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Crystallography 2018 Structural Chemistry & Crystallography Communication
ISSN: 2470-9905 Page 71
June 04-05, 2018
London, UK
3rd Edition of International Conference on
Advanced Spectroscopy,
Crystallography and Applications
in Modern Chemistry
One of the main tasks of theoretical physics is to obtain the basic
equations for all aggregate states of matter (plasma, gas, liquid,
solid). Aggregate states of matter are determined by the location,
nature of themotion and interaction of particles. The predominant
aggregative state of matter in the universe is plasma. At present,
the Vlasov’s kinetic equation is the basis of plasma physics.
It is used to describe the universe, calculate plasma devices,
tokamaks, etc. The Vlasov’s equation describes the long-range
interaction (or “action at a distance”) and, depending on the type
of interaction, distinguishes the Vlasov-Poisson, Vlasov-Maxwell,
Vlasov-Einstein, and Vlasov-Yang-Mills equations. 70 years ago
Vlasov suggested that in order to understand physical processes
in systems consisting of many particles, it is necessary to use the
equation proposed by him for describing the plasma [1]. In the
basis of such approach, Vlasov put the introduction of a unified
distribution function that depends on all the coordinates and their
derivatives up to any order (non-local statistical mechanics). In
modern crystallophysics the fact of the presence of a crystal
structure with atoms localized near the lattice sites is not derived
from the theory, but is postulated. From the Vlasov’s viewpoint,
“A crystal is not a postulated construction, but a certain state of
motion of particles”. As a result of the probabilistic approach,
Vlasov obtained themaincriterion for the existenceof a crystalline
state [2]. This criterion contains the condition for the beginning of
theprocessof crystal formationfromthehomogeneousphaseand
makes it possible to determine the numerical value of the period.
This consideration was carried out by Vlasov for an ideal crystal.
A theoretical description of the formation of a real (defective)
crystal structure from the viewpoint of the classical approach is
based on the model of high-temperature impurity precipitation.
In accordance with this model, complexes “intrinsic point defect
+ impurity atom” are formed near the crystallization front. In the
process of crystal cooling, the growth and coalescence of formed
precipitates lead to the formation of a defective structure of the
crystal. The formation of a defective crystal structure is controlled
by its thermal growth conditions (growth rate, temperature
gradients, cooling rate) [3]. We checked the positions of Vlasov’s
physics for real single crystals of semiconductor silicon. We
confirmed the fact of complex formation near the crystallization
front [4, 5]. The classical and probabilistic models for the
formation of a defective crystal structure lead to identical results.
The probabilistic approach allows give a new interpretation of the
known results of studies of heat-treated crystals. The formation
of thermal donors and thermal acceptors occurs as a result of
the process of coalescence of impurity precipitates. Based on
the solution obtained, three main conclusions can be drawn: (1)
Vlasov’s theory is a far-reaching and natural extension of classical
mechanics. (2) Vlasov’s equation can be used to describe any
aggregate state of matter. (3) Vlasov’s equation is a universal tool
for describing the processes taking place in the physical world
(both in the macrocosm and in the microcosm).
THE VLASOV’S EQUATION FOR DESCRIPTION OF SOLIDS STRUCTURE
V.I.Talanin1 and I.E. Talanin
Institute of Economics and Information Technologies, Ukraine
Struct Chem Crystallogr Commun 2018, Volume 4
DOI: 10.21767/2470-9905-C1-006