Symmetry of Crystals and Molecules /
Ladd, M. F. C.
Symmetry of Crystals and Molecules / Symmetry of Crystals & Molecules Mark Ladd, Formerly Head of Chemical Physics, University of Surrey. - 1st Ed. - United Kingdom Oxford University Press 2014 - xxi, 433 pages : illustrations 26 cm
Includes bibliographical references and index.
Symmetry everywhere -- Introduction -- Looking at symmetry -- Some symmetrical objects -- Denning symmetry -- Symmetry in science -- Symmetry in music -- Symmetry in architecture -- Summary and notation -- Introducing symmetry notation -- References 1 -- Problems 1 -- Geometry of crystals and molecules -- Introduction -- Reference axes -- Crystallographic axes -- Equation of a plane -- Miller indices -- Miller -- Bravais indices -- Zones -- Weiss zone equation -- Addition rule for crystal planes -- Projection of three-dimensional features -- Stereographic projection -- Calculations in stereographic projections -- Axial ratios and interaxial angles -- Molecular geometry: VSEPR theory -- Molecular geometry: experimental determination -- Interatomic distances and angles -- Conformational parameters 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.8.1. 2. 2.1. 2.2. 2.2.1. 2.3. 2.4. 2.4.1. 2.5. 2.5.1. 2.5.2. 2.6. 2.6.1. 2.6.2. 2.6.3. 2.7. 2.8. 2.8.1. 2.8.2. Internal coordinates -- Errors and precision -- Molecular geometry: theoretical determination -- The Schrodinger equation -- Atomic orbitals -- Normalization -- Probability distributions -- Atomic's and p orbitals -- Chemical species and molecular orbitals -- Crystal packing -- References 2 -- Problems 2 -- Point group symmetry -- Introduction -- Symmetry elements, symmetry operations and symmetry operators -- Point groups -- Symmetry in two dimensions -- Rotation symmetry -- Reflection symmetry -- Combinations of symmetry operations in two dimensions -- Two-dimensional systems and point group notation -- Subgroups -- Three-dimensional point groups -- Rotation symmetry in three dimensions -- Reflection symmetry in three dimensions -- Roto-inversion symmetry -- Stereogram representations of three-dimensional point groups -- Crystallographic point groups -- Crystal classes 2.8.3. 2.8.4. 2.9. 2.9.1. 2.9.2. 2.9.3. 2.9.4. 2.9.5. 2.9.6. 2.10. 3. 3.1. 3.2. 3.3. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.4.5. 3.5. 3.5.1. 3.5.2. 3.5.3. 3.5.4. 3.5.5. 3.5.6. Crystal systems -- Derivation of point groups -- Ten simple point groups -- Combinations of symmetry operations in three dimensions -- Euler's construction -- Centrosymmetric point groups (Laue groups) and Laue classes -- Projected symmetry -- Point groups and physical properties of crystals and molecules -- Enantiomorphism and chirality -- Optical properties -- Pyroelectricity and piezoelectricity -- Dipole moments -- Infrared and Raman activity -- Point groups and chemical species -- Point groups R -- Point groups R -- Point groups R1 -- Point groups R2 -- Point groups Rm -- Point groups Rm -- Point groups R2 and 1 -- Non-crystallographic point groups -- Hermann -- Mauguin and Schonflies point group symmetry notations -- Roto-reflection (alternating) axis of symmetry -- The two symmetry notations compared -- Point group recognition -- Matrix representation of point group symmetry operations 3.5.7. 3.6. 3.6.1. 3.6.2. 3.6.3. 3.6.4. 3.6.5. 3.7. 3.7.1. 3.7.2. 3.7.3. 3.7.4. 3.7.5. 3.8. 3.8.1. 3.8.2. 3.8.3. 3.8.4. 3.8.5. 3.8.6. 3.8.7. 3.9. 3.10. 3.10.1. 3.10.2. 3.11. 