International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 3.2, pp. 397-412
https://doi.org/10.1107/97809553602060000916

Chapter 3.2. Twinning and domain structures

V. Janovec,a* Th. Hahnb and H. Klapperc

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic,bInstitut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and cMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail:  janovec@fzu.cz

References

Aizu, K. (1969). Possible species of “ferroelastic” crystals and of simultaneously ferroelectric and ferroelastic crystals. J. Phys. Soc. Jpn, 27, 387–396.
Aizu, K. (1970). Possible species of ferromagnetic, ferroelectric and ferroelastic crystals. Phys. Rev. B, 2, 754–772.
Aizu, K. (1972). Electrical, mechanical and electromechanical orders of state shifts in nonmagnetic ferroic crystals. J. Phys. Soc. Jpn, 32, 1287–1301.
Blattner, H., Känzig, W., Merz, W. & Sutter, H. (1948). Die Domänenstruktur von BaTiO3-Kristallen. Helv. Phys. Acta, 21, 207–209.
Bloss, F. D. (1971). Crystallography and crystal chemistry, pp. 324–338. New York: Holt, Rinehart and Winston.
Bollmann, W. (1970). Crystal defects and crystalline interfaces, ch. 12, pp. 143–148. Berlin: Springer.
Bollmann, W. (1982). Crystal lattices, interfaces, matrices, pp. 111–249. Geneva: published by the author.
Bradley, C. J. & Cracknell, A. P. (1972). The mathematical theory of symmetry in solids. Oxford: Clarendon Press.
Budden, F. J. (1972). Fascination of groups. Cambridge University Press.
Buerger, M. J. (1945). The genesis of twin crystals. Am. Mineral. 30, 469–482.
Cady, W. G. (1946). Piezoelectricity, ch. XXV. New York: McGraw-Hill.
Cahn, R. W. (1954). Twinned crystals. Adv. Phys. 3, 202–445.
Chernysheva, M. A. (1950). Mechanical twinning in crystals of Rochelle salt. Dokl. Akad. Nauk SSSR, 74, 247–249. (In Russian.)
Donnay, G. & Donnay, J. D. H. (1974). Classification of triperiodic twins. Can. Mineral. 12, 422–425.
Donnay, J. D. H. (1940). Width of albite-twinning lamellae. Am. Mineral. 25, 578–586.
Donnay, J. D. H. & Donnay, G. (1972). Crystal geometry. In International Tables for X-ray Crystallography, Vol. II, 2nd edition, edited by J. C. Kasper & K. Lonsdale, Section 3. Birmingham: Kynoch Press.
Fischmeister, H. F. (1985). Structure and properties of high angle grain boundaries. J. Phys. (Paris), 46, Suppl. C4–3–23.
Friedel, G. (1904). Etude sur les groupements cristallins. Extrait du Bulletin de la Société d' Industrie Minérale, Quatrième Série, Tomes III et IV. Saint Etienne: Imprimerie Théolier J. et Cie.
Friedel, G. (1926). Leçons de cristallographie. Nancy, Paris, Strasbourg: Berger-Levrault. [Reprinted (1964). Paris: Blanchard.]
Fuksa, J. & Janovec, V. (1995). Permutation classification of domain pairs. Ferroelectrics, 172, 343–350.
Fuksa, J. & Janovec, V. (2002). Macroscopic symmetries and domain configurations of engineered domain structures. J. Phys. Condens. Matter, 14, 3795–3812.
Giacovazzo, C. (1992). Editor. Fundamentals of crystallography, pp. 80–87, 133–140. Oxford University Press.
Gottstein, G. & Shvindlerman, L. S. (1999). Grain boundary migration in metals, ch. 2. London: CRC Press.
Hahn, Th., Janovec, V. & Klapper, H. (1999). Bicrystals, twins and domain structures – a comparison. Ferroelectrics, 222, 11–21.
Hahn, Th. & Wondratschek, H. (1994). Symmetry of crystals. Sofia: Heron Press Ltd.
Hall, M. Jr (1959). The theory of groups. New York: The Macmillan Company.
