Origin of ω-phase formation in metastable β-type Ti-Mo alloys: cluster structure and stacking fault

The ω-phase formation and its collapsed structures in metastable β-type Ti-Mo alloys were illustrated by first-principles calculations and experimental evidence of a partially collapsed ω-phase in the nano-scale Mo-depleted region under a rapid cooling via high-angle annular dark-field scanning transmission electron microscopy. The ease of ω-phase formation within -Mo-Ti-Mo- poor cluster structure was not only due to the low energy barrier in the collapse pathway, which was caused by the reduced lattice distortion, but also due to the softening of the shear modulus (G₁₁₁) as a result of the small charge density difference. The most stable collapsed structure of the ω-phase strongly depended on the minimum stacking fault energy among different collapse degrees in accordance to the smallest charge density difference. Therefore, the concurrent compositional and structural instabilities of the ω-phase was attributed to the coupling effect of the cluster structure with stacking fault from the atomic and electronic basis.