Specific features of statistical analysis of relative grain boundary energies obtained by scanning tunneling microscopy

An approach based on statistical analysis is proposed for the processing of data obtained using scanning tunneling microscopy of grain boundaries, which allows a numerical estimation of the relative energy of grain boundaries. The proposed statistical model also gives a possibility to separate groups of grain boundaries depending on their average relative energy and fraction in general distribution. Scanning tunneling microscopy data analyses have been carried out on data obtained by investigating copper and nano-structured copper were analyzed coarse-grain commercially pure copper and on copper nanostructured by the equal-channel angular pressing (ECAP) method. Obtained results were compared with available in literature experimental data for these types of materials, received by other methods. It is established that the grain boundaries in coarse-grain copper have significantly lower relative energy in contrast to the grain boundaries of ECAP-treated copper. Besides, there is, except for boundaries with high relative energy, a fraction of boundaries in the deformed sample with energy corresponding to those in coarse-grain copper.