1. Photoelasticity of Crystals. Introduction.- 1.1. Discovery of the Phenomenon of Photoelasticity.- 1.2. Mathematical Formulation and Neumann's Constants. Pockels' Contribution.- 1.3. A Brief Historical Survey.- 1.3.1. Amorphous Solids.- 1.3.2. Cubic Crystals.- 1.3.3. Uniaxial and Biaxial Crystals.- 2. Mathematical Tools, Tensor Properties of Crystals, and Geometrical Crystallography.- 2.1. Linear Transformations.- 2.1.1. Coordinate Transformations.- 2.1.2. Orthogonality Relations.- 2.1.3. The Determinant of the Matrix [?ij] of the Direction-Cosine Scheme.- 2.2. Matrix Algebra.- 2.2.1. Introduction.- 2.2.2. Matrix Algebra and Coordinate Transformations.- 2.2.3. Some Common Types of Matrices.- 2.2.4. Orthogonal Matrix.- 2.2.5. Matrix Operators and Transformation of Tensor Components.- 2.2.6. The Diagonalization of a Matrix.- 2.3. Vectors and Their Transformation Laws.- 2.3.1. Vector Components and Coordinate Transformations.- 2.3.2. Transformations of Coordinate Differences.- 2.3.3. Transformation Law of Vectors.- 2.4. Tensor Nature of Physical Properties of Crystals and the Laws of Transformation of Cartesian Tensors.- 2.4.1. Concept of a Tensor Property and Some Examples of Tensor Properties.- 2.4.2. Transformation Law of Cartesian Tensors.- 2.4.3. Physical Properties and Crystal Symmetry.- 2.5. Crystal Symmetry and Geometrical Crystallography. The 32 Point Groups.- 2.5.1. The 32 Crystallographic Point Groups: Their Symmetry Elements and Some Examples of Crystals.- 2.5.2. Some Symmetry Operations and Their Representation by Symbols.- 2.5.3. The 32 Crystallographic Point Groups in the Schönflies Notation. Geometric Derivation.- 2.6. Symmetry Operations and Their Transformation Matrices.- 2.7. Symmetry Elements of the 32 Point Groups.- 2.7.1. Symmetry Elements of the 32 Point Groups.- 2.7.2. Comments on the 32 Crystallographic Point Groups and Their Symmetry Elements as Listed in Tables 2.3 and 2.5a.- 2.8. Neumann's Principle and Effect of Crystal Symmetry on Physical Properties.- 3. Pockels' Phenomenological Theory of Photoelasticity of Crystals.- 3.1. Introduction.- 3.2. Phenomenological Theory, Stress-Optical and Strain-Optical Constants in Four- and Two-Suffix Notations; qij and pij Matrices for the 32 Crystallographic Point Groups.- 3.2.1. The Assumptions Forming the Basis of Pockels' Theory.- 3.2.2. Mathematical Formulation of Photoelasticity in Terms of qijkl and pijkl.- 3.2.3. Mathematical Formulation of Photoelasticity in Terms of qij and pij.- 3.2.4. Crystal Symmetry and the Number of Photoelastic Constants.- 3.3. Derivation of the Nonvanishing and Independent Photoelastic Constants for the Various Crystal Classes by Different Methods.- 3.3.1. Classical Method.- 3.3.2. Tensor Method.- 3.3.3. Group Theoretical Method.- 4. Elasticity of Crystals.- 4.1. Introduction.- 4.2. Stress and Strain as Tensors.- 4.2.1. Stress as a Second-Rank Tensor.- 4.2.2. Strain as a Second-Rank Tensor.- 4.3. Hooke's Law.- 4.3.1. Generalized Form of Hooke's Law with Elastic Constants cij and sij and the Matrices of cij and sij for the 32 Point Groups.- 4.3.2. Generalized Form of Hooke's Law with Elastic Constants cijkl and sijkl.- 4.3.3. Interrelation between cijkl and cmn and between sijkl and smn.- 4.4. Experimental Methods of Determining cij and sij; Christoffel's Equation and Its Use in Determining cij of Crystals.- 4.5. Ultrasonics.- 4.5.1. Introduction.- 4.5.2. Diffraction of Light by Liquids Excited Ultrasonically.- 4.5.3. Optical Methods of Determining the Ultrasonic Velocities and Elastic Constants of Transparent Solids Employing the Schaefer-Bergmann Pattern, the Hiedemann Pattern, and the Lucas-Biquard Effect.- 4.5.4. Mayer and Hiedemann's Experiments.- 4.5.5. Raman-Nath Theory of Diffraction of Light by Ultrasonic Waves.- 4.5.6. Doppler Effect and Coherence Phenomenon.- 4.6. Brillouin Effect and Crystal Elasticity.- 4.6.1. Introduction.- 4.6.2. Theory of Light Scattering in Birefringent Crystals.- 4.6.3. Concluding Remarks.- 5
This comprehensive treatise reviews, for the first time, all the essential work over the past 160 years on the photoelastic and the closely related linear and quadratic electro-optic effects in isotropic and crystalline mate rials. Emphasis is placed on the phenomenal growth of the subject during the past decade and a half with the advent of the laser, with the use of high-frequency acousto-optic and electro-optic techniques, and with the discovery of new piezoelectric materials, all of which have offered a feedback to the wide interest in these two areas of solid-state physics. The first of these subjects, the photoelastic effect, was discovered by Sir David Brewster in 1815. He first found the effect in gels and subsequently found it in glasses and crystals. While the effect remained of academic interest for nearly a hundred years, it became of practical value when Coker and Filon applied it to measuring stresses in machine parts. With one photograph and subsequent analysis, the stress in any planar model can be determined. By taking sections of a three-dimensional model, complete three-dimensional stresses can be found. Hence this effect is widely applied in industry.
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