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

International Tables for Crystallography (2006). Vol. D, ch. 3.4, pp. 449-505

Chapter 3.4. Domain structures

V. Janoveca* and J. Přívratskáb

aDepartment of Physics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic, and bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail:


Aizu, K. (1969). Possible species of `ferroelastic' crystals and of simultaneously ferroelectric and ferroelastic crystals. J. Phys. Soc. Jpn, 27, 387–396.
Aizu, K. (1970a). Possible species of ferromagnetic, ferroelectric and ferroelastic crystals. Phys. Rev. B, 2, 754–772.
Aizu, K. (1970b). Determination of the state parameters and formulation of spontaneous strain for ferroelastics. J. Phys. Soc. Jpn, 28, 706–716.
Aizu, K. (1972). Electrical, mechanical and electromechanical orders of state shifts in nonmagnetic ferroic crystals. J. Phys. Soc. Jpn, 32, 1287–1301.
Aizu, K. (1973). Second-order ferroic state shifts. J. Phys. Soc. Jpn, 34, 121–128.
Altmann, S. L. & Herzig, P. (1994). Point-group theory tables. Oxford: Clarendon Press.
Amin, A. & Newnham, R. E. (1980). Tertiary ferroics. Phys. Status Solidi A, 61, 215–219.
Barkley, J. R. & Jeitschko, W. (1973). Antiphase boundaries and their interactions with domain walls in ferroelastic–ferroelectric Gd2(MoO4)3. J. Appl. Phys. 44, 938–944.
Bertagnolli, E., Kittinger, E. & Tichý, J. (1978). Observation of reversible elastic Dauphiné twinning in alpha-quartz. J. Phys. (Paris) Lett. 39, 295–297.
Bertagnolli, E., Kittinger, E. & Tichý, J. (1979). Ferrobielastic hysteresis in alpha-quartz. J. Appl. Phys. 50, 6267–6271.
Boulesteix, C. (1984). A survey of domains and domain walls generated by crystallographic phase transitions causing a change of the lattice. Phys. Status Solidi A, 86, 11–42.
Bradley, C. J. & Cracknell, A. P. (1972). The mathematical theory of symmetry in solids. Oxford: Clarendon Press.
Bul'bich, A. A. & Gufan, Yu. M. (1989a). Inevitable symmetry lowering in a domain wall near a reordering phase transition. Sov. Phys. JETP, 67, 1153–1157.
Bul'bich, A. A. & Gufan, Yu. M. (1989b). Phase transition in domain walls. Ferroelectrics, 172, 351–359.
Cahn, R. W. (1954). Twinned crystals. Adv. Phys. 3, 363–445.
Calleja, M., Dove, M. T. & Salje, E. K. H. (2001). Anisotropic ionic transport in quartz: the effect of twin boundaries. J. Phys. Condens. Matter, 13, 9445–9454.
Cao, W. & Barsch, G. R. (1990). Landau–Ginzburg model of interphase boundaries in improper ferroelastic perovskites of [D{_{4h}^{18}}] symmetry. Phys. Rev. B, 41, 4334–4348.
Carpenter, M. A., Salje, E. K. H. & Graeme-Barber, A. (1998). Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals. Eur. J. Mineral. 10, 621–691.
Catti, M. & Ferraris, G. (1976). Twinning by merohedry and X-ray structure determination. Acta Cryst. A32, 163–165.
Chen, X. J., Liu, J. S., Zhu, J. S. & Wang, Y. N. (2000). Group theoretical analysis of the domain structure of SrBi2Ta2O9 ferroelectric ceramic. J Phys. Condens. Matter, 12, 3745–3749.
Christian, J. W. (1975). The theory of transformations in metals and alloys. Oxford: Pergamon Press.
Chrosch, J. & Salje, E. K. H. (1999). Temperature dependence of the domain wall width in LaAlO3. J. Appl. Phys. 85, 722–727.
Curien, H. & Donnay, J. D. H. (1959). The symmetry of the complete twin. Am. Mineral. 44, 1067–1070.
Curien, H. & Le Corre, Y. (1958). Notation des macles à l'aide du symbolisme des groupes de couleurs de Chubnikov. Bull. Soc. Fr. Mineral. Cristallogr. 81, 126–132.
Dolino, G. (1985). In Modern problems in condensed matter sciences. Vol. 2, Incommensurate phases in dielectrics, edited by R. Blinc & A. P. Levanyuk, pp. 207–231. Amsterdam: North-Holland.
