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</div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" 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div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Solidus_(disambiguation)" class="mw-redirect mw-disambig" title="Solidus (disambiguation)">Solidus (disambiguation)</a>.</div> <p>While chemically pure materials have a single <a href="/wiki/Melting_point" title="Melting point">melting point</a>, <a href="/wiki/Mixture" title="Mixture">chemical mixtures</a> often partially <a href="/wiki/Melting" title="Melting">melt</a> at the temperature known as the <b>solidus</b> (<i>T</i><sub>S</sub> or <i>T</i><sub>sol</sub>), and fully melt at the higher <b>liquidus</b> temperature (<i>T</i><sub>L</sub> or <i>T</i><sub>liq</sub>). The solidus is always less than or equal to the liquidus, but they need not coincide. If a gap exists between the solidus and liquidus it is called the freezing range, and within that gap, the substance consists of a mixture of solid and liquid phases (like a <a href="/wiki/Slurry" title="Slurry">slurry</a>). Such is the case, for example, with the <a href="/wiki/Olivine" title="Olivine">olivine</a> (<a href="/wiki/Forsterite" title="Forsterite">forsterite</a>-<a href="/wiki/Fayalite" title="Fayalite">fayalite</a>) system, which is common in <a href="/wiki/Earth%27s_mantle" title="Earth's mantle">Earth's mantle</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquidus_and_solidus&action=edit&section=1" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Solid_solution.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Solid_solution.svg/250px-Solid_solution.svg.png" decoding="async" width="250" height="278" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Solid_solution.svg/375px-Solid_solution.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Solid_solution.svg/500px-Solid_solution.svg.png 2x" data-file-width="450" data-file-height="500" /></a><figcaption>The equilibrium phase diagram of a <a href="/wiki/Solid_solution" title="Solid solution">solid solution</a> of made up of mixtures of α and β. The upper curve is the line of liquidus, and the lower curve is the line of solidus.</figcaption></figure> <p>In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Materials_science" title="Materials science">materials science</a>, and <a href="/wiki/Physics" title="Physics">physics</a>, the liquidus temperature specifies the temperature above which a material is completely liquid,<sup id="cite_ref-Askeland2008_2-0" class="reference"><a href="#cite_note-Askeland2008-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and the maximum temperature at which <a href="/wiki/Crystal" title="Crystal">crystals</a> can co-exist with the melt in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. The solidus is the <a href="/wiki/Locus_(mathematics)" title="Locus (mathematics)">locus</a> of temperatures (a curve on a <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a>) below which a given substance is completely <a href="/wiki/Solid" title="Solid">solid</a> (crystallized). The solidus temperature specifies the temperature below which a material is completely solid,<sup id="cite_ref-Askeland2008_2-1" class="reference"><a href="#cite_note-Askeland2008-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and the minimum temperature at which a melt can co-exist with <a href="/wiki/Crystal" title="Crystal">crystals</a> in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. </p><p>Liquidus and solidus are mostly used for impure substances (mixtures) such as <a href="/wiki/Glass" title="Glass">glasses</a>, metal <a href="/wiki/Alloy" title="Alloy">alloys</a>, <a href="/wiki/Ceramic" title="Ceramic">ceramics</a>, <a href="/wiki/Rock_(geology)" title="Rock (geology)">rocks</a>, and <a href="/wiki/Mineral" title="Mineral">minerals</a>. Lines of liquidus and solidus appear in the phase diagrams of binary <a href="/wiki/Solid_solution" title="Solid solution">solid solutions</a>,<sup id="cite_ref-Askeland2008_2-2" class="reference"><a href="#cite_note-Askeland2008-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> as well as in <a href="/wiki/Eutectic" class="mw-redirect" title="Eutectic">eutectic</a> systems away from the invariant point.