Fundamentals of Crystalline State and Crystal Lattice p. 1 Crystalline State p. 2 Crystal Lattice and Unit Cell p. 4 Shape of the Unit Cell p.

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1 Fundamentals of Crystalline State and Crystal Lattice p. 1 Crystalline State p. 2 Crystal Lattice and Unit Cell p. 4 Shape of the Unit Cell p. 7 Crystallographic Planes, Directions, and Indices p. 8 Crystallographic Planes p. 8 Crystallographic Directions p. 11 Reciprocal Lattice p. 11 Additional Reading p. 14 Problems p. 14 Finite Symmetry Elements and Crystallographic Point Groups p. 17 Content of the Unit Cell p. 17 Asymmetric Part of the Unit Cell p. 18 Symmetry Operations and Symmetry Elements p. 19 Finite Symmetry Elements p. 22 Onefold Rotation Axis and Center of Inversion p. 25 Twofold Rotation Axis and Mirror Plane p. 26 Threefold Rotation Axis and Threefold Inversion Axis p. 26 Fourfold Rotation Axis and Fourfold Inversion Axis p. 27 Sixfold Rotation Axis and Sixfold Inversion Axis p. 28 Interaction of Symmetry Elements p. 29 Generalization of Interactions Between Finite Symmetry Elements p. 31 Symmetry Groups p. 32 Fundamentals of Group Theory p. 33 Crystal Systems p. 35 Stereographic Projection p. 36 Crystallographic Point Groups p. 38 Laue Classes p. 40 Selection of a Unit Cell and Bravais Lattices p. 41 Additional Reading p. 47 Problems p. 47 Infinite Symmetry Elements and Crystallographic Space Groups p. 51 Glide Planes p. 51 Screw Axes p. 53 Interaction of Infinite Symmetry Elements p. 54 Crystallographic Space Groups p. 56 Relationships Between Point Groups and Space Groups p. 57 Full International Symbols of Crystallographic Space Groups p. 60 Visualization of Space-Group Symmetry in Three Dimensions p. 62 Space Groups in Nature p. 63 International Tables for Crystallography p. 63

2 Equivalent Positions (Sites) p. 70 General and Special Equivalent Positions p. 70 Special Sites with Points Located on Mirror Planes p. 71 Special Sites with Points Located on Rotation and Inversions Axes p. 72 Special Sites with Points Located on Centers of Inversion p. 73 Additional Reading p. 73 Problems p. 73 Formalization of Symmetry p. 77 Symbolic Representation of Symmetry p. 77 Finite Symmetry Operations p. 77 Infinite Symmetry Operations p. 78 Algebraic Treatment of Symmetry Operations p. 79 Transformation of Coordinates of a Point p. 79 Rotational Transformations of Vectors p. 83 Translational Transformations of Vectors p. 84 Combined Symmetrical Transformations of Vectors p. 85 Augmentation of Matrices p. 87 Algebraic Representation of Crystallographic Symmetry p. 88 Interaction of Symmetry Operations p. 88 Additional Reading p. 93 Problems p. 94 Nonconventional Symmetry p. 97 Commensurate Modulation p. 98 Incommensurate Modulation p. 99 Composite Crystals p. 100 Symmetry of Modulated Structures p. 101 Quasicrystals p. 103 Additional Reading p. 105 Problems p. 105 Properties, Sources, and Detection of Radiation p. 107 Nature of X-Rays p. 109 Production of X-Rays p. 110 Conventional Sealed X-Ray Sources p. 111 Continuous and Characteristic X-Ray Spectra p. 113 Rotating Anode X-Ray Sources p. 116 Synchrotron Radiation Sources p. 117 Other Types of Radiation p. 119 Detection of X-Rays p. 121 Detector Efficiency, Linearity, Proportionality and Resolution p. 121 Classification of Detectors p. 123 Point Detectors p. 125

