Calculation of solubility in titanium alloys from first principles

We present an approach to calculate the atomic bulk solubility in binary alloys based on the statistical-thermodynamic theory of dilute lattice gas. The model considers all the appropriate ground states of the alloy and results in a simple Arrhenius-type temperature dependence determined by a 'low-solubility formation enthalpy'. This quantity, directly obtainable from first principles, is defined as the composition derivative of the compound formation enthalpy with respect to nearby ground states. We apply the framework and calculate the solubility of the A solutes in A-Ti alloys (A = Ag, Au, Cd, Co, Cr, Ir, W, Zn). In addition to determination of unknown low-temperature ground states for the eight alloys, we find qualitative agreements with solubility experimental results. The presented formalism, correct in the low-solubility limit, should be considered as an appropriate starting point for estimation of whether a more computationally expensive formalism is needed.