- Артикул:00-01038469
- Автор: Vitalij Pecharsky, Peter Zavalij
- ISBN: 978-0-387-09578-3
- Обложка: Мягкая обложка
- Издательство: Springer-Science+Business Media (все книги издательства)
- Страниц: 768
- Год: 2009
- Вес: 1914 г
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Издание на английском языке
Without a doubt, crystals such as diamonds, emeralds and rubies, whose beauty has been exposed by jewelry-makers for centuries, are enjoyed by everybody for their perfect shapes and astonishing range of colors. Far fewer people take pleasure in the internal harmony - atomic structure - which defines shapes and other properties of crystals but remains invisible to the naked eye. Ordered atomic structures are present in a variety of common materials, for example, metals, sand, rocks or ice, in addition to the easily recognizable precious stones. The former usually consist of many tiny crystals and therefore, are called polycrystals, for example metals and ice, or powders, such as sand and snow. Besides external shapes and internal structures, the beauty of crystals can be appreciated from an infinite number of distinct diffraction patterns they form upon interaction with certain types of waves, for example, X-rays. Similarly, the beauty of the sea is largely defined by a continuously changing but distinctive patterns formed by waves on the water’s surface
Contents
1 Fundamentals of Crystalline State and Crystal Lattice
1.1 Crystalline State
1.2 Crystal Lattice and Unit Cell
1.3 Shape of the Unit Cell
1.4 Crystallographic Planes, Directions, and Indices
1.4.1 Crystallographic Planes
1.4.2 Crystallographic Directions
1.5 Reciprocal Lattice
1.6 Additional Reading
1.7 Problems
2 Finite Symmetry Elements and Crystallographic Point Groups
2.1 Content of the Unit Cell
2.2 Asymmetric Part of the Unit Cell
2.3 Symmetry Operations and Symmetry Elements
2.4 Finite Symmetry Elements
2.4.1 Onefold Rotation Axis and Center of Inversion
2.4.2 Twofold Rotation Axis andMirror Plane
2.4.3 Threefold Rotation Axis and Threefold Inversion Axis
2.4.4 Fourfold Rotation Axis and Fourfold Inversion Axis
2.4.5 Sixfold Rotation Axis and Sixfold Inversion Axis
2.5 Interaction of Symmetry Elements
2.5.1 Generalization of Interactions Between Finite Symmetry Elements
2.5.2 Symmetry Groups
2.6 Fundamentals of Group Theory
2.7 Crystal Systems
2.8 Stereographic Projection
2.9 Crystallographic Point Groups
2.10 Laue Classes
2.11 Selection of a Unit Cell and Bravais Lattices
2.12 Additional Reading
2.13 Problems
3 Infinite Symmetry Elements and Crystallographic Space Groups
3.1 Glide Planes
3.2 Screw Axes
3.3 Interaction of Infinite Symmetry Elements
3.4 Crystallographic Space Groups
3.4.1 Relationships Between Point Groups and Space Groups
3.4.2 Full International Symbols of Crystallographic Space Groups
3.4.3 Visualization of Space-Group Symmetry in Three Dimensions
3.4.4 Space Groups in Nature
3.5 International Tables for Crystallography
3.6 Equivalent Positions (Sites)
3.6.1 General and Special Equivalent Positions
3.6.2 Special Sites with Points Located on Mirror Planes
3.6.3 Special Sites with Points Located on Rotation and Inversions Axes
3.6.4 Special Sites with Points Located on Centers of Inversion
3.7 Additional Reading
