Theoretical research of the temperature fields of copper during the formation of nanostructured layers in plasma environment

Abstract

The subject of study is the mathematical model for thermal processes during the formation of nanostructures in a plasma medium. In previous studies, it was shown that for the appearance of nanostructures, it is necessary that there be a certain temperature, its rate of increase, and thermal stresses. The required depth of the near-surface layer of the processed material, which is most favorable for the formation of nanostructures, is determined where the highest temperature stress gradients occur. The current work determines the technological parameters for obtaining nanostructures during ion-plasma treatment of the copper surface, as an example. The task of this work, by changing the energy of the ions, is to choose the location of the fields along the depth of the material to generate the necessary high temperature gradients in the given planes of the material. Thus, significant thermal stresses, and hence nanostructures, can be created in a large volume of material. The method used is analytical. In our work, a mathematical model was developed to describe the generation of temperature fields during ion-plasma surface treatment and tested on the process of copper treatment with oxygen ions. In this model, the joint actions of plasma flows and flows of charged particles with materials are realized through thermophysical, thermomechanical, thermal fatigue, diffusion, thermochemical, plasma-chemical processes and collisions. Therefore, the developed model will contribute to a more accurate determination of technological parameters for the formation of conditions conducive to the stable growth of nanostructures in the surface layers of processed materials. Because of numerous calculations, the dependence of the temperature of the surface layer of copper on the energy of oxygen ions was determined. The temperature fields in the zone of action of ions for three levels of the plane of the surface layer are calculated depending on the depth of penetration of ions for different times of interaction and at different current densities from 2.7∙10⁶ to 2.1∙10⁸ A/m². Studies have shown that the maximum surface temperature is reached at the end of the thermal action of the ion. Conclusions. The obtained values of thermal stresses showed the possibility of formation of nanostructures in the surface layer of copper under the action of oxygen ions at a depth of x=0.5λ_m at a current density of 2.7∙10⁶ A/m². For the x=0.5λ_m plane at a current density of 3∙10⁷ A/m², where the largest temperature gradients were found, the maximum temperature stresses were calculated, amounting to 5∙10⁸ N/m, which confirms the creation of conditions for obtaining nanostructures. But at 2.1∙10⁸ A/m², the total temperature rises, and the temperature gradients decrease, which decreases temperature stresses and failure to meet the conditions for obtaining nanostructures. The results obtained can be used to develop a technology for the production of nanostructures in a plasma environment, for example, on copper by ion-plasma treatment in an oxygen environment.in a plasma environment, for example, on copper by ion-plasma treatment in an oxygen environment.