Weibull thermodynamics: Subexponential decay in the energy spectrum of cosmic-ray nuclei

Tomaschitz, Roman

doi:10.1016/j.physa.2017.03.034

Cited by 10 publications

(2 citation statements)

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“…A discrete spectral component (Einstein terms) can be added to the Debye heat capacity at optical frequencies (cf. Meissner et al, 1978;Hoser & Madsen, 2016, 2017Sovago et al, 2020). A non-uniform phonon density of states was used by Tewari & Silotia (1990) for zinc and Malica & Dal Corso (2019) for several other monatomic crystals.…”

Section: Discussionmentioning

confidence: 99%

“…1. The isochoric heat capacity C V;eþL ðTÞ can be split into a linear component stemming from the degenerate electron gas and a multiply broken power law (Tomaschitz, 2017 , 2020c, 2021b, Isochoric heat capacity of zinc. Data points from Martin (1968Martin ( , 1969 (circles) and Eichenauer & Schulze (1959) (squares).…”

Section: Thermodynamic Functions and Debye-waller Factors Of Zinc 41 Regressed Lattice Heat Capacity Of The Zinc Structurementioning

confidence: 99%

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Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited

Tomaschitz¹

2021

Acta Cryst Sect A

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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 γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal zinc lattice, 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.

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