Tomaschitz, R.
(2021). Thermodynamics of lattice vibrations in non-cubic crystals: the zinc
structure revisited, *Acta Crystallographica *A**77**, 420-432,
DOI: 10.1107/S2053273321005507

**Abstract **IUCr
, WileyOnline

A phenomenological model of
anisotropic lattice vibrations is proposed, using a temperature-dependent
spectral cutoff and varying Debye temperatures for the vibrational normal
components. The internal lattice energy, entropy and Debye-Waller *B*
factors of non-cubic elemental crystals are derived. The formalism developed is
non-perturbative, based on temperature-dependent linear dispersion relations
for the normal modes. The Debye temperatures of the vibrational normal
components differ in anisotropic crystals; their temperature dependence and the
varying spectral cutoff can be inferred from the experimental lattice heat
capacity and *B* factors by least-squares regression. The zero-point
internal energy of the phonons is related to the low-temperature limits of the
mean-squared vibrational amplitudes of the lattice measured by X-ray and *g*-ray diffraction. A
specific example is discussed, the thermodynamic variables of the hexagonal
close-packed zinc structure, including the temperature evolution of the *B*
factors of zinc. In this case, the lattice vibrations are partitioned into
axial and basal normal components, which admit largely differing *B*
factors and Debye temperatures. The second-order *B* factors defining the
non-Gaussian contribution to the Debye-Waller damping factors of zinc are
obtained as well. Anharmonicity of the oscillator potential and deviations from
the uniform phonon frequency distribution of the Debye theory are modeled
effectively by the temperature dependence of the spectral cutoff and Debye
temperatures.

description: Roman
Tomaschitz (2021) Thermodynamics of lattice vibrations in non-cubic crystals:
the zinc structure revisited, *Acta Crystallogr. *A**77**, 420.

**Keywords:** Anisotropic
lattice vibrations; Thermodynamic functions and Debye-Waller *B*
factors of non-cubic crystals; Temperature-dependent spectral cutoff;
Directional Debye temperatures; Effective phonon speed and oscillator mass;
Heat capacity and vibrational amplitudes of zinc

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