Phase-Field Modelling of radiation induced microstructures
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Phase-Field Modelling of radiation induced microstructures L. Luneville1, G. Demange2, V. Pontikis3, D. Simeone2 1
DEN/DANS/DMN/SRMA/LA2M/LRC-CARMEN, CEA Saclay, 91191 Gif-sur-Yvette, France DEN/DANS/DM2S/SERMA/LLPR/LRC-CARMEN, CEA Saclay, 91191 Gif-sur-Yvette, France 3 DSM/IRAMIS/LSI, CEA Saclay, 91191 Gif-sur-Yvette, France 2
ABSTRACT This work shows that realistic irradiation-induced phase separation and the resulting microstructures can be obtained via an adapted Phase Field (PF) modelling combined with atomistic Monte Carlo simulations in the pseudo-grand canonical ensemble. The last allow for calculating the equilibrium phase diagram of the silver-copper alloy, chosen as a model of binary systems with large miscibility gap and, for extracting the parameters of the excess free-energy PF functional. Relying on this methodology, the equilibrium phase diagram of the alloy is predicted in excellent agreement with its experimental counterpart whereas, under irradiation, the predicted microstructures are functions of the irradiation parameters. Different irradiation conditions trigger the formation of various microstructures consistently presented as a non-equilibrium “phase diagram” aiming at facilitating the comparison with experimental observations. INTRODUCTION Microstructures in irradiated alloys are made of phases with spatial distribution in patterns and composition both differing from those observed in alloys at equilibrium [1-4]. Taking advantage of the large metastability of microstructures, radiation is now being used for tailoring materials with desired, new properties [1] such as the electronic properties of semiconductors doped by ion implantation for applications in microelectronics [5,6]. This is a main reason motivating the development of microstructural modeling capable of realistic prediction of microstructures for driving experimental preparation thus optimizing resources and shortening the time to applications. In this context, the strong requirement is that space and time scales of experimental and modeling studies of microstructures are comparable, which discriminates existing modelling techniques and points to phase field (PF) methods as the most appropriate for they naturally integrate mesoscopic time and space scales as required in microstructural modeling [7]. The present work focuses on PF description of a decomposing binary alloy under irradiation in view to study damage-related microstructures and their characteristics as functions of the irradiation parameters, energy range, flux and fluence. By numerically solving the evolution equation in discrete space and time reduced coordinates, the resulting microstructural information should be represented in real space and time units in view of the direct comparison with experiments. To this end, we have fitted the parameters of the PF excess free energy functional to the calculated equilibrium phase diagram of a silver (Ag) copper (Cu) alloy modeled using pseudo-Grand Canonical Monte Carlo (GCMC) atomistic simulations [8] and a phenomenologi
