Abstract
The coherent potential approximation has been employed to calculate the dielectric matrix in random binary alloys. The dielectric matrix so obtained has been examined to deduce the behaviour of the density-density response function, which has been used to infer the average and the random parts of the force constants that appear in the phonon Hamiltonian. The force constants between two sites have been shown to be proportional to the nuclear charges of the corresponding nuclei, within the proposed approximation. This result suggests that the fluctuations of the force constants in random binary alloys are small. The author thinks that the present calculation can give an explanation of the long phonon lifetime found experimentally in alloys with small mass disorder.