Spin models for energetics of polytypes in face-centered cubic metals

The energetics of polytypes in twelve fcc metals are systematically investigated by using advanced pseudo-Ising spin models. While the established 4P (Axial Next-Nearest-Neighbor Ising) model reliably captures energy ranges, the proposed 5P model, based on the hk notation, offers a superior microscopic perspective. It reveals that energy differences stem from the competition among three nearest-neighbor and six next-nearest-neighbor interactions. This explains the predominance of simple stacking sequences (2H, 3C, 4H, 6H(1), 9R) built from units like h, k, and hk layers. Central to our findings is the ”enthalpy polygon” framework. Its lowest-enthalpy path elucidates temperature- and pressure-induced transitions in bulk materials, while its highest-enthalpy path explains metastable phase formation during nanocrystal growth, validated against experimental data for metals such as Li, Al, Sr, Pb, and Au. This work establishes a fundamental bridge between atomic-scale interactions and macroscopic phase stability.