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

**Abstract **ScienceDirect

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

**Highlights**

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.

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