International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

A statistical model is proposed to analyze the relationship between the clustering coefficient (CC) and the temperature and atomatom interaction potential. CC is defined as the ratio of the number of atoms in clusters to the total number of atoms in a system. The proposed technique is based on the statistical concept of entropy. The clustering coefficient is considered for the equilibrium state.

It was analyzed the methods of constructions the matter with maximal of packing coefficient when the objects consist of the particles with forms either spheres or rods or plates. It was calculated the relations the partial size for relating of maximal packing coefficient. As examples of objects with coefficient of packing theirs particles we look on abrasive materials and products of the powder metallurgy and solid fuel etc.

Debye’s temperature θ_D is the temperature border between areas, C_μ^V(Т) has constant value and, when T<θ_D, begins to decrease monotonically. θ_D is the crystal parameter, which allows to calculate the dimensional border between macro- and nanostates. The statement which is found in scientific discussions that θ_D depends on temperature is incorrect because it contradicts modern crystal-physical theories. The numerical value θ_D is defined experimentally and is related to the structure of crystals and to the processes taking place in them.

Geometrically, the reciprocal lattice is built on the basis of the lattice of the crystal according to the rule
*
a j ak jk , where
the vectors
*
a j , ak are the periods of the crystal and reciprocal lattices corresponding  jk  0 at j  k and jk  1 at j  k (j, k = 1,2,3). The “weight” of the reciprocal lattice node, determined by the structural amplitude of the crystallographic plane corresponding to it, should not be zero, since in this case the reciprocal lattice node will be homologous to any point of the reciprocal space outside the lattice. Crystals with Bravais I, F, C – type cells in the reciprocal lattice are characterized by super cells, periods of which are n – times larger than ∗ = −1, where a is the period of the lattice cell. With respect to complex structures, even if they are single-element, the period of the super cell of the reciprocal lattice can exceed ∗ several times. For a diamond crystal ∗ = 4∗under the super cell of the reciprocal lattice it is necessary to use the smallest parallelepiped, the “weight” of all vertex nodes of which is not equal to zero.

The structure of the bulk crystals allow to determine the habit of the nanocrystales on their base only as a source point. It is impossible to neglect the size, form and influence of surface. The liquids surface relatively quickly passes to equilibrium form when free energy is minimum. Debye’s temperature is rather arbitrary parameter. Its determination is based on some approach. However this parameter is introduced to the reference books and is broadly used in the crystal physics. Proposed strategy allows defining habit maximum size of nanoparticles on the base well known physics representations. The L–value is determined the bounder between sizes where it can be done value description and where it’s necessary to take into account the particle sizes.

The physical properties of nanoparticles as modifiers are depend on their geometrical characteristics. These objects have 5- and 10-axis symmetry which is forbidden for crystals. The 3×3 matrices-generators of point groups of rotation in crystallographical and crystallophysics basises have as matrix elements 0 and ±1, except groups hexa- and trigonal in H-basis crystals. But these lattices too have 0 and ±1 as matrix elements for matrical representation of point moving in crystallographical basis. For describing the point groups of pentagonal and decagonal symmetries, instead of crystal lattices the so-named general regular lattices (GRL). The two dimensional GRL is known as Penrose’s sets. For 3-d pentagonal sets there are 14 groups of point symmetry, which are not crystallographic because their elements may be golden ratio.

The structure of the diamond is usually represented as two face-centered cubic cell with the same dimensions, which are shifted relative to each other by the value of +/-(1/4.1/4.1/4) That is eight different ways. However, in this case, there is a possibility of only two enantiomorphous centers, which have the same ф (hkl ) j . They do not affect on the reciprocal lattice, but allow to explain, for example, the presence of twins. The introduction of the concept of the scattering center of diamond shows that his point group is Fm3m with the full symmetry formula 3L44L3(4L3i)6L29PC, whereas the generally accepted model of the diamond structure does not correspond to such symmetry. For example, the L4 axis is missing, C is not at the origin of coordinates, there is only one L3 axis along the diagonal along which the sublattices are shifted, etc.

On the basis of modern concepts of condensed matter physics and quantum physics considered the criteria for inclusion ofdispersed particles of different composition, structure, and technological background to nanomodifiers of polymeric, oligomeric and combined matrices. There were proposed an analytical expression for the evaluation of limiting size of the dispersed particles L₀, which characterizes the manifestation of a particular energy state – nanostate.There was implemented the analysis of experimental and literature data confirming the adequacy of the calculated value of the size of particles in nanostate obtained using relation L₀=230•θ_D^-1/2, where θ_D – Debye temperature. It is shown that the provision of effective modification of macromolecular matrices necessary and sufficient condition is the presence of dispersed particles of different composition and structure of nanoscale structural fragments of the surface layer, which ensure the implementation of synergies through a combination of energy and mechanical factors in the formation of boundary layers of the optimal structure.

There were considered the physical, structural and morphological prerequisites for the realization of the nanostate phenomenon of dispersed particles of condensed matter of different composition, nature and technology for production. It was shown the role of the size factor in the occurrence of the nanostate phenomenon due to the change of the energy parameters of the surface layers of particles that contribute to their effective modifying effect on the high-molecular matrix. Physical models of the formation of a particular energy state of dispersed particles and metallic and non-metallic materials substrates, characterized by the presence of local areas ("charge-mosaic") with a long relaxation time are proposed.It was considered practical application of the nanostate phenomenon when creating high-strength and wear-resistant materials based on thermoplastic matrices (PA6, PTFE, PET), consistent lubricant and lubricating oils, tribological and protective coatings for friction units and metalwares used in mechanical engineering, automotive and mining engineering. It was made the examples of the effective use of developed nanocomposite materials in practice.

There were considered physical preconditions of appearance of dispersed particles activity in the process of the high molecular matrix modifying. The existence of a non-linear function S(r) = f (r) defining the dependence of the parameters of the characteristic physical properties of the particle of its geometrical parameters was shown. The expediency of use as modifiers dispersed particles with developed morphology of the surface layer, which provides a special energy state, was shown. Methodological approaches the optimum choice of effective modifiers while creating functional composites were developed. Practical applications of the developed approaches were exemplified.