3.12. Rotation matrices -- Non-periodic crystals -- Quasicrystals -- Buckyballs -- Icosahedral symmetry -- References 3 -- Problems 3 -- Lattices -- Introduction -- One-dimensional lattice -- Two-dimensional lattices -- Choice of unit cell -- Nets in the oblique system -- Nets in the rectangular system -- Square and hexagonal nets -- Unit cell centring -- Three-dimensional lattices -- Triclinic lattice -- Monoclinic lattices -- Orthorhombic lattices -- Tetragonal lattices -- Cubic lattices -- Hexagonal lattice -- Trigonal lattices -- Lattice directions -- Law of rational intercepts: reticular density -- Reciprocal lattice -- Rotational symmetry of lattices -- Lattice transformations -- Bravais lattice unit cell vectors -- Zone symbols and lattice directions -- Coordinates of points in the direct unit cell -- Miller indices -- Reciprocal unit cell vectors 3.12.1. 3.13. 3.13.1. 3.13.2. 3.13.3. 4. 4.1. 4.2. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.3.5. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.4.7. 4.5. 4.6. 4.7. 4.8. 4.9. 4.9.1. 4.9.2. 4.9.3. 4.9.4. 4.9.5. Volume relationships -- Reciprocity of F and I unit cells -- Wigner-Seitz cells -- References 4 -- Problems 4 -- Space groups -- Introduction -- One-dimensional space groups -- Two-dimensional space groups -- Plane groups in the oblique system -- Plane groups in the rectangular system -- Limiting conditions on X-ray reflections -- Plane groups in the square and hexagonal systems -- The seventeen plane groups summarized -- Comments on notation -- Three-dimensional space groups -- Triclinic space groups -- Monoclinic space groups -- Space groups related to point group 2 -- Screw axes -- Space groups related to point group m: glide planes -- Space groups related to point group 2/m -- Summary of the monoclinic space groups -- Half-shift rule -- Orthorhombic space groups -- Change of origin -- Standard and alternative settings of space groups -- Tetragonal space groups 4.9.6. 4.9.7. 4.9.8. 5. 5.1. 5.2. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.3.5. 5.3.6. 5.4. 5.4.1. 5.4.2. 5.4.3. 5.4.4. 5.4.5. 5.4.6. 5.4.7. 5.4.8. 5.4.9. 5.4.10. 5.4.11. 5.4.12. Space groups in the trigonal and hexagonal systems -- Cubic space groups -- Space groups and crystal structures -- Matrix representation of space group symmetry operations -- Black-white and colour symmetry -- Black-white symmetry: potassium chloride -- Colour symmetry -- The international tables and other crystallographic compilations -- The international tables for crystallography, Vol. A -- References 5 -- Problems 5 -- Symmetry and X-ray diffraction -- Introduction -- X-ray diffraction -- Recording X-ray diffraction spectra -- Reciprocal lattice and Ewald's construction -- X-ray intensity data collection -- Laue X-ray photography -- Laue projection symmetry -- X-ray precession photography -- Diffractometric and image plate recording of X-ray intensities -- X-ray scattering by a crystal: the structure factor -- Limiting conditions and the structure factor -- Geometrical structure factor for a centrosymmetric crystal 5.4.13. 5.4.14. 5.4.15. 5.5. 5.6. 5.6.1. 5.6.2. 5.7. 5.7.1. 6. 6.1. 6.2. 6.3. 6.4. 6.5. 6.5.1. 6.5.2. 6.5.3. 6.5.4. 6.6. 6.6.1. 6.6.2. Geometrical structure factor for an I centred unit cell -- Geometrical structure factor for space group P21/c -- Geometrical structure factor for space group Pmd2 -- Geometrical structure factor for space group P63/m -- Using X-ray diffraction information -- References 6 -- Problems 6 -- Elements of group theory -- Introduction -- Group requirements -- Group definitions -- Examples of groups -- Group multiplication tables -- Reference axes in group theory -- Subgroups and cosets -- Similarity transformations, conjugates and symmetry classes -- Representations and character tables -- Representations on position vectors -- Representations on basis vectors -- Representations on atom vectors -- Representations on functions -- A first look at character tables -- Transformation of atomic orbitals -- Orthonormality and orthogonality -- Notation for irreducible representations -- Complex characters 6.6.3. 