Problems

Abstract

Consider a simple lattice model for a 50–50 pseudobinary zinc blende alloy A_0.5B_0.5C. Start with a virtual crystal with an average bond length d = (d⁰_AC + d⁰ _BC )/2, in which the C atoms occupy a fcc sublattice and the averaged atoms (of A and B) occupy another sublattice. Each atom is connected to its nearest-neighboring atoms by springs with a force constant κ. There is no strain energy in this virtual crystal. Now replace a virtual atom by a real A atom, as illustrated in Fig. 3.3. Because the average bond length d is not the same as the natural bond length d⁰_AC, strain is built in the four bonds surrounding the A atom. If we only allow these four C atoms to relax while the rest of the atoms are held in their original positions, show that when the strain energy is minimized the relaxation parameter Γ (defined in Eq. 1.3.2) for these four AC bonds is exactly 75%.