<sup id="cite_ref-Callister2008_3-0" class="reference"><a href="#cite_note-Callister2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="When_distinction_is_irrelevant">When distinction is irrelevant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquidus_and_solidus&action=edit&section=2" title="Edit section: When distinction is irrelevant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For pure elements or compounds, e.g. pure copper, pure water, etc. the liquidus and solidus are at the same temperature, and the term <a href="/wiki/Melting_point" title="Melting point">melting point</a> may be used. </p><p>There are also some mixtures which melt at a particular temperature, known as <a href="/wiki/Congruent_melting" title="Congruent melting">congruent melting</a>. One example is <a href="/wiki/Eutectic_system" title="Eutectic system">eutectic mixture</a>. In a eutectic system, there is particular mixing ratio where the solidus and liquidus temperatures coincide at a point known as the invariant point. At the invariant point, the mixture undergoes a eutectic reaction where both solids melt at the same temperature.<sup id="cite_ref-Callister2008_3-1" class="reference"><a href="#cite_note-Callister2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Modeling_and_measurement">Modeling and measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquidus_and_solidus&action=edit&section=3" title="Edit section: Modeling and measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are several models used to predict liquidus and solidus curves for various systems.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Detailed measurements of solidus and liquidus can be made using techniques such as <a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">differential scanning calorimetry</a> and <a href="/wiki/Differential_thermal_analysis" title="Differential thermal analysis">differential thermal analysis</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Effects">Effects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquidus_and_solidus&action=edit&section=4" title="Edit section: Effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:SiO2_Li2O.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/a/ab/SiO2_Li2O.GIF/250px-SiO2_Li2O.GIF" decoding="async" width="250" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/a/ab/SiO2_Li2O.GIF/375px-SiO2_Li2O.GIF 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/a/ab/SiO2_Li2O.GIF/500px-SiO2_Li2O.GIF 2x" data-file-width="911" data-file-height="623" /></a><figcaption>Liquidus temperature curve in the binary glass system SiO<sub>2</sub>-Li<sub>2</sub>O</figcaption></figure> <p>For impure substances, e.g. <a href="/wiki/Alloy" title="Alloy">alloys</a>, <a href="/wiki/Honey" title="Honey">honey</a>, <a href="/wiki/Soft_drink" title="Soft drink">soft drink</a>, <a href="/wiki/Ice_cream" title="Ice cream">ice cream</a>, etc. the melting point broadens into a melting interval. If the temperature is within the melting interval, one may see "slurries" at equilibrium, i.e. the slurry will neither fully solidify nor melt. This is why new snow of high purity on mountain peaks either melts or stays solid, while dirty snow on the ground in cities tends to become slushy at certain temperatures. Weld melt pools containing high levels of sulfur, either from melted impurities of the base metal or from the welding electrode, typically have very broad melting intervals, which leads to increased risk of <a href="/wiki/Welding_defect#Hot_cracking" title="Welding defect">hot cracking</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Behavior_when_cooling">Behavior when cooling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Liquidus_and_solidus&action=edit&section=5" title="Edit section: Behavior when cooling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Above the liquidus temperature, the material is <a href="/wiki/Homogeneous_(chemistry)" class="mw-redirect" title="Homogeneous (chemistry)">homogeneous</a> and liquid at equilibrium. As the system is cooled below the liquidus temperature, more and more <a href="/wiki/Crystal" title="Crystal">crystals</a> will form in the melt if one waits a sufficiently long time, depending on the material. Alternately, <a href="/wiki/Homogeneous_(chemistry)" class="mw-redirect" title="Homogeneous (chemistry)">homogeneous</a> glasses can be obtained through sufficiently fast cooling, i.e., through kinetic inhibition of the <a href="/wiki/Crystallization" title="Crystallization">crystallization</a> process. </p><p>The crystal phase that crystallizes first on cooling a substance to its liquidus temperature is termed <i>primary crystalline phase</i> or <i>primary phase</i>. The composition range within which the primary phase remains constant is known as <i>primary crystalline phase field</i>. </p><p>The liquidus temperature is important in the glass industry because crystallization can cause severe problems during the glass melting and forming processes, and it also may lead to product failure.