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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 authors measured the thermal capacities, thermalexpansion coefficients, thermal and electrical conductivities of Nb2AlC (actual Nb:Al:C mole fractions: 0.525±0.005, 0.240±
Abstract: The heat capacities, thermal-expansion coefficients, thermal and electrical conductivities of Nb2AlC (actual Nb:Al:C mole fractions: 0.525±0.005, 0.240±0.002, and 0.235±0.005, respectively), Ti2AlC and (Ti, Nb)2AlC (actual Ti:Nb:Al:C mole fractions: 0.244±0.005, 0.273±0.005, 0.240±0.003, and 0.244±0.005, respectively) were measured as a function of temperature. These ternaries are good electrical conductors, with a resistivity that increases linearly with increasing temperatures. The resistivity of (Ti, Nb)2AlC is higher than the other members, indicating a solid-solution scattering effect. The thermal-expansion coefficients, in the 25 °C to 1000 °C temperature range, are comparable and fall in the narrow range of 8.7 to 8.9 × 10−6 K−1, with that of the solid solution being the highest. They are all good conductors of heat, with thermal conductivities in the range between 15 to 45 W/m K at room temperature. The electronic component of the thermal conductivity is the dominant mechanism at all temperatures for Nb2AlC and (Ti, Nb)2AlC. The conductivity of Ti2AlC, on the other hand, is high because the phonon contribution to the conductivity is nonnegligible.

140 citations

Journal ArticleDOI
TL;DR: It is shown that in glasses the structural disorder undermines the Debye model in a subtle way: the elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of ≈10 interatomic spacings, where it still works well for the corresponding crystalline systems.
Abstract: The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of ≈10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of ≈1 THz in the vibrational density of states or at temperatures of ≈10 K in the specific heat.

139 citations

Journal ArticleDOI
TL;DR: In this article, the effects of lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born-von Karman (BvK) force model and a single-parameters Debye model.
Abstract: The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born--von Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRDs of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.

139 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of doping on the thermal conductivity of Ge-Si alloys was investigated using the theory developed by Ziman for the scattering of phonons by electrons using the formalism of Klemens and Callaway.
Abstract: The theory developed by Ziman for the scattering of phonons by electrons is extended to high temperatures using the formalism of Klemens and Callaway. The theory is applied to the experimental results recently published by Dismukes et al. on the effect of doping on the thermal conductivity of Ge-Si alloys. After subtracting the electronic contribution from the measured thermal conductivity, the resulting lattice conductivity is analyzed. In describing the effect of doping, the deformation potential is the only free parameter; its value is adjusted for each sample to obtain agreement with the experimental data at 500\ifmmode^\circ\else\textdegree\fi{}K, which is close to the Debye temperature. The theory then predicts the correct temperature dependence of the lattice thermal conductivity. The deformation potentials, derived in this manner, are found to be higher for $n$-type than for $p$-type material, and to increase with carrier concentration. For lightly doped $p$-type and $n$-type material, values of 1.2 and 1.6 eV were obtained, respectively, which compare well with the available literature data.

139 citations

Journal ArticleDOI
TL;DR: Simultaneous momentum-space refinements of synchrotron X-ray and neutron scattering yield accurate average crystal structures, with reliable atomic displacement parameters.
Abstract: The average and local structure of the oxides Ba2SiO4, BaAl2O4, SrAl2O4, and Y2SiO5 are examined to evaluate crystal rigidity in light of recent studies suggesting that highly connected and rigid structures yield the best phosphor hosts. Simultaneous momentum-space refinements of synchrotron X-ray and neutron scattering yield accurate average crystal structures, with reliable atomic displacement parameters. The Debye temperature ΘD, which has proven to be a useful proxy for structural rigidity, is extracted from the experimental atomic displacement parameters and compared with predictions from density functional theory calculations and experimental low-temperature heat capacity measurements. The role of static disorder on the measured displacement parameters, and the resulting Debye temperatures, are also analyzed using pair distribution function of total neutron scattering, as refined over varying distance ranges of the pair distribution function. The interplay between optimal bonding in the structure, s...

138 citations


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