Surface modification of alloys by high-energy pulsed particle beams

The effect of particle beams on the surface of alloys is often used to obtain a material with desired characteristics. Mathematical modeling of such surface modification leads to the study of diffusion in the presence of an intense external source of diffusant. In this case peculiarities in material structure may be of great importance. A special role belongs to inter-grain boundaries in metals, the vicinities of which are regions of accelerated diffusion. Moreover, if the surface treatment by particle beam is carried out with short impulses comparable with relaxation times of diffusion and chemical processes to their equilibrium course, it may be necessary to explicitly consider the particle transfer rate in the material, for example, using the non-classical laws. In this paper we discuss the model of the treatment process by particle beam, which takes into account both the feature of grain boundary diffusion and finiteness of relaxation times of diffusion fluxes in the boundaries and in the volumes of grains. The problem is considered in two-dimensional formulation. The grains and their boundaries are treated as separate phases with different diffusion properties. The grains are represented in the form of rectangles, located at equal distances from each other. The relative size of the boundary phase may vary. Using generalized equations for diffusion fluxes with finite time of relaxation, we come to diffusion equations of hyperbolic type for the volume and the grain-boundary phases. It is assumed that between the diffusant and the treated material a summary chemical reaction occurs with formation of a summary product. A numerical study allowed us for the first time to establish the features of grain-boundary diffusion and to study the dynamics of reaction product formation for treatment times comparable to relaxation times. The effect of pulse duration and grain size on the diffusant concentration distribution for these conditions was investigated. [Display omitted] •Diffusion in grain boundaries are studied.•The influence of diffusion flux relaxation were analyzed.•Also, the influence of pulse duration and grain size is investigated.•The model shows wave-like pattern of diffusant concentration.•Grain size has a significant effect on the distribution of diffusant.