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  • Produktbild: Theory of Crystal Space Groups and Lattice Dynamics
  • Produktbild: Theory of Crystal Space Groups and Lattice Dynamics

Theory of Crystal Space Groups and Lattice Dynamics Infra-Red and Raman Optical Processes of Insulating Crystals

Fr. 137.00

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.05.1984

Verlag

Springer Berlin

Seitenzahl

538

Maße (L/B/H)

24.4/17/3.1 cm

Gewicht

966 g

Auflage

1974

Sprache

Englisch

ISBN

978-3-540-13395-7

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.05.1984

Verlag

Springer Berlin

Seitenzahl

538

Maße (L/B/H)

24.4/17/3.1 cm

Gewicht

966 g

Auflage

1974

Sprache

Englisch

ISBN

978-3-540-13395-7

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Theory of Crystal Space Groups and Lattice Dynamics
  • Produktbild: Theory of Crystal Space Groups and Lattice Dynamics
  • Theory of Crystal Space Groups and Infra-Red and Raman Lattice Processes of Insulating Crystals.- A. Scope and plan of the article.- 1. General survey.- 2. Plan of the article: An overview.- B. The crystal space group.- 3. Crystal symmetry — Introduction.- 4. The translation subgroup of a crystal.- ?) Translation operators {? | RL}.- ?) The translation group T.- ?) Structure of T.- ?) Born-Karman boundary conditions.- ?) A property of the {? | t].- 5. Rotational symmetry elements: The crystal point group.- ?) Rotational operators {?|0}.- ?) The point group P.- 6. General symmetry element in a crystal: Space group G.- ?) The operator {?|t(?)}.- ?) Group property of the set {?|t(?)}.- ?) Compatibility of rotation and translation.- ?) The operator {?|t} in non-Cartesian axes.- ?) Order of the space group G.- ?) Normality of translation subgroup T.- ?) Factor group.- ?) Site symmetry.- 7. The space group G as a central extension of T by P.- 8. Symmorphic space groups.- 9. Non-symmorphic space groups.- 10. Some subgroups of a space group.- C. Irreducible representations and vector spaces for finite groups.- 11. Introduction.- 12. Transformation operators on functions.- 13. Group of transformation operators on functions.- 14. Functions and representations.- 15. Irreducible representations and spaces.- 16. Idempotent transformation operators.- 17. Direct products.- ?) Direct products of representations.- ?) Reduction coefficients.- ?) Irreducible representations of direct product groups.- 18. Clebsch-Gordan coefficients.- D. Irreducible representations of the crystal translation group T.- 19. Introduction.- 20. Irreducible representations of T.- 21. The reciprocal lattice.- 22. Irreducible representations of T = T1 ? T2 ? T3.- 23. Wave vector: First Brillouin zone.- 24. Completeness and orthonormality for D(k).- 25. Irreducible vector spaces for T: Bloch vectors.- 26. Direct products in T.- E. Irreducible representations and vector spaces of space groups.- 27. Introduction.- 28. Irreducible representation D(?k)(m) of G.- 29. Representation of T subduced by D(?k)(m) of G.- 30. Transformation of Bloch vectors by rotation operators.- 31. Conjugate representations of T.- 32. Characterization of the subduced representation.- 33. Block structure of D(?k)(m) of G.- 34. Group of the canonical k: G(k).- 35. Irreducibility of the acceptable representations $${D^{\left( {{k_1}} \right)\left( m \right)}}$$ of G(k1).- 36. D(?k)(m) of G induced from D(kl) (m) of G(k1).- 37. Characters of D(?k)(m) of G; induced characters.- 38. Allowable irreducible D(k)(m) : General star with G(k1)= T.- 39. Allowable irreducible D(k)(m): Special star: Little group technique.- 40. Non-allowable irreducible D(k)(?): Little group technique.- 41. Allowable irreducible D(k)(m) as ray representations.- 42. Ray representations of P(k): The covering group P?(k).- 43. Gauge transformations of ray representations.- 44. Relationship between little group and ray representation methods.- 45. Full D(?k)(m) for symmorphic groups: Illustration.- 46. Full D(?k)(m) for non-symmorphic groups.- 47. Complete set of all D(?k)(m) for a space group.- 48. Verification of completeness of D(?k)(m).- 49. Verification of orthonormality relations for D(?k)(m).- 50. Induction of D(k)(m) from sub-space groups.- 51. Compatibility relations for D(?k)(m) and subduction.- F. Reduction coefficients for space groups: Full group methods.- 52. Introduction.- 53. Direct product D(?k)(m) ? D(?k’)(m’).- 54. Symmetrized powers [D(?k)(m)](p).- ?) Ordinary Kronecker powers.- ?) Symmetrized Kronecker powers.- 55. Definition of reduction coefficients.- 56. Wave vector selection rules.- ?) Star reduction coefficients for the ordinary product.- ?) Star reduction coefficients for the symmetrized product.