Abstract. This paper is the second
part of materials in which authors investigate the structure and electrical
properties of graphene-contained shungite. These investigations are carried
with the aim to know the possibility of shungite employment for the creating of
planar structure intended electromagnetic radiation. These investigations are
carried on the basis of conductivity maps obtained by electro-force
spectroscopy method. In the introduction it is described the brief review of
first and second parts of this work and mentioned its results. It is described
the most important properties of explored specimens. It is described the
discretization method of conductivity maps which may be possible from the
binomial maps to determine the structure parameters of specimens. It is
described the scheme of determination of carbon concentration on the basis of
calculation white and black checks on the fields which are obtained from
discretizated conductivity maps. It is described the procedure of investigation
of chains checks white and black colors on the binomial conductivity field
which is made with the purpose of detailed investigation of space distribution
of structure conducting and non-conducting phase. It is introduced in
consideration the structure discretization parameter in the measure of it’s the
single square proposed which for investigated specimens have the side 2.5
micrometers. For the characteristic of carbon distribution over the specimen volume
it is introduced the parameter of fractional which equal to quantity of single
cubes in volume unit. The determines shungite structure is compared with
proposer early models «cubes with percolation» and «sand with liquid». It is
established the satisfactory agreement. It is noted that the most important
object of present work is the investigation of distribution of checks chains on
the binomial conductivity field of each investigated specimen with the purpose
of determination of its integral conductivity. It is described the general
characteristics of specimens and methods of measuring. There was investigated
the same specimens as in first and second parts of this work. It was
investigated 32 specimens grouped to nine groups on the sign of the same carbon
concentration. The methods of specimen parameters measuring also as a whole
coincides with those described in first and second parts of this work. So the
volume concentration was determined by coulomb-metric titration. The
distribution of conducting and non-conducting regions on the flat processed
specimens surfaces was determined by electro-force microscope by resister-spreading
method. The result of these measuring was the conductivity maps for the
analysis of its it was made its discretization with binomial numerical
processing. The scanning of these binomial maps was to be able to determine the
quantity and structure of chains binomial elements distribution white and black
phases (carbon and quarts). In the quality of the original etalon it was
employed the measure of conductivity be contact methods – by two and four
contacts. By these data it was build the dependence of conductivity from the
carbon concentration which was approximated by quadratic polynomial. It is
investigated two variants of approximation polynomial determination – by the
least square method with the building of corresponding tables and with the
standard mathematic package “Matlab” with the aid of command “polyfit”. It is
established that the advantage of tables method is the high degree of
approximation and the defect – some cumbersome when the polynomial degree is
more the two. The advantage of package “Matlab” is simplicity of application so
as the polynomial of 3-4 degree and defect – comparatively low accuracy. In the
framework of this paper it was recognized that the optimal for the polynomial
of second degree which demands high accuracy to employ the table method and for
polynomial which demand less accuracy and polynomial third degree employ the
package “Matlab”. By scanning of binomial maps it is calculated the quantity of
chains having established extent. After this calculation for each value of
extent the whole quantity of chains is added. The scanning was made along the
horizontal and vertical lines after this from two determined values the middle
arithmetical value was calculated which is accepted as the measure of chains
quantity of established color. For white chains (carbon) it is found the
scattering of determined values by small extent is 25% and by the extent is
increased it is diminishing try to attain zero. It is investigated the typical
cases of dependence chain quantity from its extent by different carbon concentration.
It is made the approximation of determined values by three degree polynomials.
It is shown that by small and middle concentrations (less then 70%) the maximum
value of polynomial take place by chain extent is equal to binomial unit and by
large concentrations (more then 70%) maximum value of polynomial is fall to
maximum possible chain extent (in this case – 20 binomial units). It is made
the quality investigation of correlation between white chains extent (carbon)
and integral conductivity. It is fount that by increasing of chains extent the
integral conductivity mast increase. It is proposed the scheme of stepped
quantity analysis of dependence of chain extent from carbon concentration. It
is found that the most important moment of this task is the establishment of
normalized by own maximum polynomial dependence of chain quantity from its
extent. On the basis of determined data it is build the dependence of middle
values of chain extent on the determined level from the carbon concentration
which after this is approximated by polynomial of second degree. It is
investigated the particularity of determined data from the value of established
level. It is shown that the optimal for natural results is the level about 0,1
from maximum polynomial value in the frame of whole concentration changing from
zero to 100%. On the basis of determined data it is build the dependence of
middle extent values on established level from carbon concentration which is
approximated by polynomial of second degree. It is made the comparison of
determined polynomial with the polynomial which describes the dependence of
conductivity from concentration which is determined by contact method. It is
shown that in the case of introduction some normal coefficients both
dependences are in good agreement to each other (the distinction is less then
5%). It is proposed the model which establishes the simplification in accuracy
on normal coefficients between the chains extent on established level and
integral conductivity of specimen as a whole. It is found the analytical
formula which describes this dependence in the accuracy of about some units of
percents. It is proposed the method of measuring of integral specimen
conductivity on the basis of analysis of its binomial conductivity maps
determined by electro-force microscopy method.
Key words: carbon, shungite, electro-conductivity.
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