International Tables for Crystallography (2006). Vol. C, ch. 9.2, pp. 752-773
doi: 10.1107/97809553602060000618

Chapter 9.2. Layer stacking

Contents

  • 9.2. Layer stacking  (pp. 752-773) | html | pdf | chapter contents |
    • 9.2.1. Layer stacking in close-packed structures  (pp. 752-760) | html | pdf |
      • 9.2.1.1. Close packing of equal spheres  (pp. 752-753) | html | pdf |
        • 9.2.1.1.1. Close-packed layer  (p. 752) | html | pdf |
        • 9.2.1.1.2. Close-packed structures  (p. 752) | html | pdf |
        • 9.2.1.1.3. Notations for close-packed structures  (pp. 752-753) | html | pdf |
      • 9.2.1.2. Structure of compounds based on close-packed layer stackings  (pp. 753-755) | html | pdf |
        • 9.2.1.2.1. Voids in close packing  (p. 753) | html | pdf |
        • 9.2.1.2.2. Structures of SiC and ZnS  (pp. 753-754) | html | pdf |
        • 9.2.1.2.3. Structure of CdI 2   (p. 754) | html | pdf |
        • 9.2.1.2.4. Structure of GaSe  (pp. 754-755) | html | pdf |
      • 9.2.1.3. Symmetry of close-packed layer stackings of equal spheres  (p. 755) | html | pdf |
      • 9.2.1.4. Possible lattice types  (p. 755) | html | pdf |
      • 9.2.1.5. Possible space groups  (pp. 755-756) | html | pdf |
      • 9.2.1.6. Crystallographic uses of Zhdanov symbols  (p. 756) | html | pdf |
      • 9.2.1.7. Structure determination of close-packed layer stackings  (pp. 756-758) | html | pdf |
        • 9.2.1.7.1. General considerations  (p. 756) | html | pdf |
        • 9.2.1.7.2. Determination of the lattice type  (p. 757) | html | pdf |
        • 9.2.1.7.3. Determination of the identity period  (p. 757) | html | pdf |
        • 9.2.1.7.4. Determination of the stacking sequence of layers  (pp. 757-758) | html | pdf |
      • 9.2.1.8. Stacking faults in close-packed structures  (pp. 758-760) | html | pdf |
        • 9.2.1.8.1. Structure determination of one-dimensionally disordered crystals  (pp. 759-760) | html | pdf |
    • 9.2.2. Layer stacking in general polytypic structures  (pp. 760-773) | html | pdf |
      • 9.2.2.1. The notion of polytypism  (pp. 760-761) | html | pdf |
      • 9.2.2.2. Symmetry aspects of polytypism  (pp. 761-766) | html | pdf |
        • 9.2.2.2.1. Close packing of spheres  (p. 761) | html | pdf |
        • 9.2.2.2.2. Polytype families and OD groupoid families  (pp. 761-762) | html | pdf |
        • 9.2.2.2.3. MDO polytypes  (p. 762) | html | pdf |
        • 9.2.2.2.4. Some geometrical properties of OD structures  (pp. 762-763) | html | pdf |
        • 9.2.2.2.5. Diffraction pattern – structure analysis  (p. 763) | html | pdf |
        • 9.2.2.2.6. The vicinity condition  (pp. 763-764) | html | pdf |
        • 9.2.2.2.7. Categories of OD structures  (pp. 764-765) | html | pdf |
          • 9.2.2.2.7.1. OD structures of equivalent layers  (pp. 764-765) | html | pdf |
          • 9.2.2.2.7.2. OD structures with more than one kind of layer  (p. 765) | html | pdf |
        • 9.2.2.2.8. Desymmetrization of OD structures  (pp. 765-766) | html | pdf |
        • 9.2.2.2.9. Concluding remarks  (p. 766) | html | pdf |
      • 9.2.2.3. Examples of some polytypic structures  (pp. 766-772) | html | pdf |
        • 9.2.2.3.1. Hydrous phyllosilicates  (pp. 766-769) | html | pdf |
          • 9.2.2.3.1.1. General geometry  (pp. 767-769) | html | pdf |
          • 9.2.2.3.1.2. Diffraction pattern and identification of individual polytypes  (p. 769) | html | pdf |
        • 9.2.2.3.2. Stibivanite Sb 2 VO 5   (pp. 769-771) | html | pdf |
        • 9.2.2.3.3. γ-Hg 3 S 2 Cl 2   (pp. 771-772) | html | pdf |
        • 9.2.2.3.4. Remarks for authors  (p. 772) | html | pdf |
      • 9.2.2.4. List of some polytypic structures  (pp. 772-773) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 9.2.1.1. The close packing of equal spheres in a plane  (p. 752) | html | pdf |
      • Fig. 9.2.1.2. ( a ) Symmetry axes of a single close-packed layer of spheres and ( b ) the minimum symmetry of a three-dimensional close packing of spheres  (p. 752) | html | pdf |
