Shock Hugoniot Equation of State - Electron Band Theory Approach

Abstract

Of the various high pressure experimental data on a given material, the equation of state (EOS) is most amenable to theoretical treatment. Its interpretation involves, in principle,the straightforward application of electron band and lattice dynamical techniques for the calculation of pressure and internal energy as a function of volume and temperature. Though these formulations have been available since 1930’s, it is only during the last decade that considerable progress has been made in EOS computations by using these. Two reasons can be attributed for this advance. One is the considerable development of experiments involving lasers, electrically driven foils and underground nuclear explosions to study EOS at pressures above 100 GPa^2–5. Very recently, experimental data on iron and aluminium shocked to ~ 500 TPa have been reported⁶. These data have opened up a new area in the P-V-T surface for theoretical research, where the pressure and thermal ionisation effects are important. The second is the advent of large and fast computers and improvements in energy band methods themselves. These have made computations less time consuming and have permitted evaluation of total energies of crystalline solids to such a precision that not only can bulk properties like EOS be calculated accurately but energy differences between different phases can be determined to an accuracy of 0.1 ev per atom or better.