_Data" title="International Centre for Diffraction Data">ICDD</a></li> <li><a href="/wiki/Protein_Data_Bank" title="Protein Data Bank">PDB</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/wiki/Category:Crystallography_journals" title="Category:Crystallography journals">Journals</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Crystal_Growth_%26_Design" title="Crystal Growth & Design">Crystal Growth & Design</a></li> <li><a href="/wiki/Crystallography_Reviews" title="Crystallography Reviews">Crystallography Reviews</a></li> <li><a href="/wiki/Journal_of_Chemical_Crystallography" title="Journal of Chemical Crystallography">Journal of Chemical Crystallography</a></li> <li><a href="/wiki/Journal_of_Crystal_Growth" title="Journal of Crystal Growth">Journal of Crystal Growth</a></li> <li><a href="/wiki/Kristallografija" title="Kristallografija">Kristallografija</a></li> <li><a href="/wiki/Zeitschrift_f%C3%BCr_Kristallographie_%E2%80%93_Crystalline_Materials" title="Zeitschrift für Kristallographie – Crystalline Materials">Zeitschrift für Kristallographie – Crystalline Materials</a></li> <li><a href="/wiki/Zeitschrift_f%C3%BCr_Kristallographie_%E2%80%93_New_Crystal_Structures" title="Zeitschrift für Kristallographie – New Crystal Structures">Zeitschrift für Kristallographie – New Crystal Structures</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/wiki/Category:Crystallography_awards" title="Category:Crystallography awards">Awards</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Carl_Hermann_Medal" title="Carl Hermann Medal">Carl Hermann Medal</a></li> <li><a href="/wiki/Ewald_Prize" title="Ewald Prize">Ewald Prize</a></li> <li><a href="/wiki/Gregori_Aminoff_Prize" title="Gregori Aminoff Prize">Gregori Aminoff Prize</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#e5e5ff;"><a href="/wiki/Category:Crystallography_organizations" title="Category:Crystallography organizations">Organisation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/International_Union_of_Crystallography" title="International Union of Crystallography">IUCr</a></li> <li><a href="/wiki/International_Organization_for_Biological_Crystallization" title="International Organization for Biological Crystallization">IOBCr</a></li> <li><a href="/wiki/Shubnikov_Institute_of_Crystallography_RAS" title="Shubnikov Institute of Crystallography RAS">RAS</a></li> <li><a href="/wiki/German_Mineralogical_Society" title="German Mineralogical Society">DMG</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Associations" scope="row" class="navbox-group" style="width:1%">Associations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/European_Crystallographic_Association" title="European Crystallographic Association">Europe</a> <ul><li><a href="/wiki/French_Crystallographic_Association" title="French Crystallographic Association">France</a></li> <li><a href="/wiki/German_Crystallographic_Society" title="German Crystallographic Society">Germany</a></li> <li><a href="/wiki/British_Crystallographic_Association" title="British Crystallographic Association">UK</a></li></ul></li> <li><a href="/wiki/American_Crystallographic_Association" title="American Crystallographic Association">US</a></li> <li><a href="/wiki/Crystallographic_Society_of_Japan" title="Crystallographic Society of Japan">Japan</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Crystallography" title="Category:Crystallography">Category</a></b></li> 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