Phase Equilibria under Irradiation
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PHASE EQUILIBRIA UNDER IRRADIATION
P. BELLONW, F. SOISSONI, Y. GRANDJEAN1, 2, AND G. MARTINI I CEA, CEREM/SRMP, Centre d'Etudes de Saclay, F91191 Gif-sur-Yvette, France 2 EDF, DER/DEMA, Les Renardi~res, BP 1, Ecuelles F77250 Moret-sur-Loing, France ABSTRACT A solid under irradiation is a far-from equilibrium system, and therefore phase equilibria in such a system cannot be assessed from equilibrium thermodynamics. Starting from a kinetic description which incorporates the various processes responsible for atomic diffusion (e.g. thermally activated jumps, replacement sequences or displacement cascades), the various possible steady-states can be identified analytically or numerically, as well as their kinetic evolution on varying the control parameters of the system (e.g. temperature, average composition, irradiation flux, cascade density ...). Furthermore, from stochastic versions of the kinetic model, potentials governing the stationary probability distribution of states can be derived, allowing to build dynamical equilibrium phase diagrams. Illustrating the above approach on the A2-B2 order-disorder transition, we have identified irradiation-induced two-phase state, cascade size and density effects on phase stability. By incorporating point defects, such description is well suited to study irradiation-induced segregation at sinks in concentrated alloys.
INTRODUCTION In simple cases, an alloy under irradiation can be seen as a system where two dynamic processes are acting in parallel: thermally activated jumps and ballistic jumps, due to nuclear collisions. Kinetics and steady-state properties of such a dissipative system cannot be obtained from standard equilibrium thermodynamics. It is then fruitful to address the question of phase stability under irradiation from the point of view of dynamical systems [1-61. Starting from a mesoscopic kinetic description, the introduced by Kubo et al [71, in some specific cases stochasticusing potentials formalism governing the probability distribution of states can be built analytically [1-3,51. From these potentials, dynamical equilibrium phase diagrams are obtained, providing a map of the most stable steady-state for any given set of irradiation conditions. The existence of bursts of ballistic jumps in displacement cascades during heavy-ion or neutron irradiation can be taken into account in this approach: it will be shown that this modifies significantly the phase stability. By the use of deterministic numerical simulations, more complex cases, e.g. heterogeneous systems, can be studied [6]. Point defects can be explicitly incorporated in such descriptions, which will allow to model irradiation-induced segregation at sinks, such as free surfaces or grain boundaries. After recalling in the first section the diffusion model, dynamical equilibrium phase diagrams are built in the second section, either from deterministic or stochastic kinetic models. These techniques are used in the third section to follow microstructural evolutions, such as instability of anti-phased ordered
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