According to the Hume-Rothery rules for the substitutional solid solutions the atomic sizes of the the solute and solvent must not differ by more than 15%.

Why should it be so?


Possibly, there are two extrema to account:

a) the atomic radii of metal A and metal B do not differ significantly, and thus there are chances both metals blend statistically with each other. Which would be covered by the $< 15\%$-rule, a situation similar to mixing apples and oranges in one crate.

b) the atomic radii differ a lot. If we assume atoms as hard spheres, even the closest arrangement of spheres of one sort does not occupy fully the space available (see e.g., fcc and hcp packing). If the diameter of the other metal(s) is/are much less than the one of the host, it is possible for some of these pockets to be filled more, and for others to be filled less. Overall, the distribution of metal B and metal A in the blend of (A .and. B) no longer is even; the smaller atoms may segregate. As if you would transport a crate of filled with melons and hazel nuts. This non-regular demixing is possible because -- contrary e.g., to spinels -- you may assume absence of ions charged oppositely charged.

For the purpose of illustration, both the examples as well as the figure below intentionally exaggerate the contrast between case a) and b).

enter image description here


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