Dudnik, E. F. & Shuvalov, L. A. (1989). Domain structure and phase boundaries in ferroelastics. Ferroelectrics, 98, 207–234.
Erhart, J. & Cao, W. (2001). Effective symmetry and physical properties of twinned perovskite ferroelectric single crystals. J. Mater. Res. 16, 570–578.
Fatuzzo, E. & Merz, W. J. (1967). Ferroelectricity. Amsterdam: North-Holland.
Fesenko, E. G., Gavrilyachenko, B. G. & Semenchev, A. F. (1990). Domain structure in multiaxial ferroelectric crystals. Rostov on Don: Publishing House of the Rostov University (in Russian).
Fousek, J. (1971). Permissible domain walls in ferroelectric species. Czech. J. Phys. B, 21, 955–968.
Fousek, J. & Janovec, V. (1969). The orientation of domain walls in twinned ferroelectric crystals. J. Appl. Phys. 40, 135–142.
Friedel, G. (1926). Leçons de cristallographie. Nancy, Paris, Strasbourg: Berger-Levrault. Reprint (1964). Paris: Blanchard.
Fuksa, J. (1997). The role of the twinning group of a domain pair in tensor distinction of domain states. Ferroelectrics, 204, 135–155.
Fuksa, J. & Janovec, V. (1995). Permutation classification of domain pairs. Ferroelectrics, 172, 343–350.
Grell, H., Krause, C. & Grell, J. (1989). Tables of the 80 plane space groups in three dimensions. Berlin: Akademie der Wissenschaften der DDR.
Hahn, Th. & Wondratschek, H. (1994). Symmetry of crystals. Introduction to International Tables for Crystallography Vol. A. Sofia: Heron Press.
Hatch, D. M. & Cao, W. (1999). Determination of domain and domain wall formation at ferroic transitions. Ferroelectrics, 222, 1–10.
Hatch, D. M., Ghose, S. & Stokes, H. (1990). Phase transitions in leucite, KAl2O6. I. Symmetry analysis with order parameter treatment and the resulting microscopic distortions. Phys. Chem. Mineral. 17, 220–227.
Hatt, R. A. & Hatch, D. M. (1999). Order parameter profiles in ferroic phase transitions. Ferroelectrics, 226, 61–78.
Holser, W. T. (1958a). Relation of symmetry to structure in twinning. Z. Kristallogr. 110, 249–265.
Holser, W. T. (1958b). Point groups and plane groups in a two-sided plane and their subgroups. Z. Kristallogr. 110, 266–281.
Houchmandzadeh, B., Lajzerowicz, J. & Salje, E. K. H. (1991). Order parameter coupling and chirality of domain walls. J. Phys. Condens. Matter, 3, 5163–5169.
Huang, X. R., Jiang, S. S., Hu, X. B. & Liu, W. J. (1997). Theory of twinning structures in the orthorhombic phase of ferroelectric perovskites. J. Phys. Condens. Matter, 9, 4467–4482.
IEEE Standards on Piezoelectricity (1987). IEEE Std 176–987. New York: The Institute of Electrical and Electronics Engineers, Inc.
Indenbom, V. L. (1982). In Modern crystallography II, edited by B. K. Vainshtein, V. M. Fridkin & V. L. Indenbom, pp. 387–396. Berlin: Springer.
International Tables for Crystallography (2002). Vol. E, Subperiodic groups, edited by V. Kopský & D. B. Litvin. Dordrecht: Kluwer Academic Publishers.
International Tables for Crystallography (2005). Vol. A, Space-group symmetry, 5th edition, edited by Th. Hahn. Heidelberg: Springer.
Ishibashi, Y. (1990). Structure and physical properties of domain walls. Ferroelectrics, 104, 299–310.
Ishibashi, Y. (1992). Domain walls in crystals with incommensurate phases. II. J. Phys. Soc. Jpn, 61, 357–362.
Ishibashi, Y. (1993). The 90°-wall in the tetragonal phase of BaTiO3-type ferroelectrics. J. Phys. Soc. Jpn, 62, 1044–1047.
Janovec, V. (1972). Group analysis of domains and domain pairs. Czech. J. Phys. B, 22, 974–994.
Janovec, V. (1976). Symmetry approach to domain structures. Ferroelectrics, 12, 43–53.
Janovec, V. (1981). Symmetry and structure of domain walls. Ferroelectrics, 35, 105–110.