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <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=Liquidus_and_solidus&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Melting_point" title="Melting point">Melting/freezing point</a></li> <li><a href="/wiki/Phase_diagram" title="Phase diagram">Phase diagram</a></li> <li><a href="/wiki/Solvus" class="mw-redirect" title="Solvus">Solvus</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=Liquidus_and_solidus&action=edit&section=7" 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 mw-references-columns"><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="CITEREFHerzberg1983" class="citation journal cs1">Herzberg, Claude T. (1983). "Solidus and liquidus temperatures and mineralogies for anhydrous garnet-lherzolite to 15 GPa". <i>Physics of the Earth and Planetary Interiors</i>. <b>32</b> (2). Elsevier BV: 193–202. <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/1983PEPI...32..193H">1983PEPI...32..193H</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%2F0031-9201%2883%2990139-5">10.1016/0031-9201(83)90139-5</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9201">0031-9201</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+of+the+Earth+and+Planetary+Interiors&rft.atitle=Solidus+and+liquidus+temperatures+and+mineralogies+for+anhydrous+garnet-lherzolite+to+15+GPa&rft.volume=32&rft.issue=2&rft.pages=193-202&rft.date=1983&rft.issn=0031-9201&rft_id=info%3Adoi%2F10.1016%2F0031-9201%2883%2990139-5&rft_id=info%3Abibcode%2F1983PEPI...32..193H&rft.aulast=Herzberg&rft.aufirst=Claude+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquidus+and+solidus" class="Z3988"></span></span> </li> <li id="cite_note-Askeland2008-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Askeland2008_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Askeland2008_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Askeland2008_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAskelandFulay2008" class="citation book cs1">Askeland, Donald R.; Fulay, Pradeep P. (2008-04-23). <i>Essentials of Materials Science & Engineering</i> (2nd ed.). Toronto: Cengage Learning. p. 305. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-495-24446-2" title="Special:BookSources/978-0-495-24446-2"><bdi>978-0-495-24446-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essentials+of+Materials+Science+%26+Engineering&rft.place=Toronto&rft.pages=305&rft.edition=2nd&rft.pub=Cengage+Learning&rft.date=2008-04-23&rft.isbn=978-0-495-24446-2&rft.aulast=Askeland&rft.aufirst=Donald+R.&rft.au=Fulay%2C+Pradeep+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquidus+and+solidus" class="Z3988"></span></span> </li> <li id="cite_note-Callister2008-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Callister2008_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Callister2008_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCallisterRethwisch2008" class="citation book cs1">Callister, William D.; Rethwisch, David G. (2008). <i>Fundamentals of Materials Science and Engineering: An Integrated Approach</i> (3rd ed.). John Wiley & Sons. pp. 356–358. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-12537-3" title="Special:BookSources/978-0-470-12537-3"><bdi>978-0-470-12537-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Materials+Science+and+Engineering%3A+An+Integrated+Approach&rft.pages=356-358&rft.edition=3rd&rft.pub=John+Wiley+%26+Sons&rft.date=2008&rft.isbn=978-0-470-12537-3&rft.aulast=Callister&rft.aufirst=William+D.&rft.au=Rethwisch%2C+David+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquidus+and+solidus" 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 id="CITEREFSafarianKolbeinsenTangstad2011" class="citation journal cs1">Safarian, Jafar; Kolbeinsen, Leiv; Tangstad, Merete (2011-04-02). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs11663-011-9507-4">"Liquidus of Silicon Binary Systems"</a>. <i>Metallurgical and Materials Transactions B</i>. <b>42</b> (4). Springer Science and Business Media LLC: 852–874. <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/2011MMTB...42..852S">2011MMTB...42..852S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs11663-011-9507-4">10.1007/s11663-011-9507-4</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1073-5615">1073-5615</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Metallurgical+and+Materials+Transactions+B&rft.atitle=Liquidus+of+Silicon+Binary+Systems&rft.volume=42&rft.issue=4&rft.pages=852-874&rft.date=2011-04-02&rft.issn=1073-5615&rft_id=info%3Adoi%2F10.1007%2Fs11663-011-9507-4&rft_id=info%3Abibcode%2F2011MMTB...42..852S&rft.aulast=Safarian&rft.aufirst=Jafar&rft.au=Kolbeinsen%2C+Leiv&rft.au=Tangstad%2C+Merete&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs11663-011-9507-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquidus+and+solidus" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGalvinGrimesBurr2021" class="citation journal cs1">Galvin, C.O.T.; Grimes, R.W.; Burr, P.A. 