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Home / Issues / № 2, 2015

Phisics and Mathematics

POSSIBLE STATES OF THE DETERMINISTIC MODULAR STRUCTURES WITH CRYSTAL, NANO-DIMENSIONAL AND FRACTAL COMPONENTS IN ANTIFRICTION COMPOSITIONAL COATINGS
Ivanov V.V.
The structural states forming from nano-dimensional n, fractal f and crystal r components with account of the qualities of the corresponding nano-objects set into 3D space were analyzed [1 - 3]. The possible structural states into 1D space are may be combinatorial enumerated and presented by next square matrix А

,

where the states r, rn and rf are denotes the crystal of atoms, the crystal of nano-objects and the crystal of local fractals, the symbols n, nr and nf are denotes the nano-object only, nano-objects with crystal and fractal structures, the symbols f, fr and fn are denotes the fractal only, fractal with crystal structure and fractal of nano-objects, accordingly.

Square matrix of the possible states А(3D) = ||aij||aij||aij|||||| contains in all N = 32d = 729 states with different orientation. The possible classes of structures with nano-dimensional, crystal or fractal components are may be presented.

1 Class nano-dimensional (n n n) is contains the Rnnn3 structures from 3D-nanoparticles to 3D local fractals.

2 Class nano-dimensional crystal (r n n) is contains the Rrnn3 structures from 3D structure of ordered 2D nano-particles to 3D structure of 2D local fractals ordered after fractal law into 1D.

3 Class nano-dimensional fractal (n n f) = (n f n) is contains the Rnfn3 structures from 3D structure of 2D nano-objects ordered after fractal law into 1D space to 3D structure of 1D deterministic fractals and 2D local fractals.

4 Class nano-dimensional fractal hybrid (n f f) is contains the Rnff3 structures from 3D nanostructure of 2D fractal hybrid structure to 3D nano-fractal of 2D fractal nano-objects.

5 Class crystal fractal nano-dimensional (r f n) is contains the Rrfn3 structures from 3D fractal structure of ordered nano-objects to 3D structure of 1D deterministic fractals and 1D local fractals ordered after fractal law into 1D space.

6 Class crystal nano-dimensional (r r n) is contains the Rrrn3 structures from 3D structure of ordered chains of nano-objects into 2D space to 3D structure of fractal nano-objects ordered after fractal law into 2D space.

7 Class crystal (r r r) is contains the Rrrr3 structures from 3D-crystal of atomic chains to 3D- crystal of local 3D fractals.

8 Class crystal fractal (r r f) is contains the Rrrf3 structures from 3D structures of ordered in 2D space 1D fractals to 3D structures of local 3D fractals ordered after fractal nano-objects law into 1D space.

9 Class crystal fractal hybrid (r f f) is contains the Rrff3 structures from 3D structures of ordered 2D hybrid fractal to 3D structures of 2D fractal nano-objects ordered after fractal law into 1D space.

10 Class fractal hybrid (f f f) is contains the Rfff3 structures from 3D fractal hybrid structures to 3D fractal nano-objects.

These results were used for theoretical modeling and interpretation of tribologic surface properties of the compositional coatings based Ni-P and Ni-B systems [4-8].




References:
1. Ivanov V.V. Space components of the structural states of deterministic modular structures of composition materials with nano-dimension component into 3D space // Uspehi sovremennogo estestvoznaniya, 2014. №.12. С.79-84.

2. Ivanov V.V. Possible complex states component (r r n) and (r n n) classes deterministic modular structures of composites // Uspehi sovremennogo estest-voznaniya, 2014. №.12(2). С. 90-93.

3. Ivanov V.V. Principles of structural states forming from fractal components with account of semi-group qualities of the corresponding 1D generators multitude// Uspehi sovremennogo estestvoznaniya, 2014. №.7. С.100-104.

4. Ivanov V.V. “Concentration waves” model for the tribologic system CM1/LL,/CM2 // International journal of experimental education, 2014. № 4. Part 2. p.58-59.

5. Ivanov V.V. “Concentration waves” model for the tribologic system CM1//CM2 // International journal of experimental education, 2014. № 4. Part 2. p.59-60.

6. Ivanov V.V., Balakai V.I., Ivanov A.V., Arzumanova A.V. Synergism in composite electrolytic nickel-boron-fluoroplastic coatings // Rus. J. Appl. Chem., 2006. Т.79. №4. С.610-613.

7. Ivanov V.V., Balakai V.I., Kurnakova N.Yu. et al. Synergetic effect in nickel-teflon composite electrolytic coatings // Rus. J. Appl. Chem., 2008. Т.81. № 12. С.2169-2171.

8. Balakai V.I., Ivanov V.V., Balakai I.V., Arzumanova A.V. Analysis of the phase disorder in electroplated nickel-boron coatings // Rus. J. Appl. Chem., 2009. Т.82. №.5. С.851-856.



Bibliographic reference

Ivanov V.V. POSSIBLE STATES OF THE DETERMINISTIC MODULAR STRUCTURES WITH CRYSTAL, NANO-DIMENSIONAL AND FRACTAL COMPONENTS IN ANTIFRICTION COMPOSITIONAL COATINGS. International Journal Of Applied And Fundamental Research. – 2015. – № 2 –
URL: www.science-sd.com/461-24942 (29.03.2024).