- 57. Determination of reduction coefficients: Method of linear algebraic equations...- 58. Determination of reduction coefficients: Method of the reduction group.- 59. Determination of reduction coefficients: Use of basis functions.- 60. Theory of Clebsch-Gordan coefficients for space groups.- G. Reduction coefficients for space groups: Subgroup methods.- 61. Introduction.- 62. Complete subgroup character system.- 63. Subgroup reduction coefficients.- 64. Comparison of full group and subgroup methods.- 65. Reduction coefficients: A little group technique.- H. Space group theory and classical lattice dynamics.- 66. Introduction.- 67. Equations of motion in the harmonic approximation.- 68. Translation symmetry and particle displacements.- 69. Translation symmetry and force matrix.- 70. General symmetry and particle displacements.- 71. General symmetry and force matrix.- 72. Solution of the equations of motion: Eigenvectors [ej].- 73. Real normal coordinates qj.- 74. Crystal symmetry and the eigenvectors [ej] of [D].- 75. Necessary degeneracy of the eigenvectors [ej].- 76. Crystal symmetry and the transformation of normal coordinates qj.- 77. Fourier transformations.- 78. Fourier transformed displacements and force matrix: The dynamical matrix [D(k)].- 79. Eigenvectors of the dynamical matrix [D(k)].- 80. Complex normal coordinates.- 81. Crystal symmetry and the dynamical matrix [D(k)] and its eigenvectors.- 82. Eigenvectors of [D(k)] as bases for representation D(k)(e) of G(k).- 83. Eigenvectors of [D(k)] as bases for representations D(k)(j) of G(k).- 84. Equivalence of D(k)(e) and D(k)(j).- 85. Necessary degeneracy under G(k) and the eigenvectors of [D(k)].- 86. Complex normal coordinates $$Q\left( {\begin{array}{*{20}{c}} k \\ {{j_\mu }} \end{array}} \right)$$ as bases for the representation D(k)(j) of G(k).- I. Space-time symmetry and classical lattice dynamics.- 87. Introduction.- 88. The antilinear, antiunitary transformation operator K and time reversal.- 89. The complete space-time symmetry group G.- 90. Eigenvectors $$e\left( {\left| {\begin{array}{*{20}{c}} k \\ {{j_\lambda }} \end{array}} \right.} \right)$$ and normal coordinates $$Q\left( {\begin{array}{*{20}{c}} k \\ {{j_\lambda }} \end{array}} \right)$$ as bases for representation of G.- 91. Necessary degeneracy under the full space-time crystal symmetry group G.- 92. Test for reality of D(?k)(j) of G.- 93. Simplification of the reality test of D(?k)(m).- 94. Classification of D(?k)(m) according to reality by use of a new test.- 95. Physically irreducible representations of G as corepresentations of G.- 96. Structure of corepresentations of G: The costar, co ?k.- 97. Corepresentations of G: Class III costar.- 98. Corepresentations of G: Class II costar and general theory.- 99. Corepresentations of G: Class I costar.- 100. Acceptable irreducible corepresentations of G(k) as irreducible ray corepresentations.- 101. Complex normal coordinates as bases for irreducible corepresentations of G.- 102. Eigenvectors of D(k) as bases for irreducible corepresentations of G.- 103. Determination of actual normal mode symmetry in a crystal.- 104. Determination of eigenvectors $$e\left( {\left| {\begin{array}{*{20}{c}} k \\ j \end{array}} \right.} \right)$$ by symmetry: Factorization of the dynamical matrix.- J. Applications of results on symmetry adapted eigenvectors in classical lattice dynamics.- 105. Introduction.- 106. Tensor calculus for lattice dynamics.- ?) Effect of unitary elements.- ?) Effect of antiunitary elements.- 107. Critical points.- ?) Representation theory for the “symmetry set”.- ?) Determination of potential critical points by point symmetry.- 108. Compatibility or connectivity theory for representations.- 109. Construction crystal invariants.- ?) The crystal Hamiltonian: Harmonic and anharmonic.- ?) Force constant coupling parameters.- ?) Anharmonic terms in the potential.- 110. Construction of crystal co variants: Electric moment and polarizability.- K. Space-time symmetry and quantum lattice dynamics.- 111. Introduction.- 112. The many-body electron-ion Hamiltonian.- 113. Born-Oppenheimer adiabatic approximation.- 114. Normal coordinates and quantization.- 115. Lattice eigenfunctions in harmonic adiabatic approximation.- 116. Symmetry of harmonic lattice eigenfunctions: Introduction.- 117. Transformations of products of Hermite polynomials: Symmetrized Kronecker product.- 118. Transformation of the lattice eigenfunction: Summary and generalities.- L. Interaction of radiation and matter: Infra-red absorption and Raman scattering by phonons.- 119. Introduction.- 120. Infra-red absorption by phonons.- ?) Semi-classical radiation theory for ions and electrons.- ?) Transition rate.