International Tables for Crystallography
Volume D: Physical properties of crystals

First online edition (2006)   ISBN: 978-1-4020-0714-9   doi: 10.1107/97809553602060000104  

Edited by A. Authier

Contents

• Preface  (p. xi) | html | pdf |
  A. Authier

• Tensorial aspects of physical properties
  • 1.1. Introduction to the properties of tensors  (pp. 3-33) | html | pdf | chapter contents |
    A. Authier
    • 1.1.1. The matrix of physical properties  (pp. 3-5) | html | pdf |
    • 1.1.2. Basic properties of vector spaces  (pp. 5-7) | html | pdf |
    • 1.1.3. Mathematical notion of tensor  (pp. 7-10) | html | pdf |
    • 1.1.4. Symmetry properties  (pp. 10-31) | html | pdf |
    • 1.1.5. Thermodynamic functions and physical property tensors  (pp. 31-32) | html | pdf |
    • 1.1.6. Glossary  (pp. 32-33) | html | pdf |
    • References | html | pdf |
  • 1.2. Representations of crystallographic groups  (pp. 34-71) | html | pdf | chapter contents |
    T. Janssen
    • 1.2.1. Introduction  (pp. 34-35) | html | pdf |
    • 1.2.2. Point groups  (pp. 35-46) | html | pdf |
    • 1.2.3. Space groups  (pp. 46-51) | html | pdf |
    • 1.2.4. Tensors  (pp. 51-53) | html | pdf |
    • 1.2.5. Magnetic symmetry  (pp. 53-56) | html | pdf |
    • 1.2.6. Tables  (pp. 56-62) | html | pdf |
    • 1.2.7. Introduction to the accompanying software Tenχar  (pp. 62-70) | html | pdf |
      M. Ephraïm, T. Janssen, A. Janner and A. Thiers
    • 1.2.8. Glossary  (pp. 70-71) | html | pdf |
    • References | html | pdf |
  • 1.3. Elastic properties  (pp. 72-98) | html | pdf | chapter contents |
    A. Authier and A. Zarembowitch
    • 1.3.1. Strain tensor  (pp. 72-76) | html | pdf |
    • 1.3.2. Stress tensor  (pp. 76-80) | html | pdf |
    • 1.3.3. Linear elasticity  (pp. 80-85) | html | pdf |
    • 1.3.4. Propagation of elastic waves in continuous media – dynamic elasticity  (pp. 86-89) | html | pdf |
    • 1.3.5. Pressure dependence and temperature dependence of the elastic constants  (pp. 89-91) | html | pdf |
    • 1.3.6. Nonlinear elasticity  (pp. 91-94) | html | pdf |
    • 1.3.7. Nonlinear dynamic elasticity  (pp. 94-97) | html | pdf |
    • 1.3.8. Glossary  (p. 97) | html | pdf |
    • References | html | pdf |
  • 1.4. Thermal expansion  (pp. 99-104) | html | pdf | chapter contents |
    H. Küppers
    • 1.4.1. Definition, symmetry and representation surfaces  (pp. 99-100) | html | pdf |
    • 1.4.2. Grüneisen relation  (pp. 100-101) | html | pdf |
    • 1.4.3. Experimental methods  (pp. 101-103) | html | pdf |
    • 1.4.4. Relation to crystal structure  (pp. 103-104) | html | pdf |
    • 1.4.5. Glossary  (p. 104) | html | pdf |
    • References | html | pdf |
  • 1.5. Magnetic properties  (pp. 105-149) | html | pdf | chapter contents |
    A. S. Borovik-Romanov and H. Grimmer
    • 1.5.1. Introduction  (pp. 105-109) | html | pdf |
    • 1.5.2. Magnetic symmetry  (pp. 109-116) | html | pdf |
    • 1.5.3. Phase transitions into a magnetically ordered state  (pp. 116-125) | html | pdf |
    • 1.5.4. Domain structure  (pp. 125-127) | html | pdf |
    • 1.5.5. Weakly non-collinear magnetic structures  (pp. 127-131) | html | pdf |
    • 1.5.6. Reorientation transitions  (pp. 131-132) | html | pdf |
    • 1.5.7. Piezomagnetism  (pp. 132-137) | html | pdf |
    • 1.5.8. Magnetoelectric effect  (pp. 137-142) | html | pdf |
    • 1.5.9. Magnetostriction  (pp. 142-146) | html | pdf |
    • 1.5.10. Transformation from Gaussian to SI units  (p. 146) | html | pdf |
    • 1.5.11. Glossary  (p. 146) | html | pdf |
    • References | html | pdf |
  • 1.6. Classical linear crystal optics  (pp. 150-177) | html | pdf | chapter contents |
    A. M. Glazer and K. G. Cox
    • 1.6.1. Introduction  (p. 150) | html | pdf |
    • 1.6.2. Generalized optical, electro-optic and magneto-optic effects  (pp. 150-152) | html | pdf |
    • 1.6.3. Linear optics  (pp. 152-154) | html | pdf |
    • 1.6.4. Practical observation of crystals  (pp. 154-166) | html | pdf |
    • 1.6.5. Optical rotation  (pp. 166-172) | html | pdf |
    • 1.6.6. Linear electro-optic effect  (pp. 172-173) | html | pdf |
    • 1.6.7. The linear photoelastic effect  (pp. 173-176) | html | pdf |
    • 1.6.8. Glossary  (p. 176) | html | pdf |
    • References | html | pdf |
  • 1.7. Nonlinear optical properties  (pp. 178-219) | html | pdf | chapter contents |
    B. Boulanger and J. Zyss
    • 1.7.1. Introduction  (p. 178) | html | pdf |
    • 1.7.2. Origin and symmetry of optical nonlinearities  (pp. 178-183) | html | pdf |
    • 1.7.3. Propagation phenomena  (pp. 183-212) | html | pdf |
    • 1.7.4. Determination of basic nonlinear parameters  (pp. 212-214) | html | pdf |
    • 1.7.5. The main nonlinear crystals  (pp. 214-216) | html | pdf |
    • 1.7.6. Glossary  (p. 216) | html | pdf |
    • References | html | pdf |
  • 1.8. Transport properties  (pp. 220-227) | html | pdf | chapter contents |
    G. D. Mahan
    • 1.8.1. Introduction  (p. 220) | html | pdf |
    • 1.8.2. Macroscopic equations  (p. 220) | html | pdf |
    • 1.8.3. Electrical resistivity  (pp. 220-224) | html | pdf |
    • 1.8.4. Thermal conductivity  (pp. 224-226) | html | pdf |
    • 1.8.5. Seebeck coefficient  (pp. 226-227) | html | pdf |
    • 1.8.6. Glossary  (p. 227) | html | pdf |
    • References | html | pdf |
  • 1.9. Atomic displacement parameters  (pp. 228-242) | html | pdf | chapter contents |
    W. F. Kuhs
    • 1.9.1. Introduction  (p. 228) | html | pdf |
    • 1.9.2. The atomic displacement parameters (ADPs)  (pp. 228-232) | html | pdf |
    • 1.9.3. Site-symmetry restrictions  (p. 232) | html | pdf |
    • 1.9.4. Graphical representation  (pp. 232-242) | html | pdf |
    • 1.9.5. Glossary  (p. 242) | html | pdf |
    • References | html | pdf |
  • 1.10. Tensors in quasiperiodic structures  (pp. 243-264) | html | pdf | chapter contents |
    T. Janssen
    • 1.10.1. Quasiperiodic structures  (pp. 243-245) | html | pdf |
    • 1.10.2. Symmetry  (pp. 245-247) | html | pdf |
    • 1.10.3. Action of the symmetry group  (pp. 247-249) | html | pdf |
    • 1.10.4. Tensors  (pp. 249-255) | html | pdf |
    • 1.10.5. Tables  (pp. 255-264) | html | pdf |
    • References | html | pdf |

