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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.
At room temperature, the solubility of carbon and nitrogen in solid solutions is exceedingly small. [10] By raising, the temperature beyond 400 o C and cooling at a moderate rate, it is easy to keep a few hundredths of a percent of either element within the solution, while the remainder is supersaturated. [ 10 ]
The predominant phase was a face-centered cubic solid-solution phase, containing mainly Cr, Mn, Fe, Co, and Ni. From that result, the CrMnFeCoNi alloy, which forms only a solid-solution phase, was developed. [22] The Hume-Rothery rules have historically been applied to determine whether a mixture will form a solid solution. Research into high ...
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.
An atom diffuses in the interstitial mechanism by passing from one interstitial site to one of its nearest neighboring interstitial sites. The movement of atoms can be described as jumps, and the interstitial diffusion coefficient depends on the jump frequency. The jump frequency, , is given by: