A Thermodynamic Perspective of the Composition Dependence of Bulk Modulus in Terms of Electron Density and Molar Volume

Abstract

The variation of bulk modulus with composition of alloy phases is a core issue in any thermodynamic theory of alloy formation. Though it emerges from fundamental theory that elastic property, especially the bulk modulus is crucially dependent on interstitial electron density (ρb) distribution and its variation with respect to alloy composition, a coherent thermodynamic treatment connecting bulk modulus with electron density together with its composition dependence, is still lacking. The present study addresses this issue for solid solution alloys. A phenomenological analysis of the composition dependence of bulk modulus (BT) of single phase alloys has been presented in terms of bonding charge density (ρb) and its corresponding change with atomic volume (V). This link is developed using the fundamental interrelationship existing between bulk modulus, electron density, and molar volume. The change in bonding charge density (Δρb) with composition (x) has been modeled using an exponential scaling relation with respect to the corresponding change in atomic volume (ΔV). This scaling relation is based on the concept of the universal binding energy relation, which in turn results in a simple exponential variation of bulk modulus with composition-induced change of atomic volume. It is also shown that a common functional representation namely, BT (V) ≈ Bo exp{C × (ΔV)}, can be obtained for the temperature, pressure, and composition dependence of bulk modulus in terms of corresponding changes in volume (ΔV). The constant C takes context-dependent meaning and values. The applicability of this exponential relation towards representing the effect of composition on bulk modulus has been satisfactorily demonstrated for many substitutional alloy systems.