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Hume-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 solutions, and the other refers to interstitial solid solutions.
Interstitial solid solutions form when the solute atom is small enough (radii up to 57% the radii of the parent atoms) [2] to fit at interstitial sites between the solvent atoms. The atoms crowd into the interstitial sites, causing the bonds of the solvent atoms to compress and thus deform (this rationale can be explained with Pauling's rules ...
The propensity for any two substances to form a solid solution is a complicated matter involving the chemical, crystallographic, and quantum properties of the substances in question. Substitutional solid solutions, in accordance with the Hume-Rothery rules, may form if the solute and solvent have: Similar atomic radii (15% or less difference)
This is a schematic illustrating how the lattice is strained by the addition of interstitial solute. Notice the strain in the lattice that the solute atoms cause. The interstitial solute could be carbon in iron for example. The carbon atoms in the interstitial sites of the lattice creates a stress field that impedes dislocation movement.
[citation needed] As these interstitial atoms distort the lattice slightly, there will be an associated residual stress field surrounding the interstitial. This stress field can be relaxed by the interstitial atom diffusing towards a dislocation [ citation needed ] , which contains a small gap at its core (as it is a more open structure), see ...
In metallurgy, the Darken equations are used to describe the solid-state diffusion of materials in binary solutions. They were first described by Lawrence Stamper Darken in 1948. [ 1 ] The equations apply to cases where a solid solution's two components do not have the same coefficient of diffusion .
The iron-carbon martensitic transformation generates an increase in hardness. The martensitic phase of the steel is supersaturated in carbon and thus undergoes solid solution strengthening. [6] Similar to work-hardened steels, defects prevent atoms from sliding past one another in an organized fashion, causing the material to become harder.
Zintl phases can be prepared in regular solid state reactions, usually performed under an inert atmosphere or in a molten salt solution. Typical solid state methods include direct reduction of corresponding oxides in solution phase reactions in liquid ammonia or mercury.