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Research in the phenomenological theory of crystals

## Research in the phenomenological theory of crystals

The development of new powerful group-theoretical and tensor methods applied to the study of physical properties of crystals was the main result in this field. In particular, in [1, 2] the notion of dissymmetry and P.Curie's principle which connects physics with symmetry were analyzed; in [3, 4] the Curie's principle was generalized into the new Shubnikov-Curie principle. Shubnikov's idea of antisymmetry (or two-color symmetry) [4] was generalized into the theory of space groups of antisymmetry and polychromatic symmetry in [3]. The new derivation of Shubnikov's space groups, their magnetic interpretation, diagram and tensor representations were given in [5]. The tensor description of all the known (up to 1974) crystal physics effects can be found in the fundamental textbook [6]. The introduction of the construction of the wreath products of groups of external and internal symmetry of crystals into the generalized theory of crystal symmetry opened in 1974 a new stage in the development of the theory. The positional subgroups of this construction are isomorphous to space groups of the N- dimensional crystallography (N > 3) and constitute a powerful tool for describing the structure of such objects as incommensurate modulated crystal phases, quasicrystals and crystals with structural imperfections, where the classical space symmetry is broken [7-9]. In [3, 10] some applications of generalized colored groups beyond the scope of crystal physics were offered. The second theoretical direction was thermodynamics of phase transitions, critical phenomena and interphase boundary phenomena. Main results obtained in this field were presented in the books [11,12] by V.K.Semenchenko who worked at the Chair in 1954-1982.### References:

- A.V.Shubnikov. Problem of the Dissymetry of Material Objects - Moscow: Published by Acad. Sci. of USSR, 1961, p. 68 (in Russian)
- A.V.Shubnikov. On Works of Pierre Curie in the Field of Symmetry.
*Usp. Fiz. Nauk*, 1956, v.59, p. 591-602. - A.V.Shubnikov and V.A.Koptsik. Symmetry in Science and Art. Ed. by David Harker - New York and London, Plenum Press. 1974, p. 420 (Russian original: Moscow: Nauka, 1972)
- V.A.Koptsik. Symmetry Principles in Physics. J.Phys., 1983, vol. C 16 pp. 23-35; New group-theoretical methods in physics of imperfect crystals and the theory of structure phase transitions. Ibid. pp. 1-22
- V.A.Koptsik. Shubnikov Groups. The reference book on symmetry and physical properties of crystal structures - Moscow: published by Moscow University, 1966, p. 720
- Yu.I.Sirotin and M.P.Shaskol'skaya. Crystal Physics Fundamentals. Moscow: Nauka, 1966, p. 680
- V.A.Koptsik. Generalized Space Symmetry Groups of Quasiheteromolecular Crystals. In: Modern Problems of Physical Chemistry Ed. by Ya.I.Gerasimov and P.A.Akishin - Moscow: Published by Moscow University. 1979, pp. 139-183 (in Russian)
- V.A.Koptsik. Generalized Symmetry in Crystal Physics. Comput Math. Applic., 1988, vol. 16, No 5-7, pp. 407-424
- V.A.Koptsik. Crystallography of Quasicrystals: The Problem of Restoration of Broken Symmetry. In: Lecture Notes in Physics - Berlin: Springer Verlag, 1991, vol. 382, pp. 588-600
- V.A.Koptsik. Reflection on Symmetry-Dissemmetry in Art and Art Studies. In: Visual Mind: Art and Mathematics. Ed. by M.Emmer-Cambridge: MIT Press, 1993, pp. 193-197
- V.K.Semenchenko. The Surface Phenomena in Metals and Alloys - Moscow: Gostechizdat, 1957
- V.K.Semenchenko. Selected Chapters of Theoretical Physics -Moscow: Uchpedgiz, 1960 (Second Edition, 1966)