Fundamentals of Crystalline State p. 1 Introduction p. 1 Crystalline state p. 2 Crystal lattice and crystal structure p. 4 Shape of the unit cell p.

Transcription

1 Preface p. xvii Fundamentals of Crystalline State p. 1 Introduction p. 1 Crystalline state p. 2 Crystal lattice and crystal structure p. 4 Shape of the unit cell p. 6 Content of the unit cell p. 7 Asymmetric part of the unit cell p. 8 Symmetry operations and symmetry elements p. 10 Finite symmetry elements p. 12 One-fold rotation axis and center of inversion p. 16 Two-fold rotation axis and mirror plane p. 16 Three-fold rotation axis and three-fold inversion axis p. 17 Four-fold rotation axis and four-fold inversion axis p. 18 Six-fold rotation axis and six-fold inversion axis p. 18 Interaction of symmetry elements p. 19 Symmetry groups p. 21 Generalization of interactions between finite symmetry elements p. 22 Fundamentals of group theory p. 24 Crystal systems p. 26 Stereographic projections p. 27 Crystallographic point groups p. 29 Laue classes p. 31 Selection of a unit cell and Bravais lattices p. 32 Infinite symmetry elements p. 39 Glide planes p. 40 Screw axes p. 42 Interaction of infinite symmetry elements p. 43 Crystallographic planes, directions and indices p. 45 Indices of planes p. 46 Lattice directions and indices p. 49 Reciprocal lattice p. 50 Crystallographic space groups p. 53 Relationships between space and point groups p. 53 Full international symbols of crystallographic space groups p. 56 Visualization of space group symmetry in three dimensions p. 58 Space groups in nature p. 59 International Tables for Crystallography p. 60 Equivalent positions p. 65 General and special equivalent positions p. 66 Special sites with points located on mirror planes p. 66

2 Special sites with points located on rotation or inversion axes p. 67 Special sites with points located on centers of inversion p. 68 Symbolic description of symmetry operations p. 69 Finite symmetry operations p. 70 Infinite symmetry operations p. 71 Algebraic treatment of symmetry operations p. 72 Transformations of coordinates of a point p. 72 Rotational transformations of vectors p. 77 Translational transformations of vectors p. 78 Combined symmetrical transformations of vectors p. 79 Augmented matrices p. 81 Algebraic representation of crystallographic symmetry p. 82 Interactions between symmetry operations p. 86 Non-conventional symmetry p. 88 Commensurate modulation p. 88 Incommensurate modulation p. 90 Quasicrystals p. 91 Additional reading p. 94 Problems p. 95 Fundamentals of Diffraction p. 99 Introduction p. 99 Properties and sources of radiation p. 102 Nature and properties of x-rays p. 102 Production of x-rays p. 104 Conventional sealed x-ray sources p. 105 Continuous and characteristic x-ray spectra p. 107 Rotating anode x-ray sources p. 110 Synchrotron radiation sources p. 112 Other types of radiation p. 113 Collimation and monochromatization p. 115 Angular divergence and collimation p. 116 Monochromatization p. 119 Detection of x-rays p. 128 Detector efficiency, linearity, proportionality and resolution p. 128 Classification of detectors p. 130 Point detectors p. 132 Line and area detectors p. 136 Scattering by electrons, atoms and lattices p. 138 Scattering by electrons p. 140 Scattering by atoms and scattering factor p. 143 Scattering by lattices p. 145

