Coherent elastic energy calculation of ω particles in β matrix for Zr-Nb alloys

The misfit and coherent elastic energy caused by ω particles in β matrix is quantitatively calculated in this study. First, the coherent strain matrixes for four ω variants are established including the misfit parameters based on Khachaturyan's theory. Then, the misfit and coherent elastic energy in athermal β → ω transition, and isothermal β → ω transition are calculated, respectively. The calculation results indicate that the coherent elastic energy gets maximum value when x _Nb = 0.08 (Nb content) and gets minimum value when x _Nb = 0.1518 in quenching Zr-Nb alloys, which are in fair agreement with experimental results. For isothermal β → ω transition, the misfit and coherent elastic energy depend on composition and aging temperature. The misfit caused by isothermal ω phase is much larger than the one caused by athermal ω phase. This results in larger coherent elastic energy in isothermal β → ω transition. In addition, the misfit is found as an approximate linear function of temperature and composition for Zr-Nb alloys, and the coherent elastic energy is revealed as an increasing function of |v _F -v _S | for the two kinds of transition.