X射線晶體學基礎

內(nèi)容概要

Fundamentals of X-Ray Crystallography is the condensation and crystallization of the author's over 50 years of scientific research and teaching experience. In order to help readers to understand crystallography theory, to establish vivid three dimensional concepts of symmetry operations, simple geometry concepts and methods are employed in the analysis and derivation of the symmetry principles and diffraction theory in this book. This book is divided into three sections: fundamental principle of geometric crystallography, symmetry principle in the microscopic space and fundamental principles of crystal X-ray diffraction.In Section I and Section II, with the application of consistency principle between the distribution of general symmetry equivalent points and the spatial symmetry,the macroscopic and microscopic symmetry and their combinations are intensively analyzed and discussed. The 32 point groups and 230 microscopic symmetry combinations are systematically derived as well. In Section III, based on the relation between crystal lattice and its reciprocal lattice, the mathematical model of reciprocal lattice, Ewald sphere and their relations are adopted in the elucidation of Laue Equation and Bragg Reflection Equation. Several important single crystal diffraction measurement methods, instruments and their applications are also illustrated. In addition, through the principles of systematic absence of reciprocal lattice caused by microscopic translations, the systematic absence principle of diffraction is illustrated. The 120 diffraction groups are derived as well.

書籍目錄

Foreword to the 2nd EditionForeword to the 1st EditionPreface of the 1st EditionSection Ⅰ Fundamental Principles of Geometric CrystallographyChapter 1 Principal Characteristics of Crystalline Solids1.1.1 Periodicity of internal crystal structure1.1.2 Space lattice and crystal lattice1.1.3 Other basic properties of crystalChapter 2 The Identity Theorem of the Facial Angle1.2.1 Apparent crystal face and actual crystal face1.2.2 Identity of the crystal faces angles1.2.3 Crystal projectionsChapter 3 Principles of Crystal Symmetry1.3.1 Symmetry and symmetry in crystals1.3.2 Identity,symmetry center,and reflection plane1.3.3 Symmetry axis(rotation symmetry axis)1.3.4 Rotoinversion axes Lni1.3.5 Rotoreflection axes LnsChapter 4 Combination of Symmetry Elements1.4.1 Symmetry element combinations without the generation of higher-fold rotation axes1.4.2 Symmetry element combinations involving only 1 higher-fold axis1.4.3 Intersection of higher-fold axes with symmetry planes in a perpendicular positionChapter 5 Symmetry Combinations Allowed in Crystals1.5.1 Symmetry combinations involving no more than 1 higher-fold axis1.5.2 Combination of symmetry axes involving more than 1 higher-fold axis1.5.3 Combination of symmetry axes involving more than one high-fold axis with one symmetry planeChapter 6 Orientation of Crystals and Crystal Systems1.6.1 Zone and zone axis1.6.2 Orientation of Crystals1.6.3 Classification of Crystal SystemsChapter 7 Crystal Face Indices and Crystal Edge Indices1.7.1 Crystal Face Indices1.7.2 Crystal Edge Indices1.7.3 Relationship Between Edge Indices and Face IndicesChapter 8 The Equivalent Point Set1.8.1 The General and Special Equivalent Points sets1.8.2 Orientation of the international notations of point groups1.8.3 The deduction of coordinates for equivalent point sets1.8.4 Numbers and coordinates of the equivalent points in equivalent point setsChapter 9 Monomorphous crystal forms, composite crystal forms, and their examples1.9.1 Monomorphous crystal form1.9.2 Composite crystal formSection Ⅱ Symmetry Principle of Microscopic SpaceChapter 1 Translation in Microscopic Space2.1.1 Periodic Translation2.1.2 Translation Symmetry Operation2.1.3 Non-primitive translationChapter 2 Symmetry Elements in Microscopic Space2.2.1 Characteristics of symmetry elements in microscopic space2.2.2 The glide symmetry planes2.2.3 The screw symmetry axis2.2.4 Coordinates of symmetry equivalent points in various screw axesChapter 3 Combinations of Microscopic Symmetry Elements and Periodic Translations2.3.1 Combination of the nonhigh-fold axis of microscopic symmetry elements and the periodic translation2.3.2 Combination of a 4-fold axis and the periodic translation2.3.3 Combination of a 3-fold axis and the periodic translation2.3.4 Combination of 6-fold axis and periodic translationChapter 4 Combination of Symmetry Elements in Microscopic Space2.4.1 General properties of "combination of symmetry elements in microscopic space2.4.2 Perpendicular intersection between the symmetry axis and the symmetry plane2.4.3 Intersections between symmetry