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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.
Substitutional solute in lattice. Depending on the size of the alloying element, a substitutional solid solution or an interstitial solid solution can form. [2] In both cases, atoms are visualised as rigid spheres where the overall crystal structure is essentially unchanged.
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)
At 0-D there is precipitate and solid solution strengthening with particulates strengthening structure, at 1-D there is work/forest hardening with line dislocations as the hardening mechanism, and at 2-D there is grain boundary strengthening with surface energy of granular interfaces providing strength improvement.
Iron, for example, can hold a maximum of 6.67% carbon. Although the elements of an alloy usually must be soluble in the liquid state, they may not always be soluble in the solid state. If the metals remain soluble when solid, the alloy forms a solid solution, becoming a homogeneous structure consisting of identical crystals, called a phase.
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