Specific Features of Statistical Analysis for Grain Nanostructures Formed by Solid-State Diffusion at Annealing

Abstract

Analysis of structure of Nb3Sn layers, formed by solid-state diffusion in Nb/Cu-Sn composites, has been carried out, using statistical analysis methods. The three different statistical models of grain size distributions, which consist of both a single logarithmic standard distribution and a combination of a logarithmic and a standard distribution with scale factors were considered. It was shown that, during the formation and further evolution of the structure by solid-state diffusion processes, there is a strong correlation between the average crystallite sizes and their deviations from mean values. The dependence of the standard deviation on the average crystallite size, calculated from parameters of logarithmic distribution, falls on the straight line with small deviations. Taking into consideration the relationship between the parameters of grain size distribution, one can conclude that an approximation with the model which involves the dependence between standard deviation of the standard distribution and the logarithmic one provides better accuracy, despite a little bit worse fitting quality of the experimental distributions.