The heart of crystalline materials

Primary solid solutions are defined by the solubility limit of the alloying element(s) (\(\ce{B}\)) in the base metal (\(\ce{A}\)). There are some empirical rules, called the Hume-Rothery rules, that allow the order of magnitude of the solubility limit to be qualitatively evaluated:

• size effect:

  this effect is related to the variation in elastic energy due to solution heat treatment. If the atomic diameters of elements \(\ce{A}\) and \(\ce{B}\) differ by more than 15 %, the solubility of \(\ce{B}\) in \(\ce{A}\) will be very limited (only a few atomic %),

• electronegativity effect:

  if elements\(\ce{A}\) and \(\ce{B}\) have very different electronegativities, they will tend to form bonds with a non-metallic character (ionic or covalent), which will considerably decrease the primary solubility,

• valence effect:

  the solubility of an element with high valence is greater in a solvent of low valence than in the opposite case,

• electronic concentration effect:

  the solubility limit is governed by the electronic concentration (number of valence electrons per atom).