Study of self-organization in disordered materials using information theory

Determination of the degree of ordering of materials’ structure by calculating the information-correlation characteristics

“…Previously [3], we developed a method for cal culating the AMI for a surface; the method was imple mented in the form of a software package. We remind that the AMI between the arbitrary pair of points A and B is given by (1) where z is a random quantity (the height of the profile of the material's surface at the point with the coordi nates (x, y); D is the range of determination of the ran dom quantity z (the plane of the sample); Z is the range of values of the random quantity z (heights in the pro file of points at the surface); p A (z 1 ) and p B (z 2 ) are prob abilities that the random quantity representing the height of the profile takes the values z 1 and z 2 at the points A and B; and p AB (z 1 , z 2 ) is the joint probability of the simultaneous adoption of specified values at two points.…”

“…We stud ied the following surface models: first, a model, which entirely excludes correlation in long range order and, second, a model with a completely regular structure. The main calculated characteristics of the tests are listed in Table 1 [3]. On the basis of studying the test models for the surfaces of materials, we suggested cri teria for the degree of ordering of a material's structure ( Table 2).…”

Investigation of the formation of fractal structures in SiO2 · SnO x · CuO y thin films prepared by the sol-gel method

“…In [7][8][9][10][11], the authors proposed to consider the film formation processes of disordered semiconductor mate rials in terms of the theory of self organization, which allows one to estimate the degree of disorder of a system without its detailed description. Such an approach allows one to control the processes of formation of the nanoma terial and predict its properties.…”

Multifractal Detrended fluctuation Analysis in Examining Surface Properties of the Gas-Sensing Metal-Containing Polyacrylonitrile

“…The film surface images received by means of microscopy can serve as a starting point for the analysis by methods of nonlinear dynamics and the information theory (Vikhrov et al, 2005, Bodyagin et al, 1997, Mursalov et al, 2000, Vikhrov et al, 2012, Avacheva et al, 2008. The processes in solid-state formation are characterized by the basic features of self-organizing systems (Vikhrov et al, 2005).…”

“…Vikhrov S.P. showed the ability of the methods to reveal change of structure under influence of technology parameters that is impossible to make by traditional methods (Vikhrov et al, 2012, Avacheva et al, 2008.…”