Janovec, V., Litvin, D. B. & Fuksa, J. (1995). Transposable domain pairs and domain distinction. Ferroelectrics, 172, 351–359.
Janovec, V., Richterová, L. & Litvin, D. B. (1993). Non-ferroelastic twin laws and distinction of domains in non-ferroelastic phases. Ferroelectrics, 140, 95–100.
Janovec, V., Schranz, W., Warhanek, H. & Zikmund, Z. (1989). Symmetry analysis of domain structure in KSCN crystals. Ferroelectrics, 98, 171–189.
Janovec, V. & Zikmund, Z. (1993). Microscopic structure of domain walls and antiphase boundaries in calomel crystals. Ferroelectrics, 140, 89–93.
Jerphagnon, J., Chemla, D. & Bonneville, R. (1978). The description of the physical properties of condensed matter using irreducible tensors. Adv. Phys. 27, 609–650.
Jona, F. & Shirane, G. (1962). Ferroelectric crystals. Oxford: Pergamon Press.
Kalonji, G. (1985). A roadmap for the use of interfacial symmetry groups. J. Phys. (Paris) Colloq. 46, 49–556.
Känzig, W. (1957). Ferroelectrics and antiferroelectrics. In Solid state physics IV, edited by F. Seitz & D. Turnbull, pp. 1–197. New York: Academic Press.
Klassen-Neklyudova, M. V. (1964). Mechanical twinning of crystals. New York: Consultants Bureau.
Knox, R. S. & Gold, A. (1967). Symmetry in the solid state. Introduction. New York: W. A. Benjamin.
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.
Koňák, Č., Kopský, V. & Smutný, F. (1978). Gyrotropic phase transitions. J. Phys. Solid State Phys. 11, 2493–2518.
Kopský, V. (1979). Tensorial covariants for the 32 crystal point groups. Acta Cryst. A35, 83–95.
Kopský, V. (1982). Group lattices, subduction of bases and fine domain structures for magnetic point groups. Prague: Academia.
Kopský, V. (1993). Translation normalizers of Euclidean motion groups. J. Math. Phys. 34, 1548–1576.
Kopský, V. (2001). Tensor parameters of ferroic phase transitions I. Theory and tables. Phase Transit. 73, 1–422.
Lines, M. E. & Glass, A. M. (1977). Principles and applications of ferroelectric and related materials. Oxford: Clarendon Press.
Litvin, D. B. & Janovec, V. (1999). Classification of domain pairs and tensor distinction. Ferroelectrics, 222, 87–93.
Locherer, K. R., Chrosch, J. & Salje, E. K. H. (1998). Diffuse X-ray scattering in WO3. Phase Transit. 67, 51–63.
Mitsui, T., Tatsuzaki, I. & Nakamura, E. (1976). An introduction to the physics of ferroelectrics. New York: Gordon & Breach.
Newnham, R. E. (1974). Domains in minerals. Am. Mineral. 59, 906–918.
Newnham, R. E. (1975). Structure–property relations. Berlin: Springer.
Newnham, R. E. & Cross, L. E. (1974a). Symmetry of secondary ferroics I. Mater. Res. Bull. 9, 927–934.
Newnham, R. E. & Cross, L. E. (1974b). Symmetry of secondary ferroics II. Mater. Res. Bull. 9, 1021–1032.
Newnham, R. E., Miller, C. S., Cross, L. E. & Cline, T. W. (1975). Tailored domain patterns in piezoelectric crystals. Phys. Status Solidi A, 32, 69–78.
Newnham, R. E. & Skinner, D. P. Jr (1976). Polycrystalline secondary ferroics. Mater. Res. Bull. 11, 1273–1284.
Nye, J. F. (1985). Physical properties of crystals. Oxford: Clarendon Press.
Opechowski, W. (1986). Crystallographic and metacrystallographic groups. Amsterdam: North-Holland.
Palmer, D. C., Putnis, A. & Salje, E. K. H. (1988). Twinning in tetragonal leucite. Phys. Chem. Mineral. 16, 298–303.
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.
Přívratská, J. & Janovec, V. (1997). Pyromagnetic domain walls connecting antiferromagnetic non-ferroelastic domains. Ferroelectrics, 204, 321–331.
Přívratská, J. & Janovec, V. (1999). Spontaneous polarization and/or magnetization in non-ferroelastic domain walls: symmetry predictions. Ferroelectrics, 222, 23–32.
Přívratská, J., Janovec, V. & Machonský, L. (2000). Tensor properties discriminating domain walls from non-ferroelastic domains. Ferroelectrics, 240, 83–92.
