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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)
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. This is a schematic illustrating how the lattice is strained by the addition of substitutional solute.
Interstitial atoms (blue) occupy some of the spaces within a lattice of larger atoms (red) In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure.
Steel is an example of an interstitial alloy, because the very small carbon atoms fit into interstices of the iron matrix. Stainless steel is an example of a combination of interstitial and substitutional alloys, because the carbon atoms fit into the interstices, but some of the iron atoms are substituted by nickel and chromium atoms. [8]
In interstitial lattice diffusion, a diffusant (such as C in an iron alloy), will diffuse in between the lattice structure of another crystalline element. In substitutional lattice diffusion ( self-diffusion for example), the atom can only move by substituting place with another atom.
In the case of an impurity, the atom is often incorporated at a regular atomic site in the crystal structure. This is neither a vacant site nor is the atom on an interstitial site and it is called a substitutional defect. The atom is not supposed to be anywhere in the crystal, and is thus an impurity.