Relation between the Grüneisen constant and Poisson’s ratio of vitreous systems

Сандитов, Б. Д.; Цыдыпов, Ш. Б.; Сандитов, Д. С.

doi:10.1134/s1063771007050090

Cited by 47 publications

(17 citation statements)

References 2 publications

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“…Thermal conductivity can also be simply estimated using Slack's model :

k = A \cdot \frac{\overset{true¯}{M} Θ_{normalD}^{3} δ}{(γ^{2} n^{2 ∖ 3} T)}

, where A is a constant ( A = 3.1 × 10 −6 if k is in W m −1 K −1 and δ in Å), Θ D is the Debye temperature obtained by Eq. , δ 3 is the volume per atom, γ is the Grüneisen parameter of the acoustic phonons at high temperature and can be deduced from Poisson's ratio through the expression

γ = \frac{3 (1 + ν)}{[2 (2 - 3 ν)]}

and other parameters are defined as these in Eq. .…”

Section: Resultsmentioning

confidence: 99%

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Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Cui

Wang

et al. 2017

Physica Status Solidi (b)

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Na3OBr is expected to be a promising superionic conductor for use as solid state electrolyte in large scale energy storage systems, but its lattice dynamic and thermal conductivity properties have not been well studied till now. In this work, we performed a detailed study on these properties as well as its electronic and elastic properties using first principles method. The results indicate that Na3OBr is a direct band gap crystal. It is mechanically stable but elastically anisotropic. Its phonons at the Brillouin zone center were classified using group theory analysis and its Born effective charges, LO–TO splitting, and dielectric constants were calculated and discussed. Its phonon dispersion curves were obtained and their origins were revealed. Based on the phonon dispersion curves, its thermal conductivity as a function of temperature was predicted, which give a value of 7.30 Wm−1 K−1 at 300 K. Further study reveals that, for Na3OBr, the simple Slack's model can give almost the same thermal conductivity curve as that obtained from the phonon dispersion curves.

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“…Thermal conductivity can also be simply estimated using Slack's model :

k = A \cdot \frac{\overset{true¯}{M} Θ_{normalD}^{3} δ}{(γ^{2} n^{2 ∖ 3} T)}

γ = \frac{3 (1 + ν)}{[2 (2 - 3 ν)]}

and other parameters are defined as these in Eq. .…”

Section: Resultsmentioning

confidence: 99%

“…, Q D is the Debye temperature obtained by Eq. (8), d 3 is the volume per atom, g is the Gr€ uneisen parameter of the acoustic phonons at high temperature and can be deduced from Poisson's ratio through the expression g ¼ 3ð1þnÞ ½2ð2À3nÞ [33] and other parameters are defined as these in Eq. (8).…”

Section: Phonons and Thermal Conductivitymentioning

confidence: 99%

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Cui

Wang

et al. 2017

Physica Status Solidi (b)

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“…The temperature‐dependent thermal conductivity was calculated using the Slack's model:

{normalκ}_{normalL} = A \frac{\bar{M} {normalΘ}_{D}^{3} δ}{{normalγ}^{2} n^{2 / 3} T}

where n the number of atoms in the primitive cell, δ 3 the volume per atom, Θ D the Debye temperature,

\overset{M}{true}

the average mass of the atoms in the crystal, and A is a physical constants ( A ≈ 3.1 × 10 −6 if κ L is in W·(m·K) −1 , and δ in Å). γ is the high limit of the acoustic phonon‐mode Grüneisen parameter, and can be calculated from Poisson's ratio:

γ = \frac{9 (υ_{normall}^{2} - \frac{4}{3} υ_{normals}^{2})}{2 (υ_{normall}^{2} - 2 υ_{normals}^{2})} = \frac{3}{2} ()(, \frac{1 + v}{2 - 3 v})

…”

Section: Calculation Methodsmentioning

confidence: 99%

Al₅BO₉: A Wide Band Gap, Damage‐Tolerant, and Thermal Insulating Lightweight Material for High‐Temperature Applications

