Modeling of nanostructure formation in silumin during electron beam treatment

Abstract

The paper presents a mathematical model describing formation of nano-scaled structures in the top layers of aluminum and silicon alloy treated by low-energy high-current electron beams. The model is based on the ideas of nano-structures, forming due to thermo-capillary instability on the edge of melt and electron beam plasma. This instability arises because of the temperature gradient in the melted layer. Linearized Navier–Stocks equations, and convective thermal conductivity equations, as well as kinematic and dynamic boundary conditions were stated for the melted layer. The solution was found as normal modes of disturbances. The relation decrement vs. wave length was found out. The length of wave with the maximal decrement of instability is revealed to be 1140 nm. The further increase in the temperature gradient and the density of the electron beam, respectively, causes its shortening. The findings of the critical wave length differ from the dimensions of crystallization cells (400–600 nm) estimated by SEM. The reason for this is that silicon causes deviations from the linear relation of the surface tension to the temperature.