Thermocapillary model of formation of surface nanostructure in metals at electron beam treatment

The paper presents the thermocapillary model for the formation of nanostructures in surface layers of materials. It is based on Navier-Stokes hydrodynamic equations, the thermal conductivity equation, the state equation and the boundary conditions. A search for the solutions in the form of a progressive wave has been carried out. The dispersion equation has been obtained and analyzed. The dependence of the instability increment on wavelength has been built. The values of the critical wavelength, at which thermocapillary instability for iron and titanium comes, have been obtained. Value comparison of the calculated wavelengths with cell sizes of crystallization has showed a satisfactory agreement. (paper)