Volumetric and structural contributions to the interatomic potentials and elastic moduli of cubic metals

A popular model for metals considers the binding energy $E_{\mathrm{bind}}$ to consist of a structure-dependent part $E_{\mathrm{str}}$ and a volume-dependent part $E_{\mathrm{vol}}$. An analysis of each part’s contributions to the pressure, the bulk modulus κ, and the shear moduli μ and μ’ reveals combinations of elastic moduli that are evidently fundamental as is evidenced by their systematic variation in the Periodic Table. If ${\kappa }_{\mathrm{vol}}$ and $P_{\mathrm{vol}}$ are the contributions of $E_{\mathrm{vol}}$ to κ and P, respectively, at arbitrary applied pressure P, ${\kappa }_{\mathrm{vol}}$-2$P_{\mathrm{vol}}$=κ-2P-μ’-(2 /3)μ.