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<title>Solid solution</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Solid solution</span></span>

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<p>A <b>solid solution,</b> a term popularly used for metals, is a homogeneous mixture of two compounds in solid state and having a single <a href="Crystal_structure" title="Crystal structure">crystal structure</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> Many examples can be found in <a href="Metallurgy" title="Metallurgy">metallurgy</a>, <a href="Geology" title="Geology">geology</a>, and <a href="Solid-state_chemistry" title="Solid-state chemistry">solid-state chemistry</a>. The word "solution" is used to describe the intimate mixing of components at the atomic level and distinguishes these <a href="Homogeneity_and_heterogeneity" title="Homogeneity and heterogeneity">homogeneous</a> materials from physical <a href="Mixture" title="Mixture">mixtures</a> of components. Two terms are mainly associated with solid solutions – <i>solvents</i> and <i>solutes,</i> depending on the relative abundance of the atomic species.

</p><p>In general if two compounds are <a href="Isostructural" title="Isostructural">isostructural</a> then a solid solution will exist between the end members (also known as parents). For example <a href="Sodium_chloride" title="Sodium chloride">sodium chloride</a> and <a href="Potassium_chloride" title="Potassium chloride">potassium chloride</a> have the same cubic crystal structure so it is possible to make a pure compound with any ratio of sodium to potassium (Na<sub>1-x</sub>K<sub>x</sub>)Cl by dissolving that ratio of NaCl and KCl in water and then evaporating the solution. A member of this family is sold under the brand name <a href="Lo_Salt" class="mw-redirect" title="Lo Salt">Lo Salt</a> which is (Na<sub>0.33</sub>K<sub>0.66</sub>)Cl, hence it contains 66% less sodium than normal table salt (NaCl). The pure minerals are called <a href="Halite" title="Halite">halite</a> and <a href="Sylvite" title="Sylvite">sylvite</a>; a physical mixture of the two is referred to as <a href="Sylvinite" title="Sylvinite">sylvinite</a>.

</p><p>Because minerals are natural materials they are prone to large variations in composition. In many cases specimens are members for a solid solution family and geologists find it more helpful to discuss the composition of the family than an individual specimen. <a href="Olivine" title="Olivine">Olivine</a> is described by the formula (Mg, Fe)<sub>2</sub>SiO<sub>4</sub>, which is equivalent to (Mg<sub>1−x</sub>Fe<sub>x</sub>)<sub>2</sub>SiO<sub>4</sub>. The ratio of magnesium to iron varies between the two endmembers of the solid solution series: forsterite (Mg-endmember: Mg<sub>2</sub>SiO<sub>4</sub>) and fayalite (Fe-endmember: Fe<sub>2</sub>SiO<sub>4</sub>)<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> but the ratio in olivine is not normally defined. With increasingly complex compositions the geological notation becomes significantly easier to manage than the chemical notation.

</p>

<div class="mw-heading mw-heading2"><h2 id="Nomenclature">Nomenclature</h2></div>

<p>The <a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a> definition of a solid solution is a "solid in which components are compatible and form a unique phase".<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>

</p><p>The definition "crystal containing a second constituent which fits into and is distributed in the lattice of the host crystal" given in refs.,<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> is not general and, thus, is not recommended.

</p><p>The expression is to be used to describe a solid phase containing more than one substance when, for convenience, one (or more) of the substances, called the solvent, is treated differently from the other substances, called solutes.

</p><p>One or several of the components can be <i>macromolecules</i>. Some of the other components can then act as plasticizers, i.e., as molecularly dispersed substances that decrease the glass-transition temperature at which the amorphous phase of a <i>polymer</i> is converted between glassy and rubbery states.

</p><p>In pharmaceutical preparations, the concept of solid solution is often applied to the case of mixtures of <i>drug</i> and <i>polymer</i>.

