A Nonisothermal Mechanodiffusion Model of the Initial Stage of Particle Beam Penetration into a Target Surface

Abstract

A coupled mathematical model of the initial stage of particle penetration into a metal surface in the nonisothermal approximation is presented. It is assumed that at the moment of collision with the target the implanted particles have enough energy to generate elastic mechanical disturbances that affect the redistribution of the implanted material. In the general case, the model includes the equation of continuity, the heat conduction equation, the balance equations for implanted component balance, and the equation of motion. The governing relationships correspond to the theory of generalized thermoelastic diffusion. The model takes the finiteness of relaxation times of heat and mass fluxes and the interaction of waves of different physical nature (waves of impurity concentration, stresses (strain), and temperature) into account. The simplifying approximations, nondimensionalization of the equation system, and the method of their solution are described in detail. The problem was implemented numerically using the double sweep method. Examples of coupled problem solving for the system of Mo(Ni) materials are presented. The processes of penetration and redistribution of the impurity in the surface layer of the target are considered in detail at times before and after the relative relaxation times of heat and mass fluxes. It is shown that the interaction of waves of different physical natures leads to temperature and concentration distributions that do not comply with the classical ideas following from models with the Fourier and Fick laws. The results demonstrate distortions in deformation and temperature waves, which is indicative of the interaction between the processes. It is revealed that wave profiles change more noticeably as the current time is closer to the relative relaxation time of the mass flux and the time of the external pulse action.