6.6.4. 6.6.5. 6.6.6. 6.7. 7. 7.1. 7.2. 7.3. 7.4. 7.4.1. 7.4.2. 7.4.3. 7.4.4. 7.5. 7.5.1. 7.5.2. 7.5.3. 7.5.4. 7.6. 7.6.1. 7.6.2. 7.6.3. 7.6.4. Linear groups -- Some properties of character tables -- The great orthogonality theorem -- Reduction of reducible representations -- Constructing a character table -- Summary of the properties of character tables -- Constructing the character table for point group D3h -- Handling complex characters -- Direct products -- Representations on direct product functions -- Formation of a character table by direct products -- How the direct product has been used -- References 7 -- Problems 7 -- Applications of group theory -- Introduction -- Structure and symmetry in molecules and ions -- Application of models -- Application of diffraction studies -- Application of theoretical studies -- Monte Carlo and molecular dynamics techniques -- Symmetry adapted molecular orbitals -- Transition metal compounds: crystal-field and ligand-field theories -- The hexacyanoferrate(II) ion -- Vibrational studies 7.6.5. 7.6.6. 7.7. 7.8. 7.9. 7.9.1. 7.9.2. 7.9.3. 7.10. 7.10.1. 7.10.2. 7.10.3. 8. 8.1. 8.2. 8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.2.6. 8.2.7. 8.3. Symmetry of normal modes -- Boron trifluoride -- Selection rules for infrared and Raman activity: dipole moment and polarizability -- Harmonics and combination vibrations -- Group theory and point groups -- Cyclic point groups -- Dihedral point groups -- Cubic rotation point groups -- Point groups from combinations of operators -- Group theory and space groups -- Triclinic and monoclinic space groups -- Orthorhombic space groups -- Tetragonal space groups -- Cubic space groups -- Factor groups -- Factor group analysis of iron(II) sulphide -- Symmetry ascent and correlation -- Site group and factor group analyses -- References 8 -- Problems 8 -- Computer-assisted studies -- Introduction 8.3.1. 8.3.2. 8.3.3. 8.3.4. 8.4. 8.4.1. 8.4.2. 8.4.3. 8.4.4. 8.5. 8.5.1. 8.5.2. 8.5.3. 8.5.4. 8.6. 8.6.1. 8.6.2. 8.6.3. 9. 9.1. Derivation of point groups -- Recognition of point groups -- Internal and Cartesian coordinates -- Molecular geometry -- Best-fit plane -- Reduction of a representation in point group D6h -- Unit cell reduction -- Matrix operations -- Zone symbol or Miller indices -- Linear least squares -- Reference 9 -- Stereoviews and crystal models -- Stereoviews and stereoviewing -- Crystal models -- References -- Analytical geometry of direction cosines -- Direction cosines of a line -- Angle between two lines -- Vectors and matrices -- Introduction -- Vectors -- Volume of a parallelepiped -- Matrices -- Normal to a plane (hkl) -- Solution of linear simultaneous equations -- Useful matrices -- Stereographic projection of a circle is a circle 9.2. 9.3. 9.4. 9.5. 9.6. 9.7. 9.8. 9.9. 9.10. 9.11. A1. A1.1. A1.2. A2. A2.1. A2.2. A3. A3.1. A3.2. A3.3. A3.4. A3.5. A3.6. A3.7. A4.
This text provides a comprehensive study of the symmetry and geometry of crystals and molecules, starting from first principles. The pre-knowledge assumed is mathematics and physical science to about A-level; additional mathematical topics are discussed in appendices. It is copiously illustrated, including many stereoviews, with instructions both for stereoviewing and for constructing a stereoviewer. Problems for each chapter are provided, with fully worked tutorial solutions.--
Text in English.
9780199670888 0199670889
2013944301
Crystallography.
Symmetry.
Crystallography.
Symmetry.
Kristallsymmetrie.