</p><p>The number of drug molecules that do behave as solvent (plasticizer) of polymers is small.<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>

</p>

<div class="mw-heading mw-heading2"><h2 id="Phase_diagrams">Phase diagrams</h2></div>

<p>On a <a href="Phase_diagram" title="Phase diagram">phase diagram</a> a solid solution is represented by an area, often labeled with the structure type, which covers the compositional and temperature/pressure ranges. Where the end members are not isostructural there are likely to be two solid solution ranges with different structures dictated by the parents. In this case the ranges may overlap and the materials in this region can have either structure, or there may be a <a href="Miscibility_gap" title="Miscibility gap">miscibility gap</a> in solid state indicating that attempts to generate materials with this composition will result in mixtures. In areas on a phase diagram which are not covered by a solid solution there may be line phases, these are compounds with a known crystal structure and set stoichiometry. Where the crystalline phase consists of two (non-charged) organic molecules the line phase is commonly known as a <a href="Cocrystal" title="Cocrystal">cocrystal</a>. In metallurgy alloys with a set composition are referred to as <a href="Intermetallic" title="Intermetallic">intermetallic</a> compounds. A solid solution is likely to exist when the two elements (generally <a href="Metal" title="Metal">metals</a>) involved are close together on the <a href="Periodic_table" title="Periodic table">periodic table</a>, an intermetallic compound generally results when two metals involved are not near each other on the periodic table.<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>

<div class="mw-heading mw-heading2"><h2 id="Details">Details</h2></div>

<p>The solute may incorporate into the solvent <a href="Crystal_lattice" class="mw-redirect" title="Crystal lattice">crystal lattice</a> <i><a href="Crystallographic_defect#substit" title="Crystallographic defect">substitutionally</a></i>, by replacing a solvent particle in the lattice, or <i><a href="Interstitial_defect" title="Interstitial defect">interstitially</a></i>, by fitting into the space between solvent particles. Both of these types of solid solution affect the properties of the material by distorting the crystal lattice and disrupting the physical and electrical homogeneity of the solvent material.<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> Where the atomic radii of the solute atom is larger than the solvent atom it replaces the crystal structure (<a href="Unit_cell" title="Unit cell">unit cell</a>) often expands to accommodate it, this means that the composition of a material in a solid solution can be calculated from the unit cell volume a relationship known as <a href="Vegard's_law" title="Vegard's law">Vegard's law</a>.<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>

</p><p>Some mixtures will readily form solid solutions over a range of concentrations, while other mixtures will not form solid solutions at all. The propensity for any two substances to form a solid solution is a complicated matter involving the <a href="Chemistry" title="Chemistry">chemical</a>, <a href="Crystallography" title="Crystallography">crystallographic</a>, and <a href="Quantum_mechanics" title="Quantum mechanics">quantum</a> properties of the substances in question. Substitutional solid solutions, in accordance with the <a href="Hume-Rothery_rules" title="Hume-Rothery rules">Hume-Rothery rules</a>, may form if the solute and solvent have:

</p>

<ul><li>Similar <a href="Atomic_radius" title="Atomic radius">atomic radii</a> (15% or less difference)</li>

<li>Same crystal structure</li>

<li>Similar <a href="Electronegativity" title="Electronegativity">electronegativities</a></li>

<li>Similar <a href="Valence_(chemistry)" title="Valence (chemistry)">valency</a></li></ul>

<p>a solid solution mixes with others to form a new solution

</p><p>The <a href="Phase_diagram" title="Phase diagram">phase diagram</a> in the above diagram displays an <a href="Alloy" title="Alloy">alloy</a> of two metals which forms a solid solution at all relative <a href="Concentration" title="Concentration">concentrations</a> of the two species. In this case, the pure phase of each element is of the same crystal structure, and the similar properties of the two elements allow for unbiased substitution through the full range of relative concentrations. Solid solution of pseudo-binary systems in complex systems with three or more components may require a more involved representation of the phase diagram with more than one <a href="Solvus" class="mw-redirect" title="Solvus">solvus</a> curves drawn corresponding to different equilibrium chemical conditions.<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>

</p><p>Solid solutions have important commercial and industrial applications, as such mixtures often have superior properties to pure materials. Many metal alloys are solid solutions. Even small amounts of solute can affect the electrical and physical properties of the solvent.

