Application of block-discretization method for analysis of electrical conductivity of graphene-containing shungite.
Authors:   Syktyvkar State University, Oktyabrskiy prosp. 55, Syktyvkar 167001, Russia, Antonets I.V. , Golubev E.A. ,   Geology Institute Komy SC UrD RAS, Pervomaiskaya 54, Syktyvkar 167982, Russia, Shavrov V.G. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia, Shcheglov V.I. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia
Published: March 2021

The block-discretization method for calculation of electrical conductivity of graphene-contained shungite is proposed and realized in practice. It is established that in the basis of forming of shungite carbon conductivity is presented the structure and arrangement of graphene packets which may be investigated only by electron microscopy method. The card of space allocation of graphene packets on the flat section of shungite specimen is brought. It is found two varieties of graphene packets distribution – regular when packets forms the ribbons one after the other and irregular when the packets are oriented in arbitrary directions. As a result of this cards character it is proposed to distinguish two varieties of observed structure – power-contrast which is formed by regulated ribbons and weak-contrast which is formed by chaotic oriented graphene packets. On the basis of model of current-tubes the valuing of electrical resistance for both kinds of structure is made. As a maximum cases for conditions of current flow it is investigated two orientation of packets inside of tube – suitable when the layers of graphene are oriented along the axis of tube and unsuitable when the layers of graphene are oriented across the axis of tube. In this case it is taken into account that the resistance of graphene packet across the layer is more then the resistance of its layer along the plane on three orders and more. It is found that the main resistance of tube is formed not only by graphene layers but in the most influence of joint from neighbouring graphene packets. The method of making of contour card which consist of the construction of boundaries between two kinds of structure and tracing the contour lines which correspond to individual ribbons in these boundaries is proposed. From the consideration of cards of flat section of structure it is established that the arrangement of packets, its orientation and conditions of grouping in general have same character in different parts of whole card. It is established that the extracted from the whole structure sufficient small area has the same specific conductivity as the whole structure. For the analysis of whole structure the method of block-discretization is proposed. This method consist of the breaking the whole massif on parts which are sufficiently similar to each other and analysis of several parts with subsequent averaging. It is supposed that the parameters of this averaged part may be calculated using simple means. After these actions the received meanings of parameters are repeated so times as it is necessary and as a result it is found the parameters of whole structure. The detailed step-by-step algorithm of using block-discretization method for the founding the specific conductivity of whole structure using the contour card of flat section of specimen is proposed. As a procedure of discretization it is proposed the breaking of whole card on square parts which are named as “blocks”. After this breaking from the different localizations from whole card it is chooses several blocks which parameters are subjected to averaging. After these actions it is constructed the net which is the same as initial net on the whole card but in this case the cells of this net are filled by equal averaged blocks. The calculation of parameters of whole card which consist of equal blocks gives the parameters of initial task. The application of block-discretization method is considered on the example of real shungite specimen from the deposit Nigozero which structure contains the ribbons intermitted by unregulated packets. It is constructed the contour card of specimen part having dimensions 40 x 40 nm. On this card is applied the net with square cells having dimension 10 x 10 nm which breaks the whole card into 16 blocks. It is made the secondary block discretization of blocks so as on the each block applied the net having cells 1 x 1 nm. Using this net the areas of block which contain the ribbons and unregulated packets and also the length and quantity of ribbons in block are found. The results of these measuring are averaged above all blocks. On the basis of averaged values of block parameters the geometrical structure of averaged block is constructed. It is found that the block may be presented as the closely packed on the flat of structure which consist of the equal single current tubes. In this case equal single tube consist of two successive connected parts. The first of these parts correspond to suitable orientation of grapheme packets and the second correspond to unsuitable orientation of the same packets. Using the received by electron microscopy methods parameters of grapheme layers and packets and also the gaps between its the resistance of single tube and averaged block consisted of these tubes is calculated. In supposition that the shungite structure is uniform in three axis on the basis of single tube and averaged block parameters the specific conductivity of carbon part of shungite is calculated. It is found that the obtained value of specific conductivity in comparison of specific conductivity of real shungite containing 97% carbon is larger approximate in three-four times. It is proposed the optimization of model by consideration into account the gap between packets and volume distribution of tubes in isotropic structure. These additions allows to obtain the good agreement between received data and meanings of conductivity of real shungites. In briefly mentioned some possibilities of development this work, mentioned the universal character of block-discretization method and mentioned some possible tasks for its application.