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Debye model

About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.


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TL;DR: In this paper, the effect of the equilibrium and nonequilibrium properties of the crystal lattice on the thermal conductivity of monatomic crystals was studied by splitting the total anharmonic interatomic lattice potential into its diagonal and nondiagonal contributions.
Abstract: The lattice thermal conductivity for monatomic crystals is discussed for high temperatures, above and around the Debye temperature. While this problem cannot be treated in a suitable way by conventional methods for calculating transport coefficients, it represents an excellent example of the use of correlation-function techniques. By splitting the total anharmonic interatomic lattice potential into its diagonal and nondiagonal contributions, $V={V}_{\mathrm{d}}+{V}_{\mathrm{nd}}$, the effect of the equilibrium and nonequilibrium properties of the crystal lattice on the thermal conductivity can be studied separately. The current-current correlation function is calculated to second order in $V$ in a single-phonon-lifetime approximation. While ${V}_{\mathrm{nd}}$ only contributes in this approximation to the space-time-dependent part of the correlation function, ${V}_{\mathrm{d}}$ contributes as well to the space-time-independent part. The latter contribution ${{V}_{\mathrm{d}}}^{0}$ represents a temperature-dependent Hartree approximation of the lattice potential and determines the equilibrium properties of the crystal lattice. At constant pressure ${{V}_{\mathrm{d}}}^{0}$ gives rise to the thermal expansion of the system, which causes a decrease of the Debye frequency with increasing temperature, resulting in a depression of the conductivity below the $\frac{1}{T}$ behavior. Even in the case of constant volume, the temperature dependence of ${{V}_{\mathrm{d}}}^{0}$ causes a decrease of the phonon frequency with increasing temperature. This again gives rise to a depression of the conductivity below the $\frac{1}{T}$ behavior and leads to a ${T}^{2}$ term in the resistivity in the region around the Debye temperature. This latter effect is studied by taking into account the entire anharmonicity of the lattice potential which leads to ${{V}_{\mathrm{d}}}^{0}$ and calculating the space-time-dependent part of the correlation function in lowest order in the atomic displacements. Thus Peierls' expression for the conductivity is rederived in terms of the renormalized phonon frequency and group velocity due to ${{V}_{\mathrm{d}}}^{0}$, rather than the pure harmonic approximation of the lattice potential. The entire dissipative mechanism of the system, which is given by the space-time-dependent part of the correlation function, calculated to second order in $V$, cancels partially the effect of ${{V}_{\mathrm{d}}}^{0}$ on the conductivity. For temperatures around and just above the Debye temperature the temperature dependence of the lattice thermal conductivity is given by $\frac{1}{T}(1+\ensuremath{\alpha}T)$. With increasing temperature the conductivity reaches a minimum, which is followed by a steep rise as one approaches a dynamical instability of the system.

49 citations

Journal ArticleDOI
TL;DR: In this article, a tunnel splitting of (64±2)cm−1 associated with the quantum mechanical motion of the hydrogen atom in the intramolecular O-H-O hydrogen bond was derived along with the Debye temperature 60.8 K and two Einstein temperatures 131.4 K.
Abstract: The heat capacities of 5-bromo-9-hydroxyphenalenone (BHP) and its deuteroxy derivative (BDP) were measured at temperatures between 2 and 310 K. The heat capacity of BHP is a smooth function of temperature and that of BDP has two peaks at 21.3 and 33.9 K. By analyzing the data on BHP, a tunnel splitting of (64±2) cm−1 associated with the quantum mechanical motion of the hydrogen atom in the intramolecular O–H–O hydrogen bond was derived along with the Debye temperature 60.8 K and two Einstein temperatures 131.4 (nondegenerate) and 210.4 K (doubly degenerate). The enthalpy change of 225 J mol−1 and entropy change of 6.8 J K−1 mol−1 were determined for the total thermal effects associated with the two phase transitions in BDP. The value of the transition entropy is consistent with the twofold disorder in the high temperature phase. The tunneling energy and transition enthalpy satisfy an inequality demanded, on the assumption that the potential energies experienced by the proton and deuteron are the same, by ...

49 citations

Journal ArticleDOI
TL;DR: In this article, the structural, elastic, electronic and thermal properties of cubic perovskite-type BaSnO 3 were investigated and the ground-state properties were in agreement with experimental data.

49 citations

Journal ArticleDOI
TL;DR: In this paper, simple models for the heat capacity and thermal conductivity of a solid are introduced, with emphasis on the density of vibrational states, and the importance of these Einstein oscillators for impeding thermal transport is discussed.
Abstract: The Einstein model of a solid usually lacks a clear illustration in introductory solid-state physics courses because most solids are much better described by the Debye model. Filled antimony skutterudites, materials that have recently attracted much attention because of their potential for thermoelectric applications, provide a canonical illustration of the Einstein model. The filling atoms are loosely bound in the atomic cage formed by their neighbors, and hence their description as independent harmonic oscillators is adequate. Simple models for the heat capacity and thermal conductivity of a solid are introduced, with emphasis on the density of vibrational states. These models are used in conjunction with experimental results obtained from heat capacity and inelastic neutron scattering measurements to demonstrate the applicability of the concept of the Einstein oscillator to the filling guests in antimony skutterudites. The importance of these Einstein oscillators for impeding thermal transport is discussed and some simple problems involving the heat capacity, thermal conductivity, and inelastic neutron scattering are proposed.

49 citations

Journal ArticleDOI
TL;DR: In this article, the Housley-Hess approach has been used to determine the static disorder term of the temperature factors for both the Zr/Y and O atoms in 10mol% Y2O3-ZrO2 over the temperature range 15 to 1323
Abstract: Neutron powder diffraction has been used to measure the temperature factors of both the cation and the anion atoms in 10mol% Y2O3–ZrO2 over the temperature range 15 to 1323 K. The Housley–Hess approach has been used to determine the static disorder term of the temperature factors for both the Zr/Y and O atoms. The static contribution was determined to be 1.04 (6) A2 for Zr/Y and 2.2 (1) A2 for O. From these results, a Debye temperature of 527 (20) K was calculated for this sample.

49 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023178
2022346
2021303
2020242
2019285
2018304