International Tables for Crystallography (2013). Vol. D, ch. 3.4, pp. 484-559
doi: 10.1107/97809553602060000918

Chapter 3.4. Domain structures

Contents

  • 3.4. Domain structures  (pp. 484-559) | html | pdf | chapter contents |
    • 3.4.1. Introduction  (pp. 484-486) | html | pdf |
      • 3.4.1.1. Basic concepts  (pp. 484-485) | html | pdf |
      • 3.4.1.2. Scope of this chapter  (pp. 485-486) | html | pdf |
    • 3.4.2. Domain states  (pp. 486-505) | html | pdf |
      • 3.4.2.1. Principal and basic domain states  (pp. 486-490) | html | pdf |
      • 3.4.2.2. Degenerate (secondary) domain states, partition of principal domain states  (pp. 490-493) | html | pdf |
        • 3.4.2.2.1. Ferroelastic domain state  (pp. 491-492) | html | pdf |
        • 3.4.2.2.2. Ferroelectric domain states  (p. 492) | html | pdf |
        • 3.4.2.2.3. Domain states with the same stabilizer  (pp. 492-493) | html | pdf |
      • 3.4.2.3. Property tensors associated with ferroic domain states  (pp. 493-495) | html | pdf |
      • 3.4.2.4. Synoptic table of ferroic transitions and domain states  (pp. 495-497) | html | pdf |
        • 3.4.2.4.1. Explanation of Table 3.4.2.7  (pp. 496-497) | html | pdf |
      • 3.4.2.5. Basic (microscopic) domain states and their partition into translation subsets  (pp. 497-505) | html | pdf |
    • 3.4.3. Domain pairs: domain twin laws, distinction of domain states and switching  (pp. 505-528) | html | pdf |
      • 3.4.3.1. Domain pairs and their symmetry, twin law  (pp. 506-508) | html | pdf |
      • 3.4.3.2. Twinning group, distinction of two domain states  (pp. 508-510) | html | pdf |
      • 3.4.3.3. Switching of ferroic domain states  (pp. 510-511) | html | pdf |
      • 3.4.3.4. Classes of equivalent domain pairs and their classifications  (pp. 511-512) | html | pdf |
      • 3.4.3.5. Non-ferroelastic domain pairs: twin laws, domain distinction and switching fields, synoptic table  (pp. 512-515) | html | pdf |
        • 3.4.3.5.1. Explanation of Table 3.4.3.4  (pp. 512-515) | html | pdf |
      • 3.4.3.6. Ferroelastic domain pairs  (pp. 515-528) | html | pdf |
        • 3.4.3.6.1. Spontaneous strain  (pp. 516-517) | html | pdf |
        • 3.4.3.6.2. Equally deformed planes of a ferroelastic domain pair  (pp. 517-518) | html | pdf |
        • 3.4.3.6.3. Disoriented domain states, ferroelastic domain twins and their twin laws  (pp. 518-521) | html | pdf |
        • 3.4.3.6.4. Ferroelastic domain pairs with compatible domain walls, synoptic table  (pp. 521-527) | html | pdf |
          • 3.4.3.6.4.1. Explanation of Table 3.4.3.6  (pp. 526-527) | html | pdf |
        • 3.4.3.6.5. Ferroelastic domain pairs with no compatible domain walls, synoptic table  (pp. 527-528) | html | pdf |
      • 3.4.3.7. Domain pairs in the microscopic description  (p. 528) | html | pdf |
    • 3.4.4. Domain twins and domain walls  (pp. 528-539) | html | pdf |
      • 3.4.4.1. Formal description of simple domain twins and planar domain walls of zero thickness  (pp. 528-529) | html | pdf |
      • 3.4.4.2. Layer groups  (pp. 529-530) | html | pdf |
      • 3.4.4.3. Symmetry of simple twins and planar domain walls of zero thickness  (pp. 530-533) | html | pdf |
      • 3.4.4.4. Non-ferroelastic domain twins and domain walls  (pp. 533-535) | html | pdf |
      • 3.4.4.5. Ferroelastic domain twins and walls. Ferroelastic twin laws  (p. 535) | html | pdf |
      • 3.4.4.6. Domain walls of finite thickness – continuous description  (pp. 535-538) | html | pdf |
      • 3.4.4.7. Microscopic structure and symmetry of domain walls  (p. 538) | html | pdf |
