Systematic of polymorphous transformation of crystals, generalized on the base of M.J. Burger’s criteria

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Abstract

The paper proposes an extended (3 × 3) classification of polymorphous transformations, which includes the 0th coordination sphere in addition to the M. J. Burger’s I and II coordination spheres. As a result, the first parameter of this classification is the number of a transformable coordination sphere — it takes the value equal to 0 (atom, ion), 1 (the coordination polyhedra) and 2 (the nearest to the coordination polyhedra environment). The second parameter of the classification is determined by the Burger’s energy barrier for a transformation. And here, in addition to transformations with a break of chemical bonds (reconstructive) and without it (deformational), some intermediate types of transformations take place — with a disordering of structural units (atoms, molecules and other atomic complexes). As examples of polymorphous transformations with transformation of the 0th coordination sphere, there are considered electron transitions in an atom, changes of the atom’s spin, and magnetic ordering of atoms in a crystal structure. Transformations with disordering are illustrated by substitutions-jumps of structural units and their slowed down or free rotation. There is developing the concept of “polymorphism” of chemical elements.

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About the authors

Stanislav K. Filatov

Saint-Petersburg State University

Author for correspondence.
Email: filatov.stanislav@gmail.com
Russian Federation, Universitetskaya embankment, 7/9; Saint-Petersburg, Russia

Peter Paufler

Dresden technical university

Email: peter.paufler@tu-dresden.de
Germany, Drezden

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Supplementary files

Supplementary Files
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2. Fig. 1. Structures of ferromagnetic tetragonal α-Fe (а) and paramagnetic cubic β-Fe (б) polymorphic modifications of iron (Filatov, 1995).

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3. Fig. 2. Example of succession in reconstruction of the structure during deformations and polymorphous transition of crystals while the increase of temperature (Filatov, 2011). Coordination 7-verteces monoclinic modification ZrO2 (baddeleite) and principal features of its reconstruction (dark arrows (а)) in the 8-verteces tetragonal modification (б) in comparison with patterns of thermal expansion coefficients of these two modifications. 1 — Zr, 2 — upper atoms of oxygen, 3 — lower atoms of oxygen.

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4. Fig. 3. Polymorphous transitions accompanied by different in value jumps of the modification volume (Filatov, 1990, p. 68, 99, 124): а — ZrO2, ΔV = –3.4 %; б — quartz, ΔV = +0.6 %; в — LaNbO4, ΔV = 0. Footnote indices M and T specify monoclinic and tetragonal modifications.

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5. Fig. 4. Crystal structure of n-paraffin’s (Filatov et al., 1993; 1997; Kotelnikova, Filatov, 2002): even (а) and odd (б) aliphatic chains of C8H18 and C9H20 homolog’s; position of chains in structure ob orthorhombic (в) and hexagonal (г) modifications (axis c perpendicular to pictures); light and dark circles — atoms at different levels along the axis c; large circles — sections of «cylinders» of rotating chains.

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6. Fig. 5. Thermal dependence of a√3, b, c parameters and the volume V of n-paraffin’s unit cells (Filatov et al., 1993; 1997; Kotelnikova, Filatov, 2002): а — orthorhombic crystalline (Orcryst), orthorhombic rotation-crystalline (Orrot.1) and hexagonal rotation-crystalline (Hrot.2) modifications of the C23H48 homolog; б — the same for the solid solution of C22H46 and C24H50 homolog’s in the 1:1 ratio. Additional designations of phases are in text.

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7. Fig. 6. Crystal structures of CuZn alloy: а — low temperature cubic modification, с. т. CsCl; б — high temperature cubic modification, с. т. β-Fe (Fig. 1).

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8. Fig. 7. Scheme of distribution of Si and Al atoms in tetrahedrical positions in sanidine (а), orthoclase (б) and the maximum microcline (в) (Dolivo-Dobrovolsky, 1999). Tetrahedra are marked according to the nomenclature of feldspars. Vertical lines — planes of symmetry, small circles — inversion centers.

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9. Fig. 8. To the question of polytypism of layered silicates: а — crystal structure of mica; б — six simple modes of the ordered overlapping of layers in mica.

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