A short survey is presented of recent advances in the theory of stability criteria for phases under irradiation. The reason why standard thermodynamical criteria do not apply is discussed. As an example we show that among the many cases of irradiation induced stabilization of metastable phases, some are simple enough to deserve a detailed quantitative theoretical interpretation. Such is the case for the Ni4Mo compound where irradiationinduced inversion of the respective stability of two ordered structures was first reported, as well as irradiation-induced bistability. The Lyapunov function formalism introduced by the authors, makes it possible to describe quantitatively the competition between the chemically driven formation of compounds with their ballistic destruction and to assess the respective stability of various compound structures under irradiation. The model has now reached a degree of sophistication such that good quantitative agreement with the reported behaviour is achieved. We argue that a similar type of approach might be useful for predicting the type of phase to be stabilized by mechanical alloying.
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