TY - JOUR

T1 - Vibrational properties of model monatomic crystals under pressure

AU - Wolf, George H.

AU - Jeanloz, Raymond

PY - 1985

Y1 - 1985

N2 - 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-Gr̈neisen 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-Gr̈neisen 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 Gr̈neisen parameter decreases with pressure, but the commonly assumed power-law relation of the thermal Gr̈neisen 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.

AB - 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-Gr̈neisen 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-Gr̈neisen 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 Gr̈neisen parameter decreases with pressure, but the commonly assumed power-law relation of the thermal Gr̈neisen 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.

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U2 - 10.1103/PhysRevB.32.7798

DO - 10.1103/PhysRevB.32.7798

M3 - Article

AN - SCOPUS:0001343370

VL - 32

SP - 7798

EP - 7810

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 12

ER -