Putnis, A. (1992). Introduction to mineral sciences. Cambridge University Press.
Rosenman, G., Skliar, A., Eger, D., Oron, M. & Katz, M. (1998). Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals. Appl. Phys. Lett. 73, 3650–3652.
Rosová, A. (1999). Real domain structure origination in (110) mechanical twinning in YBa2Cu3O7−y. In Studies of high temperature superconductors, Vol. 28, edited by A. Narlikar, pp. 125–148. New York: Nova Science Publishers.
Rosová, A., Boulesteix, C. & Vávra, I. (1993). Role of microtwins in twin lamella intersections and interconnections in YBa2Cu3O7−y. Physica C, 214, 247–256.
Rychetský, I. & Schranz, W. (1993). Antiphase boundaries in Hg2Br2 and KSCN. J. Phys. Condens. Matter, 5, 1455–1472.
Rychetský, I. & Schranz, W. (1994). Ferroelastic domain walls in Hg2Br2 and KSCN. J. Phys. Condens. Matter, 6, 11159–11165.
Saint-Grégoire, P. & Janovec, V. (1989). Modulated phases in crystals: Symmetry of walls and wall lattices. Example of quartz. In Nonlinear coherent structures, edited by M. Bartes & J. Léon. Lecture notes in physics, Vol. 353, pp. 117–126. Berlin: Springer.
Saint-Grégoire, P., Janovec, V. & Kopský, V. (1997). A sample analysis of domain walls in simple cubic phase of C60. Ferroelectrics, 191, 73–78.
Salje, E. K. H. (1990). Phase transitions in ferroelastic and co-elastic crystals, 1st edition. Cambridge University Press.
Salje, E. K. H. (1991). Strain-related transformation twinning in minerals. Neues Jahrb. Mineral. Abh. 163, 43–86.
Salje, E. K. H. (2000a). Mesoscopic twin patterns in ferroelastic and co-elastic minerals. Rev. Mineral. Geochem. 39, 65–84.
Salje, E. K. H. (2000b). Ferroelasticity. Contemp. Phys. 41, 79–91.
Sapriel, J. (1975). Domain-wall orientations in ferroelastics. Phys. Rev. B, 12, 5128–5140.
Schlenker, J. L., Gibbs, G. V. & Boisen, M. B. (1978). Strain-tensor components expressed in terms of lattice parameters. Acta Cryst. A34, 52–54.
Schmid, H. (1991). Polarized light microscopy of the ferroelastic domains of YBa2Cu3O7−x. Phase Transit. 30, 205–214.
Schmid, H. (1993). Polarized light microscopy (PLM) of ferroelectric and ferroelastic domains in transmitted and reflected light. In Ferroelectric ceramics, edited by N. Setter & E. L. Colla, pp. 107–126. Basel: Birkhäuser.
Schmid, H., Burkhardt, E., Walker, E., Brixel, W., Clin, M., Rivera, J.-P., Jorda, J.-L., François, M. & Yvon, K. (1988). Polarized light and X-ray precession study of the ferroelastic domains of YBa2Cu3O7−δ. Z. Phys. B Condens. Matter, 72, 305–322.
Schranz, W. (1995). Domains and interfaces near ferroic phase transitions. Key Eng. Mater. 101102, 41–60.
Scott, J. (1998). The physics of ferroelectric ceramic thin films for memory applications. Ferroelectrics Rev. 1, 1–129.
Scott, J. (2000). Ferroelectric memories. Heidelberg: Springer.
Shmyt'ko, I. M., Shekhtman, V. Sh., Ossipyan, Yu. A. & Afonikova, N. S. (1987). Twin structure and structure of twin boundaries in 1–2–3-O7−δ crystals. Ferroelectrics, 97, 151–170.
Shubnikov, A. V. & Kopcik, V. A. (1974). Symmetry in science and art. New York: Plenum Press.
Shur, V. Ya., Batchko, R. G., Rumyantsev, E. L., Miller, G. D., Fejer, M. M. & Byer, R. L. (1999). Domain engineering: periodic domain pattering in lithium niobate. Proc. 11th ISAF, pp. 399–406. Piscataway, NJ: IEEE.
Shur, V. Ya., Gruverman, A. L., Letuchev, V. V., Rumyantsev, E. L. & Subbotin, A. L. (1989). Domain structure of lead germanate. Ferroelectrics, 98, 29–49.
