Atomic mean-square displacements in f.c.c. metals

Abstract

In two recent letters, one by Zoli in 1991, and the other by Schober in 1992, the evaluation of the quasiharmonic and anharmonic contributions to the atomic mean-square displacement (MSD) for f.c.c. metals has been discussed. In Zoli's work, the difference in the two contributions is found to be 91%. Schober, on the other hand, has not evaluated the explicit anharmonic contribution to MSD. The huge difference in Zoli's work is shown here to be due to an inaccurate evaluation of the explicit anharmonic contribution to MSD. A proper self-contained method as presented here, which employs the same model in the quasiharmonic and anharmonic calculations of MSD or Debye-Waller factor, indeed shows that the two contributions differ from each other by 10–15% depending on the temperature. Larger differences exist at higher temperatures. Some numerical results are given for a model of the f.c.c. lattice, namely a nearest-neighbour central force model employing a Lennard-Jones potential (applicable to rare-gas solids) and the Morse potential as a model for Cu.