Solid solution

A solid solution is a solid phase whose composition can vary as components share one crystal structure. In a substitutional solid solution, atoms replace host atoms on lattice sites; interstitial solutions place smaller atoms between them.

This is distinct from a macroscopic mixture of separate solid phases. Composition-dependent lattice distortion can affect strength and transport, linking atomic placement with the properties of an alloy or mineral.

For ideal independent mixing on crystallographic sublattices, an endmember’s thermodynamic activity is the product of its required site fractions, with multiplicities. If one component occupies $q$ equivalent mixing positions per formula unit and has site fraction $X$, then $a=X^q$, not generally $X$.

For a binary example, the mixing Gibbs free energy per mole of formula units is $qRT[X\ln X+(1-X)\ln (1-X)]$. Differentiating the total free energy with respect to the amount of the all-component endmember gives a mixing chemical-potential term $qRT\ln X$. Comparison with $RT\ln a$ proves $a=X^q$. This derivation assumes ideal mixing and equal site fractions; nonideal interactions and preferential site occupancy require a different model. Mg endmembers of biotite and garnet commonly use $X_{\mathrm{Mg}}^3$ in this simplified three-site approximation.

An activity model in which distinct atomic positions in a crystal structure are occupied independently by specified species. For ideal random mixing, a pure mineral endmember requiring ${\nu }_s$ specified atoms on site type $s$ has thermodynamic activity $a={\prod }_s{X}_s^{{\nu }_s}$ relative to that pure endmember, with other occupations held fixed. Its mixing contribution to the chemical potential is $RT\ln a$. The powers count occupied positions per formula unit; they are not always the mole fraction of whole endmember formulae.

Resistance to dislocation motion caused by substitutional or interstitial solutes and their interactions with the dislocation strain field and core.

An approximate linear interpolation of a substitutional solid solution's lattice parameter with atomic composition. Converting the inferred atomic fraction to mass fraction requires molar masses. Ordering, nonideal mixing, strain and multiple phases can invalidate a simple two-endpoint interpolation.

The composition boundary beyond which one homogeneous phase cannot accommodate additional solute under the stated conditions. Phase separation or a new structure can appear beyond that range.

Coupled changes in ions, oxidation states or vacancies that preserve charge balance when a lattice substitution changes formal charge.

Replacement of a lattice ion by another of the same formal charge. charge neutrality alone does not ensure unlimited solubility; size and coordination preferences also matter.

A solid solution adjoining a pure-component end of a composition phase diagram. Its solute content can be small but need not be zero. A phase label such as (Bi) therefore does not by itself mean exactly pure bismuth.

A semiconductor solid solution whose composition changes its band gap.