High temperature and pressure thermodynamics of strontium: A macroscopic approach

High-Temperature Vibrational Properties and Melting Curve of Aluminum

“…Indeed, at elevated temperatures (T > θ D ; the Debye temperature), one may expect weakening of atomic correlations and the use of the mean-field approach is justified. In a recent paper [17], we have examined this point and calculated several thermodynamic properties for strontium in a high-T and high-P environment including finite temperature frequency shifts, and this validates the use of the MFP and pseudopotential coupling scheme. The characteristic temperature obtained by the MFP approach is used to define a Debye temperature along the line suggested by Wang [19];…”

“…As noted earlier, different authors have used different means to construct the MFP [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], but we follow the one due to Wang and co-workers in conjunction with the local pseudopotential due to Fiolhais et al [22,23]. Assuming the vibration of the lattice ion is symmetrical with respect to its equilibrium position, Wang and Li [9] have proposed an analytical form for the MFP, as given by…”

“…They have compared and analyzed their MFP-based predictions with the Debye-Grüneisen theory within the same scaled binding energy formalism and with experiments. In another recent study [17], we have examined the physical significance of the MFP approach in conjunction with the local pseudopotential for fcc-Sr. We demonstrated that the results for high-temperature frequency shifts calculated through a pdc and p-dos within the quasiharmonic approximation (QHA) are very similar to the one estimated through the MFP approach, and with a better account of intrinsic anharmonism by the MFP scheme. This observation also implies that the mean frequency calculated by the MFP approach is sufficient to characterize the crystal in the high-T and high-P regime.…”

“…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.…”

“…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.…”