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Madison A.E.,Admiral Makarov State University of Maritime and Inland Shipping
RSC Advances | Year: 2015

An original well-defined substitution algorithm on how to construct the icosahedral packings is proposed, simple inflation/deflation rules for icosahedral quasicrystals are described, and natural local matching rules are derived. This journal is © The Royal Society of Chemistry 2015. Source


Madison A.E.,Admiral Makarov State University of Maritime and Inland Shipping
RSC Advances | Year: 2015

An effective tiling approach is proposed for the structural description of icosahedral quasicrystals based on the original substitution algorithm. The atomic structure of icosahedral quasicrystals may by derived by using the iterative and recursive inflation/deflation procedure with subsequent decoration of quasi-unit cells. The quasi-unit cells are stacked in three-dimensional space face-to-face without any gaps between them producing the whole infinite icosahedral structure in the same manner as the usual periodic crystals are generated by multiplication of their unit cells containing one or more atoms in a specific spatial arrangement. A variety of examples illustrating the efficiency of the general algorithm is presented. Stacking of quasi-unit cells along the five-fold axis, as well as the arrangement of cells normal to the five-fold, three-fold, and two-fold axes are presented. The possible atomic structure of an icosahedral single-component quasicrystal is derived. Three types of inequivalent sites with exact icosahedral symmetry may simultaneously exist in the quasicrystalline structure. The structure of characteristic clusters enforced by the compatibility with the quasicrystalline type of ordering is discussed. © The Royal Society of Chemistry 2015. Source


Ol'Khovik E.,Admiral Makarov State University of Maritime and Inland Shipping
IOP Conference Series: Materials Science and Engineering | Year: 2015

Today there are many computer systems for modeling of the casting technology processes. All of them allow calculating the availability and distribution of the shrinkage porosity in the test casting, but this information allows only making changes in existing casting technology. In this paper you obtain the information about changes in the local and structural mechanical properties of the casting in the presence of its volume shrinkage porosity. Article presents the results of direct experimental studies of technological defects (shrinkage and gas porosity) impact on the mechanical properties of low carbon steel castings. Methods of investigation are also disclosed, including the methods for producing of molded samples obtained at different process conditions and the crystallization apparatus which is described for the measuring of the density of the samples. There are the mathematical relationship for the elastic modulus, yield stress, elongation and fatigue characteristics fracture cast steel with low carbon content in the presence of the volumetric shrinkage porosity. © Published under licence by IOP Publishing Ltd. Source


Madison A.E.,Admiral Makarov State University of Maritime and Inland Shipping
Structural Chemistry | Year: 2016

An example of substitution rules for the construction of heptagonal rhombic tilings is proposed. Rigorous inflation/deflation rules make it possible to expand the tiling up to infinity without additional ad hoc rearrangements. The derived tilings are self-similar and consist of characteristic patterns with seven-pointed stars surrounded by similar seven-pointed stars. © 2016 Springer Science+Business Media New York Source


Madison A.E.,Admiral Makarov State University of Maritime and Inland Shipping
Structural Chemistry | Year: 2015

Abstract The concept of infinitely fragmented fractal tiling is proposed for the description of the structure and symmetry of quasicrystals. Fractal tilings may serve as unique "parent" structures for the corresponding local isomorphism class. The generating symmetry elements and some special features of the resulting symmetry groups of the fractal tilings are analyzed. Simple inflation/deflation rules for icosahedral quasicrystals are proposed, and natural local matching rules are derived. © 2015 Springer Science+Business Media New York. Source

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