</p>

<p>The binary phase diagram in the above diagram shows the phases of a mixture of two substances in varying concentrations, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span>. The region labeled "<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

</semantics>

</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span>" is a solid solution, with <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span> acting as the solute in a matrix of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span>. On the other end of the concentration scale, the region labeled "<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>

</semantics>

</math></span><img src="./7ed48a5e36207156fb792fa79d29925d2f7901e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" loading="lazy"></span>" is also a solid solution, with <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> acting as the solute in a matrix of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span>. The large solid region in between the <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

</semantics>

</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>

</semantics>

</math></span><img src="./7ed48a5e36207156fb792fa79d29925d2f7901e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" loading="lazy"></span> solid solutions, labeled "<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

</semantics>

</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> + <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>

</semantics>

</math></span><img src="./7ed48a5e36207156fb792fa79d29925d2f7901e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" loading="lazy"></span>", is <i>not</i> a solid solution. Instead, an examination of the <a href="Microstructure" title="Microstructure">microstructure</a> of a mixture in this range would reveal two phases—solid solution <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span>-in-<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span> and solid solution <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math></span><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"></span>-in-<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> would form separate phases, perhaps <a href="Lamellar_structure" title="Lamellar structure">lamella</a> or <a href="Crystallite" title="Crystallite">grains</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Application">Application</h2></div>

<p>In the phase diagram, at three different concentrations, the material will be solid until heated to its <a href="Melting_point" title="Melting point">melting point</a>, and then (after adding the <a href="Heat_of_fusion" class="mw-redirect" title="Heat of fusion">heat of fusion</a>) become liquid at that same temperature:

</p>

<ul><li>the unalloyed extreme left</li>

<li>the unalloyed extreme right</li>

<li>the dip in the center (the <a href="Eutectic" class="mw-redirect" title="Eutectic">eutectic</a> composition).</li></ul>

<p>At other proportions, the material will enter a mushy or pasty phase until it warms up to being completely melted.

</p><p>The mixture at the dip point of the diagram is called a <a href="Eutectic_point" class="mw-redirect" title="Eutectic point">eutectic</a> alloy. Lead-tin mixtures formulated at that point (37/63 mixture) are useful when soldering electronic components, particularly if done manually, since the solid phase is quickly entered as the solder cools. In contrast, when lead-tin mixtures were used to solder seams in automobile bodies a pasty state enabled a shape to be formed with a wooden paddle or tool, so a 70–30 lead to tin ratio was used. (Lead is being removed from such applications owing to its <a href="Toxicity" title="Toxicity">toxicity</a> and consequent difficulty in recycling devices and components that include lead.)

</p>

<div class="mw-heading mw-heading2"><h2 id="Exsolution">Exsolution</h2></div>

<p>When a solid solution becomes unstable—due to a lower temperature, for example—exsolution occurs and the two phases separate into distinct microscopic to megascopic <a href="Lamella_(materials)" title="Lamella (materials)">lamellae</a>. This is mainly caused by difference in cation size. Cations which have a large difference in radii are not likely to readily substitute.<sup id="cite_ref-test_11-0" class="reference"><a href="#cite_note-test-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

</p><p>Alkali <a href="Feldspar" title="Feldspar">feldspar</a> <a href="Minerals" class="mw-redirect" title="Minerals">minerals</a>, for example, have <a href="Endmember" title="Endmember">end members</a> of <a href="Albite" title="Albite">albite</a>, NaAlSi<sub>3</sub>O<sub>8</sub> and <a href="Microcline" title="Microcline">microcline</a>, KAlSi<sub>3</sub>O<sub>8</sub>. At high temperatures Na<sup>+</sup> and K<sup>+</sup> readily substitute for each other and so the minerals will form a solid solution, yet at low temperatures albite can only substitute a small amount of K<sup>+</sup> and the same applies for Na<sup>+</sup> in the microcline. This leads to exsolution where they will separate into two separate phases. In the case of the alkali feldspar minerals, thin white albite layers will alternate between typically pink microcline,<sup id="cite_ref-test_11-1" class="reference"><a href="#cite_note-test-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> resulting in a <a href="Perthite" title="Perthite">perthite</a> texture.

</p>

<ul><li><a href="Solid_solution_strengthening" title="Solid solution strengthening">Solid solution strengthening</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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</style><cite id="CITEREFAbbaschianReed-Hill2008" class="citation book cs1">Abbaschian, Reza; Reed-Hill, Robert E. (2008-12-11). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=wh4v6UWjYdIC"><i>Physical Metallurgy Principles</i></a>. Cengage Learning. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-495-08254-5</bdi>.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://publications.iupac.org/pac/pdf/2012/pdf/8402x0377.pdf">"Terminology for biorelated polymers and applications (IUPAC Recommendations 2012)"</a> <span class="cs1-format">(PDF)</span>. <i>iupac.org</i>. p. 395<span class="reference-accessdate">. Retrieved <span class="nowrap">4 November</span> 2022</span>.</cite></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFAlan_D._MacNaughtAndrew_R._Wilkinson1997" class="citation book cs1">Alan D. MacNaught; Andrew R. Wilkinson, eds. (1997). <i>Compendium of Chemical Terminology: IUPAC Recommendations</i> (2nd ed.). Blackwell Science. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0865426848</bdi>.</cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation book cs1"><span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/compendiumofanal0000unse"><i>Compendium of Analytical Nomenclature (the "Orange Book")</i></a></span>. Oxford: Blackwell Science. 1998. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0865426155</bdi>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFVertDoiHellwichHess2012" class="citation journal cs1">Vert, Michel; Doi, Yoshiharu; Hellwich, Karl-Heinz; Hess, Michael; Hodge, Philip; Kubisa, Przemyslaw; Rinaudo, Marguerite; Schué, François (2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150319032817/http://pac.iupac.org/publications/pac/pdf/2012/pdf/8402x0377.pdf">"Terminology for biorelated polymers and applications (IUPAC Recommendations 2012)"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Pure_and_Applied_Chemistry" title="Pure and Applied Chemistry">Pure and Applied Chemistry</a></i>. <b>84</b> (2): <span class="nowrap">377–</span>410. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2FPAC-REC-10-12-04">10.1351/PAC-REC-10-12-04</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:98107080">98107080</a>. Archived from <a rel="nofollow" class="external text" href="http://pac.iupac.org/publications/pac/pdf/2012/pdf/8402x0377.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2015-03-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-07-25</span></span>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFCottrell1967" class="citation book cs1"><a href="Alan_Cottrell" title="Alan Cottrell">Cottrell, Alan Howard</a> (1967). <i>An Introduction to Metallurgy</i>. Institute of Materials. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-8448-0767-2</bdi>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFCallister_Jr.2006" class="citation book cs1">Callister Jr., William D. (2006). <i>Materials Science and Engineering: An Introduction</i> (7th ed.). John Wiley & Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-35446-5</bdi>.</cite></span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFAxonHume-Rothery1948" class="citation journal cs1">Axon, H.J.; Hume-Rothery, William (22 April 1948). "The lattice spacings of solid solutions of different elements in aluminium". <i>Proceedings of the Royal Society A</i>. <b>193</b> (1032): <span class="nowrap">1–</span>24. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1948RSPSA.193....1A">1948RSPSA.193....1A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1948.0030">10.1098/rspa.1948.0030</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:96915827">96915827</a>.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite id="CITEREFAnandWolvertonSnyder2022" class="citation journal cs1">Anand, Shashwat; Wolverton, Chris; Snyder, Jeff (2022). "Thermodynamic Guidelines for Maximum Solubility". <i>Chemistry of Materials</i>. <b>34</b> (4): <span class="nowrap">1638–</span>1648. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Facs.chemmater.1c03715">10.1021/acs.chemmater.1c03715</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:246516386">246516386</a>.</cite></span>

