Prediction of the zirconium hydride precipitation barrier with an anisotropic 3D phase-field model incorporating bulk thermodynamics and elasticity

A phase-field model is developed to elucidate a long-standing question about zirconium hydride nucleation by extending the applicability of bulk equilibrium thermodynamics to the nanoscale. A significant hysteresis is observed between the conditions of hydride dissolution and precipitation during power cycling which can degrade the mechanical stability of nuclear fuel cladding but depends on availability of heterogeneous nucleation sites. The modelling approach combines anisotropic interfacial energy, a comprehensive 3D anisotropic elastic treatment, and stress driven diffusion with quadratic approximations of thermodynamic potentials. New experimental evidence of the effect of thermal history on hydride precipitation is presented which provides support and enhanced interpretation of the model predictions. Simulation results indicate that the interfacial energy of an embryotic hydride is augmented by the elastic contribution from the coherent interface, resulting in effective interfacial energies in the basal and prismatic planes in excess of 0.80 and 1.44 J m−2 respectively, more than a factor of 20 larger than typically considered. Along with the strain energy of accommodation, a significant homogenous nucleation barrier is formed which is overcome by a sufficient thermodynamic driving force for the growth of the embryo, determined by the H supersaturation in the surrounding matrix and the bulk equilibrium thermodynamics, which changes dramatically with temperature.