Atomic mean-square displacement in fcc metals: repulsive potentials

摘要

We present a method for the calculation of the atomic mean-square displacement (u2) of an anharmonic crystal from potentials involving repulsive interactions. The quasiharmonic and the lowest-order cubic and quartic anharmonic contributions to (u2) are evaluated from the knowledge of seven Brillouin zone (BZ) sums which are tabulated in the interval -0.1 a1 0.0. The parameter a1 characterizes the volume dependence of the BZ sums and is negative for repulsive potentials. All the BZ sums are evaluated in the limit L , where L is the step length from the origin to the boundary of the BZ. The method is applicable to a nearest-neighbour central force model of the fcc lattice, and it can be extended to a bcc lattice. We present two applications of the method. One is the calculation of (u2) from the r-1 2 repulsive potential, and our results are in good agreement with those obtained by Monte Carlo methods. The other is to the nearest-neighbour Born-Mayer potential with a volume-dependent e ective coe cient alpha. In the case of Cu, the agreement with other theoretical calculations as well as the experimental values from X-ray data at 300 and 400 K is excellent.