Irradiation-induced formation of metastable phases: A master-equation approach

We propose a new formalism, based on a master equation, for elaborating criteria of phase stability under irradiation. This technique is applied to the order-disorder transition in ${\mathrm{Ni}}_4$Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been reported, as well as a temperature domain where bistability is observed. The technique consists in describing the time evolution of the configuration of the system at the atomistic level and writing a master equation for the probability distribution of configurations defined at a mesoscopic level. The transition probabilities of the former are expressed in terms of the atomic jump frequencies which enter the atomistic description, to a level of sophistication compatible with a simple mean-field description of the thermodynamics of the system outside irradiation. The identity between the thermodynamical equilibrium states and fluctuations on the one hand and the dynamical steady states outside irradiation on the other hand is thus built into the formalism. Irradiation effects are then introduced by enhancing the overall atomic mobility (defect supersaturation) and by adding to the atomic exchange frequencies a ballistic contribution which forces mixing whatever the local configuration (infinite-temperature dynamics). The same formal expression for the probability of the various dynamical steady states is obtained, but with some potential replacing the free energy. The former has no simple intuitive meaning but may be evaluated numerically. The probabilities of various steady-state configurations can then be assessed. When applied to ${\mathrm{Ni}}_4$Mo under high-energy-electron irradiation, the technique fully reproduces the sequence of behaviors which has been observed experimentally in the whole irradiation temperature range. The temperature thresholds where stability inversion or bistability are observed may be fitted reasonably well despite the crudeness of the mean-field description underlying the treatment.