Molekülsymmetrie.
548.81 / LAN
Symmetry of Crystals and Molecules / Symmetry of Crystals & Molecules Mark Ladd, Formerly Head of Chemical Physics, University of Surrey. - 1st Ed. - United Kingdom Oxford University Press 2014 - xxi, 433 pages : illustrations 26 cm
Includes bibliographical references and index.
Symmetry everywhere -- Introduction -- Looking at symmetry -- Some symmetrical objects -- Denning symmetry -- Symmetry in science -- Symmetry in music -- Symmetry in architecture -- Summary and notation -- Introducing symmetry notation -- References 1 -- Problems 1 -- Geometry of crystals and molecules -- Introduction -- Reference axes -- Crystallographic axes -- Equation of a plane -- Miller indices -- Miller -- Bravais indices -- Zones -- Weiss zone equation -- Addition rule for crystal planes -- Projection of three-dimensional features -- Stereographic projection -- Calculations in stereographic projections -- Axial ratios and interaxial angles -- Molecular geometry: VSEPR theory -- Molecular geometry: experimental determination -- Interatomic distances and angles -- Conformational parameters 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.8.1. 2. 2.1. 2.2. 2.2.1. 2.3. 2.4. 2.4.1. 2.5. 2.5.1. 2.5.2. 2.6. 2.6.1. 2.6.2. 2.6.3. 2.7. 2.8. 2.8.1. 2.8.2. Internal coordinates -- Errors and precision -- Molecular geometry: theoretical determination -- The Schrodinger equation -- Atomic orbitals -- Normalization -- Probability distributions -- Atomic's and p orbitals -- Chemical species and molecular orbitals -- Crystal packing -- References 2 -- Problems 2 -- Point group symmetry -- Introduction -- Symmetry elements, symmetry operations and symmetry operators -- Point groups -- Symmetry in two dimensions -- Rotation symmetry -- Reflection symmetry -- Combinations of symmetry operations in two dimensions -- Two-dimensional systems and point group notation -- Subgroups -- Three-dimensional point groups -- Rotation symmetry in three dimensions -- Reflection symmetry in three dimensions -- Roto-inversion symmetry -- Stereogram representations of three-dimensional point groups -- Crystallographic point groups -- Crystal classes 2.8.3. 2.8.4. 2.9. 2.9.1. 2.9.2. 2.9.3. 2.9.4. 2.9.5. 2.9.6. 2.10. 3. 3.1. 3.2. 3.3. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.4.5. 3.5. 3.5.1. 3.5.2. 3.5.3. 3.5.4. 3.5.5. 3.5.6. Crystal systems -- Derivation of point groups -- Ten simple point groups -- Combinations of symmetry operations in three dimensions -- Euler's construction -- Centrosymmetric point groups (Laue groups) and Laue classes -- Projected symmetry -- Point groups and physical properties of crystals and molecules -- Enantiomorphism and chirality -- Optical properties -- Pyroelectricity and piezoelectricity -- Dipole moments -- Infrared and Raman activity -- Point groups and chemical species -- Point groups R -- Point groups R -- Point groups R1 -- Point groups R2 -- Point groups Rm -- Point groups Rm -- Point groups R2 and 1 -- Non-crystallographic point groups -- Hermann -- Mauguin and Schonflies point group symmetry notations -- Roto-reflection (alternating) axis of symmetry -- The two symmetry notations compared -- Point group recognition -- Matrix representation of point group symmetry operations 3.5.7. 3.6. 3.6.1. 3.6.2. 3.6.3. 3.6.4. 3.6.5. 3.7. 3.7.1. 3.7.2. 3.7.3. 3.7.4. 3.7.5. 3.8. 3.8.1. 3.8.2. 3.8.3. 3.8.4. 3.8.5. 3.8.6. 3.8.7. 3.9. 3.10. 3.10.1. 3.10.2. 3.11. 