• Symmetry aspects of excitations
  • 2.1. Phonons  (pp. 266-293) | html | pdf | chapter contents |
    G. Eckold
    • 2.1.1. Introduction  (p. 266) | html | pdf |
    • 2.1.2. Fundamentals of lattice dynamics in the harmonic approximation  (pp. 266-274) | html | pdf |
    • 2.1.3. Symmetry of lattice vibrations  (pp. 274-291) | html | pdf |
    • 2.1.4. Conclusion  (p. 291) | html | pdf |
    • 2.1.5. Glossary  (pp. 291-292) | html | pdf |
    • References | html | pdf |
  • 2.2. Electrons  (pp. 294-313) | html | pdf | chapter contents |
    K. Schwarz
    • 2.2.1. Introduction  (p. 294) | html | pdf |
    • 2.2.2. The lattice  (p. 294) | html | pdf |
    • 2.2.3. Symmetry operators  (pp. 294-295) | html | pdf |
    • 2.2.4. The Bloch theorem  (pp. 295-296) | html | pdf |
    • 2.2.5. The free-electron (Sommerfeld) model  (p. 297) | html | pdf |
    • 2.2.6. Space-group symmetry  (pp. 297-298) | html | pdf |
    • 2.2.7. The vector and the Brillouin zone  (p. 298) | html | pdf |
    • 2.2.8. Bloch functions  (p. 299) | html | pdf |
    • 2.2.9. Quantum-mechanical treatment  (pp. 299-300) | html | pdf |
    • 2.2.10. Density functional theory  (pp. 300-301) | html | pdf |
    • 2.2.11. Band-theory methods  (pp. 301-303) | html | pdf |
    • 2.2.12. The linearized augmented plane wave method  (pp. 303-304) | html | pdf |
    • 2.2.13. The local coordinate system  (pp. 304-305) | html | pdf |
    • 2.2.14. Characterization of Bloch states  (pp. 305-307) | html | pdf |
    • 2.2.15. Electric field gradient tensor  (pp. 307-310) | html | pdf |
    • 2.2.16. Examples  (pp. 310-312) | html | pdf |
    • 2.2.17. Conclusion  (p. 312) | html | pdf |
    • References | html | pdf |
  • 2.3. Raman scattering  (pp. 314-328) | html | pdf | chapter contents |
    I. Gregora
    • 2.3.1. Introduction  (p. 314) | html | pdf |
    • 2.3.2. Inelastic light scattering in crystals – basic notions  (pp. 314-315) | html | pdf |
    • 2.3.3. First-order scattering by phonons  (pp. 315-322) | html | pdf |
    • 2.3.4. Morphic effects in Raman scattering  (pp. 322-325) | html | pdf |
    • 2.3.5. Spatial-dispersion effects  (pp. 325-326) | html | pdf |
    • 2.3.6. Higher-order scattering  (pp. 326-327) | html | pdf |
    • 2.3.7. Conclusions  (pp. 327-328) | html | pdf |
    • 2.3.8. Glossary  (p. 328) | html | pdf |
    • References | html | pdf |
  • 2.4. Brillouin scattering  (pp. 329-335) | html | pdf | chapter contents |
    R. Vacher and E. Courtens
    • 2.4.1. Introduction  (p. 329) | html | pdf |
    • 2.4.2. Elastic waves  (pp. 329-330) | html | pdf |
    • 2.4.3. Coupling of light with elastic waves  (p. 330) | html | pdf |
    • 2.4.4. Brillouin scattering in crystals  (pp. 330-331) | html | pdf |
    • 2.4.5. Use of the tables  (p. 331) | html | pdf |
    • 2.4.6. Techniques of Brillouin spectroscopy  (pp. 331-335) | html | pdf |
    • References | html | pdf |