Hámos, L. von & Thiessen, P. A. (1931). Über die Sichtbarmachung von Bezirken verschiedenen ferromagnetischen Zustandes fester Körper. Z. Phys. 71, 442–444.
Haüy, R.-J. (1801). Traité de minéralogie I, p. 273. Paris: Delance.
Indenbom, V. L. (1960). Phase transitions without change in the number of atoms in the unit cell of the crystal. Sov. Phys. Crystallogr. 5, 106–115.
International Tables for Crystallography (2004). Vol. A1. Symmetry relations between space groups, edited by H. Wondratschek & U. Müller. Dordrecht: Kluwer Academic Publishers.
International Tables for Crystallography (2005). Vol. A. Space-group symmetry, 5th edition, edited by Th. Hahn. Heidelberg: Springer.
Janovec, V. (1972). Group analysis of domains and domain pairs. Czech. J. Phys. B, 22, 974–994.
Janssen, T. (1973). Crystallographic groups. Amsterdam: North-Holland.
Kalonji, G. (1985). A roadmap for the use of interfacial symmetry groups. J. Phys. (Paris) Colloq. 46, C4–249–255.
Kay, H. F. (1948). Preparation and properties of crystals of barium titanate, BaTiO3. Acta Cryst. 1, 229–237.
Kerber, A. (1991). Algebraic combinatorics via finite group action. Mannheim: B. I. Wissenschaftsverlag.
Kerber, A. (1999). Applied finite group actions. Berlin: Springer.
Klassen-Neklyudova, M. V. (1964). Mechanical twinning of crystals. New York: Consultants Bureau.
Klassen-Neklyudova, M. V., Chernysheva, M. A. & Shternberg, A. A. (1948). The real structure of crystals of Rochelle salt. Dokl. Akad. Nauk SSSR, 63, 527–530. (In Russian.)
Klein, C. (1869). Zwillingsverbindungen und Verzerrungen. Heidelberg: G. Mohr.
Koch, E. (2004). Twinning. In International tables for crystallography, Vol. C. Mathematical, physical and chemical tables, 3rd edition, edited by E. Prince, ch. 1.3. Dordrecht: Kluwer Academic Publishers.
Kopský, V. (1983). Algebraic investigations in Landau model of structural phase transitions, I, II, III. Czech. J. Phys. B, 33, 485–509, 720–744, 845–869.
Kuratowski, K. & Mostowski, A. (1968). Set theory. Amsterdam: North-Holland.
Landau, L. D. (1937). On the theory of phase transitions. I and II. Zh. Eksp. Teor. Fiz. 7, pp. 19, 627 (in Russian); Phys. Z. Sowjet. 11, pp. 26, 545 (in German). Collected papers of L. D. Landau, edited by D. Ter Haar (1967). New York: Gordon and Breach.
Lang, S. (1965). Algebra. Reading, MA: Addison-Wesley.
Ledermann, W. (1973). Introduction to group theory. London: Longman Group Ltd.
Lipschutz, S. (1981). Theory and problems of set theory and related topics. Singapore: McGraw-Hill.
Mallard, E. (1879). Traité de cristallographie, géométrie et physique. Vol. I. Paris: Dunod.
Matthias, B. & von Hippel, A. (1948). Domain structure and dielectric response of barium titanate single crystals. Phys. Rev. 73, 1378–1384.
Michel, L. (1980). Symmetry defects and broken symmetry. Configurations. Hidden symmetry. Rev. Mod. Phys. 52, 617–651.
Mohs, F. (1822, 1824). Grundriss der Mineralogie, two volumes. Dresden: Arnold. [English translation by Haidinger, W. (1825): Treatise on mineralogy, three volumes. Edinburgh: Constable.]
Mohs, F. (1823). On the crystallographic discoveries and systems of Mohs and Weiss. Edinburgh Philos. J. 8, 275–290.
Mueller, H. (1935). Properties of Rochelle salt. Phys. Rev. 47, 175–191.
Naumann, C. F. (1830). Lehrbuch der reinen und angewandten Krystallographie. Vol. II, p. 203. Leipzig: Brockhaus.
Naumann, C. F. (1856). Elemente der theoretischen Krystallographie. p. 67. Leipzig: W. Engelmann.
Niggli, P. (1919). Geometrische Kristallographie des Diskontinuums. Leipzig: Borntraeger. [Reprinted (1973). Wiesbaden: Sändig.]
