Thermodynamics of concentrated solid solution alloys

This paper reviews the three main approaches for predicting the formation of concentrated solid solution alloys (CSSA) and for modeling their thermodynamic properties, in particular, utilizing the methodologies of empirical thermo-physical parameters, CALPHAD method, and first-principles calculations combined with hybrid Monte Carlo/Molecular Dynamics (MC/MD) simulations. In order to speed up CSSA development, a variety of empirical parameters based on Hume-Rothery rules have been developed. Herein, these parameters have been systematically and critically evaluated for their efficiency in predicting solid solution formation. The phase stability of representative CSSA systems is then illustrated from the perspectives of phase diagrams and nucleation driving force plots of the σ phase using CALPHAD method. The temperature-dependent total entropies of the FCC, BCC, HCP, and σ phases in equimolar compositions of various systems are presented next, followed by the thermodynamic properties of mixing of the BCC phase in Al-containing and Ti-containing refractory metal systems. First-principles calculations on model FCC, BCC and HCP CSSA reveal the presence of both positive and negative vibrational entropies of mixing, while the calculated electronic entropies of mixing are negligible. Temperature dependent configurational entropy is determined from the atomic structures obtained from MC/MD simulations. Current status and challenges in using these methodologies as they pertain to thermodynamic property analysis and CSSA design are discussed