Pressure induced phase transition in tin: Ab-initio calculations

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First principles total energy calculations as a function of unit cell volume have been performed on α (diamond structure), β (double bct), bct, bcc and hcp structures of tin. The comparison of total energies of these structures at various volumes suggests high pressure structural transitions of α → β → bet → bct at pressures of ~ 0.15 GPa, 2.7 GPa and 28 GPa. Also, 300 K isotherm upto maximum pressures of ~ 400 GPa has been determined for this metal. Using theoretical isotherm, shock Hugoniot of tin has been derived. Further, theoretically evaluated volume dependent Gruneisen parameter in conjunction with Lindeman melting law has been used to determine the pressure dependent melting of tin. The intersection of the theoretical melting curve with theoretically determined temperature rise with shock pressure reveals that this metal will melt at shock pressure of ~ 38 GPa (temperature ~ 1428 K) in good agreement with experimental value of 39 GPa (1550+100 K).