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abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Glass_science" title="Template:Glass science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Glass_science" title="Template talk:Glass science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Glass_science" title="Special:EditPage/Template:Glass science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Glass_science_topics" style="font-size:114%;margin:0 4em"><a href="/wiki/Glass" title="Glass">Glass</a> science topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glass" title="Glass">Glass</a></li> <li><a href="/wiki/Glass_transition" title="Glass transition">Glass transition</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AgInSbTe" title="AgInSbTe">AgInSbTe</a></li> <li><a href="/wiki/Bioglass" class="mw-redirect" title="Bioglass">Bioglass</a></li> <li><a href="/wiki/Borophosphosilicate_glass" title="Borophosphosilicate glass">Borophosphosilicate glass</a></li> <li><a href="/wiki/Borosilicate_glass" title="Borosilicate glass">Borosilicate glass</a></li> <li><a href="/wiki/Ceramic_glaze" title="Ceramic glaze">Ceramic glaze</a></li> <li><a href="/wiki/Chalcogenide_glass" title="Chalcogenide glass">Chalcogenide glass</a></li> <li><a href="/wiki/Cobalt_glass" title="Cobalt glass">Cobalt glass</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Cranberry glass</a></li> <li><a href="/wiki/Crown_glass_(optics)" title="Crown glass (optics)">Crown glass</a></li> <li><a href="/wiki/Flint_glass" title="Flint glass">Flint glass</a></li> <li><a href="/wiki/Fluorosilicate_glass" title="Fluorosilicate glass">Fluorosilicate glass</a></li> <li><a href="/wiki/Fused_quartz" title="Fused quartz">Fused quartz</a></li> <li><a href="/wiki/GeSbTe" title="GeSbTe">GeSbTe</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Gold ruby glass</a></li> <li><a href="/wiki/Lead_glass" title="Lead glass">Lead glass</a></li> <li><a href="/wiki/Milk_glass" title="Milk glass">Milk glass</a></li> <li><a href="/wiki/Phosphosilicate_glass" title="Phosphosilicate glass">Phosphosilicate glass</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens glass</a></li> <li><a href="/wiki/Glass#Silicate_glass" title="Glass">Silicate glass</a></li> <li><a href="/wiki/Soda%E2%80%93lime_glass" title="Soda–lime glass">Soda–lime glass</a></li> <li><a href="/wiki/Sodium_hexametaphosphate" title="Sodium hexametaphosphate">Sodium hexametaphosphate</a></li> <li><a href="/wiki/Sodium_silicate" title="Sodium silicate">Soluble glass</a></li> <li><a href="/wiki/Tellurite_glass" title="Tellurite glass">Tellurite glass</a></li> <li><a href="/wiki/Thoriated_glass" title="Thoriated glass">Thoriated glass</a></li> <li><a href="/wiki/Ultra_low_expansion_glass" title="Ultra low expansion glass">Ultra low expansion glass</a></li> <li><a href="/wiki/Uranium_glass" title="Uranium glass">Uranium glass</a></li> <li><a href="/wiki/Vitreous_enamel" title="Vitreous enamel">Vitreous enamel</a></li> <li><a href="/wiki/Wood%27s_glass" title="Wood's glass">Wood's glass</a></li> <li><a href="/wiki/ZBLAN" title="ZBLAN">ZBLAN</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glass-ceramic" title="Glass-ceramic">Glass-ceramics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bioactive_glass" title="Bioactive glass">Bioactive glass</a></li> <li><a href="/wiki/CorningWare" title="CorningWare">CorningWare</a></li> <li><a href="/wiki/Glass-ceramic-to-metal_seals" title="Glass-ceramic-to-metal seals">Glass-ceramic-to-metal seals</a></li> <li><a href="/wiki/Macor" title="Macor">Macor</a></li> <li><a href="/wiki/Zerodur" title="Zerodur">Zerodur</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Preparation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Annealing_(glass)" title="Annealing (glass)">Annealing</a></li> <li><a href="/wiki/Chemical_vapor_deposition" title="Chemical vapor deposition">Chemical vapor deposition</a></li> <li><a href="/wiki/Glass_batch_calculation" title="Glass batch calculation">Glass