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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.
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)
Substitutional solid solution strengthening occurs when the solute atom is large enough that it can replace solvent atoms in their lattice positions. Some alloying elements are only soluble in small amounts, whereas some solvent and solute pairs form a solution over the whole range of binary compositions.
The solvus or solubility line (or curve) is the line (or lines) on a phase diagram that give the limits of solute addition. That is, the lines show the maximum amount of a component that can be added to another component and still be in solid solution. In the solid's crystalline structure, the 'solute' element can either take the place of the ...
In metal alloys with substitutional solute elements, such as aluminum-magnesium alloys, dynamic strain aging leads to negative strain rate sensitivity which causes instability in plastic flow. [4] The diffusion of solute elements around a dislocation can be modeled based on the energy required to move a solute atom across the slip plane of the ...
A Lippmann diagram is a graphical plot showing the solidus/solutus equilibrium states for a given binary solid solution (e.g., (Ba 1-x Sr x)SO 4, barite/celestite) in equilibrium with an aqueous solution containing the two substituting ions: Ba 2+ and Sr 2+ (solid solution – aqueous solution system, or SS-AS).
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]
Then there is the Hume-Rothery rule, which states that two metals that differ by more than 15% in their atomic radius will not form substitutional solid solutions. This rule can only be used reliably (90 % success) to predict poor solubility; it cannot predict good solubility.