</li>

<li id="cite_note-test-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-test_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-test_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Nesse, William D. (2000). <i>Introduction to Mineralogy</i>. New York: Oxford University Press. p91–92. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-510691-6</bdi></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

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<ul><li><cite id="CITEREFChen,_JingXu,_Zhi-qinChen,_Z-Z.Li,_T-F.2005" class="citation journal cs1">Chen, Jing; Xu, Zhi-qin; Chen, Z-Z.; Li, T-F. & Chen, F-Y. (December 2005). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060509120657/http://www.uni-graz.at/IEC-7/PDF-files/Chen.pdf">"Pargasite and ilmenite exsolution texture in clinopyroxene from the Hujialing Garnet-Pyroxenite, Su-lu U.H.P. Terrane, Central China: A geodynamic Implication"</a> <span class="cs1-format">(PDF)</span>. <i><a href="European_Journal_of_Mineralogy" class="mw-redirect" title="European Journal of Mineralogy">European Journal of Mineralogy</a></i>. <b>17</b> (6): <span class="nowrap">895–</span>903. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005EJMin..17..895C">2005EJMin..17..895C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1127%2F0935-1221%2F2005%2F0017-0895">10.1127/0935-1221/2005/0017-0895</a>. Archived from <a rel="nofollow" class="external text" href="http://www.uni-graz.at/IEC-7/PDF-files/Chen.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2006-05-09.</cite></li>

<li><cite id="CITEREFPetersen" class="citation web cs1">Petersen, U. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060411131454/http://www.mines.utah.edu/~wmep/59298/592PDF/rlm2.pdf">"Introduction to Ore Microscopy II; Mineral Paragenesis"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.mines.utah.edu/~wmep/59298/592PDF/rlm2.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2006-04-11.</cite></li></ul>

</div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.doitpoms.ac.uk/tlplib/solid-solutions/index.php">DoITPoMS Teaching and Learning Package—"Solid Solutions"</a></li></ul>

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</style><div id="Chemical_solutions144" style="font-size:114%;margin:0 4em"><a href="Solution_(chemistry)" title="Solution (chemistry)">Chemical solutions</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Solution_(chemistry)" title="Solution (chemistry)">Solution</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="Ideal_solution" title="Ideal solution">Ideal solution</a></li>

<li><a href="Aqueous_solution" title="Aqueous solution">Aqueous solution</a></li>

<li><a href="Buffer_solution" title="Buffer solution">Buffer solution</a></li>

<li><a href="Flory%E2%80%93Huggins_solution_theory" title="Flory–Huggins solution theory">Flory–Huggins</a></li>

<li><a href="Mixture" title="Mixture">Mixture</a></li>

<li><a href="Suspension_(chemistry)" title="Suspension (chemistry)">Suspension</a></li>

<li><a href="Colloid" title="Colloid">Colloid</a></li>

<li><a href="Phase_diagram" title="Phase diagram">Phase diagram</a></li>

<li><a href="Phase_separation" title="Phase separation">Phase separation</a></li>

<li><a href="Eutectic_system" title="Eutectic system">Eutectic point</a></li>

<li><a href="Alloy" title="Alloy">Alloy</a></li>

<li><a href="Saturation_concentration" class="mw-redirect" title="Saturation concentration">Saturation</a></li>

<li><a href="Supersaturation" title="Supersaturation">Supersaturation</a></li>

<li><a href="Serial_dilution" title="Serial dilution">Serial dilution</a></li>

<li><a href="Dilution_(equation)" title="Dilution (equation)">Dilution (equation)</a></li>

