This book, which covers the essence of crystallography, crystal structure analysis,protein crystallography, may be served as the fundamental reading material for undergraduate and postgraduate students who pursue the crystallography major,and it also can be used as the reference book for researchers majored in crystallography.

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.

Foreword to the 2nd Edition

Foreword to the 1st Edition

Preface of the 1st Edition

Section Ⅰ Fundamental Principles of Geometric Crystallography

 Chapter 1 Principal Characteristics of Crystalline Solids

1.1.1 Periodicity of internal crystal structure

1.1.2 Space lattice and crystal lattice

1.1.3 Other basic properties of crystal

 Chapter 2 The Identity Theorem of the Facial Angle

1.2.1 Apparent crystal face and actual crystal face

1.2.2 Identity of the crystal faces angles

1.2.3 Crystal projections

 Chapter 3 Principles of Crystal Symmetry

1.3.1 Symmetry and symmetry in crystals

1.3.2 Identity,symmetry center,and reflection plane

1.3.3 Symmetry axis(rotation symmetry axis)

1.3.4 Rotoinversion axes Lni

1.3.5 Rotoreflection axes Lns

 Chapter 4 Combination of Symmetry Elements

1.4.1 Symmetry element combinations without the generation of higher-fold rotation axes

1.4.2 Symmetry element combinations involving only 1 higher-fold axis

1.4.3 Intersection of higher-fold axes with symmetry planes in a perpendicular position

 Chapter 5 Symmetry Combinations Allowed in Crystals

1.5.1 Symmetry combinations involving no more than 1 higher-fold axis

1.5.2 Combination of symmetry axes involving more than 1 higher-fold axis

1.5.3 Combination of symmetry axes involving more than one high-fold axis with one symmetry plane

 Chapter 6 Orientation of Crystals and Crystal Systems

1.6.1 Zone and zone axis

1.6.2 Orientation of Crystals

1.6.3 Classification of Crystal Systems

 Chapter 7 Crystal Face Indices and Crystal Edge Indices

1.7.1 Crystal Face Indices

1.7.2 Crystal Edge Indices

1.7.3 Relationship Between Edge Indices and Face Indices

 Chapter 8 The Equivalent Point Set

1.8.1 The General and Special Equivalent Points sets

1.8.2 Orientation of the international notations of point groups

1.8.3 The deduction of coordinates for equivalent point sets

1.8.4 Numbers and coordinates of the equivalent points in equivalent point sets

 Chapter 9 Monomorphous crystal forms, composite crystal forms, and their examples

1.9.1 Monomorphous crystal form

1.9.2 Composite crystal form

Section Ⅱ Symmetry Principle of Microscopic Space

 Chapter 1 Translation in Microscopic Space

2.1.1 Periodic Translation

2.1.2 Translation Symmetry Operation

2.1.3 Non-primitive translation

 Chapter 2 Symmetry Elements in Microscopic Space

2.2.1 Characteristics of symmetry elements in microscopic space

2.2.2 The glide symmetry planes

2.2.3 The screw symmetry axis

2.2.4 Coordinates of symmetry equivalent points in various screw axes

 Chapter 3 Combinations of Microscopic Symmetry Elements and Periodic Translations

2.3.1 Combination of the nonhigh-fold axis of microscopic symmetry elements and the periodic translation

2.3.2 Combination of a 4-fold axis and the periodic translation

2.3.3 Combination of a 3-fold axis and the periodic translation

2.3.4 Combination of 6-fold axis and periodic translation

 Chapter 4 Combination of Symmetry Elements in Microscopic Space

2.4.1 General properties of "combination of symmetry elements in microscopic space

2.4.2 Perpendicular intersection between the symmetry axis and the symmetry plane

2.4.3 Intersections between symmetry planes

2.4.4 Combination between 2-fold axes

2.4.5 Non-perpendicular intersection between 2-fold axes and symmetry planes

 Chapter 5 Fourteen Bravais Lattices

2.5.1 Selection of the unit lattice,primitive lattice,and nonprimitive lattice

2.5.2 Fourteen Bravais lattices

2.5.3 R lattice in the trigonal crystal system

2.5.4 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 system

 Chapter 6 Combinations of Microscopic Symmetry Elements and Nonprimitive Translations

2.6.1 Combinations of symmetry center and nonprimitive translations

2.6.2 Combination of symmetry planes and nonprimitive translations

2.6.3 Glide plane d in a nonprimitive lattice

2.6.4 Combination of a 2-fold axis and nonprimitive translation

2.6.5 Combination of a 4-fold axis and a nonprimitive translation

2.6.6 Three-fold axes in the cubic crystal system

 Chapter 7 Deduction of the Spatial Symmetry Groups

2.7.1 Selection principles of the origin in the coordinate system

2.7.2 International notation of the spatial symmetry group

2.7.3 Principles for the deduction of the 230 space groups

2.7.4 Transposition and rotation of coordinate axes and transformation of space group notation

2.7.5 Space groups of the triclinic crystal system and the monoclinic crystal system

2.7.6 Space groups of the orthorhombic crystal system

2.7.7 Space groups of the tetragonal crystal system

2.7.8 Space groups of the hexagonal crystal system

2.7.9 Space groups of the trigonal crystal system

2.7.10 Space groups of the cubic crystal system

2.7.11 Deduction of equivalent point systems from the international notation for space groups

Section Ⅲ Fundamental Principles of Crystal X-ray Diffraction

 Chapter 1 Generation and Basic Characteristics of X-rays

3.1.1 Generation of X-rays

3.1.2 Basic characteristics of X-rays

 Chapter 2 The Crystal Lattice and the Reciprocal Lattice

3.2.1 Establishment of the reciprocal lattice

3.2.2 Mathematical expression of the crystal lattice and the reciprocal lattice

3.2.3 Example of the crystal lattice and the reciprocal lattice

3.2.4 Unit cell and reciprocal unit cell of the crystal lattice

 Chapter 3 Nonprimitive Crystal Lattice and Its Reciprocal Lattice

3.3.I Two-dimensional point planes in crystal lattice and their reciprocal lattice point planes

3.3.2 The primitive lattice and the reciprocal lattice of a crystal

3.3.3 Face-centered C lattice and the reciprocal lattice of a crystal

3.3.4 Body-centered I lattice and the reciprocal lattice of a crystal

3.3.5 The all-faces-centered F lattice and the reciprocal lattice of a crystal

3.3.6 The principle of the partial lattice points' systematic absence in a nonprimitive crystal lattice

 Chapter 4 X-ray Diffraction in Crystals

3.4.1 The Laue equation

3.4.2 Expression of the Laue equation in a reflection sphere

3.4.3 The Bragg equation

3.4.4 Diffraction of non-elementary substance structures

 Chapter 5 Diffraction Sphere and Diffraction Space

3.5.1 Reciprocal latticeand reflection sphere

3.5.2 Upper limit of the diffraction

3.5.3 Symmetry of a diffraction space

3.5.4 Systematic extinction of diffractions caused by translation characteristics

3.5.5 The 120 diffraction groups

3.5.6 Symmetric equivalence of diffractions in diffraction space

3.5.7 Transformation among diffraction indices of symmetry equivalence in diffraction space

3.5.8 Diffraction of real crystals

 Chapter 6 Method and Fundamental Principle of Single-crystal Diffraction

3.6.1 The Laue method

3.6.2 The Oscillation method

3.6.3 The Weissenberg method

3.6.4 The Precession method

3.6.5 Fundamental principles of the 4-circle diffractometer

Figure Caption Index

Table Title Index