International Tables for Crystallography
Volume D: Physical properties of crystals

Second online edition (2013)   ISBN: 978-1-118-76229-5   doi: 10.1107/97809553602060000113  

Edited by A. Authier

Contents

• Preface to the second edition  (p. xii) | html | pdf |
  André Authier

• Tensorial aspects of physical properties
  • 1.1. Introduction to the properties of tensors  (pp. 3-34) | 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. 72-100) | 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. 92-95) | html | pdf |
    • 1.3.7. Nonlinear dynamic elasticity  (pp. 95-98) | html | pdf |
    • 1.3.8. Glossary  (p. 98) | html | pdf |
    • References | html | pdf |
  • 1.4. Thermal expansion  (pp. 100-105) | html | pdf | chapter contents |
    H. Küppers
    • 1.4.1. Definition, symmetry and representation surfaces  (pp. 100-101) | html | pdf |
    • 1.4.2. Grüneisen relation  (pp. 101-102) | html | pdf |
    • 1.4.3. Experimental methods  (pp. 102-104) | html | pdf |
    • 1.4.4. Relation to crystal structure  (pp. 104-105) | html | pdf |
    • 1.4.5. Glossary  (p. 105) | html | pdf |
    • References | html | pdf |
  • 1.5. Magnetic properties  (pp. 106-153) | html | pdf | chapter contents |
    A. S. Borovik-Romanov, H. Grimmer and M. Kenzelmann
    • 1.5.1. Introduction  (pp. 106-110) | html | pdf |
    • 1.5.2. Magnetic symmetry  (pp. 110-117) | html | pdf |
    • 1.5.3. Phase transitions into a magnetically ordered state  (pp. 117-126) | html | pdf |
    • 1.5.4. Domain structure  (pp. 126-128) | html | pdf |
    • 1.5.5. Weakly non-collinear magnetic structures  (pp. 128-132) | html | pdf |
    • 1.5.6. Reorientation transitions  (pp. 132-133) | html | pdf |
    • 1.5.7. Piezomagnetism  (pp. 133-139) | html | pdf |
    • 1.5.8. Magnetoelectric effect  (pp. 139-145) | html | pdf |
    • 1.5.9. Magnetostriction  (pp. 145-148) | html | pdf |
    • 1.5.10. Connection between Gaussian and SI units  (p. 148) | html | pdf |
    • 1.5.11. Glossary  (p. 149) | html | pdf |
    • References | html | pdf |
  • 1.6. Classical linear crystal optics  (pp. 153-180) | html | pdf | chapter contents |
    A. M. Glazer and K. G. Cox
    • 1.6.1. Introduction  (p. 153) | html | pdf |
    • 1.6.2. Generalized optical, electro-optic and magneto-optic effects  (pp. 153-155) | html | pdf |
    • 1.6.3. Linear optics  (pp. 155-157) | html | pdf |
    • 1.6.4. Practical observation of crystals  (pp. 157-169) | html | pdf |
    • 1.6.5. Optical rotation  (pp. 169-175) | html | pdf |
    • 1.6.6. Linear electro-optic effect  (pp. 175-176) | html | pdf |
    • 1.6.7. The linear photoelastic effect  (pp. 176-179) | html | pdf |
    • 1.6.8. Glossary  (p. 179) | html | pdf |
    • References | html | pdf |
  • 1.7. Nonlinear optical properties  (pp. 181-222) | html | pdf | chapter contents |
    B. Boulanger and J. Zyss
    • 1.7.1. Introduction  (p. 181) | html | pdf |
    • 1.7.2. Origin and symmetry of optical nonlinearities  (pp. 181-186) | html | pdf |
    • 1.7.3. Propagation phenomena  (pp. 186-215) | html | pdf |
    • 1.7.4. Determination of basic nonlinear parameters  (pp. 215-217) | html | pdf |
    • 1.7.5. The main nonlinear crystals  (pp. 217-219) | html | pdf |
    • 1.7.6. Glossary  (p. 219) | html | pdf |
    • References | html | pdf |
  • 1.8. Transport properties  (pp. 223-230) | html | pdf | chapter contents |
    G. D. Mahan
    • 1.8.1. Introduction  (p. 223) | html | pdf |
    • 1.8.2. Macroscopic equations  (p. 223) | html | pdf |
    • 1.8.3. Electrical resistivity  (pp. 223-227) | html | pdf |
    • 1.8.4. Thermal conductivity  (pp. 227-229) | html | pdf |
    • 1.8.5. Seebeck coefficient  (pp. 229-230) | html | pdf |
    • 1.8.6. Glossary  (p. 230) | html | pdf |
    • References | html | pdf |
  • 1.9. Atomic displacement parameters  (pp. 231-245) | html | pdf | chapter contents |
    W. F. Kuhs
    • 1.9.1. Introduction  (p. 231) | html | pdf |
    • 1.9.2. The atomic displacement parameters (ADPs)  (pp. 231-235) | html | pdf |
    • 1.9.3. Site-symmetry restrictions  (p. 235) | html | pdf |
    • 1.9.4. Graphical representation  (pp. 235-245) | html | pdf |
    • 1.9.5. Glossary  (p. 245) | html | pdf |
    • References | html | pdf |
  • 1.10. Tensors in quasiperiodic structures  (pp. 246-270) | html | pdf | chapter contents |
    T. Janssen
    • 1.10.1. Quasiperiodic structures  (pp. 246-248) | html | pdf |
    • 1.10.2. Symmetry  (pp. 248-252) | html | pdf |
    • 1.10.3. Action of the symmetry group  (pp. 252-253) | html | pdf |
    • 1.10.4. Tensors  (pp. 253-262) | html | pdf |
    • 1.10.5. Tables  (pp. 262-268) | html | pdf |
    • References | html | pdf |
  • 1.11. Tensorial properties of local crystal susceptibilities  (pp. 269-283) | html | pdf | chapter contents |
    V. E. Dmitrienko, A. Kirfel and E. N. Ovchinnikova
    • 1.11.1. Introduction  (pp. 269-270) | html | pdf |
    • 1.11.2. Symmetry restrictions on local tensorial susceptibility and forbidden reflections  (pp. 270-272) | html | pdf |
    • 1.11.3. Polarization properties and azimuthal dependence  (pp. 272-274) | html | pdf |
    • 1.11.4. Physical mechanisms for the anisotropy of atomic X-ray susceptibility  (p. 274) | html | pdf |
    • 1.11.5. Non-resonant magnetic scattering  (p. 275) | html | pdf |
    • 1.11.6. Resonant atomic factors: multipole expansion  (pp. 275-280) | html | pdf |
    • 1.11.7. Glossary  (p. 281) | html | pdf |
    • References | html | pdf |