3.12. Rotation matrices -- Non-periodic crystals -- Quasicrystals -- Buckyballs -- Icosahedral symmetry -- References 3 -- Problems 3 -- Lattices -- Introduction -- One-dimensional lattice -- Two-dimensional lattices -- Choice of unit cell -- Nets in the oblique system -- Nets in the rectangular system -- Square and hexagonal nets -- Unit cell centring -- Three-dimensional lattices -- Triclinic lattice -- Monoclinic lattices -- Orthorhombic lattices -- Tetragonal lattices -- Cubic lattices -- Hexagonal lattice -- Trigonal lattices -- Lattice directions -- Law of rational intercepts: reticular density -- Reciprocal lattice -- Rotational symmetry of lattices -- Lattice transformations -- Bravais lattice unit cell vectors -- Zone symbols and lattice directions -- Coordinates of points in the direct unit cell -- Miller indices -- Reciprocal unit cell vectors 3.12.1. 3.13. 3.13.1. 3.13.2. 3.13.3. 4. 4.1. 4.2. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.3.5. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.4.7. 4.5. 4.6. 4.7. 4.8. 4.9. 4.9.1. 4.9.2. 4.9.3. 4.9.4. 4.9.5. Volume relationships -- Reciprocity of F and I unit cells -- Wigner-Seitz cells -- References 4 -- Problems 4 -- Space groups -- Introduction -- One-dimensional space groups -- Two-dimensional space groups -- Plane groups in the oblique system -- Plane groups in the rectangular system -- Limiting conditions on X-ray reflections -- Plane groups in the square and hexagonal systems -- The seventeen plane groups summarized -- Comments on notation -- Three-dimensional space groups -- Triclinic space groups -- Monoclinic space groups -- Space groups related to point group 2 -- Screw axes -- Space groups related to point group m: glide planes -- Space groups related to point group 2/m -- Summary of the monoclinic space groups -- Half-shift rule -- Orthorhombic space groups -- Change of origin -- Standard and alternative settings of space groups -- Tetragonal space groups 4.9.6. 4.9.7. 4.9.8. 5. 5.1. 5.2. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.3.5. 5.3.6. 5.4. 5.4.1. 5.4.2. 5.4.3. 5.4.4. 5.4.5. 5.4.6. 5.4.7. 5.4.8. 5.4.9. 5.4.10. 5.4.11. 5.4.12. Space groups in the trigonal and hexagonal systems -- Cubic space groups -- Space groups and crystal structures -- Matrix representation of space group symmetry operations -- Black-white and colour symmetry -- Black-white symmetry: potassium chloride -- Colour symmetry -- The international tables and other crystallographic compilations -- The international tables for crystallography, Vol. A -- References 5 -- Problems 5 -- Symmetry and X-ray diffraction -- Introduction -- X-ray diffraction -- Recording X-ray diffraction spectra -- Reciprocal lattice and Ewald's construction -- X-ray intensity data collection -- Laue X-ray photography -- Laue projection symmetry -- X-ray precession photography -- Diffractometric and image plate recording of X-ray intensities -- X-ray scattering by a crystal: the structure factor -- Limiting conditions and the structure factor -- Geometrical structure factor for a centrosymmetric crystal 5.4.13. 5.4.14. 5.4.15. 5.5. 5.6. 5.6.1. 5.6.2. 5.7. 5.7.1. 6. 6.1. 6.2. 6.3. 6.4. 6.5. 6.5.1. 6.5.2. 6.5.3. 6.5.4. 6.6. 6.6.1. 6.6.2. Geometrical structure factor for an I centred unit cell -- Geometrical structure factor for space group P21/c -- Geometrical structure factor for space group Pmd2 -- Geometrical structure factor for space group P63/m -- Using X-ray diffraction information -- References 6 -- Problems 6 -- Elements of group theory -- Introduction -- Group requirements -- Group definitions -- Examples of groups -- Group multiplication tables -- Reference axes in group theory -- Subgroups and cosets -- Similarity transformations, conjugates and symmetry classes -- Representations and character tables -- Representations on position vectors -- Representations on basis vectors -- Representations on atom vectors -- Representations on functions -- A first look at character tables -- Transformation of atomic orbitals -- Orthonormality and orthogonality -- Notation for irreducible representations -- Complex characters 6.6.3. 