planes2.4.4 Combination between 2-fold axes2.4.5 Non-perpendicular intersection between 2-fold axes and symmetry planesChapter 5 Fourteen Bravais Lattices2.5.1 Selection of the unit lattice,primitive lattice,and nonprimitive lattice2.5.2 Fourteen Bravais lattices2.5.3 R lattice in the trigonal crystal system2.5.4 The [-110] orientation in the Bravais lattice of the tetragonal crystal system and [100] and [120] orientations in the Bravais lattice of the hexagonal crystal systemChapter 6 Combinations of Microscopic Symmetry Elements and Nonprimitive Translations2.6.1 Combinations of symmetry center and nonprimitive translations2.6.2 Combination of symmetry planes and nonprimitive translations2.6.3 Glide plane d in a nonprimitive lattice2.6.4 Combination of a 2-fold axis and nonprimitive translation2.6.5 Combination of a 4-fold axis and a nonprimitive translation2.6.6 Three-fold axes in the cubic crystal systemChapter 7 Deduction of the Spatial Symmetry Groups2.7.1 Selection principles of the origin in the coordinate system2.7.2 International notation of the spatial symmetry group2.7.3 Principles for the deduction of the 230 space groups2.7.4 Transposition and rotation of coordinate axes and transformation of space group notation2.7.5 Space groups of the triclinic crystal system and the monoclinic crystal system2.7.6 Space groups of the orthorhombic crystal system2.7.7 Space groups of the tetragonal crystal system2.7.8 Space groups of the hexagonal crystal system2.7.9 Space groups of the trigonal crystal system2.7.10 Space groups of the cubic crystal system2.7.11 Deduction of equivalent point systems from the international notation for space groupsSection Ⅲ Fundamental Principles of Crystal X-ray DiffractionChapter 1 Generation and Basic Characteristics of X-rays3.1.1 Generation of X-rays3.1.2 Basic characteristics of X-raysChapter 2 The Crystal Lattice and the Reciprocal Lattice3.2.1 Establishment of the reciprocal lattice3.2.2 Mathematical expression of the crystal lattice and the reciprocal lattice3.2.3 Example of the crystal lattice and the reciprocal lattice3.2.4 Unit cell and reciprocal unit cell of the crystal latticeChapter 3 Nonprimitive Crystal Lattice and Its Reciprocal Lattice3.3.I Two-dimensional point planes in crystal lattice and their reciprocal lattice point planes3.3.2 The primitive lattice and the reciprocal lattice of a crystal3.3.3 Face-centered C lattice and the reciprocal lattice of a crystal3.3.4 Body-centered I lattice and the reciprocal lattice of a crystal3.3.5 The all-faces-centered F lattice and the reciprocal lattice of a crystal3.3.6 The principle of the partial lattice points' systematic absence in a nonprimitive crystal latticeChapter 4 X-ray Diffraction in Crystals3.4.1 The Laue equation3.4.2 Expression of the Laue equation in a reflection sphere3.4.3 The Bragg equation3.4.4 Diffraction of non-elementary substance structuresChapter 5 Diffraction Sphere and Diffraction Space3.5.1 Reciprocal latticeand reflection sphere3.5.2 Upper limit of the diffraction3.5.3 Symmetry of a diffraction space3.5.4 Systematic extinction of diffractions caused by translation characteristics3.5.5 The 120 diffraction groups3.5.6 Symmetric equivalence of diffractions in diffraction space3.5.7 Transformation among diffraction indices of symmetry equivalence in diffraction space3.5.8 Diffraction of real crystalsChapter 6 Method and Fundamental Principle of Single-crystal Diffraction3.6.1 The Laue method3.6.2 The Oscillation method3.6.3 The Weissenberg method3.6.4 The Precession method3.6.5 Fundamental principles of the 4-circle diffractometerFigure Caption IndexTable Title Index

章節(jié)摘錄

版權頁：插圖：In discussions on crystal projection in chapter 2, we showed that to study the relationships between the crystal faces of a crystal polyhedron, it is necessary to study only the internal point-to-point relationships between a group of points on the plane of the projection sphere. The symmetry pattern formed by the crystalfaces is represented by the symmetry pattern composed of a group of points, and the symmetry relationships between the crystal faces are expressed by the symmetry relationships between the geometric locations of those points. There fore,each of the symmetry classes in geometric crystallography can be represented by a group of points with specific symmetry relationships in which the group of points fully characterizes the symmetric features of the corresponding symmetry class. Here,the symmetry transformation refers to the relationships between the geometric locations of the points. We are more accustomed to calling the 32symmetry classes the 32 point groups.

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