3 Line and Area Detectors p. 128 Additional Reading p. 131 Problems p. 131 Fundamentals of Diffraction p. 133 Scattering by Electrons, Atoms and Lattices p. 134 Scattering by Electrons p. 136 Scattering by Atoms and Atomic Scattering Factor p. 138 Scattering by Lattices p. 140 Geometry of Diffraction by Lattices p. 142 Laue Equations p. 142 Braggs' Law p. 142 Reciprocal Lattice and Ewald's Sphere p. 144 Additional Reading p. 148 Problems p. 148 The Powder Diffraction Pattern p. 151 Origin of the Powder Diffraction Pattern p. 152 Representation of Powder Diffraction Patterns p. 157 Understanding of Powder Diffraction Patterns p. 159 Positions of Powder Diffraction Peaks p. 162 Peak Positions as a Function of Unit Cell Dimensions p. 163 Other Factors Affecting Peak Positions p. 165 Shapes of Powder Diffraction Peaks p. 168 Peak-Shape Functions p. 170 Peak Asymmetry p. 179 Intensity of Powder Diffraction Peaks p. 182 Integrated Intensity p. 182 Scale Factor p. 185 Multiplicity Factor p. 186 Lorentz-Polarization Factor p. 187 Absorption Factor p. 188 Preferred Orientation p. 194 Extinction Factor p. 199 Additional Reading p. 201 Problems p. 201 Structure Factor p. 203 Structure Amplitude p. 203 Population Factor p. 204 Temperature Factor (Atomic Displacement Factor) p. 206 Atomic Scattering Factor p. 211 Phase Angle p. 215 Effects of Symmetry on the Structure Amplitude p. 217

4 Friedel Pairs and Friedel's Law p. 218 Friedel's Law and Multiplicity Factor p. 220 Systematic Absences p. 220 Lattice Centering p. 221 Glide Planes p. 222 Screw Axes p. 223 Space Groups and Systematic Absences p. 225 Additional Reading p. 235 Problems p. 236 Solving the Crystal Structure p. 239 Fourier Transformation p. 239 Phase Problem p. 245 Patterson Technique p. 246 Direct Methods p. 250 Structure Solution from Powder Diffraction Data p. 253 Total Scattering Analysis Using Pair Distribution Function p. 255 Additional Reading p. 261 Problems p. 262 Powder Diffractometry p. 263 Brief History of the Powder Diffraction Method p. 264 Beam Conditioning in Powder Diffractometry p. 269 Collimation p. 271 Monochromatization p. 274 Principles of Goniometer Design in Powder Diffractometry p. 280 Goniostats with Strip and Point Detectors p. 283 Goniostats with Area Detectors p. 287 Nonambient Powder Diffractometry p. 292 Variable Temperature Powder Diffractometry p. 292 Principles of Variable Pressure Powder Diffractometry p. 294 Powder Diffractometry in High Magnetic Fields p. 296 Additional Reading p. 299 Problems p. 299 Collecting Quality Powder Diffraction Data p. 301 Sample Preparation p. 301 Powder Requirements and Powder Preparation p. 301 Powder Mounting p. 304 Sample Size p. 310 Sample Thickness and Uniformity p. 311 Sample Positioning p. 313 Effects of Sample Preparation on Powder Diffraction Data p. 314 Data Acquisition p. 318

5 Wavelength p. 318 Monochromatization p. 320 Incident Beam Aperture p. 322 Diffracted Beam Aperture p. 325 Variable Aperture p. 329 Power Settings p. 330 Classification of Powder Diffraction Experiments p. 331 Step Scan p. 331 Continuous Scan p. 334 Scan Range p. 336 Quality of Experimental Data p. 338 Quality of Intensity Measurements p. 339 Factors Affecting Resolution p. 342 Additional Reading p. 343 Problems p. 344 Preliminary Data Processing and Phase Analysis p. 347 Interpretation of Powder Diffraction Data p. 348 Preliminary Data Processing p. 353 Background p. 355 Smoothing p. 359 K p. 361 Peak Search p. 363 Profile Fitting p. 366 Phase Identification and Quantitative Analysis p. 377 Crystallographic Databases p. 377 Phase Identification p. 382 Quantitative Analysis p. 390 Phase Contents from Rietveld Refinement p. 394 Determination of Amorphous Content or Degree of Crystallinity p. 395 Additional Reading p. 399 Problems p. 400 Determination and Refinement of the Unit Cell p. 407 The Indexing Problem p. 407 Known Versus Unknown Unit Cell Dimensions p. 410 Indexing: Known Unit Cell p. 412 High Symmetry Indexing Example p. 414 Other Crystal Systems p. 420 Reliability of Indexing p. 421 The F p. 424 The M p. 425 Introduction to Ab Initio Indexing p. 426

