Calculation of solubility in titanium alloys from first-principles

TL;DR

This paper introduces a first-principles based thermodynamic model to accurately calculate atomic solubility in binary titanium alloys, considering ground states and providing a simple Arrhenius-type temperature dependence.

Contribution

It develops a novel approach linking first-principles calculations with thermodynamic theory to predict solubility in alloys, including identification of ground states and low-solubility behavior.

Findings

Calculated solubility for A in A-Ti alloys matches experimental trends.

Identified new low-temperature ground states for eight alloys.

Provided a simple, accurate model for low-solubility thermodynamics.

Abstract

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 {\it "low-solubility formation enthalpy"}. This quantity, directly obtainable from first-principle calculations, 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 specie in A-Ti alloys (A=Ag,Au,Cd,Co,Cr,Ir,W,Zn). In addition to determining 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 determining if more computationally expensive formalisms are otherwise needed.