Order-Disorder Phase Transition in Binary Alloys—Coherent Potential Approximation

The electronic density of states of a one-dimensional $\mathrm{AB}$ model alloy with long-range order is calculated in the coherent potential approximation. Impurity states are found inside the energy gap and the energy gap disappears long before the alloy becomes completely disordered. The temperature-dependent long-range order exhibits a first-order order-disorder phase transition which causes a discontinuity in the electronic density of states at the middle of the energy gap at the critical temperature $T_c$.