Free-energy-based thermodynamic and kinetic landscapes of Cu–Nb alloys

Abstract

Understanding phase stability in immiscible alloys is essential for designing materials for extreme environments, including high-temperature and irradiation conditions. Here, Cu–Nb is used as a model system with a positive enthalpy of mixing, in which enthalpic and entropic contributions compete across composition and temperature. Molecular dynamics and well-tempered metadynamics simulations were combined to investigate thermodynamic preferences and transformation kinetics over the full composition range from 300 to 1700 K. Helmholtz free-energy trends for FCC, BCC, and liquid/amorphous structures were estimated from lattice-static and vibrational contributions derived from velocity autocorrelation functions and vibrational densities of states (VDOS). Lattice-static energy governs structural preference near the terminal compositions, favoring FCC in Cu-rich alloys and BCC in Nb-rich alloys. At approximately 30–50 at. % Nb, competing structures have comparable static energies, and the vibrational contribution increasingly favors liquid/amorphous configurations at elevated temperatures. VDOS analysis reveals phonon softening in FCC alloys with increasing Nb content, whereas BCC Nb primarily exhibits thermal broadening and spectral-weight redistribution with modest peak shifts. Metadynamics simulations show that increasing Nb from 30 to 40 at. % at 300 K stabilizes the amorphous state relative to FCC, while Nb-rich alloys retain an overall preference for BCC order. Increasing temperature from 300 to 1000 K reduces transformation barriers between crystalline and amorphous states in both composition regimes. These findings clarify how composition and temperature govern competing ordered and disordered states and provide guidance for designing heterogeneous immiscible alloys and interfaces for extreme environments.