Shur, V. Ya., Rumyantsev, E. L., Nikolaeva, E. V., Shishkin, E. I., Batchko, R. G., Fejer, M. M. & Byer, R. L. (2001). Recent achievements in domain engineering in lithium niobate and lithium tantalate. Ferroelectrics, 257, 191–202.
Shuvalov, L. A. (1988). Editor. Modern crystallography IV. Physical properties of crystals. Berlin: Springer.
Shuvalov, L. A., Dudnik, E. F. & Wagin, S. V. (1985). Domain structure geometry of real ferroelastics. Ferroelectrics, 65, 143–152.
Shuvalov, L. A. & Ivanov, N. R. (1964). Change in the optical activity of ferroelectric crystals on reversal of polarization. Sov. Phys. Crystallogr. 9, 290–299. (Kristallografiya, 9, 363–372.)
Sidorkin, A. S. (2002). Domain structure in ferroelectrics and related materials. Moscow: Fizmatlit (in Russian).
Sirotin, Yu. I. & Shaskolskaya, M. P. (1982). Fundamentals of crystal physics. Moscow: Mir.
Smolenskii, G. A., Bokov, V. A., Isupov, V. A., Krainik, N. N., Pasynkov, R. E. & Shur, M. S. (1984). Physics of ferroelectric phenomena. New York: Gordon & Breach.
Snoeck, E., Saint-Grégoire, P., Janovec, V. & Roucau, C. (1994). TEM study of 3-q modulated phase of quartz-type under electric field. Ferroelectrics, 155, 171–176.
Sonin, E. B. & Tagancev, A. K. (1989). Structure and phase transitions in antiphase boundaries of improper ferroelectrics. Ferroelectrics, 98, 291–295.
Strukov, B. A. & Levanyuk, A. P. (1998). Ferroelectric phenomena in crystals. Berlin: Springer.
Sutton, A. P. & Balluffi, R. W. (1995). Interfaces in crystalline materials. Oxford: Clarendon Press.
Tagancev, A. R. & Sonin, E. B. (1989). Linear singularities and their motion in improper ferroelectrics. Ferroelectrics, 98, 297–300.
Tolédano, J.-C. & Tolédano, P. (1987). The Landau theory of phase transitions. Singapore: World Scientific.
Tolédano, P. & Dmitriev, V. (1996). Reconstructive phase transitions. Singapore: World Scientific.
Tomaszewski, P. E. (1992). Structural phase transitions in crystals. I. Database. II. Statistical analysis. Phase Transit. 38, 127–220, 221–228.
Uchino, K. (2000). Ferroelectric devices. New York: Marcel Dekker.
Vainshtein, B. K. (1994). Modern crystallography I. Symmetry of crystals. Berlin: Springer.
Van Landuyt, J., Van Tendeloo, G., Amelinckx, S. & Walker, M. B. (1985). Interpretation of Dauphiné-twin-domain configurations resulting from the α–β phase transition in quartz and aluminium phosphate. Phys. Rev. B, 31, 2986–2992.
Van Tendeloo, G. & Amelinckx, S. (1974). Group-theoretical considerations concerning domain formation in ordered alloys. Acta Cryst. A30, 431–440.
Wadhawan, V. K. (1991). Ferroelasticity: introductory survey and present status. Phase Transit. 34, 3–18.
Wadhawan, V. K. (2000). Introduction to ferroic materials. The Netherlands: Gordon and Breach.
Wondratschek, H. & Aroyo, M. I. (2001). The application of Hermann's group [{\cal M}] in group–subgroup relations between space groups. Acta Cryst. A57, 311–320.
Wondratschek, H. & Jeitschko, W. (1976). Twin domains and antiphase domains. Acta Cryst. A32, 664–666.
Xu, Y. (1991). Ferroelectric materials and their applications. Amsterdam: North-Holland.
Yin, J. & Cao, W. (2000). Domain configurations in domain engineered 0.995Pb(Zn1/3Nb2/3)O30.045PbTiO3 single crystals. J. Appl. Phys. 87, 7438–7441.
Zheludev, I. S. (1988). Electrical properties of crystals. In Modern crystallography IV. Physical properties of crystals, edited by L. A. Shuvalov, pp. 178–266. Berlin: Springer-Verlag.
Zieliński, P. (1990). Group-theoretical description of domains and phase boundaries in crystalline solids. Surf. Sci. Rep. 11, 179–223.
Zikmund, Z. (1984). Symmetry of domain pairs and domain walls. Czech. J. Phys. B, 34, 932–949.