Theory of chemical trends in simple-metal elastic moduli

For most simple metals the shear modulus $\mu$ (which measures the resistance to volume-preserving structure-changing deformations) is comparable in magnitude to the bulk modulus $B$ (which measures the resistance to structure-preserving volume-changing deformations). That this is also true for the alkali metals, for which $\frac{\mu }{B}\approx 0.5$, is surprising in view of the successful Wigner-Seitz description of simple-metal cohesion in terms of purely volume-dependent forces. To resolve this apparent contradiction, and to understand the trends exhibited by the elastic moduli of monovalent and polyvalent simple metals, an expression for the total energy, accurate to second order in the electron-ion pseudopotential, is used to examine both the bulk and shear moduli for a broad range of simple metals. It is shown that a single-parameter model potential of simple form gives an accurate representation of the pseudopotential in both the $q\sim 0$ and $q\sim 2k_F$ regions. A connection (based on the Ewald energy) between the shear and bulk moduli of the alkali metals is discovered, leading to the prediction $\frac{\mu }{B}\approx 0.6$, in good agreement with experiment. $B$ and $\mu$ are examined as functions of valence and electron density, and the systematics of the simple-metal elastic moduli are thus understood in a simple and intuitive way.