International Tables for Crystallography (2013). Vol. D, ch. 1.10, pp. 246-270
doi: 10.1107/97809553602060000909

Chapter 1.10. Tensors in quasiperiodic structures

Contents

  • 1.10. Tensors in quasiperiodic structures  (pp. 246-270) | html | pdf | chapter contents |
    • 1.10.1. Quasiperiodic structures  (pp. 246-248) | html | pdf |
      • 1.10.1.1. Introduction  (p. 246) | html | pdf |
      • 1.10.1.2. Types of quasiperiodic crystals  (pp. 246-247) | html | pdf |
      • 1.10.1.3. Embedding in superspace  (pp. 247-248) | html | pdf |
    • 1.10.2. Symmetry  (pp. 248-252) | html | pdf |
      • 1.10.2.1. Symmetry transformations  (pp. 248-249) | html | pdf |
      • 1.10.2.2. Point groups  (pp. 249-250) | html | pdf |
      • 1.10.2.3. Superspace groups  (p. 250) | html | pdf |
      • 1.10.2.4. Magnetic superspace groups  (pp. 250-251) | html | pdf |
      • 1.10.2.5. Pseudotensors  (pp. 251-252) | html | pdf |
    • 1.10.3. Action of the symmetry group  (pp. 252-253) | html | pdf |
      • 1.10.3.1. Action of superspace groups  (p. 252) | html | pdf |
      • 1.10.3.2. Compensating gauge transformations  (p. 252) | html | pdf |
      • 1.10.3.3. Irreducible representations of three-dimensional space groups  (pp. 252-253) | html | pdf |
    • 1.10.4. Tensors  (pp. 253-262) | html | pdf |
      • 1.10.4.1. Tensors in higher-dimensional spaces  (p. 253) | html | pdf |
      • 1.10.4.2. Tensors in superspace  (p. 254) | html | pdf |
      • 1.10.4.3. Inhomogeneous tensors  (pp. 254-255) | html | pdf |
      • 1.10.4.4. Irreducible representations  (p. 255) | html | pdf |
      • 1.10.4.5. Determining the number of independent tensor elements  (pp. 255-257) | html | pdf |
        • 1.10.4.5.1. Piezoelectric tensor  (pp. 255-256) | html | pdf |
        • 1.10.4.5.2. Elasticity tensor  (p. 256) | html | pdf |
        • 1.10.4.5.3. Electric field gradient tensor  (pp. 256-257) | html | pdf |
      • 1.10.4.6. Determining the independent tensor elements  (pp. 257-262) | html | pdf |
        • 1.10.4.6.1. Metric tensor for an octagonal three-dimensional quasicrystal  (p. 257) | html | pdf |
        • 1.10.4.6.2. EFG tensor for Pcmn   (p. 257) | html | pdf |
        • 1.10.4.6.3. Elasticity tensor for a two-dimensional octagonal quasicrystal  (pp. 257-258) | html | pdf |
        • 1.10.4.6.4. Piezoelectric tensor for a three-dimensional octagonal quasicrystal  (pp. 258-259) | html | pdf |
        • 1.10.4.6.5. Elasticity tensor for an icosahedral quasicrystal  (p. 259) | html | pdf |
        • 1.10.4.6.6. Coupling to magnetism  (pp. 259-262) | html | pdf |
    • 1.10.5. Tables  (pp. 262-268) | html | pdf |
    • References | html | pdf |
    • Tables
      • Table 1.10.2.1. Allowable three-dimensional point groups for systems up to rank six  (p. 251) | html | pdf |
      • Table 1.10.4.1. Characters of the point group [10\,mm(10^3\,mm)] for representations relevant for elasticity  (p. 256) | html | pdf |
      • Table 1.10.4.2. Sign change of [\partial_iE_j] under the generators A , B , C   (p. 257) | html | pdf |
      • Table 1.10.4.3. Elastic constants for icosahedral quasicrystals  (p. 260) | html | pdf |
      • Table 1.10.5.1. Character tables of some point groups for quasicrystals  (pp. 260-261) | html | pdf |
      • Table 1.10.5.2. Matrices of the irreducible representations of dimension [d \geq 2] corresponding to the irreps of Table 1.10.5.1  (pp. 262-267) | html | pdf |
      • Table 1.10.5.3. The representation matrices for [\Gamma_3]   (p. 268) | html | pdf |
      • Table 1.10.5.4. Number of free parameters for some tensors and their symmetry groups  (p. 268) | html | pdf |