<li><a href="Apparent_molar_property" title="Apparent molar property">Apparent molar property</a></li>

<li><a href="Miscibility_gap" title="Miscibility gap">Miscibility gap</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Concentration" title="Concentration">Concentration</a><br>and related quantities</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="Molar_concentration" title="Molar concentration">Molar concentration</a></li>

<li><a href="Mass_concentration_(chemistry)" title="Mass concentration (chemistry)">Mass concentration</a></li>

<li><a href="Number_density" title="Number density">Number concentration</a></li>

<li><a href="Volume_fraction" title="Volume fraction">Volume concentration</a></li>

<li><a href="Equivalent_concentration" title="Equivalent concentration">Normality</a></li>

<li><a href="Molality" title="Molality">Molality</a></li>

<li><a href="Mole_fraction" title="Mole fraction">Mole fraction</a></li>

<li><a href="Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">Mass fraction</a></li>

<li><a href="Natural_abundance" title="Natural abundance">Isotopic abundance</a></li>

<li><a href="Mixing_ratio" title="Mixing ratio">Mixing ratio</a></li>

<li><a href="Ternary_plot" title="Ternary plot">Ternary plot</a></li>

<li><a href="Total_dissolved_solids" title="Total dissolved solids">Total dissolved solids</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Solubility" title="Solubility">Solubility</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="Solubility_equilibrium" title="Solubility equilibrium">Solubility equilibrium</a></li>

<li><a href="Solvation" title="Solvation">Solvation</a></li>

<li><a href="Solvation_shell" title="Solvation shell">Solvation shell</a></li>

<li><a href="Enthalpy_change_of_solution" title="Enthalpy change of solution">Enthalpy of solution</a></li>

<li><a href="Lattice_energy" title="Lattice energy">Lattice energy</a></li>

<li><a href="Raoult's_law" title="Raoult's law">Raoult's law</a></li>

<li><a href="Henry's_law" title="Henry's law">Henry's law</a></li>

<li><a href="Solubility_table" title="Solubility table">Solubility table (data)</a></li>

<li><a href="Solubility_chart" title="Solubility chart">Solubility chart</a></li>

<li><a href="Miscibility" title="Miscibility">Miscibility</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Solvent" title="Solvent">Solvent</a></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>(Category)</li>

<li><a href="Acid_dissociation_constant" title="Acid dissociation constant">Acid dissociation constant</a></li>

<li><a href="Protic_solvent" title="Protic solvent">Protic solvent</a></li>

<li><a href="Polar_aprotic_solvent" title="Polar aprotic solvent">Polar aprotic solvent</a></li>

<li><a href="Inorganic_nonaqueous_solvent" title="Inorganic nonaqueous solvent">Inorganic nonaqueous solvent</a></li>

<li><a href="Solvation" title="Solvation">Solvation</a></li>

<li><a href="List_of_boiling_and_freezing_information_of_solvents" title="List of boiling and freezing information of solvents">List of boiling and freezing information of solvents</a></li>

<li><a href="Partition_coefficient" title="Partition coefficient">Partition coefficient</a></li>

<li><a href="Chemical_polarity" title="Chemical polarity">Polarity</a></li>

<li><a href="Hydrophobe" title="Hydrophobe">Hydrophobe</a></li>

<li><a href="Hydrophile" title="Hydrophile">Hydrophile</a></li>

<li><a href="Lipophilicity" title="Lipophilicity">Lipophilic</a></li>

<li><a href="Amphiphile" title="Amphiphile">Amphiphile</a></li>

<li><a href="Lyonium_ion" title="Lyonium ion">Lyonium ion</a></li>

<li><a href="Lyate_ion" title="Lyate ion">Lyate ion</a></li></ul>

</div></td></tr></tbody></table></div>

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This article is issued from <a class="external text" title="Last edited on 2025-05-09" href="https://en.wikipedia.org/wiki/?title=Solid_solution&oldid=1289499068">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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