Correlation between the Electron Gas Bulk Modulus andc12−c44of Monovalent Metals

Abstract

When the shear elastic constants of the monovalent metals are assumed to be due to central forces, the deviation from the Cauchy relations of elasticity can be attributed to the bulk modulus of the electron gas. This modulus may be calculated from the total gas energy using the exchange and correlation contributions due to Gell-Mann and Brueckner (GB) and to Fletcher and Larson (FL). The bulk modulus of Cu based on the FL energies is found to agree quantitatively with the experimental ${c}_{12}\ensuremath{-}{c}_{44}$ and to have also the correct volume dependence from 0 to 300\ifmmode^\circ\else\textdegree\fi{}K. The bulk modulus of the Na gas at 300\ifmmode^\circ\else\textdegree\fi{}K based on the exchange and correlation energies of GB agrees within 6% with ${c}_{12}\ensuremath{-}{c}_{44}$ observed. Comparisons are also made for Ag but no agreement is found. These correlations seem inconsistent in that the same formula should work for both Cu and Na if there are central forces, and the GB result should work for neither because it is supported to be invalid in the range of real metallic densities. The correlations provide no final criteria for the determination of the proper exchange and correlation energies of the electron gas.