This collection of problems in physical properties of crystals, first published in 1972, has survived a rigorous test of time and proved its merits for lecturers and students at the Moscow Institute of Steel and Alloys. The problems were compiled on the basis of university textbooks, special monographs, and journal articles. The book is intended for graduate and post-graduate students, as well as for engineers dealing with practical applications of crystals. It has been translated into German and French. N. V. Perelomova, Cand.Sc. (Phys. and Math.), is a lecturer at the Chair of Crystallography of the Moscow Institute of Steel and Alloys. She is the author of the monograph “Acoustic Crystals” and of about 50 published works in crystal physics. M. M. Tagieva, Cand.Sc. (Phys. and Math.), is a senior instructor at the Chair of Crystallography of the Moscow Institute of Steel and Alloys, the author of 32 scientific papers.Contents Preface to English Edition 5 Editor’s Foreword 6 From the Preface to the First Russian Edition 7Preface to the Second Russian Edition 8 List of Symbols 9 1. Matrix Representation of Symmetry Operations and Symmetry Classes 13 2. Symmetry Principle in Crystal Physics. Symmetry of Physical Phenomena and Properties of Crystals 22 3. Physical Properties of Crystals Described by Tensors of Rank One 35 4. Physical Properties of Crystals Described by Tensors of Rank Two 45 5. Stress and Strain in Crystals. Analysis of Stressed State 69 6. Piezoelectric Properties of Crystals. Electrostriction 87 7. Elastic Properties of Crystals. Hook’s law 115 8. Piezoresistivity in Semiconductor Crystals 136 9. Optical Properties of Crystals 151 10. Piezooptical Properties of Crystals 170 11. Electrooptical Properties of Crystals 181 12. Generation of Optical Harmonics 208 13. Rotation of Polarization Plane (Optical Activity) 225 14. Elastic Waves in Crystals 231 15. Thermodynamics of Crystals 274 Answers to Problems 290 References 295 AppendixTable 1. Notation of 32 Symmetry Classes 296 Table 2. Symbols of Symmetry Elements on Stereographic Projections 297 Table 3. Rules for Setting of Crystals According to Symmetry System 298 Table 4. Symmetry Elements and Rules for Choosing Axes for 32 Table 5. Crystallographic Classes 298 Rules for Choosing Crystallophysical Axes 301 Table 6. Matrices of Piezoelectric Moduli (d_{ij}) and Piezoelectric Constants (g_{ij}) 302Table 7. Matrices of Piezoelectric Constants (h_{ij}) and (e_{ij}) for Crystals in Which These Matrices Differ from (d_{ij}) and (g_{ij}) 304Table 8. Matrices of Piezoelectric Moduli (d_{ij}) for Piezoelectric Textures 304Table 9. Matrices of Elastic Compliances (s_{ij}) and Elastic Stiffnesses (c_{ij}) 304Table 10. Matrices of Piezoresistivity Constants (𝚷_{ij}) 308Table 11. Matrices of Piezooptical Constants (𝛑_{ij}) and Elastooptical Constants (p_{kl}) 310Table 12. Matrices of Linear Electrooptical Effect Constants (r_{ij}) 314Table 13. Matrices of Quadratic Electrooptical Effect Constants (R_{ij}) 317Table 13.a Tensor [g_{ij}] 319 Table 14. Reference Data Required for Solving the Problems 321 Table 15. Units of Physical Quantities and Conversion Factors for the Corresponding Units in the SI and CGSE Systems 331 Table 16. Tensor of Physical Properties of Crystals Mentioned in the Book 336