Abstract:Calculations of the Hugoniot Pressure and Pressure Derivative of the Bulk Modulus for Transition Metals​

U. Walzer. Calculations of Hugoniot pressure and pressure derivative of bulk modulus for transition metals. High Temp. - High Pressures, 19:161-176, 1987.

Calculations of the Hugoniot Pressure and Pressure Derivative of the Bulk Modulus for Transition Metals

U. Walzer

Abstract

A bonding theory for transition metals has been derived which permits good to very good predictions for the energy, static pressure, Hugoniot pressure, bulk modulus, and its pressure derivative with respect to their dependence on the relative volume. The d-band structure has been expressed through a combination of the transition-metal pseudopotential theory and the muffin-tin orbital theory. The nearly free s-electrons contribute four terms to the energy: kinetic energy, exchange energy, a Madelung term, and its pseudopotential correction. Three further assumptions are made: the ratio of the nearest-neighbour separation to the atomic radius remains constant for each pressure; at least for elements with full d-shells the pressure must exactly disappear at zero-pressure volume; and at least for elements with full d-shells the calculated and the experimental bulk modulus must be in exact agreement at vanishing pressure. The essential aspect of this theory, called MC theory, is that it is applicable in a unified manner to all transition metals. In addition to seven well-known microphysical input parameters, two macrophysical input parameters are required.

Key words: solid-state physics, metals, pseudopotentials, pressure, Hugoniot pressure, bulk modulus, bonding, d-band, muffin-tin orbital theory, Birch-Murnaghan equation, kinetic energy, exchange energy, Madelung energy, Grüneisen parameter, Periodic Table, Grüneisen ratio, Hamiltonian, Fermi surface, transition metals, high pressure, equation of state