Statistical Mechanics of Solids

Chapter 8: Order-Disorder Alloys

8.1 Order-Disorder Structures

A binary order-disorder structure is defined as a two-component crystal with the following properties:

  1. At absolute zero of temperature, atoms of each component separately occupy a sublattice of the crystal. Each of the two interpenetrating sublattices contains only one type of atom. The structure is then said to be completely ordered.

  2. At sufficiently high temperatures, both types of atoms are distributed throughout both sublattices at random. The structure is then said to be completely disordered.

Two examples of order-disorder structures are shown in figure 8.1, in which A represents the structure of ?-brass (CuZn). If we ignore the identity of the atoms, the structure is body-centered cubic (BCC). The BBC lattice contains two interpenetrating simple cubic (SC) sublattices, one sublattice consisting of the cube corners, and the other sublattice consisting of the cube centers, as shown in figure 8.1A. In the completely ordered state, the body centers of the unit cubes are all occupied by atoms of one type (say, Cu) while the cube corners are all occupied by atoms of the other type (say, Zn). The two sublattices are completely equivalent, and it is immaterial which type of atom is assigned to a given sublattice. In the completely disordered state, any site can be occupied by an atom of either type, the probability that a given site contains an atom of a given type being one half.


Figure 8.1: Order-disorder lattice structures. A, Body-centered cubic stimustince of ?-brass (CuZu). B, Face-centered cubic structure of...

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