Photoelastic and electro-optic properties of crystals

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書誌事項

Photoelastic and electro-optic properties of crystals

T.S. Narasimhamurty

Plenum Press, c1981

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注記

Bibliography: p. 421-501

Includes indexes

内容説明・目次

内容説明

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.

目次

  • 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 Schoenflies 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. Experimental Methods of Determining the Photoelastic Constants.- 5.1. Optical Behavior of a Solid under a Mechanical Stress, and Neumann's Constants.- 5.2. Derivation of Expressions for the Stress Birefringence in Terms of qij for Cubic and Noncubic Crystals.- 5.2.1. Stress Birefringence in Cubic Crystals.- 5.2.2. Stress Birefringence in Noncubic Crystals.- 5.2.3. Tensor Method of Deriving q?ijkl in Terms of qmnop.- 5.2.4. Expression for the Change of Thickness in Terms of sij for an Orthorhombic Crystal for a Specific Orientation.- 5.3. Experimental Determination of qij and pij by Optical Methods.- 5.3.1. Measurement of Stress Birefringence, and Relative Path Retardation.- 5.3.2. Measurement of Absolute Path Retardation by Interferometric Methods.- 5.3.3. Photoelastic Studies of Optically Active Crystals.- 5.4. Dispersion of qij by Spectroscopic Methods.- 5.4.1. Birefringent Compensator for Studying Very Small Changes in Double Refraction.- 5.4.2. Dispersion of the Individual Stress-Optical Coefficients q11 and q12 of Vitreous Silica.- 5.4.3. Interference-Spectroscope Method of Studying the Absolute Photoelastic Coefficients of Glasses and Their Variation with Wavelength.- 5.5. Elliptic Vibrations and Elliptically Polarized Light.- 5.5.1. Composition of Two Rectangular Vibrations Giving an Ellipse: Use of the Senarmont Compensator.- 5.5.2. Photometric Method for the Measurement of Photoelastic Birefringence.- 5.5.3. The Poincare Sphere and Its Application to the Study of the Photoelastic Behavior of Optically Active Crystals.- 5.6. Ultrasonic Methods of Studying the Elasto-Optic Behavior of Crystals.- 5.6.1. Introduction.- 5.6.2. Mueller's Theory.- 5.6.3. Experimental Determination of Pij/pkl by Three Different Methods Due to Mueller.- 5.6.4. Pettersen's Method of Determining Pij/pkl.- 5.6.5. Bragg Diffraction Method of Determining the Individual Values of pij.- 5.6.6. Borrelli and Miller's Method of Determining the pij of Glass.- 5.6.7. Technological Applications of the Acousto-Optic Effect.- 5.7. Brillouin Scattering and Photoelasticity of Crystals.- 6. Atomistic Theory of Photoelasticity of Cubic Crystals.- 6.1. Introduction.- 6.2. Mueller's Theory-A Brief Survey.- 6.3. Effect of Hydrostatic Pressure on the Index of Refraction n
  • The Strain Polarizability Constant ?0.- 6.4. Anisotropy of Rj and ?itj.- 6.5. Thermo-Optic Behavior of Crystals and Photoelastic behavior.- 6.6. Pockels' Photoelastic Groups in Cubic Crystals and Mueller's Theory.- 6.7. Photoelastic Dispersion in Cubic Crystals
  • ?0 as a Function of Crystalline Material, Wavelength of Light, and Temperature.- 6.8. Effect of Elastic Deformation on the Oscillator Strengths and Dispersion Frequencies of Optical Electrons.- 6.9. Temperature Dependence of Stress-Optical Dispersion.- 6.10. Reversal of the Sign of Stress Birefringence in Pure and Mixed Crystals.- 6.10.1. Pure Crystals.- 6.10.2. Mixed Crystals of KCl and KBr.- 6.11. Stress-Optical and Strain-Optical Isotropy in Cubic Crystals.- 6.12. Optic Axial Angle and Its Dispersion in Stressed Cubic Crystals of T and Th Classes.- 7. Piezoelectricity.- 7.1. Introduction.- 7.2. Direct and Converse Piezoelectric Effects.- 7.3. Mathematical Formulation, Piezoelectric Constants dijk in Tensor Notation, and dij in Two-Suffix Notation
  • Relation between dijl and dij.- 7.4. Deduction of the Surviving dijk for Some Crystal Classes by Tensor Method, and the dij Matrices for the 21 Noncentrosymmetric Classes.- 7.5. Concluding Remarks.- 8. Electro-Optic Effects in Crystals: Pockels Linear Electro-Optic and Kerr Quadratic Electro-Optic Effects.- 8.1. Introduction.- 8.2. Demonstration of the Electro-Optic Effects, Linear and Quadratic.- 8.3. Historical Survey.- 8.3.1. Earlier Work.- 8.3.2. More Recent Work.- 8.4. Pockels' Phenomenological Theory of the Linear Electro-Optic Effect in Three- and Two-Suffix Notations, Rijk and rij.- 8.5. Derivation of the Relation between the Linear Electro-Optic Constants of a Crystal: Free and Clamped Constants.- 8.5.1. Discussion: Primary and Secondary Electro-Optic Effects, and Clamped and Unclamped Electro-Optic Coefficients.- 8.5.2. Methods of Obtaining the Primary and Secondary Linear Electro-Optic Effects.- 8.6. Kerr Quadratic Electro-Optic Effect: Pockels' Phenomenological Theory.- 8.7. Crystal Symmetry and the Number of Surviving Linear Electro-Optic Coefficients Rijk and rij and Their Deduction by Tensor Method: rij Matrices for the 21 Noncentrosymmetric Classes.- 8.7.1. Crystal Symmetry and the Surviving Linear Electro-Optic Constants.- 8.7.2. Tensor Method of Deducing the Nonvanishing Independent Rijk.- 8.8. Derivation of the Expressions for ? = f(rij) for Some Typical Crystal Classes and Orientations.- 8.8.1. Cubic System: Classes 23(T) and $$\bar 43m$$ (Td).- 8.8.2. Tetragonal System: Class $$\bar 42m$$ (D2d).- 8.8.3. Trigonal System: Class 32 (D3).- 8.9. Experimental Methods of Determining rij.- 8.9.1. General Description and Application to Some Typical Crystal Classes.- 8.9.2. Some Experimental Methods.- 8.9.3. Methods of Applying the Electric Field to the Crystal Prism.- 8.9.4. Experimental Determination of rij in Some Specific Cases of Crystals.- 8.10. Some Points of Interest on the Use of the Pockels Effect in Crystals, and Half-Wave Voltage V?/2.- 8.11. Some Technological Applications of Pockels Cells (Linear Electro-Optic Devices).- 8.11.1. Use of the Electro-Optic Effect in Technology.- 8.11.2. Some Applications of Electro-Optic Devices.- Author Index.

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