    • 3.4.5. Glossary  (p. 539) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 3.4.1.1. Domain structure of tetragonal barium titanate (BaTiO 3 )  (p. 484) | html | pdf |
      • Fig. 3.4.1.2. Domain structure of a BaGa 2 O 4 crystal seen by high-resolution transmission electron microscopy  (p. 484) | html | pdf |
      • Fig. 3.4.1.3. Elastic hysteresis of ferroelastic lead phosphate Pb 3 (PO 4 ) 2 (Salje, 1990)  (p. 485) | html | pdf |
      • Fig. 3.4.1.4. Transmission electron microscopy image of the ferroelastic domain structure in a YBa 2 Cu 3 O 7− y crystal  (p. 485) | html | pdf |
      • Fig. 3.4.1.5. Non-ferroelastic ferroelectric domains in triglycine sulfate (TGS) revealed by a liquid-crystal method  (p. 485) | html | pdf |
      • Fig. 3.4.2.1. Hierarchy in domain-structure analysis  (p. 487) | html | pdf |
      • Fig. 3.4.2.2. Exploded view of single-domain states [{\bf S}_1], [{\bf S}_2], [{\bf S}_3] and [{\bf S}_4 ] (solid rectangles with arrows of spontaneous polarization) formed at a phase transition from a parent phase with symmetry [G=4_z/m_zm_xm_{xy} ] to a ferroic phase with symmetry [F_1=2_xm_ym_z]  (p. 487) | html | pdf |
      • Fig. 3.4.2.3. Oriented symmetry operations of the cubic group [m\bar3m] and of its subgroups  (p. 495) | html | pdf |
      • Fig. 3.4.2.4. Oriented symmetry operations of the hexagonal group [6/mmm ] and of its hexagonal and trigonal subgroups  (p. 496) | html | pdf |
      • Fig. 3.4.2.5. Four basic single-domain states [{{\sf S}_1}= 1_1], [{{\sf S}_2}= 1_2], [{{\sf S}_3}= 2_1], [{{\sf S}_4}= 2_2 ] of the ferroic phase of a calomel (Hg 2 Cl 2 ) crystal  (p. 505) | html | pdf |
      • Fig. 3.4.3.1. Transposable domain pairs  (p. 507) | html | pdf |
      • Fig. 3.4.3.2. Non-transposable domain pairs  (p. 507) | html | pdf |
      • Fig. 3.4.3.3. Domain structure in lead germanate observed using a polarized-light microscope  (p. 515) | html | pdf |
      • Fig. 3.4.3.4. Temperature dependence of lattice parameters in leucite  (p. 516) | html | pdf |
      • Fig. 3.4.3.5. Two ways of constructing a ferroelastic domain twin  (p. 517) | html | pdf |
      • Fig. 3.4.3.6. High-resolution electron microscopy image of a ferroelastic twin in the orthorhombic phase of WO 3   (p. 519) | html | pdf |
      • Fig. 3.4.3.7. Ferroelastic twins in a very thin YBa 2 Cu 3 O 7−δ crystal observed in a polarized-light microscope  (p. 519) | html | pdf |
      • Fig. 3.4.3.8. Exploded view of four ferroelastic twins with disoriented ferroelastic domain states [{\bf R}_1^+, {\bf R}_2^-] and [{\bf R}_1^-, {\bf R}_2^+ ] formed from a single-domain pair [({\bf S}_1,{\bf S}_2)]  (p. 520) | html | pdf |
      • Fig. 3.4.3.9. Splitting of diffraction spots at a tetragonal-to-orthorhombic transition  (p. 520) | html | pdf |
      • Fig. 3.4.3.10. Domain pairs in calomel  (p. 528) | html | pdf |
      • Fig. 3.4.4.1. Symbols of a simple twin  (p. 529) | html | pdf |
      • Fig. 3.4.4.2. A simple twin under the action of four types of operation that do not change the orientation of the wall plane p   (p. 531) | html | pdf |
      • Fig. 3.4.4.3. Engineered periodic non-ferroelastic ferroelectric stripe domain structure within a lithium tantalate crystal with symmetry descent [\bar 6\supset 3 ]  (p. 534) | html | pdf |
      • Fig. 3.4.4.4. Microscopic structure of two domain states and two parallel mutually reversed domain walls in the [\alpha] phase of quartz  (p. 534) | html | pdf |