• Symmetry aspects of excitations
  • 2.1. Phonons  (pp. 286-313) | html | pdf | chapter contents |
    G. Eckold
    • 2.1.1. Introduction  (p. 286) | html | pdf |
    • 2.1.2. Fundamentals of lattice dynamics in the harmonic approximation  (pp. 286-294) | html | pdf |
    • 2.1.3. Symmetry of lattice vibrations  (pp. 294-311) | html | pdf |
    • 2.1.4. Conclusion  (p. 311) | html | pdf |
    • 2.1.5. Glossary  (pp. 311-312) | html | pdf |
    • References | html | pdf |
  • 2.2. Electrons  (pp. 314-333) | html | pdf | chapter contents |
    K. Schwarz
    • 2.2.1. Introduction  (p. 314) | html | pdf |
    • 2.2.2. The lattice  (p. 314) | html | pdf |
    • 2.2.3. Symmetry operators  (pp. 314-315) | html | pdf |
    • 2.2.4. The Bloch theorem  (pp. 315-316) | html | pdf |
    • 2.2.5. The free-electron (Sommerfeld) model  (p. 317) | html | pdf |
    • 2.2.6. Space-group symmetry  (pp. 317-318) | html | pdf |
    • 2.2.7. The vector and the Brillouin zone  (p. 318) | html | pdf |
    • 2.2.8. Bloch functions  (p. 319) | html | pdf |
    • 2.2.9. Quantum-mechanical treatment  (pp. 319-320) | html | pdf |
    • 2.2.10. Density functional theory  (pp. 320-321) | html | pdf |
    • 2.2.11. Band-theory methods  (pp. 321-323) | html | pdf |
    • 2.2.12. The linearized augmented plane wave method  (pp. 323-324) | html | pdf |
    • 2.2.13. The local coordinate system  (pp. 324-325) | html | pdf |
    • 2.2.14. Characterization of Bloch states  (pp. 325-327) | html | pdf |
    • 2.2.15. Electric field gradient tensor  (pp. 327-330) | html | pdf |
    • 2.2.16. Examples  (pp. 330-332) | html | pdf |
    • 2.2.17. Conclusion  (p. 332) | html | pdf |
    • References | html | pdf |
  • 2.3. Raman scattering  (pp. 334-348) | html | pdf | chapter contents |
    I. Gregora
    • 2.3.1. Introduction  (p. 334) | html | pdf |
    • 2.3.2. Inelastic light scattering in crystals – basic notions  (pp. 334-335) | html | pdf |
    • 2.3.3. First-order scattering by phonons  (pp. 335-342) | html | pdf |
    • 2.3.4. Morphic effects in Raman scattering  (pp. 342-345) | html | pdf |
    • 2.3.5. Spatial-dispersion effects  (pp. 345-346) | html | pdf |
    • 2.3.6. Higher-order scattering  (pp. 346-347) | html | pdf |
    • 2.3.7. Conclusions  (pp. 347-348) | html | pdf |
    • 2.3.8. Glossary  (p. 348) | html | pdf |
    • References | html | pdf |
  • 2.4. Brillouin scattering  (pp. 349-355) | html | pdf | chapter contents |
    R. Vacher and E. Courtens
    • 2.4.1. Introduction  (p. 349) | html | pdf |
    • 2.4.2. Elastic waves  (pp. 349-350) | html | pdf |
    • 2.4.3. Coupling of light with elastic waves  (p. 350) | html | pdf |
    • 2.4.4. Brillouin scattering in crystals  (pp. 350-351) | html | pdf |
    • 2.4.5. Use of the tables  (p. 351) | html | pdf |
    • 2.4.6. Techniques of Brillouin spectroscopy  (pp. 351-355) | html | pdf |
    • References | html | pdf |

