High-temperature vibrational response and high-pressure melting curve of lead

The concept of mean-field potential (MFP) is an adequate description to evaluate vibrational contribution to the Helmholtz free energy at finite temperatures and pressures for condensed-state of matter. Once the total free energy is available, as an explicit function of temperature and volume (≡pressure), several thermodynamic properties can be calculated numerically using the text-book equations. While the MFP approach is robust, its applicability is extended to estimate atomic and vibrational properties of materials within the Debye model. In the present scheme, we propose energy-calculation based formula to calculate the Debye temperature. We discuss temperature dependence of Debye temperature, entropy and atomic mean-square displacements for elemental fcc-Pb. It is demonstrated that the present extended MFP (EMFP) scheme, allows one to include the effect of three choices for thermodynamic Grüneisen parameter, namely, due to Slater, due to Dugdale and MacDonald and the one due to free volume theory, on different physical properties. A much debatable dynamical phenomenon, a high pressure melting curve is also obtained, where melting temperature is now explicitly dependent on these three assumptions for the Grüneisen parameter. Results so obtained are discussed and compared with the recent first principles theoretical and experimental findings.