A simplified method for calculating the debye temperature from elastic constants

Anderson, Orson L.

doi:10.1016/0022-3697(63)90067-2

Cited by 2,867 publications

(989 citation statements)

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“…Hence, at low temperatures the Debye temperature calculated from elastic constants is the same as that determined from specific heat measurements. One of the standard methods to calculate the Debye temperature (θ D ) is from elastic constants data, since θ D may be estimated from the average sound velocity, ν m by the following equation [38,39]:…”

Section: Calculation Of Debye Temperaturementioning

confidence: 99%

First-principles study of structural, electronic and elastic properties of Nb4AlC3

Bouhemadou¹

2010

Braz. J. Phys.

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Using First-principles calculations, we have studied the structural, electronic and elastic properties of Nb 4 AlC 3 , a new compound belonging to the MAX phases. Geometrical optimization of the unit cell is in good agreement with the experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions are higher along the c-axis than along the a-axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The band structure shows that this compound is electrical conductor. The analysis of the site and momentum projected densities shows that bonding is due to Nb d-C p and Nb d-Al p hybridizations. The Nb d-C p bond is lower in energy and stiffer than Nb d-Al p bond. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus and Poisson's ratio for ideal polycrystalline Nb 4 AlC 3 aggregate. We estimated the Debye temperature of Nb 4 AlC 3 from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Nb 4 AlC 3 compound, and it still awaits experimental confirmation.

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Section: Calculation Of Debye Temperaturementioning

confidence: 99%

First-principles study of structural, electronic and elastic properties of Nb4AlC3

Bouhemadou¹

2010

Braz. J. Phys.

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“…Хорошо известно, что температура Дебая принадлежит к числу наиболее важных тепловых па-раметров кристаллов и разделяет области высоко-и низкотемпературные, когда при T < θ D колебательные возбуждения возникают исключительно из акустических мод. Температуру Дебая можно оценить [63], используя среднюю скорость звука (ν m ), как…”

Section: дв суетин ир шеинunclassified

Электронная структура, механическая и динамическая стабильность гексагональных субкарбидов M-=SUB=-2-=/SUB=-C (M = Tc, Ru, Rh, Pd, Re, Os, Ir, Pt): ab initio расчеты

Suetin¹,

Shein²

2018

Физика Твердого Тела

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Физика твердого тела, 2018, том 60, вып Посредством ab initio расчетов были изучены свойства серии гексагональных (Fe 2 N-подобных) суб-карбидов M 2 C, где M = Tc, Ru, Rh, Pd, Re, Os, Ir, Pt, и рассчитаны их равновесные структурные параметры, электронные свойства, фазовая стабильность, константы упругости, модули сжатия, сдвига и Юнга, сжимаемость, индикатор Пуга, коэффициент Пуассона, индексы упругой анизотропии, а также твердость, температура Дебая, скорости звука, низкотемпературная теплоемкость. На основании полученных данных установлено, что все эти субкарбиды механически устойчивы, однако их энергии формирования E form относительно смеси d-металла и графита положительны. Кроме того, расчет фононных спектров этих субкарбидов показал наличие отрицательных мод, что указывает на их динамическую нестабильность. Таким образом, успешный синтез данных карбидов при нормальных условиях маловероятен.

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“…The knowledge of such a numerical figure is essential for developing and manufacturing electronic devices [24,27]. The Debye temperature (θ D ) of the considered compounds is estimated from the average sound velocity ν m in terms of the following equation [28]:…”

Section: Debye Temperaturementioning

confidence: 99%

“…ν m is the average wave velocity and it is dependent on the transverse (ν t ) and the longitudinal (ν l ) wave velocities according to the following formulas [28]: ν l and ν t can be estimated from the shear modulus G and the bulk modulus B by using Navier's equation as follows [28]:…”

Section: Debye Temperaturementioning

confidence: 99%

Density Functional Study of the Carbon Dependence of the Structural, Mechanic, Thermodynamic, and Dynamic Properties of SiC Alloys

Langueur

Kassali

2017

Int J Thermophys

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Using a density functional scheme, for the first time the carbon dependence on the structural, dynamic, thermodynamic, and dynamic properties of Si 1−x C x alloys (x = 0.0 to 1.0 in steps of 0.125) has been investigated. The structural properties of these materials, in particular, the composition dependence of the lattice parameter and bulk modulus, are in excellent agreement with experimental data and follow a quadratic law in (x). A nonlinear relationship is found between the elastic constants C 11 , C 12 , and C 44 and the carbon concentration (x). The behavior of the acoustical and optical phonon frequencies at high-symmetry points Γ , X , and L is predicted. Through the quasi-harmonic Debye model, in which the photonic effects are taken into account, the Debye temperature, the heat capacity, the Helmholtz free energy, the internal energy, and the entropy are determined for the Si 1−x C x compounds.

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A simplified method for calculating the debye temperature from elastic constants

Cited by 2,867 publications

References 1 publication

First-principles study of structural, electronic and elastic properties of Nb4AlC3

First-principles study of structural, electronic and elastic properties of Nb4AlC3

Электронная структура, механическая и динамическая стабильность гексагональных субкарбидов M-=SUB=-2-=/SUB=-C (M = Tc, Ru, Rh, Pd, Re, Os, Ir, Pt): ab initio расчеты

Density Functional Study of the Carbon Dependence of the Structural, Mechanic, Thermodynamic, and Dynamic Properties of SiC Alloys

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