High temperature and pressure thermodynamics of strontium: A macroscopic approach

Abstract

Close proximity of d-bands (above) to the Fermi level (E _F) makes the heavy alkaline earth metals (Ca, Sr and Ba) fairly sensitive to external influences like temperature and pressure. Softening of some of the phonon modes at high temperatures and/or pressures implies that anharmonic effects can play an important role in determining lattice dynamics and related properties. In the conventional approach, phonon density of states (p-dos) have to be calculated at each volume to compute free energy and thereby the other thermodynamic properties, which is computationally quite demanding. Using an alternative technique, the mean-field potential (MFP) approach was combined with the relatively soft local pseudopotential to obtain the free energy at different temperatures and pressures. The results for phonon frequency shifts at finite temperatures using the MFP approach and those calculated from p-dos within the quasiharmonic approximation are very similar. This validates the use of the MFP approach coupled with the local pseudopotential to estimate vibrational response of the system at high-temperature and high-pressure environments. The present scheme was used to study various thermophysical properties for elemental strontium at elevated temperatures and pressures, including the high-pressure melting curve and temperature along the shock Hugoniot. Computed results are affirmatively compared and analyzed with other reported data. The present scheme completely bypasses traditional cumbersome calculations, and it is computationally convenient yet accurate.

Keywords:

• phonon frequency shift
• mean-field potential
• thermal dynamics
• melting curve
• strontium

Acknowledgements

The authors are very grateful to Prof. V.B. Gohel for stimulating discussions of the topic, and NKB is thankful to UGC, New Delhi, for providing necessary support under the Project No. F. 34-504\2008 (SR).