6.6.4. 6.6.5. 6.6.6. 6.7. 7. 7.1. 7.2. 7.3. 7.4. 7.4.1. 7.4.2. 7.4.3. 7.4.4. 7.5. 7.5.1. 7.5.2. 7.5.3. 7.5.4. 7.6. 7.6.1. 7.6.2. 7.6.3. 7.6.4. Linear groups -- Some properties of character tables -- The great orthogonality theorem -- Reduction of reducible representations -- Constructing a character table -- Summary of the properties of character tables -- Constructing the character table for point group D3h -- Handling complex characters -- Direct products -- Representations on direct product functions -- Formation of a character table by direct products -- How the direct product has been used -- References 7 -- Problems 7 -- Applications of group theory -- Introduction -- Structure and symmetry in molecules and ions -- Application of models -- Application of diffraction studies -- Application of theoretical studies -- Monte Carlo and molecular dynamics techniques -- Symmetry adapted molecular orbitals -- Transition metal compounds: crystal-field and ligand-field theories -- The hexacyanoferrate(II) ion -- Vibrational studies 7.6.5. 7.6.6. 7.7. 7.8. 7.9. 7.9.1. 7.9.2. 7.9.3. 7.10. 7.10.1. 7.10.2. 7.10.3. 8. 8.1. 8.2. 8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.2.6. 8.2.7. 8.3. Symmetry of normal modes -- Boron trifluoride -- Selection rules for infrared and Raman activity: dipole moment and polarizability -- Harmonics and combination vibrations -- Group theory and point groups -- Cyclic point groups -- Dihedral point groups -- Cubic rotation point groups -- Point groups from combinations of operators -- Group theory and space groups -- Triclinic and monoclinic space groups -- Orthorhombic space groups -- Tetragonal space groups -- Cubic space groups -- Factor groups -- Factor group analysis of iron(II) sulphide -- Symmetry ascent and correlation -- Site group and factor group analyses -- References 8 -- Problems 8 -- Computer-assisted studies -- Introduction 8.3.1. 8.3.2. 8.3.3. 8.3.4. 8.4. 8.4.1. 8.4.2. 8.4.3. 8.4.4. 8.5. 8.5.1. 8.5.2. 8.5.3. 8.5.4. 8.6. 8.6.1. 8.6.2. 8.6.3. 9. 9.1. Derivation of point groups -- Recognition of point groups -- Internal and Cartesian coordinates -- Molecular geometry -- Best-fit plane -- Reduction of a representation in point group D6h -- Unit cell reduction -- Matrix operations -- Zone symbol or Miller indices -- Linear least squares -- Reference 9 -- Stereoviews and crystal models -- Stereoviews and stereoviewing -- Crystal models -- References -- Analytical geometry of direction cosines -- Direction cosines of a line -- Angle between two lines -- Vectors and matrices -- Introduction -- Vectors -- Volume of a parallelepiped -- Matrices -- Normal to a plane (hkl) -- Solution of linear simultaneous equations -- Useful matrices -- Stereographic projection of a circle is a circle 9.2. 9.3. 9.4. 9.5. 9.6. 9.7. 9.8. 9.9. 9.10. 9.11. A1. A1.1. A1.2. A2. A2.1. A2.2. A3. A3.1. A3.2. A3.3. A3.4. A3.5. A3.6. A3.7. A4.
This text provides a comprehensive study of the symmetry and geometry of crystals and molecules, starting from first principles. The pre-knowledge assumed is mathematics and physical science to about A-level; additional mathematical topics are discussed in appendices. It is copiously illustrated, including many stereoviews, with instructions both for stereoviewing and for constructing a stereoviewer. Problems for each chapter are provided, with fully worked tutorial solutions.--
Text in English.
9780199670888 0199670889
2013944301
Crystallography.
Symmetry.
Crystallography.
Symmetry.
Kristallsymmetrie.
Molekülsymmetrie.
548.81 / LAN