Tomaschitz, R.
(2020). Effective partition function of crystals: Reconstruction from heat
capacity data and Debye-Waller factor, *Physica *B* ***593**,
412243, DOI:
10.1016/j.physb.2020.412243

**Abstract **ScienceDirect

A semi-empirical method to define a
partition function for phonons is proposed, which is capable of accurately
reproducing thermodynamic functions, especially in the intermediate temperature
range, where the Debye theory occasionally fails to describe the emerging
phonon peaks in the heat capacity. The phonon partition function is defined
with a temperature-dependent spectral cutoff L(*T*) and Debye temperature q(*T*). The
varying q(*T*) can be
reconstructed from heat capacity measurements by least-squares regression, and
the spectral cutoff is chosen so that the partition function defines a genuine
equilibrium system consistent with the equilibrium condition ¶*S*/¶*U*=1/*T* on the
internal-energy derivative of entropy. The zero-point energy of the phonons is
not predetermined by the amplitude of the cubic low-temperature slope of the
heat capacity but emerges as an integration constant, which can be inferred
from X-ray diffraction measurements of the Debye-Waller *B*-factor. The
formalism is put to test with the rutile polymorph of TiO_{2}.

description: Roman
Tomaschitz (2020) Effective partition function of crystals: Reconstruction from
heat capacity data and Debye-Waller factor, *Physica B ***593**,
412243.

**Keywords:** Varying Debye temperature; Temperature-dependent
spectral cutoff; Zero-point energy; Internal energy and entropy; Debye-Waller *B*-factor;
Rutile polymorph of titanium dioxide

**Highlights**

The phonon partition function is assembled with a temperature-dependent spectral cutoff and Debye temperature.

The formalism is
illustrated with the heat capacity of rutile TiO_{2}, which largely
deviates from the Debye theory.

The temperature variation of the spectral cutoff is determined by an equilibrium condition on the partition function.

The variation of the Debye temperature is reconstructed from a least-squares fit to heat capacity data.

The zero-point energy
of the phonons is inferred from a measurement of the Debye-Waller *B*-factor.

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