ATOMIC MEAN-SQUARE DISPLACEMENT IN FCC METALS - REPULSIVE POTENTIALS

We present a method for the calculation of the atomic mean-square disp lacement [mu(2)] of an anharmonic crystal from potentials involving re pulsive interactions. The quasiharmonic and the lowest-order cubic and quartic anharmonic contributions to [mu(2)] are evaluated from the kn owledge of seven Brillouin zone (BZ) sums which are tabulated in the i nterval -0.1 less than or equal to a(1) less than or equal to 0.0. The parameter a(1) characterizes the volume dependence of the BZ sums and is negative for repulsive potentials. All the BZ sums are evaluated i n the limit L --> infinity, where L is the step length from the origin to the boundary of the BZ. The method is applicable to a nearest-neig hbour central force model of the fee lattice, and it can be extended t o a bcc lattice. We present two applications of the method. One is the calculation of [mu(2)] from the r(-12) repulsive potential, and our r esults are in good agreement with those obtained by Monte Carlo method s. The other is to the nearest-neighbour Born-Mayer potential with a v olume-dependent effective coefficient alpha. In the case of Cu, the ag reement with other theoretical calculations as well as the experimenta l values from X-ray data at 300 and 400 K is excellent.