THE ZERO STATIC INTERNAL-STRESS APPROXIMATION IN LATTICE-DYNAMICS, AND THE CALCULATION OF ISOTOPE EFFECTS ON MOLAR VOLUMES

For crystals in which relative positions of atoms within the unit cell are not wholly determined by symmetry, a complete application of the quasiharmonic approximation requires the minimization of the free ener gy with respect to both external (eta(lambda) and internal (epsilon(j) ) strains. The zero static internal stress approximation first minimiz es the static lattice energy with respect to the epsilon(j) for each s tate of external strain; the total free energy is then minimized only with respect to the eta(lambda). We show that although this gives an i ncorrect internal strain, to the first order it gives the correct exte rnal strain at each temperature; in principle, errors are thus of the same order as those due to the use of the quasiharmonic approximation. In particular, recent calculations by Lacks [D. J. Lacks, J. Chem. Ph ys. 103, 5085 (1995)] of the effect of deuteration on the molar volume of polyethylene are shown by the present analysis to include indirect ly the effect of vibrational stretching of the C-H(D) bonds, and their reasonable agreement with room temperature measurements may after all not be fortuitous. (C) 1996 American Institute of Physics.