Mesoscopic Modelling of Irradiation Damage Processes: Bridging Many-Body Mechanics and Thermodynamics in Rate Processes

Abstract

The integration of atomistic mechanics into the macroscopic modeling of rate-processes in solids should ensure the principles of statistical and thermal physics are not violated. Rate constants are customarily derived based on the transition state theory or its variants such as kinetic Monte Carlo simulation, phase-field model, and classical nucleation theory. In this perspective, we examine the assumptions traditionally made in constructing the mesoscopic connection between molecular mechanics and macroscopic thermodynamics, (1) separability of the reaction path from the noise created by lattice vibrations, (2) validity of classical statistics, and (3) existence of quasi-equilibrium among the reactants, the transition state, and the product. We find that the first assumption excludes rate processes at high temperatures or low reaction barrier, while the second excludes those at low temperatures or low reaction barrier. The third assumption has to reconcile with the nonequilibrium nature of rate processes, such as the neglect of entropy production which is proportional to the reaction rate, and thus excludes processes proceeding at fast rates. On this basis, the traditional approach in mesoscopic modeling is only reliable for rate processes in irradiation-damage accumulation with a high activation barrier and at not-too-high temperatures. The mitigation of these restrictions and evaluation of consequences due to their neglect can be formulated in a mesoscopic model in which the atomic processes in the many-body system are treated dynamically and energy quantization and quantum uncertainty are taken into account explicitly through the Mori-Zwanzig formalism of nonequilibrium statistical mechanics and the quantum fluctuation-dissipation relation.