Software Tools for Integrating Special Quasirandom Structures and the Cluster Variation Method into the CALPHAD Formalism

The CALPHAD method provides an effective way to parameterize alloy free energies computed from first-principles. While the Special Quasirandom Structure (SQS) formalism offers a natural and efficient tool to generate input data for disordered solid solution phases, accounting for Short Range Order (SRO) effects in a computationally efficient way presents a challenge. In this work we introduce a Python based software pipeline which utilize the Cluster Variation Method (CVM) method in tandem with the SQS formalism to determine closed-form nonlinear expressions for temperature-dependent SRO corrections to the formation free energies. Our approach, which implements the CVM to any level of accuracy, has been integrated into the sqs2tdb software pipeline. As a proof of concept, we perform a thermodynamic assessment of the Ir-Ru binary alloy with SRO correction and show its effectiveness in accurately reproducing the known experimental phase diagram. We also perform SRO corrections to an equimolar MoNbTaVW SQS and show significant SRO effects at temperatures far above room temperature.