Thermodynamic properties of the alkali metals at high temperatures and high pressures using mean-field potential model

Bhatt, N. K.; Vyas, P. R.; Jani, A. R.; Gohel, V. B.

doi:10.1016/j.jpcs.2004.08.050

Cited by 21 publications

(13 citation statements)

References 42 publications

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“…(2) is the potential energy of a molecule as it roams from the center to a distance . In terms of the AMFP approach [16][17][18][19][20][21][22], ( V ) can be expressed by the static energy E ( ) of a molecule,…”

Section: Analytic Equation Of Statementioning

confidence: 99%

“…Several years ago, Wang et al proposed the AMFP approach, and applied it to many materials. Bhatt et al [20,21] further applied the AMFP to lead and alkali metals, and concluded that in comparison with other theoretical models the AMFP is computationally simple, physically transparent and reliable for the study of thermodynamic properties in the high pressure and high temperature environment. Recently, Sun et al prove that the AMFP is an analytic approximation of the free volume theory (FVT) [22].…”

Section: Introductionmentioning

confidence: 99%

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An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

et al. 2008

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Abstract:The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.

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Section: Analytic Equation Of Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

et al. 2008

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“…In the past, different philosophies were used to compute the mean-field potential (MFP): free volume theory [2][3][4][5][6], Debye-Grüneisen theory [7], classical cell-model [8], and 0 K isotherm-based MFP [9,[11][12][13][14][15][16][17][18][19][20][21]. Wang and his coworkers [9,10,[18][19][20], and others [11][12][13][14][15][16][17]21] have proposed a method of modeling the vibrational free energy in terms of the 0 K total energy from the concept of the MFP approach. The concept of the MFP due to Wang and co-workers does not require detailed electronic band structure calculations over the complete density range of interest.…”

Section: Introductionmentioning

confidence: 99%

High-Temperature Vibrational Properties and Melting Curve of Aluminum

et al. 2010

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The mean-field theory due to Wang and Li (Phys Rev B 63:196, 2000) to calculate the effective mean potential experienced by vibrating ions in a crystal is used to compute the ion-motional free energy. An improvement is sought by treating the parameter λ, entering an expression of the mean-field potential (MFP), as a free parameter for the case of aluminum. Although a corresponding expression for the Grüneisen parameter (γ ) is significantly different then the known cases, namely, those due to (i) Slater, (ii) Dugdale and MacDonald, (iii) free volume theory, and (iv) Barton and Stacey, its value is very close to the experimental result. Significant improvement is observed for high-temperature thermodynamics of aluminum with the new choice of λ, or equivalently γ . Also, the present improved scheme is extended to measure the vibrational response of the crystal. Recently, Bhatt et al. (Philos Mag 90:1599, 2010 have demonstrated that the mean frequency (ω ) calculated by the MFP approach in conjunction with the density-dependent local pseudopotential suffices to characterize the crystal at finite temperatures. Relating ω to the Debye frequency, vibrational properties like the Debye temperature, the mean-square displacement, and entropy are obtained as a function of temperature. Further, a generalized melting law is derived by combining the MFP approach to Lindemann's law, where the effect of different choices of the parameter λ is now explicitly included into the description. Results so obtained for different physical properties are analyzed and discussed in the light of recent first principles and experimental findings.

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“…Several years ago, Wang et al [19][20][21][22] proposed the analytic mean field potential (AMFP) approach, and applied it to many materials. Bhatt et al [23,24] further applied the AMFP to lead and alkali metals, and concluded that in comparison with other theoretical models the AMFP is computationally simple, physically transparent and reliable to study the thermodynamic properties in the high pressures and high temperatures environment. Recently, Sun et al have proven that the AMFP is an analytic approximation of the free volume theory (FVT) [25].…”

Section: Introductionmentioning

confidence: 99%

Analytic Equation of State and Thermodynamic Properties for α-, β-, and γ-Si₃N₄Based on Analytic Mean Field Approach

et al. 2008

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The analytic mean field potential approach is applied to α-, β-, and γ-Si 3 N 4 . The analytic expressions for the Helmholtz free energy, internal energy, and equation of state were derived. The formalism for the case of the Morse potential is used in this work. Its six potential parameters are determined through fitting the compression experimental data of α-, β-, and γ-Si 3 N 4 . The calculated compression curves of α-, β-, and γ-Si 3 N 4 are in good agreement with the available experimental data. This suggests that the analytic mean field potential approach is a very useful approach to study the thermodynamic properties of Si 3 N 4 . Furthermore, we predict the variation of the free energy and internal energy with the molar volume at several higher temperatures and calculate the temperature dependence of the molar volume, bulk modulus, thermal expansion coefficient and isochoric heat capacity at zero pressure.

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Thermodynamic properties of the alkali metals at high temperatures and high pressures using mean-field potential model

Cited by 21 publications

References 42 publications

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

High-Temperature Vibrational Properties and Melting Curve of Aluminum

Analytic Equation of State and Thermodynamic Properties for α-, β-, and γ-Si₃N₄Based on Analytic Mean Field Approach

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Thermodynamic properties of the alkali metals at high temperatures and high pressures using mean-field potential model

Cited by 21 publications

References 42 publications

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

High-Temperature Vibrational Properties and Melting Curve of Aluminum

Analytic Equation of State and Thermodynamic Properties for α-, β-, and γ-Si3N4Based on Analytic Mean Field Approach

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Product

Resources

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Analytic Equation of State and Thermodynamic Properties for α-, β-, and γ-Si₃N₄Based on Analytic Mean Field Approach