Molar volume prediction in unary and binary alloy metals using cross-validated regression models

Molar volumes of selected elemental metals and binary alloys were estimated from room temperature up to the melting points at atmospheric pressure. The coefficients of linear thermal expansions (CLTEs) are assessed by linear regression based on available experimental data in b c c , f c c and h c p crystal structures. With these coefficients, the molar volumes of elements at their stable or metastable phases are calculated. For selected binary compounds, at room temperature and atmospheric pressure, a non-linear regression model based on the Levenberg–Marquardt algorithm is applied to estimate the excess molar volume using Redlich–Kister polynomials. While previous studies based on CALculation of PHase Diagram (CALPHAD) assessments used one basis function, (i.e. a fit with only the leading order interaction parameter) to estimate the excess molar volume from experimental data, in the present study it is shown that improved prediction accuracy can be achieved using higher order polynomials in the Redlich–Kister expansion in many binary alloys, provided cross-validation is performed to avoid overfitting. We report higher-order Redlich–Kister parameters valid at room-temperature and ambient pressure. The estimated excess molar volumes are used to obtain the mixture molar volumes for selected Ni-X, Ti-X, and Co-X compounds.