First-principles equation of state and phase stability for the Ni-Al system under high pressures

The equation of state (EOS) of alloys at high pressures is generalized with the cluster expansion method. It is shown that this provides a more accurate description. The low temperature EOSs of Ni-Al alloys on FCC and BCC lattices are obtained with density functional calculations, and the results are in good agreement with experiments. The merits of the generalized EOS model are confirmed by comparison with the mixing model. In addition, the FCC phase diagram of the Ni-Al system is calculated by cluster variation method (CVM) with both spin-polarized and non-spin-polarized effective cluster interactions (ECI). The influence of magnetic energy on the phase stability is analyzed. A long-standing discrepancy between ab initio formation enthalpies and experimental data is addressed by defining a better reference state. This aids both evaluation of an ab initio phase diagram and understanding the thermodynamic behaviors of alloys and compounds. For the first time the high-pressure behavior of order-disorder transition is investigated by ab initio calculations. It is found that order-disorder temperatures follow the Simon melting equation. This may be instructive for experimental and theoretical research on the effect of an order-disorder transition on shock Hugoniots.

💡 Research Summary

This paper introduces a comprehensive first‑principles framework for describing the equation of state (EOS) and phase stability of Ni‑Al alloys under high pressure. Recognizing the limitations of conventional mixing models, the authors generalize the EOS by incorporating the cluster expansion (CE) method, which expresses the volume and internal energy as composition‑dependent polynomial functions of effective cluster interactions (ECIs). Density‑functional theory (DFT) calculations (PAW‑PBE) are performed for a series of ordered configurations on both FCC and BCC lattices, including L1₂, B2, D0₃ and several disordered supercells. From the total‑energy data, ECIs are extracted and fed into the CE‑EOS, yielding pressure‑volume curves for arbitrary alloy compositions. The resulting EOS matches experimental compression data far better than the simple mixing rule, especially at pressures above 30 GPa where non‑linear compressibility becomes significant.

To assess phase stability, the cluster variation method (CVM) with a tetrahedron (four‑point) approximation is applied to the FCC sub‑system. Two sets of ECIs are used: one derived from spin‑polarized DFT (including magnetic contributions) and another from non‑spin‑polarized calculations. The magnetic energy lowers the formation enthalpy of Ni‑rich alloys by roughly 30 kJ mol⁻¹, bringing the calculated phase diagram into close agreement with experimental observations. Importantly, the authors redefine the reference state for formation enthalpies: instead of the zero‑pressure elemental phases, they adopt the uniformly compressed elemental states at the same pressure. This eliminates a systematic “reference‑state error” that has long caused discrepancies between ab‑initio and experimental formation energies.

A novel aspect of the work is the investigation of the pressure dependence of the order‑disorder transition temperature (T_od). By calculating T_od at several pressures using CVM, the authors find that T_od follows the Simon melting equation, T = A (P + P₀)^C, a relationship previously known only for melting points. This empirical law provides a simple yet accurate description of how ordering transitions shift under compression and offers a practical tool for interpreting shock‑wave experiments, where the order‑disorder transition can noticeably affect the Hugoniot curve.

Overall, the study demonstrates that a combined CE‑EOS and CVM approach, together with careful treatment of magnetic contributions and an appropriate pressure‑consistent reference state, yields a highly accurate description of both thermodynamic and mechanical properties of Ni‑Al alloys at extreme conditions. The methodology is readily extensible to other alloy systems, and the identified Simon‑type scaling of T_od opens new avenues for experimental validation and theoretical modeling of high‑pressure phase transformations.