When solute atoms substitute the parent lattice atoms from their original sites, the solid solution is called a substitutional solid solution. There could be two possibilit­ies: First, solute atoms can substitute the host lattice atoms randomly, forming a random (or disordered) substitutional solid solution. An overwhelming majority of substitutional alloys are of this type. Second, an ordered (substitutional) solid solu­tion results when the solute and solvent atoms are arranged in a regular fashion on the lattice sites (Figure 2.27). Perfect order becomes possible when the two metals are mixed in some fixed proportions such as 3 : 1, 1: 1, and so on and at under certain temperature. For example, Cu3Au (75 at% of Cu and 25 at% of Au) alloy can exhibit an ordered structure at lower temperature range, but above a certain tem­perature range the ordered alloy loses perfect order, thus becoming disordered. However, the Cu-Ni alloy system at all compositions and in all conditions are dis­ordered, which is the norm most times.

Hume-Rothery studied a number of substitutional alloys and developed a set of

basic rules for substitutional solid solubility. The principles derived from his study

are known as the Hume-Rothery’s rules:

1) “The atom size difference between the host atom and the solute atom should be less than 15%.” If the size difference becomes higher, more intense stress fields are created. This observation is true for both large and small solute atoms. Generally, a large atom induces a compressive stress field around itself, while a small atom tends to introduce a tensile stress field. These stress fields can increase the potential energy of the crystal. Therefore, the solid solubility becomes more limited as the size difference increases. This is known as the size factor effect. For example, the atomic radii of copper and nickel are 145 and 149 pm., respectively. The percentage size difference is only about 2.8%. They have wide solid solubility in each other.

2) “The electronegativity difference between the solvent and the solute should be small.” Electronegativity is defined as the ability of an atom to attract electrons to itself. The electronegativity difference between two elements can be calcu­lated from Pauling’s electronegativity scale. The difference is generally quite small between typical metallic elements. If the electronegativity difference is more, the tendency would be to create compounds rather than alloys. This is called chemical affinity effect. For example, the Pauling electronegativity values of copper and nickel are 1.9 and 1.91, respectively, thus giving the difference of only 0.01.

3) “The valency of the atoms constituting the alloy must be the same for extensive solid solubility.” However, when the valencies are different, a metal with lower valency tends to dissolve in a metal of higher valency more readily than vice versa. It is found that an excess of electrons is more readily tolerated rather than a deficiency of bonding electrons. This is known as relative valency effect. For instance, zinc (two valence electrons) dissolves appreciable amount of copper (up to 38%), whereas copper (one valence electron) dissolves only about 3% in zinc.

4) “The crystal structures of the solvent and solute should be the same for achiev­ing extensive solid solubility, known as crystal structure effect.” This implies that solute atoms can substitute the host lattice atoms continuously, forming a series of solid solutions. A nice example of this is the isomorphous system of copper and nickel (both have FCC crystal structure).