Tomaschitz, R. (2021). Effective real-space correlations of crystal lattice vibrations, Journal of Physics and Chemistry of Solids 152, 109773, DOI: 10.1016/j.jpcs.2020.109773
Effective phonon fields coupled to a temperature-dependent permeability tensor are introduced to model empirical thermodynamic functions of crystal lattices and the temperature variation of Debye-Waller factors inferred by X-ray, g-ray or neutron diffraction. The permeabilities generate a varying Debye temperature and a temperature-dependent spectral cutoff in the partition function as well as an effective temperature-dependent oscillator mass, to be calculated from diffraction and heat capacity data. The zero-point internal energy of the phonon field is extracted from low-temperature Debye-Waller B-factor measurements. The varying spectral cutoff, Debye temperature and oscillator mass determine the temperature evolution of real-space correlation functions. Closed integral representations are derived for the effective two-point function correlating isotropic lattice vibrations in monatomic cubic crystals as well as for the reduced four-point function correlating fluctuations around the mean-squared atomic displacement. The correlations are long-range with power-law tails and become oscillatory at low temperature. The formalism is illustrated with the correlation functions of copper.
description: Roman Tomaschitz (2021) Effective real-space correlations of crystal lattice vibrations, J. Phys. Chem. Solids 152, 109773.
Keywords: Effective phonon fields; Temperature-dependent permeabilities; Lattice heat capacity and Debye-Waller B-factors; Zero-point energy of lattice vibrations; Correlation functions of the copper lattice; Anisotropic compounds
Effective phonon fields coupled to a temperature-dependent permeability tensor are introduced to model lattice vibrations.
The permeabilities generate a temperature-dependent spectral cutoff and Debye temperature defining the partition function.
The empirical thermodynamic functions and the temperature evolution of Debye-Waller B-factors are accurately reproduced.
The effective real-space correlations of fluctuations around the mean-squared vibrations in cubic lattices are calculated.
The formalism is put to test with the heat capacity, internal energy, entropy and B-factor of the copper lattice.