3 Geometry of diffraction by lattices p. 146 Laue equations and Braggs' law p. 147 Reciprocal lattice and Ewald's sphere p. 149 Origin of the powder diffraction pattern p. 153 Representation of powder diffraction patterns p. 158 Understanding of powder diffraction patterns p. 161 Positions of powder diffraction peaks p. 164 Peak positions as a function of unit cell dimensions p. 164 Other factors affecting peak positions p. 167 Shapes of powder diffraction peaks p. 171 Peak shape functions p. 173 Peak asymmetry p. 182 Intensity of powder diffraction peaks p. 184 Integrated intensity p. 185 Scale factor p. 188 Multiplicity factor p. 189 Lorentz-polarization factor p. 190 Absorption factor p. 193 Preferred orientation p. 196 Extinction factor p. 202 Structure factor p. 203 Structure amplitude p. 203 Population factor p. 204 Temperature factor p. 207 Atomic scattering factor p. 212 Phase angle p. 216 Effects of symmetry on the structure amplitude p. 218 Friedel pairs and Friedel's law p. 219 Friedel's law and multiplicity factor p. 221 Systematic absences p. 222 Space groups and systematic absences p. 227 Fourier transformation p. 237 Phase problem p. 243 Patterson technique p. 245 Direct methods p. 249 Structure solution from powder diffraction data p. 253 Additional reading p. 256 Problems p. 258 Experimental Techniques p. 261 Introduction p. 261 Brief history of the powder diffraction method p. 262

4 Powder diffractometers p. 267 Principles of goniometer design in powder diffractometry p. 269 Goniostats with point detectors p. 273 Goniostats with area detectors p. 276 Safety p. 279 Radiation quantities and terms p. 280 Biological effects of ionizing radiation p. 281 Exposure limits p. 282 Radiation hazards of analytical x-ray systems p. 283 Hazard control measures for analytical x-ray systems p. 284 Sample preparation p. 287 Powder requirements and powder preparation p. 287 Powder mounting p. 290 Sample size p. 295 Sample thickness and uniformity p. 297 Positioning the sample with respect to the goniometer axis p. 298 Effects of sample preparation on powder diffraction data p. 301 Data acquisition p. 305 Wavelength selection p. 305 Monochromatization p. 306 Incident beam aperture p. 309 Diffracted beam aperture p. 313 Variable aperture p. 316 Power settings p. 317 Classification of powder diffraction experiments p. 318 Step scan p. 319 Continuous scan p. 322 Scan range p. 324 Quality of experimental data p. 326 Quality of intensity measurements p. 328 Factors affecting resolution p. 331 Additional reading p. 333 Problems p. 335 Preliminary Data Processing and Phase Analysis p. 339 Introduction p. 339 Interpretation of powder diffraction data p. 340 Preliminary data processing p. 345 Background p. 347 Smoothing p. 352 K[alpha subscript 2] stripping p. 354 Peak search p. 356

5 Profile fitting p. 360 Phase identification and analysis p. 371 Crystallographic databases p. 372 Phase identification and qualitative analysis p. 377 Quantitative analysis p. 384 Additional reading p. 390 Problems p. 392 Unit Cell Determination and Refinement p. 399 Introduction p. 399 The indexing problem p. 399 Known versus unknown unit cell dimensions p. 402 Indexing: known unit cell p. 405 High symmetry indexing example p. 407 Other crystal systems p. 413 Reliability of indexing p. 415 The F[subscript N] figure of merit p. 418 The M[subscript 20] figure of merit p. 419 Introduction to ab initio indexing p. 420 Cubic crystal system p. 422 Primitive cubic unit cell: LaB[subscript 6] p. 425 Body-centered cubic unit cell: U[subscript 3]Ni[subscript 6]Si[subscript 2] p. 427 Tetragonal and hexagonal crystal systems p. 429 Indexing example: LaNi[subscript 4.85]Sn[subscript 0.15] p. 433 Automatic ab initio indexing algorithms p. 436 Trial-and-error method p. 438 Zone search method p. 439 Unit cell reduction algorithms p. 440 Delaunay-Ito reduction p. 441 Niggli reduction p. 442 Automatic ab initio indexing: computer codes p. 443 TREOR p. 444 DICVOL p. 447 ITO p. 448 Selecting a solution p. 449 Ab initio indexing examples p. 451 Hexagonal indexing: LaNi[subscript 4.85]Sn[subscript 0.15] p. 451 Monoclinic indexing: (CH[subscript 3]NH[subscript 3])[subscript 2]Mo[subscript 7]O[subscript 22] p. 457 Triclinic indexing: Fe[subscript 7](PO[subscript 4])[subscript 6] p. 460 Precise lattice parameters and linear least squares p. 464 Linear least squares p. 466 Precise lattice parameters from linear least squares p. 469

