Vibrational properties of model monatomic crystals under pressure

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Abstract
The roles of the attractive and repulsive forces in controlling the vibrational properties of monatomic crystals are systematically evaluated as a function of compression. Face-centered-cubic, hexagonal, and body-centered-cubic structures are considered with Lennard-Jones and Buckingham-type interatomic potentials. At zero pressure, the phonon frequencies and their mode-Grüneisen parameters deviate strongly from those of a reference state where the atoms interact solely through the corresponding purely repulsive potential. In detail, the degree of deviation depends on the structure, relative range of the repulsive and attractive forces, and the vibrational wavelength. With increasing pressure, the phonon frequencies asymptotically approach values of the purely repulsive reference state. Higher-order properties such as the mode-Grüneisen parameters and their logarithmic volume derivatives approach the repulsive limiting values more rapidly than do the frequencies, provided the associated modes do not become unstable. The close-packed lattices are dynamically stable at all positive pressures and display only a small variation among different orders of the frequency spectra Debye moments. However, this variation can be quite large for any structure at strains near that where the lattice is dynamically unstable. We find that the thermal Grüneisen parameter decreases with pressure, but the commonly assumed power-law relation of the thermal Grüneisen parameter with volume is violated. Average anharmonic vibrational properties are well described by a cell model in these monatomic systems at both low and high pressures. In addition, a strong correlation is found between the static-lattice compressional properties and the average vibrational properties; free-volume relations give good estimates of the high-temperature thermal properties, especially at high pressures.