International Journal of Thermophysics

, Volume 31, Issue 11–12, pp 2159–2175 | Cite as

High-Temperature Vibrational Properties and Melting Curve of Aluminum

  • N. K. Bhatt
  • B. Y. Thakore
  • P. R. Vyas
  • A. R. Jani


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.


Aluminum Debye temperature Grüneisen parameter Mean-square displacement MFP Melting curve 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • N. K. Bhatt
    • 1
  • B. Y. Thakore
    • 1
  • P. R. Vyas
    • 2
  • A. R. Jani
    • 1
  1. 1.Department of PhysicsSardar Patel UniversityVallabh VidyanagarIndia
  2. 2.Department of PhysicsGujarat UniversityAhmedabadGujaratIndia

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