Niggli, P. (1920, 1924, 1941). Lehrbuch der Mineralogie und Kristallchemie, 1st ed. 1920, 2nd ed. 1924, 3rd ed., Part I, 1941, pp. 136–153, 401–414. Berlin-Zehlendorf: Gebrüder Borntraeger.
Opechowski, W. (1986). Crystallographic and metacrystallographic groups. Amsterdam: North-Holland.
Pond, R. C. & Bollmann, W. (1979). The symmetry and interfacial structure of bicrystals. Philos. Trans. R. Soc. London Ser. A, 292, 449–472.
Pond, R. C. & Vlachavas, D. S. (1983). Bicrystallography. Proc. R. Soc. London Ser. A, 386, 95–143.
Robinson, D. J. S. (1982). A course in the theory of groups. New York: Springer.
Romé de l'Isle, J. B. L. (1783). Cristallographie. Vol. I, 2nd edition, p. 93. Paris: Imprimerie de Monsieur.
Rosen, J. (1995). Symmetry in science. Berlin: Springer.
Shubnikov, A. V. & Koptsik, V. A. (1974). Symmetry in science and art, pp. 348, 372. New York: Plenum.
Speiser, A. (1927). Theorie der Gruppen von endlicher Ordnung. Berlin: Springer.
Sutton, A. P. & Balluffi, R. W. (1995). Interfaces in crystalline materials, Section 1.5, pp. 25–41. Oxford: Clarendon Press.
Tertsch, H. (1936). Bemerkungen zur Frage der Verbreitung und zur Geometrie der Zwillingsbildungen. Z. Kristallogr. 94, 461–490.
Tschermak, G. (1904). Einheitliche Ableitung der Kristallisations- und Zwillingsgesetze. Z. Kristallogr. 39, 433–462.
Tschermak, G. (1906). Lehrbuch der Mineralogie. Wien: Hölder.
Tschermak, G. & Becke, F. (1915). Lehrbuch der Mineralogie. 7th edition, pp. 93–114. Wien: Hölder.
Vainshtein, B. K. (1994). Modern crystallography I. Symmetry of crystals, 2nd edition. Berlin: Springer.
Vainshtein, B. K., Fridkin, V. M. & Indenbom, V. L. (1995). Modern crystallography II. Structure of crystals, 2nd edition, Section 5.7. Berlin: Springer.
Valasek, J. (1921). Piezoelectricity and allied phenomena in Rochelle salt. Phys. Rev. 17, 475–481.
Van Tendeloo, G. & Amelinckx, S. (1974). Group-theoretical considerations concerning domain formation in ordered alloys. Acta Cryst. A30, 431–440.
Wadhawan, V. K. (1997). A tensor classification of twinning in crystals. Acta Cryst. A53, 546–555.
Wadhawan, V. K. (2000). Introduction to ferroic materials. Amsterdam: Gordon and Breach.
Weiss, Chr. S. (1809). De Indagando Formarum Crystallinarum Charactere Geometrico Principali. Dissertatio. Leipzig: Tauchnitz. [French translation by Brochant de Villiers, A. (1811): Mémoire sur la détermination du caractère géométrique principal des formes cristallines. J. Mines, 29, 349–391, 401–444.]
Weiss, Chr. S. (1814). Schweigers Journal für Physik und Chemie, Vol. X, p. 223.
Weiss, Chr. S. (1817, 1818). Magazin der Gesellschaft naturforschender Freunde zu Berlin, Vol. VII, p. 183, Vol. VIII, p. 27.
Weiss, P. (1907). L'hypothèse du champ moléculaire et la propriété ferromagnétique. J. Phys. Radium, 6, 661–690.
Wondratschek, H. (1995). Splitting of Wyckoff positions (orbits). Z. Kristallogr. 210, 567–573.
Wondratschek, H. & Aroyo, M. (2001). The application of Hermann's group [\cal M] in group–subgroup relations between space groups. Acta Cryst. A57, 311–320.
Zheludev, I. S. & Shuvalov, L. A. (1956). Seignettoelectric phase transitions and crystal symmetry. Kristallografiya, 1, 681–688. (In Russian.) [English translation: Sov. Phys. Crystallogr. 1, 537–542].
Zwicker, B. & Scherrer, P. (1944). Elektrooptische Eigenschaften der seignette-elektrischen Kristalle KH2PO4 und KD2PO4. Helv. Phys. Acta, 17, 346–373.