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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, Volume 21, Number 3, Pages 481–495 (Mi vsgtu1553)  

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics of Solids

Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals

V. N. Aptukov*, V. Yu. Mitin

Perm State National Research University, Perm, 614000, Russian Federation

Abstract: This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.

Keywords: salt rock crystals, fractal dimension, multifractals, method of minimal coverings, nanoindentation, hardness
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1553

Full text: PDF file (4721 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 51-7:51:548; 548.0:539.3/.8
MSC: 74E15
Received: July 11, 2017
Revised: September 13, 2017
Accepted: September 18, 2017
First online: September 28, 2017

Citation: V. N. Aptukov, V. Yu. Mitin, “Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:3 (2017), 481–495

Citation in format AMSBIB
\Bibitem{AptMit17}
\by V.~N.~Aptukov, V.~Yu.~Mitin
\paper Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 3
\pages 481--495
\mathnet{http://mi.mathnet.ru/vsgtu1553}
\crossref{https://doi.org/10.14498/vsgtu1553}
\zmath{https://zbmath.org/?q=an:06964799}
\elib{https://elibrary.ru/item.asp?id=32248392}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Aptukov, V. Yu. Mitin, “Otsenka mekhanicheskikh kharakteristik kristallov solyanykh porod na osnove matematicheskoi modeli protsessa nanoindentirovaniya na zondovom silovom mikroskope Dimension Icon”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 256–269  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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