• Symmetry aspects of phase transitions, twinning and domain structures
  • 3.1. Structural phase transitions  (pp. 338-376) | html | pdf | chapter contents |
    J.-C. Tolédano, V. Janovec, V. Kopský, J. F. Scott and P. Boček
    • 3.1.1. Introduction  (pp. 338-340) | html | pdf |
      J.-C. Tolédano
    • 3.1.2. Thermodynamics of structural transitions  (pp. 340-349) | html | pdf |
      J.-C. Tolédano
    • 3.1.3. Equitranslational phase transitions. Property tensors at ferroic phase transitions  (pp. 350-361) | html | pdf |
      V. Janovec and V. Kopský
    • 3.1.4. Example of a table for non-equitranslational phase transitions  (p. 361) | html | pdf |
      J.-C. Tolédano
    • 3.1.5. Microscopic aspects of structural phase transitions and soft modes  (pp. 361-372) | html | pdf |
      J. F. Scott
    • 3.1.6. Group informatics and tensor calculus  (pp. 372-374) | html | pdf |
      V. Kopský and P. Boček
    • 3.1.7. Glossary  (p. 374) | html | pdf |
    • References | html | pdf |
  • 3.2. Twinning and domain structures  (pp. 377-392) | html | pdf | chapter contents |
    V. Janovec, Th. Hahn and H. Klapper
    • 3.2.1. Introduction and history  (pp. 377-378) | html | pdf |
    • 3.2.2. A brief survey of bicrystallography  (pp. 378-379) | html | pdf |
    • 3.2.3. Mathematical tools  (pp. 379-390) | html | pdf |
    • References | html | pdf |
  • 3.3. Twinning of crystals  (pp. 393-448) | html | pdf | chapter contents |
    Th. Hahn and H. Klapper
    • 3.3.1. Crystal aggregates and intergrowths  (pp. 393-394) | html | pdf |
    • 3.3.2. Basic concepts and definitions of twinning  (pp. 394-398) | html | pdf |
    • 3.3.3. Morphological classification, simple and multiple twinning  (pp. 398-399) | html | pdf |
    • 3.3.4. Composite symmetry and the twin law  (pp. 399-402) | html | pdf |
    • 3.3.5. Description of the twin law by black–white symmetry  (pp. 402-403) | html | pdf |
    • 3.3.6. Examples of twinned crystals   (pp. 403-412) | html | pdf |
    • 3.3.7. Genetic classification of twins  (pp. 412-416) | html | pdf |
    • 3.3.8. Lattice aspects of twinning  (pp. 416-422) | html | pdf |
    • 3.3.9. Twinning by merohedry and pseudo-merohedry  (pp. 422-425) | html | pdf |
    • 3.3.10. Twin boundaries  (pp. 426-444) | html | pdf |
    • 3.3.11. Glossary  (pp. 444-445) | html | pdf |
    • References | html | pdf |
  • 3.4. Domain structures  (pp. 449-505) | html | pdf | chapter contents |
    V. Janovec and J. Přívratská
    • 3.4.1. Introduction  (pp. 449-451) | html | pdf |
    • 3.4.2. Domain states  (pp. 451-470) | html | pdf |
    • 3.4.3. Domain pairs: domain twin laws, distinction of domain states and switching  (pp. 470-491) | html | pdf |
    • 3.4.4. Domain twins and domain walls  (pp. 491-502) | html | pdf |
    • 3.4.5. Glossary  (pp. 502-503) | html | pdf |
    • References | html | pdf |

• List of terms and symbols used in this volume  (pp. 507-508) | html | pdf |
  A. Authier

• Resources  | html |