Abstract
Basic symmetry properties of transformation twins and of ferroelectric or ferromagnetic domains are examined in terms of the abstract group theory. It is shown that the crystallographical relations between domains (twin components) and between domain pairs can be deduced from the decomposition of the symmetry group of the high symmetry phase into the left and double cosets of the group of the low symmetry phase. Expressions are derived for the numbers of proper and improper domains, for the number of crystallographically equivalent low symmetry phases, and for the number of crystallographically non-equivalent domain pairs. A classification of domain pairs according to their symmetry is proposed. The domain structure of the monoclinic phase in WO3 and the Dauphiné twinning in quartz are analysed as illustrative examples.
Similar content being viewed by others
References
Zheludev I. S., Shuvalov L. A.: Kristallografiya1 (1956), 681.
Shuvalov L. A.: J. Phys. Soc. Japan28, Supplement (1970), 38.
Zheludev I. S.:in Solid State Physics. Edited by H. Ehrenreich, F. Seitz, D. Turnbull, Academic Press, New York 1971, Vol. 26, p. 429.
Aizu K.: J. Phys. Soc. Japan27 (1969), 387.
Aizu K.: Phys. Rev.B 2 (1970), 754.
Ascher E.: Helv. Phys. Acta39 (1966), 466.
Ascher E.: Group-theoretical Considerations on Ferroelectric Phase Transitions and Polarisation Reversals, Lecture Notes, Battelle Institute, Geneva 1967; Chem. Phys. Letters1 (1967), 69.
Indenbom V. L.:in Physics of Imperfect Crystals, Proc. of the School held in Telavi. Tbilisi 1966, Vol. I, p. 5.
Kroupa F., Janovec V.: to be published.
Dvořák V.: J. Phys. Soc. Japan28, Supplement (1970), 252.
Landau L., Lifshitz E. M.: Statistical Physics. Addison-Wesley, New York 1958, Ch. 14.
Ascher E.: Physics Letters20 (1966), 352.
Tisza L.: Ann. Phys. (N.Y.)13 (1961), 1.
Gränicher H., Müller K. A.: Materials Research Bulletin6 (1971), 977.
Lang S.: Algebra. Addison-Wesley, Reading, Mass. 1965, Ch. I, § 5.
Birman J. L.:in Proc. of the Symposium on Ferroelectricity. Edited by E. F. Weller, Elsevier Publ. Co, New York 1967, p. 20.
Devonshire A. F.: Phil. Mag.40 (1949), 1040; ibid.42 (1951), 1065.
Levanyuk A. P., Sannikov D. G.: Zh. eksper. teor. Fiz.60 (1971), 1109.
Jansen L., Boon M.: Theory of Finite Groups. North-Holland Publ. Co., Amsterdam 1967.
Hall M.: The Theory of Groups. The Macmillan Co., New York 1959.
Speiser A.: Theorie der Gruppen von endlicher Ordnung. J. Springer, Berlin 1937.
Känzig W.:in Solid State Physics. Edited by F. Seitz, D. Turnbull, Academic Press, New York 1957, Vol. 4, p. 1.
Kovalev O. V.: Irreducible Representations of the Space Groups. Gordon and Breach, New York 1965.
Fousek J.: private communication.
Ascher E.: Properties of Shubnikov Point Groups (Part 1). Report from Battelle Institute, Geneva.
Author information
Authors and Affiliations
Additional information
Na Slovance 2, Praha 8, Czechoslovakia.
The author is grateful to Dr. V. Dvořák and to Dr. F. Kroupa for critical comments on the manuscript.
Rights and permissions
About this article
Cite this article
Janovec, V. Group analysis of domains and domain pairs. Czech J Phys 22, 974–994 (1972). https://doi.org/10.1007/BF01690203
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01690203