Comparison of hexagonal close packed and cubic close packed rare gas solids

Hexagonal close packed and cubic close packed structures of heavy rare gas atoms are compared. Lattice expansion effects are examined for a model in which atoms interact via Lennard-Jones (12-6) potentials, lattice motion is according to the quasiharmonic approximation, and the model crystals are in equilibrium at constant temperature and pressure. Phonon frequencies are found to depend sensitively upon lattice parameters. In the cubic (hexagonal) structure the phonon modes most strongly affected by expansion are long (short) wavelength, longitudinal (transverse), acoustic (optic) modes. Phonon frequencies for the cubic structure all remain real for expansions considerably greater than would cause imaginary frequencies for the hexagonal structure. Equilibrium lattice parameters are found to deviate from their static equilibrium values by amounts depending upon the De Boer parameter, the deviations being slightly greater for the hexagonal structure, which exhibits nonideal stacking. The problem of explaining the observed stability of the cubic structures of real rare gas solids is discussed.Science, Faculty ofPhysics and Astronomy, Department ofGraduat