      • Fig. 3.4.4.5. Transmission electron microscopy (TEM) image of the incommensurate triangular ([3-q] modulated) phase of quartz  (p. 535) | html | pdf |
      • Fig. 3.4.4.6. Profile of the one-component order parameter [\eta(\xi)] in a symmetric wall (S)  (p. 536) | html | pdf |
      • Fig. 3.4.4.7. Profiles of the one-component order parameter [\eta(\xi)] in a sym­metric wall (solid curve) and in the reversed wall (dotted curve)  (p. 537) | html | pdf |
      • Fig. 3.4.4.8. Profiles of the one-component order parameter [\eta(\xi)] in an asymmetric wall (solid curve) and in the reversed asymmetric wall (dotted curve)  (p. 537) | html | pdf |
      • Fig. 3.4.4.9. Profiles of the one-component order parameter [\eta(\xi)] in an asymmetric wall (solid curve) and in the reversed asymmetric wall (dotted curve)  (p. 537) | html | pdf |
      • Fig. 3.4.4.10. A profile of the second order parameter component in a degenerate domain wall  (p. 538) | html | pdf |
      • Fig. 3.4.4.11. Microscopic structure of a ferroelastic domain wall in calomel  (p. 539) | html | pdf |
    • Tables
      • Table 3.4.2.1. Left and double cosets, principal and secondary domain states and their tensor parameters for the phase transition with [G=4_z/m_zm_xm_{xy} ] and [F_1=2_xm_ym_z]   (p. 489) | html | pdf |
      • Table 3.4.2.2. Crystal systems, holohedries, crystal families and number of spontaneous strain components  (p. 491) | html | pdf |
      • Table 3.4.2.3. Classification of ferroic phases according to ferroelastic and ferroelectric domain states  (p. 492) | html | pdf |
      • Table 3.4.2.4. Morphic properties, tensor parameters, order parameters and domain states  (p. 494) | html | pdf |
      • Table 3.4.2.5. Symbols of symmetry operations of the point group [m\bar 3m ]   (p. 495) | html | pdf |
      • Table 3.4.2.6. Symbols of symmetry operations of the point group [6/mmm]   (p. 496) | html | pdf |
      • Table 3.4.2.7. Group–subgroup symmetry descents [G \supset F_1]   (pp. 498-502) | html | pdf |
      • Table 3.4.3.1. Classification of domain pairs, ferroic phases and of switching (state shifts)  (p. 510) | html | pdf |
      • Table 3.4.3.2. Four types of domain pairs  (p. 511) | html | pdf |
      • Table 3.4.3.3. Decomposition of [G=6_z/m_z] into left cosets of [F_1=2_z/m_z ]   (p. 512) | html | pdf |
      • Table 3.4.3.4. Non-ferroelastic domain pairs, domain twin laws and distinction of non-ferroelastic domains  (pp. 513-514) | html | pdf |
      • Table 3.4.3.5. Property tensors and switching fields  (p. 514) | html | pdf |
      • Table 3.4.3.6. Ferroelastic domain pairs and twins with compatible domain walls  (pp. 521-526) | html | pdf |
      • Table 3.4.3.7. Ferroelastic domain pairs with no compatible domain walls  (p. 527) | html | pdf |
      • Table 3.4.4.1. Crystallographic layer groups with continuous translations  (p. 530) | html | pdf |
      • Table 3.4.4.2. Action of four types of operations g on a twin [({\bf S}_1 |{\bf n}| {\bf S}_j) ]   (p. 531) | html | pdf |
      • Table 3.4.4.3. Classification of domain walls and simple twins  (p. 532) | html | pdf |
      • Table 3.4.4.4. Symmetries of non-ferroelastic domain twins and walls  (p. 533) | html | pdf |
      • Table 3.4.4.5. Symmetry properties of domain walls in α quartz  (p. 534) | html | pdf |
      • Table 3.4.4.6. Symmetry properties of ferroelastic domain twins and compatible domain walls  (p. 536) | html | pdf |
      • Table 3.4.4.7. Sectional layer groups and twin (wall) symmetries of the twin [({\sf S}_1|[100];s{\bf d}|{\sf S}_3)] in a calomel crystal  (p. 539) | html | pdf |