Atomic mass transport in binary metallic glasses: a case study of Mg₂Ca, Al₂Ca and Al₄Ca

The phenomenological framework of non-equilibrium thermodynamics links atomic transport processes to observable quantities. In this study, we examine mass transport mechanisms in binary bulk metallic glasses (BMGs) using a combined approach: (i) the darken-manning (DM) equation, derived from irreversible thermodynamics, to compute interdiffusion coefficients and related thermodynamic factors, and (ii) thefree volumetheory, applicable to glass and liquid phases. Inputs for the DM equation were obtained from molecular dynamics simulations, enabling us to quantify cross-correlation effects during diffusion. In our previous work Shankaret al(2024J. Appl. Phys.13635107), we simulated the amorphous phase of biocompatible Mg₂Ca, Al₂Ca, and Al₄Ca systems. Applying the composite theory to these BMGs, we identify distinct mass transport behaviors in glass and liquid phases. Our results suggest that diffusion in the glassy state is dominated by solid-like, elastic vibrations, whereas in the liquid phase, anharmonicity drives diffusion. In the glass phase, this anharmonicity arises from the interatomic potential; in the liquid phase, it stems from dynamic structural rearrangements. The liquid phase exhibits non-phononic, unstable vibrational modes that diminish in the glass phase, which adopts a more harmonic, phonon-like character. At low temperatures, low-frequency vibrations rarely lead to atomic jumps, confining atoms within potential wells. This is analyzed through the frequency-dependent diffusion coefficient and vibrational density of states. The hole theory effectively describes the energetics of both phases: in glasses, holes act as vacancies governed by interatomic forces, while in liquids, they are short-lived, fluctuating cavities. These fluctuations, governed by hole formation energy, drive mass transport in the liquid phase. Our findings further show that glass transition and stability correlate with hole formation energy and elastic moduli. Finally, manning parameters reveal the influence of phase transitions on atomic interdiffusion, especially under stochastic forces in thet→ 0 limit.