3.8 Problems
4 Formalization of Symmetry
4.1 Symbolic Representation of Symmetry
4.1.1 Finite Symmetry Operations
4.1.2 Infinite Symmetry Operations
4.2 Algebraic Treatment of Symmetry Operations
4.2.1 Transformation of Coordinates of a Point
4.2.2 Rotational Transformations of Vectors
4.2.3 Translational Transformations of Vectors
4.2.4 Combined Symmetrical Transformations of Vectors
4.2.5 Augmentation of Matrices
4.2.6 Algebraic Representation of Crystallographic Symmetry
4.2.7 Interaction of Symmetry Operations
4.3 Additional Reading
4.4 Problems
5 Nonconventional Symmetry
5.1 Commensurate Modulation
5.2 Incommensurate Modulation
5.3 Composite Crystals
5.4 Symmetry of Modulated Structures
5.5 Quasicrystals
5.6 Additional Reading
5.7 Problems
6 Properties, Sources, and Detection of Radiation
6.1 Nature of X-Rays
6.2 Production of X-Rays
6.2.1 Conventional Sealed X-Ray Sources
6.2.2 Continuous and Characteristic X-Ray Spectra
6.2.3 Rotating Anode X-Ray Sources
6.2.4 Synchrotron Radiation Sources
6.3 Other Types of Radiation
6.4 Detection of X-Rays
6.4.1 Detector Efficiency, Linearity, Proportionality and Resolution
6.4.2 Classification of Detectors
6.4.3 Point Detectors
6.4.4 Line and Area Detectors
6.5 Additional Reading
6.6 Problems
7 Fundamentals of Diffraction
7.1 Scattering by Electrons, Atoms and Lattices
7.1.1 Scattering by Electrons
7.1.2 Scattering by Atoms and Atomic Scattering Factor
7.1.3 Scattering by Lattices
7.2 Geometry of Diffraction by Lattices
7.2.1 Laue Equations
7.2.2 Braggs’ Law
7.2.3 Reciprocal Lattice and Ewald’s Sphere
7.3 Additional Reading
7.4 Problems
8 The Powder Diffraction Pattern
8.1 Origin of the Powder Diffraction Pattern
8.2 Representation of Powder Diffraction Patterns
8.3 Understanding of Powder Diffraction Patterns
8.4 Positions of Powder Diffraction Peaks
8.4.1 Peak Positions as a Function of Unit Cell Dimensions
8.4.2 Other Factors Affecting Peak Positions
8.5 Shapes of Powder Diffraction Peaks
8.5.1 Peak-Shape Functions
8.5.2 Peak Asymmetry
8.6 Intensity of Powder Diffraction Peaks
8.6.1 Integrated Intensity
8.6.2 Scale Factor
8.6.3 Multiplicity Factor
8.6.4 Lorentz-Polarization Factor
8.6.5 Absorption Factor
8.6.6 Preferred Orientation
8.6.7 Extinction Factor
8.7 Additional Reading
8.8 Problems
9 Structure Factor
9.1 Structure Amplitude
9.1.1 Population Factor
9.1.2 Temperature Factor (Atomic Displacement Factor)
9.1.3 Atomic Scattering Factor
9.1.4 Phase Angle
9.2 Effects of Symmetry on the Structure Amplitude
9.2.1 Friedel Pairs and Friedel’s Law
9.2.2 Friedel’s Law and Multiplicity Factor
9.3 Systematic Absences
9.3.1 Lattice Centering
9.3.2 Glide Planes
9.3.3 Screw Axes
9.4 Space Groups and Systematic Absences
9.5 Additional Reading
9.6 Problems
10 Solving the Crystal Structure
10.1 Fourier Transformation
10.2 Phase Problem
10.2.1 Patterson Technique
10.2.2 Direct Methods
10.2.3 Structure Solution from Powder Diffraction Data
10.3 Total Scattering Analysis Using Pair Distribution Function
10.4 Additional Reading
10.5 Problems
11 Powder Diffractometry
11.1 Brief History of the Powder DiffractionMethod
11.2 Beam Conditioning in Powder Diffractometry
11.2.1 Collimation
11.2.2 Monochromatization
11.3 Principles of Goniometer Design in Powder Diffractometry