6 Cubic Crystal System p. 428 Primitive Cubic Unit Cell: LaB p. 430 Body-Centered Cubic Unit Cell: U p. 432 Tetragonal and Hexagonal Crystal Systems p. 434 Indexing Example: LaNi p. 437 Automatic Ab Initio Indexing Algorithms p. 440 Indexing in Direct Space p. 441 Indexing in Reciprocal Space p. 444 Unit Cell Reduction Algorithms p. 447 Delaunay-Ito Transformation p. 448 Niggli Reduction p. 449 Automatic Ab Initio Indexing: Computer Codes p. 450 TREOR p. 451 DICVOL p. 453 ITO p. 454 Selecting a Solution p. 455 Ab Initio Indexing Examples p. 457 Hexagonal Indexing: LaNi p. 457 Monoclinic Indexing: (CH p. 462 Triclinic Indexing: Fe p. 466 Pseudo-Hexagonal Indexing: LiB(C p. 470 Precise Lattice Parameters and Linear Least Squares p. 473 Linear Least Squares p. 475 Precise Lattice Parameters from Linear Least Squares p. 477 Concluding Remarks p. 485 Additional Reading p. 485 Problems p. 486 Solving Crystal Structure from Powder Diffraction Data p. 497 Ab Initio Methods of Structure Solution p. 497 Conventional Reciprocal Space Methods p. 498 Conventional Direct Space Modeling p. 499 Unconventional Direct, Reciprocal, and Dual Space Methods p. 500 Validation and Completion of the Model p. 505 The Content of the Unit Cell p. 506 Pearson's Classification p. 509 Finding Structure Factors from Powder Diffraction Data p. 510 Nonlinear Least Squares p. 513 Quality of Profile Fitting p. 517 Visual Assessment of the Quality of Profile Fitting p. 518 Figures of Merit p. 521 The Rietveld Method p. 524

7 Fundamentals of the Rietveld Method p. 527 Classes of Rietveld Refinement Parameters p. 529 Restraints, Constraints, and Rigid-Bodies p. 531 Figures of Merit and Quality of Rietveld Refinement p. 538 Common Problems and How to Deal with Them p. 539 Termination of Rietveld Refinement p. 542 Concluding Remarks p. 543 Additional Reading p. 544 Crystal Structure of LaNi p. 547 Full Pattern Decomposition p. 549 Solving the Crystal Structure p. 556 Rietveld Refinement Using Cu K p. 560 Scale Factor and Profile Parameters p. 561 Overall Atomic Displacement Parameter p. 563 Individual Parameters, Free and Constrained Variables p. 564 Anisotropic Atomic Displacement Parameters p. 567 Multiple Phase Refinement p. 567 Refinement Results p. 568 Rietveld Refinement Using Mo K p. 569 Combined Refinement Using Different Sets of Diffraction Data p. 573 Crystal Structure of CeRhGe p. 579 Full Pattern Decomposition p. 579 Solving the Crystal Structure from X-Ray Data p. 583 Highest Symmetry Attempt p. 584 Low-Symmetry Model p. 586 Solving the Crystal Structure from Neutron Data p. 589 Rietveld Refinement p. 595 X-Ray Data, Correct Low Symmetry Model p. 595 X-Ray Data, Wrong High-Symmetry Model p. 598 Neutron Data p. 599 Crystal Structure of Nd p. 603 Full Pattern Decomposition p. 603 Solving the Crystal Structure p. 604 Rietveld Refinement p. 607 Empirical Methods of Solving Crystal Structures p. 611 Crystal Structure of Gd p. 612 Crystal Structure of Gd p. 615 Crystal Structure of Gd p. 616 Rietveld Refinement of Gd p. 620 Gd p. 620 Gd p. 623

8 Gd p. 627 Structure-Property Relationships p. 630 Crystal Structure of NiMnO p. 633 Observed Structure Factors from Experimental Data p. 633 Solving the Crystal Structure p. 636 A Few Notes About Using GSAS p. 640 Completion of the Model and Rietveld Refinement p. 643 Initial Refinement Steps p. 643 Where Is Mn and Where Is Ni? p. 647 Finalizing the Refinement of the Model Without Hydrogen p. 648 Locating Hydrogen p. 648 Combined Rietveld Refinement p. 650 Crystal Structure of tma V p. 655 Observed Structure Factors p. 656 Solving the Crystal Structure p. 658 Completion of the Model and Rietveld Refinement p. 661 Unrestrained Rietveld Refinement p. 662 Rietveld Refinement with Restraints p. 665 Crystal Structure of ma p. 669 Possible Model of the Crystal Structure p. 669 Rietveld Refinement and Completion of the Model p. 672 Crystal Structure of Mn p. 679 Solving the Crystal Structure p. 680 Rietveld Refinement p. 682 Determining Chemical Composition p. 685 Crystal Structure of FePO p. 691 Building and Optimizing the Model of the Crystal Structure p. 692 Rietveld Refinement p. 696 Crystal Structure of Acetaminophen, C p. 703 Ab Initio Indexing and Le Bail Fitting p. 705 Solving the Crystal Structure p. 709 Creating a Model p. 709 Optimizing the Model (Solving the Structure) p. 713 Restrained Rietveld Refinement p. 717 Chapters 15-25: Additional Reading p. 721 Chapters 15-25: Problems p. 723 Index p. 729 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.