6 Epilogue p. 479 Additional reading p. 481 Problems p. 482 Crystal Structure Determination p. 493 Introduction p. 493 Ab initio methods of structure solution p. 494 Conventional reciprocal space techniques p. 495 Conventional direct space techniques p. 495 Unconventional reciprocal and direct space strategies p. 496 Validation and completion of the model p. 499 The content of the unit cell p. 500 Pearson's classification p. 503 Structure factors from powder diffraction data p. 504 Non-linear least squares p. 507 Figures of merit in full pattern decomposition p. 512 Structure solution from powder data p. 515 Crystal structure of LaNi[subscript 4.85]Sn[subscript 0.15] p. 516 Crystal structure of CeRhGe[subscript 3] from x-ray data p. 530 Crystal structure of CeRhGe[subscript 3] from neutron data p. 541 Crystal structure of Nd[subscript 5]Si[subscript 4] p. 548 Crystal structure of NiMnO[subscript 2](OH) p. 553 Crystal structure of tmav[subscript 3]O[subscript 7] p. 561 Crystal structure of ma[subscript 2]Mo[subscript 7]O[subscript 22] p. 568 Crystal structure of Mn[subscript 7](OH)[subscript 3](VO[subscript 4])[subscript 4] p. 571 Crystal structure of FePO[subscript 4] p. 575 Empirical methods of solving crystal structures p. 580 Crystal structure of Gd[subscript 5]Ge[subscript 4] p. 583 Crystal structure of Gd[subscript 5]Si[subscript 4] p. 585 Crystal structure of Gd[subscript 5]Si[subscript 2]Ge[subscript 2] p. 587 Additional reading p. 591 Problems p. 594 Crystal Structure Refinement p. 599 Introduction p. 599 The Rietveld method p. 601 Rietveld method basics p. 603 Classes of Rietveld parameters p. 606 Figures of merit and quality of refinement p. 608 Termination of Rietveld refinement p. 609 Rietveld refinement of LaNi[subscript 4.85]Sn[subscript 0.15] p. 610 Scale factor and profile parameters p. 611 Overall atomic displacement parameter p. 614

7 Individual parameters, free and constrained variables p. 614 Anisotropic atomic displacement parameters p. 617 Multiple phase refinement p. 617 Refinement results p. 618 Different radiation p. 619 Combined refinement using different diffraction data p. 623 Rietveld refinement of CeRhGe[subscript 3] p. 628 Refinement using x-ray diffraction data p. 628 Refinement using neutron diffraction data p. 632 Rietveld refinement of Nd[subscript 5]Si[subscript 4] p. 635 Rietveld refinement using GSAS p. 639 Completion of the model and Rietveld refinement of NiMnO[subscript 2](OH) p. 643 Completion of the model and Rietveld refinement of tmav[subscript 3]O[subscript 7] p. 654 Rietveld refinement and completion of the ma[subscript 2]Mo[subscript 7]O[subscript 22] structure Rietveld refinement of Mn[subscript 7](OH)[subscript 3](VO[subscript 4])[subscript 4] p. 662 p. 669 Rietveld refinement of the monoclinic FePO[subscript 4] p. 677 Rietveld refinement of Gd[subscript 5]Ge[subscript 4], Gd[subscript 5]Si[subscript 4] and Gd[subscript 5]Si[subscript 2]Ge[subscript 2] p. 684 Gd[subscript 5]Ge[subscript 4] p. 685 Gd[subscript 5]Si[subscript 4] p. 687 Gd[subscript 5]Si[subscript 2]Ge[subscript 2] p. 692 Epilogue p. 697 Additional reading p. 699 Problems p. 700 Index p. 703 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.