11.3.1 Goniostats with Strip and Point Detectors
11.3.2 Goniostats with Area Detectors
11.4 Nonambient Powder Diffractometry
11.4.1 Variable Temperature Powder Diffractometry
11.4.2 Principles of Variable Pressure Powder Diffractometry
11.4.3 Powder Diffractometry in High Magnetic Fields
11.5 Additional Reading
11.6 Problems
12 Collecting Quality Powder Diffraction Data
12.1 Sample Preparation
12.1.1 Powder Requirements and Powder Preparation
12.1.2 PowderMounting
12.1.3 Sample Size
12.1.4 Sample Thickness and Uniformity
12.1.5 Sample Positioning
12.1.6 Effects of Sample Preparation on Powder Diffraction Data
12.2 Data Acquisition
12.2.1 Wavelength
12.2.2 Monochromatization
12.2.3 Incident Beam Aperture
12.2.4 Diffracted Beam Aperture
12.2.5 Variable Aperture
12.2.6 Power Settings
12.2.7 Classification of Powder Diffraction Experiments
12.2.8 Step Scan
12.2.9 Continuous Scan
12.2.10 Scan Range
12.3 Quality of Experimental Data
12.3.1 Quality of Intensity Measurements
12.3.2 Factors Affecting Resolution
12.4 Additional Reading
12.5 Problems
13 Preliminary Data Processing and Phase Analysis
13.1 Interpretation of Powder Diffraction Data
13.2 Preliminary Data Processing
13.2.1 Background
13.2.2 Smoothing
13.2.3 K?2 Stripping
13.2.4 Peak Search
13.2.5 Profile Fitting
13.3 Phase Identification and Quantitative Analysis
13.3.1 Crystallographic Databases
13.3.2 Phase Identification
13.3.3 Quantitative Analysis
13.3.4 Phase Contents from Rietveld Refinement
13.3.5 Determination of Amorphous Content or Degree of Crystallinity
13.4 Additional Reading
13.5 Problems
14 Determination and Refinement of the Unit Cell
14.1 The Indexing Problem
14.2 Known Versus Unknown Unit Cell Dimensions
14.3 Indexing: Known Unit Cell
14.3.1 High Symmetry Indexing Example
14.3.2 Other Crystal Systems
14.4 Reliability of Indexing
14.4.1 The FN Figure ofMerit
14.4.2 The M20(MN) Figure ofMerit
14.5 Introduction to Ab Initio Indexing
14.6 Cubic Crystal System
14.6.1 Primitive Cubic Unit Cell: LaB6
14.6.2 Body-Centered Cubic Unit Cell: U3Ni6Si2
14.7 Tetragonal and Hexagonal Crystal Systems
14.7.1 Indexing Example: LaNi4.85 Sn0.15
14.8 Automatic Ab Initio Indexing Algorithms
14.8.1 Indexing in Direct Space
14.8.2 Indexing in Reciprocal Space
14.9 Unit Cell Reduction Algorithms
14.9.1 Delaunay–Ito Transformation
14.9.2 Niggli Reduction
14.10 Automatic Ab Initio Indexing: Computer Codes
14.10.1 TREOR
14.10.2 DICVOL
14.10.3 ITO
14.10.4 Selecting a Solution
14.11 Ab Initio Indexing Examples
14.11.1 Hexagonal Indexing: LaNi4.85Sn0.15
14.11.2 Monoclinic Indexing: (CH3NH3)2Mo7O22
14.11.3 Triclinic Indexing: Fe7(PO4)6
14.11.4 Pseudo-Hexagonal Indexing: LiB(C2O4)2
14.12 Precise Lattice Parameters and Linear Least Squares
14.12.1 Linear Least Squares
14.12.2 Precise Lattice Parameters from Linear Least Squares
14.13 Concluding Remarks
14.14 Additional Reading
14.15 Problems
15 Solving Crystal Structure from Powder Diffraction Data
15.1 Ab Initio Methods of Structure Solution
15.1.1 Conventional Reciprocal Space Methods
15.1.2 Conventional Direct Space Modeling
15.1.3 Unconventional Direct, Reciprocal, and Dual Space Methods
15.1.4 Validation and Completion of the Model
15.2 The Content of the Unit Cell
15.3 Pearson’s Classification
