Substitutional Solid Solutions

          If the atoms of the solvent or parent metal are replaced in the crystal lattice by atoms of the solute metal then the solid solution is known as 'Substitutional solid solution'.

For example, copper atoms may substitute for nickel atoms without disturbing the F.C.C. structure of nickel (Fig. a). In the substitutional solid solutions, the substitution can be either disordered or ordered.

Fig. b shows disordered substitutional solid solution. Here the solute atoms have substituted disorderly for the solvent atoms on their lattice site.

Fig. c shows an ordered substitutional solid solution. Here the solute atoms have substituted in an orderly manner for the solvent atoms on their lattice site.

Hume Rothery rules for the formation of substitutional solid solutions:

          By studying a number of alloy systems, Hume Rothery formulated certain rules which govern the formation of substitutional solid solutions. These are:

(a) Crystal structure factor:

          For complete solid solubility, the two elements should have the same type of crystal structure i.e., both elements should have either F.C.C or B.C.C or H.C.P structure.

(b) Relative size factor: 

         As the size (atomic radii) difference between two elements increases, the solid solubility becomes more restricted. For extensive solid solubility the difference in atomic radii of two elements should be less than about 15%. If the relative size factor is more than 15%, solid solubility is limited. For example, both silver and lead have F.C.C Structure and the relative size factor is about 20%. Therefore the solubility of lead in solid silver is about 1.5% and he solubility of silver in solid lead is about 0.1%. Copper and Nickel are completely soluble in each other in all proportions. They have the same type of crystal structure (F.C.C) and differ in atomic radii by about 2%.    

(c) Chemical affinity factor:

          Solid solubility is favored when the two metals have lesser chemical affinity. If the chemical affinity of the two metals is greater then greater is the tendency towards compound formation. Generally, if the two metals are separated in the periodic table widely then they possess greater chemical affinity and are very likely to form some type of compound instead of solid solution.  

(d) Relative  valence  factor:

          It is found that a metal of lower valance tends to dissolve more of a metal of higher valance than vice versa. For example in Aluminium-nickel alloy system, nickel (lower valance) dissolve 5% aluminium but aluminium (higher valance) dissolve 0.04% nickel.