Zhou

Xiang

2016

J. Am. Ceram. Soc.

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The electronic structure, chemical bonding, mechanical, and thermal properties of a B‐containing mullite Al5BO9 were investigated using a combination of first‐principles calculations, Debye model, Clack model, and Slack's equation. The results show that Al5BO9 has a wide band gap of 6.4 eV. The bonding in BO3 triangle and AlO4 tetrahedron is covalent‐ionic, whereas that in AlO6 octahedra and AlO5 bipyramids is ionic‐covalent. The maximum (245 GPa) and minimum Young's modulus (161 GPa) are along [100] and [010] direction, respectively. Based on the low shear modulus (78 GPa) and low Pugh's ratio (G/B = 0.497), Al5BO9 is predicted as a damage‐tolerant ceramic. The most likely slip systems are [010](100) and [100](010). The high Debye temperature (956 K) indicates good high‐temperature stability. The minimum thermal conductivity is estimated to be 1.59 W·(m·K)−1, and the thermal conductivity decreases with temperature as 2071.9/T.

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“…Clarke's equations suggest a fundamental guideline for the selection of potential high‐temperature TBC materials according to the minimum thermal conductivity, but pale when investigating thermal properties over wide range of temperatures. In the present calculation, the temperature dependence of thermal conductivity is calculated from Slack's equation:

κ = A \cdot \frac{\overset{M}{true} {θ_{D}}^{3} normalδ}{γ^{2} n^{2 false/ 3} T} (T \geq θ)

where

\overset{M}{true}

[kg/mol] is the mean atomic mass, δ 3 [m 3 ] is the average volume of one atom in the primitive unit cell, θ D [K] is the Debye temperature, T [K] is the absolute temperature, n is the number of atoms per primitive unit cell, γ is the Grüneisen constant derived from Poisson's ratio according to the following expression, and A [W mol/kg/m 2 /K 3 ] is a coefficient determined by γ:

γ = \frac{9 ({normalν}_{l}^{2} - \frac{4}{3} {normalν}_{s}^{2})}{2 ({normalν}_{l}^{2} - 2 {normalν}_{normals}^{2})} = \frac{3}{2} (\frac{1 + normalν}{2 - 3 normalν})

A (normalγ) = \frac{5.720 \times 10^{7} \times 0.849}{2 \times (1 - \frac{0.514}{normalγ} + \frac{0.228}{γ^{2}})}

…”

Section: Calculation Methodsmentioning

confidence: 99%

Theoretical Predictions on Elastic Stiffness and Intrinsic Thermal Conductivities of Yttrium Silicates

Luo

Wang

et al. 2014

J. Am. Ceram. Soc.

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Yttrium silicates are promising candidates for environmental and thermal barrier coatings owing to their excellent high-temperature performances. Previous works have experimentally attested to their low thermal conductivity, nevertheless, the experimental data were significantly affected by measurement inaccuracy and the existence of defects such as point defects, dislocations, grain boundaries, and pores in measured samples. In this study, the temperature dependences of intrinsic lattice thermal conductivities of c-Y 2 Si 2 O 7 and Y 2 SiO 5 are predicted based on the first-principles calculations of crystal structure, elastic moduli, Debye temperature, and Gr€ uneisen constant. Both silicates display very low thermal conductivities over the range of 300-2000 K; and in addition, Y 2 SiO 5 exhibits relatively lower thermal conductivity than c-Y 2 Si 2 O 7 . We also show certain discrepancies between experimental and theoretical thermal conductivities, and it strengthens the important role of theoretical prediction of intrinsic lattice thermal conductivities of promising materials.

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Relation between the Grüneisen constant and Poisson’s ratio of vitreous systems

Cited by 47 publications

References 2 publications

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Al₅BO₉: A Wide Band Gap, Damage‐Tolerant, and Thermal Insulating Lightweight Material for High‐Temperature Applications

Theoretical Predictions on Elastic Stiffness and Intrinsic Thermal Conductivities of Yttrium Silicates

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Relation between the Grüneisen constant and Poisson’s ratio of vitreous systems

Cited by 47 publications

References 2 publications

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na3OBr via first principles

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na3OBr via first principles

Al5BO9: A Wide Band Gap, Damage‐Tolerant, and Thermal Insulating Lightweight Material for High‐Temperature Applications

Theoretical Predictions on Elastic Stiffness and Intrinsic Thermal Conductivities of Yttrium Silicates

Contact Info

Product

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Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Electronic, elastic, lattice dynamic and thermal conductivity properties of Na₃OBr via first principles

Al₅BO₉: A Wide Band Gap, Damage‐Tolerant, and Thermal Insulating Lightweight Material for High‐Temperature Applications