Solid solution

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A solid solution describes a family of materials which have a range of compositions (e.g. AxB1−x) and a single
crystal structure In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen ...

. Many examples can be found in
metallurgy Metallurgy is a domain of Materials science, materials science and engineering that studies the physical and chemical behavior of metallic Chemical element, elements, their Inter-metallic alloy, inter-metallic compounds, and their mixtures, which ...
,
geology Geology (from the Ancient Greek γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is an Earth science concerned with the solid Earth, the rock (geology), rocks of which it is composed, and the processes by which th ...

, and
solid-state chemistrySolid-state chemistry, also sometimes referred as materials chemistry, is the study of the synthesis, structure, and properties of solid phase materials, particularly, but not necessarily exclusively of, non-molecular solids. It therefore has a stro ...
. The word "solution" is used to describe the intimate mixing of components at the atomic level and distinguishes these homogeneous materials from physical
mixture In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, ...

s of components. In general if two compounds are
isostructuralIsostructural chemical compounds have similar chemical structures. "Isomorphism (crystallography), Isomorphous" when used in the relation to crystal structures is not synonymous: in addition to the same atomic connectivity that characterises isostruc ...
then a solid solution will exist between the end members (also known as parents). For example
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With Molar mass, molar ...
and
potassium chloride Potassium chloride (KCl, or potassium salt) is a metal halide Metal halides are compounds between metals and halogens. Some, such as sodium chloride are ionic, while others are covalently bonded. Covalently bonded metal halides may be discrete m ...

have the same cubic crystal structure so it is possible to make a pure compound with any ratio of sodium to potassium (Na1-xKx)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 Lo Salt which is (Na0.33K0.66)Cl hence why it contains 66% less sodium than normal table salt (NaCl). The pure minerals are called
halite Halite ( or ), commonly known as rock salt, is a type of salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of Salt (chemistry), salts; salt in its natural form as a cry ...

and
sylvite Sylvite, or sylvine, is potassium chloride Potassium chloride (KCl, or potassium salt) is a metal halide Metal halides are compounds between metals and halogens. Some, such as sodium chloride are ionic, while others are covalently bonded. Cova ...

, a physical mixture of the two is referred to as . 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.
Olivine The mineral In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Ra ...

is described by the formula (Mg, Fe)2SiO4, which is equivalent to (Mg1−xFex)2SiO4. The ratio of magnesium to iron varies between the two endmembers of the solid solution series: forsterite (Mg-endmember: Mg2SiO4) and fayalite (Fe-endmember: Fe2SiO4) 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.

# Phase diagrams

On a phase diagram 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
miscibility gapA miscibility gap is a region in a phase diagram for a mixture of components where the mixture exists as two or more Phase (matter), phases – any region of composition of mixtures where the constituents are not completely miscible. The IUPAC_book# ...
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 maybe 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
cocrystalCocrystals are "solids that are crystalline single phase materials composed of two or more different molecular or ionic compounds generally in a stoichiometric ratio which are neither solvates nor simple salts." A broader definition is that cocrystal ...
. In metallurgy alloys with a set composition are referred to as
intermetallic An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy An alloy is an admixture of metal A metal (from Ancient Greek, Gree ...
compounds. A solid solution is likely to exist when the two elements (generally
metal A metal (from Ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts Electrical resistivity and conductivity, el ...

s) involved are close together on the
periodic table The periodic table, also known as the periodic table of (the) chemical elements, is a tabular display of the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical element ...

, an intermetallic compound generally results when two metals involved are not near each other on the periodic table.

# Details

The solute may incorporate into the solvent
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of Translation operator (quantum mechanics)#Discrete Translational Symmetry, discrete translation operations described in th ...
'' substitutionally'', by replacing a solvent particle in the lattice, or '' interstitially'', 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. Where the atomic radii of the solute atom is larger than the solvent atom it replaces the crystal structure (
unit cell In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen ...

) 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 Vegard's law. 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
chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wit ...

,
crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen drop", with its mean ...

, and
quantum In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
properties of the substances in question. Substitutional solid solutions, in accordance with the
Hume-Rothery rulesHume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules; one refers to substitutional solid s ...
, may form if the solute and solvent have: * Similar
atomic radii The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the Atomic nucleus, nucleus to the boundary of the surrounding Electron shell, shells of electrons. Since the bou ...