batch calculation</a></li> <li><a href="/wiki/Glass_production" title="Glass production">Glass forming</a></li> <li><a href="/wiki/Glass_production#Hot_end" title="Glass production">Glass melting</a></li> <li><a href="/wiki/Calculation_of_glass_properties" title="Calculation of glass properties">Glass modeling</a></li> <li><a href="/wiki/Ion_implantation" title="Ion implantation">Ion implantation</a></li> <li><a href="/wiki/Liquidus" class="mw-redirect" title="Liquidus">Liquidus temperature</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Viscosity#Viscosity_of_amorphous_materials" title="Viscosity">Viscosity</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Optics" title="Optics">Optics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Achromatic_lens" title="Achromatic lens">Achromat</a></li> <li><a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">Dispersion</a></li> <li><a href="/wiki/Gradient-index_optics" title="Gradient-index optics">Gradient-index optics</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Optical_amplifier" title="Optical amplifier">Optical amplifier</a></li> <li><a href="/wiki/Optical_fiber" title="Optical fiber">Optical fiber</a></li> <li><a href="/wiki/Optical_lens_design" title="Optical lens design">Optical lens design</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens</a></li> <li><a href="/wiki/Photosensitive_glass" title="Photosensitive glass">Photosensitive glass</a></li> <li><a href="/wiki/Refraction" title="Refraction">Refraction</a></li> <li><a href="/wiki/Transparency_and_translucency" title="Transparency and translucency">Transparent materials</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Surface<br />modification</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anti-reflective_coating" title="Anti-reflective coating">Anti-reflective coating</a></li> <li><a href="/wiki/Chemically_strengthened_glass" title="Chemically strengthened glass">Chemically strengthened glass</a></li> <li><a href="/wiki/Corrosion#Corrosion_of_glasses" title="Corrosion">Corrosion</a></li> <li><a href="/wiki/Dealkalization" title="Dealkalization">Dealkalization</a></li> <li><a href="/wiki/DNA_microarray" title="DNA microarray">DNA microarray</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Insulated_glazing" title="Insulated glazing">Insulated glazing</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Self-cleaning_glass" title="Self-cleaning glass">Self-cleaning glass</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Tempered_glass" title="Tempered glass">Tempered glass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diverse<br />topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Conservation_and_restoration_of_glass_objects" title="Conservation and restoration of glass objects">Conservation and restoration of glass objects</a></li> <li><a href="/wiki/Glass-coated_wire" title="Glass-coated wire">Glass-coated wire</a></li> <li><a href="/wiki/Safety_glass" title="Safety glass">Safety glass</a></li> <li><a href="/wiki/Glass_databases" title="Glass databases">Glass databases</a></li> <li><a href="/wiki/Glass_electrode" title="Glass electrode">Glass electrode</a></li> <li><a href="/wiki/Glass_fiber_reinforced_concrete" title="Glass fiber reinforced concrete">Glass fiber reinforced concrete</a></li> <li><a href="/wiki/Glass_ionomer_cement" title="Glass ionomer cement">Glass ionomer cement</a></li> <li><a href="/wiki/Glass_microsphere" title="Glass microsphere">Glass microspheres</a></li> <li><a href="/wiki/Fiberglass" title="Fiberglass">Glass-reinforced plastic</a></li> <li><a href="/wiki/Glass_cloth" title="Glass cloth">Glass cloth</a></li> <li><a href="/wiki/Glass-to-metal_seal" title="Glass-to-metal seal">Glass-to-metal seal</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Pre-preg" title="Pre-preg">Pre-preg</a></li> <li><a href="/wiki/Prince_Rupert%27s_drop" title="Prince Rupert's drop">Prince Rupert's drops</a></li> <li><a href="/wiki/Radioactive_waste#Vitrification" title="Radioactive waste">Radioactive waste vitrification</a></li> <li><a href="/wiki/Windshield" title="Windshield">Windshield</a></li> <li><a href="/wiki/Glass_fiber" title="Glass fiber">Glass fiber</a></li></ul> </div></td></tr></tbody></table></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="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Liquidus_and_solidus&oldid=1258339093">https://en.wikipedia.org/w/index.php?title=Liquidus_and_solidus&oldid=1258339093</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" 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