- ?) Analysis of the transition matrix element for infra-red lattice absorption.- ?) Symmetry of the matrix element for infra-red absorption.- ?) One phonon and multiphonon processes.- 121. Raman scattering by phonons: Generalized Placzek theory.- ?) Hamiltonian.- ?) Transition rate for scattering.- ?) Simplification of the scattering matrix elements for an insulator.- ?) Symmetry of the Raman scattering matrix element.- ?) One phonon and multiphonon processes.- ?) The A • A term in scattering Hamiltonian.- 122. A mutual exclusion selection rule for certain two phonon overtones in infra-red and Raman processes in crystals with an inversion.- 123. Polarization effects in infra-red and Raman lattice processes.- ?) Raman tensor and Clebsch-Gordan coefficients.- ?) Polarization effects in Raman scattering: The Raman tensor in a cubic crystal with inversion.- ?) Polarization effects due to macroscopic electric field.- i) Cubic crystals with inversion symmetry.- ii) Cubic crystals without inversion.- ?) Polarization effects and two phonon bound states.- ?) Polarization in infra-red absorption due to anisotropy.- 124. Aspects of modern quantum theories of lattice Raman scattering and infra-red absorption.- ?) Many-body polarizability theory of Raman scattering.- ?) Many-body theory of infra-red absorption.- ?) Group theory and the thermal phonon Green functions.- ?)Microscopic theory of Raman scattering: Bloch picture.- ?) Microscopic theory of Raman scattering: Exciton picture.- ?) Microscopic theory of Raman scattering: Polariton picture.- ?) Resonance Raman scattering and symmetry breaking.- M. Group theory of diamond and rocksalt space groups.- 125. Introduction.- 126. Geometry of the rocksalt and diamond space groups.- 127. Irreducible representations in rocksalt.- 128. Some wave vector selection rules in rocksalt.- 129. Reduction of ?X(4?) ? ?X(5?) in rocksalt.- 130. Reduction of ?L(3?) ? ?L(3+) in rocksalt.- 131. Additional reduction coefficients in rocksalt.- 132. Irreducible representations D(?)(m), D(?X)(m)D(?L)(m) in diamond.- 133. Reduction coefficients.- ?) Products D(?)(m), D(?X)(m)D(?L)(m) in diamond.- ?) Additional reduction coefficients in diamond.- 134. Clebsch-Gordan coefficients in diamond structure for D(?X)(m) ? D(?X)(m’).- 135. Test of effect of time reversal symmetry in diamond and rocksalt structure.- 136. Connectivity and labelling of irreducible representations in diamond and rocksalt structures: Consequences for selection rules.- N. Phonon symmetry, infra-red absorption and Raman scattering in diamond and rocksalt space groups.- 137. Introduction.- 138. Phonon symmetry in rocksalt and diamond.- 139. Compatibility and phonon symmetry in diamond and rocksalt.- 140. Critical points for phonons in diamond structure: Germanium, silicon and diamond.- Diamond structure: Point ?.- Diamond structure: Point X1.- Point L1.- Point W1.- Line ?.- Line Q.- 141. Two phonon density of states and critical points in diamond structure.- 142. Interpretation of lattice Raman and infra-red spectra in crystals of the diamond structure.- Diamond.- Silicon.- Germanium.- C, Si, Ge.- 143. Symmetry set of critical points in rocksalt structure.- 144. Two phonon density of states and critical points in rocksalt—NaCl.- 145. Interpretation of lattice Raman and infra-red spectra in some rocksalt structure crystals.- NaCl.- NaF.- Other alkali halides.- 146. Polarization effects in two phonon Raman scattering in rocksalt and diamond structures.- ?) Rocksalt.- ?) Diamond.- O. Some aspects of the optical properties of crystals with broken symmetry: Point imperfections and external stresses.- 147. Introduction.- 148. Symmetry group of the imperfect crystal with a point defect.- 149. “Band” phonons in imperfect diamond and rocksalt crystals.- 150. Local phonons in imperfect diamond and rocksalt crystals.- 151. Dynamical aspects of perturbed crystal vibrations.- 152. Infra-red absorption in the perturbed system.- 153. Raman scattering in the perturbed system.- 154. Symmetry breaking and induced lattice absorption and scattering.- ?) Symmetry breaking.- ?) Morphic Effects.- P. Respice, adspice, prospice.- Q. Acknowledgements.- Appendix A: Complete tables of reduction coefficients-selection rules for rocksalt structure Of Oh5 (Tables A.1 to A.11).- Appendix B: Complete tables of reduction coefficients-selection rules for the diamond space group Oh7 (Tables B.1 to B.10).- Appendix C: Illustration of ray representation method: Point X in diamond (Table C.1).- Appendix D: Tables for the zincblende structure: $$F\bar 43m$$; Td2 (Tables D.1 to D.10).- References.- Index of key equations.- Index of tables.- Index of figures.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).