      • Fig. 9.2.1.3. Voids in a close packing: ( a ) tetrahedral void; ( b ) tetrahedron formed by the centres of spheres; ( c ) octahedral void; ( d ) octahedron formed by the centres of spheres  (p. 753) | html | pdf |
      • Fig. 9.2.1.4. Tetrahedral arrangement of Si and C atoms in the SiC-6 H structure  (p. 753) | html | pdf |
      • Fig. 9.2.1.5. The layer structure of CdI 2 : small circles represent Cd ions and larger ones I ions  (p. 754) | html | pdf |
      • Fig. 9.2.1.6. The primitive unit cell of the 2 H close packing  (p. 755) | html | pdf |
      • Fig. 9.2.1.7. A rhombohedral lattice ( a 1 , a 2 , a 3 ) referred to hexagonal axes ( A 1 , A 2 , C )  (p. 755) | html | pdf |
      • Fig. 9.2.1.8. The relationship between the f.c.c. and the primitive rhombohedral unit cell of the c.c.p. structure  (p. 756) | html | pdf |
      • Fig. 9.2.1.9. The a *− b * reciprocal-lattice net for close-packed layer stackings  (p. 756) | html | pdf |
      • Fig. 9.2.2.1. Symmetry interpretation of close packings of equal spheres  (p. 761) | html | pdf |
      • Fig. 9.2.2.2. Schematic representation of three structures belonging to the OD groupoid family P (1) m 1|1  (p. 762) | html | pdf |
      • Fig. 9.2.2.3. Schematic examples of the three categories of OD structures consisting of equivalent layers (perpendicular to the plane of the drawing)  (p. 764) | html | pdf |
      • Fig. 9.2.2.4. Schematic examples of the four categories of OD structures consisting of more than one kind of layer (perpendicular to the plane of the drawing)  (p. 764) | html | pdf |
      • Fig. 9.2.2.5. Hierarchy of VC structures indicating the position of OD structures within it  (p. 765) | html | pdf |
      • Fig. 9.2.2.6. ( a ) Tetrahedral sheet in a normal projection  (p. 767) | html | pdf |
      • Fig. 9.2.2.7. Two possible combinations of one tetrahedral and one octahedral sheet ( a ) by shared apical O atoms, ( b ) by hydrogen bonds (side projection)  (p. 767) | html | pdf |
      • Fig. 9.2.2.8. Combination of two adjacent tetrahedral sheets ( a ) in the mica group, ( b ) in the talc–pyrophyllite group (side projection)  (p. 767) | html | pdf |
      • Fig. 9.2.2.9. The nine possible displacements in the structures of polytypes of phyllosilicates  (p. 768) | html | pdf |
      • Fig. 9.2.2.10. The NFZ relations ( a ) for the pair tetrahedral sheet–homo-octahedral sheet (with shared apical O atoms), ( b ), ( c ) for the pair homo-octahedral sheet–tetrahedral sheet (by hydrogen bonds)  (p. 768) | html | pdf |
      • Fig. 9.2.2.11. Stereopair showing the sequence of sheets in the structures of the serpentine–kaolin group  (p. 769) | html | pdf |
      • Fig. 9.2.2.12. Stereopair showing the sequence of sheets in the structures of the mica group  (p. 770) | html | pdf |
      • Fig. 9.2.2.13. Stereopair showing the sequence of sheets in the structures of the talc–pyrophyllite group  (p. 770) | html | pdf |
      • Fig. 9.2.2.14. Stereopair showing the sequence of sheets in the structures of the chlorite–vermiculite group (chlorite-1 M , courtesy of Zoltai & Stout, 1985)  (p. 770) | html | pdf |
      • Fig. 9.2.2.15. Clinographic projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates  (p. 771) | html | pdf |
      • Fig. 9.2.2.16. Normal projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates  (p. 771) | html | pdf |
      • Fig. 9.2.2.17. The structure of stibivanite-2 M   (p. 771) | html | pdf |
      • Fig. 9.2.2.18. The two kinds of OD layers in the stibivanite family  (p. 772) | html | pdf |
      • Fig. 9.2.2.19. The structure of stibivanite-2 O   (p. 772) | html | pdf |
      • Fig. 9.2.2.20. The structural principle of γ -Hg 3 S 2 Cl 2   (p. 772) | html | pdf |
    • Tables
      • Table 9.2.1.1. Common close-packed metallic structures  (p. 753) | html | pdf |
      • Table 9.2.1.2. List of SiC polytypes with known structures in order of increasing periodicity  (p. 754) | html | pdf |
      • Table 9.2.1.3. Intrinsic fault configurations in the 6 H ( A 0 B 1 C 2 A 3 C 4 B 5 ;. . .) structure  (p. 758) | html | pdf |
      • Table 9.2.1.4. Intrinsic fault configurations in the 9 R ( A 0 B 1 A 2 C 0 A 1 C 2 B 0 C 1 B 2 ;. . .) structure  (p. 759) | html | pdf |