A new method of calculation of the thermodynamic properties of point defects in concentrated solid solutions: An application to VNbMoTaW alloy

Abstract

Up to now, the problem of accurate calculation of the enthalpy and Gibbs energy of formation of self-point defects (SPDs) in crystalline solid solutions at given temperatures remains. In this paper, we present an accurate method for calculating the thermodynamic properties of SPDs in solid solutions, including high-entropy alloys, using molecular dynamics (MD), which exactly takes into account the effects of anharmonicity at temperatures above the Debye temperature. The method is implemented within the supercell approach and includes the integration of the Gibbs-Helmholtz equation in combination with a computer experiment to determine the concentration of vacancies and self-interstitial atoms (SIA) at high temperatures. The method was validated for the equiatomic bcc VNbMoTaW alloy in the temperature range from 1000 to 2700 K. Simulations revealed that local chemical ordering, neglected in random solid solution approximations, critically impacts defect energetics, with its omission leading to significant underestimation of SPD’s formation enthalpies in MD calculations. The enthalpy and entropy of vacancy formation in VNbMoTaW exhibit weak temperature dependence, contrasting with pure metals such as vanadium and tungsten. Self-interstitial atoms (SIAs) display formation enthalpies substantially higher than those of vacancies, consistent with trends in pure metals. Vacancy concentrations in VNbMoTaW at equivalent temperatures lie between values for pure tungsten (highest melting point) and vanadium (lowest melting point). Equilibrium SIA concentrations remain two or more times lower than vacancy concentrations across the studied temperature range. Notably, vacancy concentrations near the alloy’s melting temperature align closely with experimentally observed values in pure metals ($10^{-4}$ – $10^{-3}$). This work establishes a robust computational protocol for defect thermodynamics in complex alloys, with implications for designing materials resistant to radiation damage and high-temperature degradation.