• Symmetry aspects of phase transitions, twinning and domain structures
  • 3.1. Structural phase transitions  (pp. 358-396) | html | pdf | chapter contents |
    J.-C. Tolédano, V. Janovec, V. Kopský, J. F. Scott and P. Boček
    • 3.1.1. Introduction  (pp. 358-360) | html | pdf |
      J.-C. Tolédano
    • 3.1.2. Thermodynamics of structural transitions  (pp. 360-369) | html | pdf |
      J.-C. Tolédano
    • 3.1.3. Equitranslational phase transitions. Property tensors at ferroic phase transitions  (pp. 370-381) | html | pdf |
      V. Janovec and V. Kopský
    • 3.1.4. Example of a table for non-equitranslational phase transitions  (p. 381) | html | pdf |
      J.-C. Tolédano
    • 3.1.5. Microscopic aspects of structural phase transitions and soft modes  (pp. 381-392) | html | pdf |
      J. F. Scott
    • 3.1.6. Group informatics and tensor calculus  (pp. 392-394) | html | pdf |
      V. Kopský and P. Boček
    • 3.1.7. Glossary  (p. 394) | html | pdf |
    • References | html | pdf |
  • 3.2. Twinning and domain structures  (pp. 397-412) | html | pdf | chapter contents |
    V. Janovec, Th. Hahn and H. Klapper
    • 3.2.1. Introduction and history  (pp. 397-398) | html | pdf |
    • 3.2.2. A brief survey of bicrystallography  (pp. 398-399) | html | pdf |
    • 3.2.3. Mathematical tools  (pp. 399-410) | html | pdf |
    • References | html | pdf |
  • 3.3. Twinning of crystals  (pp. 413-487) | html | pdf | chapter contents |
    Th. Hahn and H. Klapper
    • 3.3.1. Crystal aggregates and intergrowths  (pp. 413-414) | html | pdf |
    • 3.3.2. Basic concepts and definitions of twinning  (pp. 414-418) | html | pdf |
    • 3.3.3. Morphological classification, simple and multiple twinning  (pp. 418-419) | html | pdf |
    • 3.3.4. Composite symmetry and the twin law  (pp. 419-423) | html | pdf |
    • 3.3.5. Description of the twin law by black–white symmetry  (p. 423) | html | pdf |
    • 3.3.6. Examples of twinned crystals   (pp. 423-436) | html | pdf |
    • 3.3.7. Genetic classification of twins  (pp. 436-440) | html | pdf |
    • 3.3.8. Lattice aspects of twinning  (pp. 440-446) | html | pdf |
    • 3.3.9. Twinning by merohedry and pseudo-merohedry  (pp. 446-450) | html | pdf |
    • 3.3.10. Twin boundaries  (pp. 450-469) | html | pdf |
    • 3.3.11. Effect of twinning in reciprocal space  (pp. 469-477) | html | pdf |
    • 3.3.12. Domain structures (by V. Janovec)  (p. 477) | html | pdf |
    • 3.3.13. Glossary  (pp. 477-478) | html | pdf |
    • References | html | pdf |
  • 3.4. Domain structures  (pp. 484-559) | html | pdf | chapter contents |
    V. Janovec and J. Přívratská
    • 3.4.1. Introduction  (pp. 484-486) | html | pdf |
    • 3.4.2. Domain states  (pp. 486-505) | html | pdf |
    • 3.4.3. Domain pairs: domain twin laws, distinction of domain states and switching  (pp. 505-528) | html | pdf |
    • 3.4.4. Domain twins and domain walls  (pp. 528-539) | html | pdf |
    • 3.4.5. Glossary  (p. 539) | html | pdf |
    • References | html | pdf |

• List of terms and symbols used in this volume  (pp. 545-547) | html | pdf |
  A. Authier

• Resources  | html |