(15% or less difference) * Same crystal structure * Similar
electronegativities Electronegativity, symbolized as '' χ'', is the tendency of an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. ...

* Similar valency a solid solution mixes with others to form a new solution The
phase diagram A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phase (matter), phases (such as solid, liqu ...

in ''Fig. 1'' displays an
alloy An alloy is an admixture of metal A metal (from Ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts Elec ...
of two metals which forms a solid solution at all relative
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...

s 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 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. The binary phase diagram in ''Fig. 2'' shows the phases of a mixture of two substances in varying concentrations, $A$ and $B$. The region labeled "$\alpha$" is a solid solution, with $B$ acting as the solute in a matrix of $A$. On the other end of the concentration scale, the region labeled "$\beta$" is also a solid solution, with $A$ acting as the solute in a matrix of $B$. The large solid region in between the $\alpha$ and $\beta$ solid solutions, labeled "$\alpha$ + $\beta$", is ''not'' a solid solution. Instead, an examination of the
microstructure Microstructure is the very small scale structure of a material, defined as the structure of a prepared surface of material as revealed by an optical microscope above 25× magnification. The microstructure of a material (such as metals, polymer ...
of a mixture in this range would reveal two phases—solid solution $A$-in-$B$ and solid solution $B$-in-$A$ would form separate phases, perhaps lamella or
grains A grain is a small, hard, dry seed A seed is an embryonic plant enclosed in a protective outer covering. The formation of the seed is part of the process of reproduction Reproduction (or procreation or breeding) is the biological pro ...

.

# Application

In the phase diagram, at three different concentrations, the material will be solid until its heated to its
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state of matter, state from solid to liquid. At the melting point the solid and liquid phase exist in Thermodynamic equilibrium, equilibrium. ...

, and then (after adding the
heat of fusion The enthalpy of fusion of a substance, also known as (latent) heat of fusion is the change in its enthalpy Enthalpy is a property of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls ...
) become liquid at that same temperature: * the unalloyed extreme left * the unalloyed extreme right * the dip in the center (the eutectic composition). At other proportions, the material will enter a mushy or pasty phase until it warms up to being completely melted. The mixture at the dip point of the diagram is called a eutectic 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
toxicity Toxicity is the degree to which a chemical substance or a particular mixture of substances can damage an organism. Toxicity can refer to the effect on a whole organism, such as an animal, bacteria, bacterium, or plant, as well as the effect on a ...

and consequent difficulty in recycling devices and components that include lead.)

# Exsolution

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
lamellae Lamella (plural lamellae) means a small plate or flake in Latin, and in English may refer to: Biology * Lamella (mycology) File:Trompetenpfifferling Teufelskanzel.jpg, "False" gills of ''Craterellus tubaeformis'' A lamella, or gill, is a papery h ...
. This is mainly caused by difference in cation size. Cations which have a large difference in radii are not likely to readily substitute.Nesse, William D. (2000). ''Introduction to Mineralogy''. New York: Oxford University Press. p91-92. Take the alkali
feldspar Feldspars are a group of rock-forming aluminium tectosilicate minerals, containing sodium, calcium, potassium or barium. The most common members of the feldspar group are the ''plagioclase'' (sodium-calcium) feldspars and the ''alkali'' (potas ...
minerals In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. (20 ...

for example, whose end members are
albite Albite is a plagioclase feldspar Feldspars () are a group of rock-forming tectosilicate minerals that make up about 41% of the Earth's continental crust by weight. Feldspars crystallize from magma as both Intrusive rock, intrusive and extru ...

, NaAlSi3O8 and
microcline Microcline (KAlSi3O8) is an important igneous rock Igneous rock (derived from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in ...

, KAlSi3O8. At high temperatures Na+ and K+ 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+ and the same applies for Na+ 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, resulting in a
perthite and a first-order red plate. The K-feldspar host (orthoclase) appears orange, and albite exsolution lamellae appear yellow. Long dimension of field is 0.4 mm. Perthite is used to describe an intergrowth of two feldspar Feldspars () are a group ...
texture.

*
Solid solution strengthening Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), ...

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