Application of second discretization method for analysis of graphene-containing shungite structure on scanning electron microscopy data

The application of the secondary discretization method to analyze the structure of graphene-containing shungite using carbon distribution maps in shungite samples taken by high-resolution scanning electron microscopy is proposed. To analyze the degree of homogeneity of the maps, the method of primary structural discretization by three levels was used, for which the map was divided into cells using a grid overlay with square cells. The determination of the degree of order was carried out by manual and machine methods, after which a comparison of the obtained results was performed. A scheme of hierarchy of degree of order was proposed. Five degrees of order are distinguished. A definition of “neighborhood order” is proposed, which characterizes the degree of change in the homogeneity of the structure at the boundary between neighboring cells. A scheme for calculating the neighborhood order on a map row with subsequent summation over the whole map is proposed. A procedure of secondary map discretization is proposed, which consists in superimposing a new grid including an integer number of primary cells on the primary discretized map. A first-level secondary discretization is performed, resulting in a complete map divided into four partial maps. Based on the processing of the partial maps, it is shown that the neighborhood order in manual processing exceeds the neighborhood order in machine processing by a factor of 1.3. The homogeneity parameter of the map as a whole is introduced according to the deviation of the neighborhood order for each of the partial maps from the average value. Anisotropy of the neighborhood order, consisting in the difference of order values by rows and by columns of the same map, is revealed. The anisotropy parameter, defined by the difference between the unit and the ratio of row and column neighborhood orders, is introduced. The homogeneity parameter of the map is introduced into consideration, which consists in the percentage value of the deviation of the anisotropy parameter from the average value of the map as a whole. It is found that the anisotropy parameter, compared to the neighborhood order parameter, provides a more sensitive tool for determining the homogeneity of the map as a whole. Using the same methodology as for each partial map, the neighborhood order of the full map is examined. It is found that the neighborhood order for manual processing exceeds a similar value for machine processing by a factor of 1.33 with an accuracy of 0.8%, which is consistent with a similar result obtained when considering partial maps. The anisotropy of the neighborhood order over the complete map is considered. It is shown that the use of machine processing compared to manual processing provides more accurate results. Some recommendations for possible development of the work are given, including variation of primary and secondary sampling cell parameters, identification of the cause and mechanism of excess of neighborhood order in manual processing over the same order in machine processing, investigation of the degree of homogeneity over several maps of a single sample, as well as over several samples from different deposits with subsequent comparison with the electrical conductivity of the samples. )