Shell Structure Effects in Compressed Aluminum

Abstract

It is now possible to make equation of state measurements on compressed matter up to pressures in excess of 1 TPa, by carrying out shock compression studies on samples placed in the vicinity of underground explosions [1]. While these shock wave experiments measure very hot samples, current research in laser implosion techniques is aimed at reaching comparable compressions with much lower final temperatures.† This increasing experimental access to TPa and higher pressures provides the theoretician with an impetus to examine the problem of calculating very high pressure equations of state. To date, almost all theoretical determinations in this range have been based on statistical, Thomas-Fermi models [2–4]. The Soviet shock compression work, for example, uses a comparative measurement technique which depends critically on a simplistic extrapolation of experimental data below 1 TPa over an order of magnitude in pressure to the predictions of statistical models above 10 TPa. The major disadvantage of the statistical models is that they ignore the electron shell structure of the atoms. Attempts to correct these models [5] must be considered tentative. A more satisfactory treatment of electrons in solids rigorously including shell structure is the self-consistent augmented-plane-wave (APW) method. This method has become widely used in recent years to calculate T = 0 isotherms and cohesive energies of metals.

Work performed under the auspices of the U.S. Energy Research and Development Administration under Contract No. W-7405-Eng-48.