15.4 Finding Structure Factors from Powder Diffraction Data
15.5 Nonlinear Least Squares
15.6 Quality of Profile Fitting
15.6.1 Visual Assessment of the Quality of Profile Fitting
15.6.2 Figures of Merit
15.7 The Rietveld Method
15.7.1 Fundamentals of the Rietveld Method
15.7.2 Classes of Rietveld Refinement Parameters
15.7.3 Restraints, Constraints, and Rigid-Bodies
15.7.4 Figures of Merit and Quality of Rietveld Refinement
15.7.5 Common Problems and How to Deal with Them
15.7.6 Termination of Rietveld Refinement
15.8 Concluding Remarks
15.9 Additional Reading
16 Crystal Structure of LaNi4.85Sn0.15
16.1 Full Pattern Decomposition
16.2 Solving the Crystal Structure
16.3 Rietveld Refinement Using Cu K?1,2 Radiation
16.3.1 Scale Factor and Profile Parameters
16.3.2 Overall Atomic Displacement Parameter
16.3.3 Individual Parameters, Free and Constrained Variables
16.3.4 Anisotropic Atomic Displacement Parameters
16.3.5 Multiple Phase Refinement
16.3.6 Refinement Results
16.4 Rietveld Refinement Using Mo K?1,2 Radiation
16.5 Combined Refinement Using Different Sets of Diffraction Data
17 Crystal Structure of CeRhGe3
17.1 Full Pattern Decomposition
17.2 Solving the Crystal Structure from X-Ray Data
17.2.1 Highest Symmetry Attempt
17.2.2 Low-Symmetry Model
17.3 Solving the Crystal Structure from Neutron Data
17.4 Rietveld Refinement
17.4.1 X-Ray Data, Correct Low Symmetry Model
17.4.2 X-Ray Data, Wrong High-Symmetry Model
17.4.3 Neutron Data
18 Crystal Structure of Nd5Si4
18.1 Full Pattern Decomposition
18.2 Solving the Crystal Structure
18.3 Rietveld Refinement
19 Empirical Methods of Solving Crystal Structures
19.1 Crystal Structure of Gd5Ge4
19.2 Crystal Structure of Gd5Si4
19.3 Crystal Structure of Gd5Si2Ge2
19.4 Rietveld Refinement of Gd5Ge4, Gd5Si4, and Gd5Si2Ge2
19.4.1 Gd5Ge4
19.4.2 Gd5Si4
19.4.3 Gd5Si2Ge2
19.5 Structure–Property Relationships
20 Crystal Structure of NiMnO2(OH)
20.1 Observed Structure Factors from Experimental Data
20.2 Solving the Crystal Structure
20.3 A Few Notes About Using GSAS
20.4 Completion of the Model and Rietveld Refinement
20.4.1 Initial Refinement Steps
20.4.2 Where Is Mn and Where Is Ni?
20.4.3 Finalizing the Refinement of the Model Without Hydrogen
20.4.4 Locating Hydrogen
20.4.5 Combined Rietveld Refinement
21 Crystal Structure of tmaV3O7
21.1 Observed Structure Factors
21.2 Solving the Crystal Structure
21.3 Completion of the Model and Rietveld Refinement
21.3.1 Unrestrained Rietveld Refinement
21.3.2 Rietveld Refinement with Restraints
22 Crystal Structure of ma2Mo7O22
22.1 Possible Model of the Crystal Structure
22.2 Rietveld Refinement and Completion of the Model
23 Crystal Structure of Mn7(OH)3(VO4)4
23.1 Solving the Crystal Structure
23.2 Rietveld Refinement
23.3 Determining Chemical Composition
24 Crystal Structure of FePO4
24.1 Building and Optimizing the Model of the Crystal Structure
24.2 Rietveld Refinement
25 Crystal Structure of Acetaminophen, C8H9NO2
25.1 Ab Initio Indexing and Le Bail Fitting
25.2 Solving the Crystal Structure
25.2.1 Creating a Model
25.2.2 Optimizing the Model (Solving the Structure)
25.3 Restrained Rietveld Refinement
25.4 Chapters 15-25: Additional Reading
25.5 Chapters 15-25: Problems
Index
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