Introduction to X-Ray Powder Diffractometry

by Jenkins, Ron; Snyder, Robert

• ISBN13: 9780471513391
• ISBN10: 0471513393
• Edition: 1st
• Format: Hardcover
• Copyright: 1996-07-12
• Publisher: Wiley-Interscience

Summary

Introduction to X-ray Powder Diffractometry, a collaboration between two internationally known and respected experts in the field, provides invaluable guidance to anyone using X-ray powder diffractometers and diffractometry in materials science, ceramics, the pharmaceutical industry, and elsewhere.

Author Biography

Ron Jenkins is General Manager at the International Centre for Diffraction Data in Newtown Square, Pennsylvania. He has been involved in X-ray research for over thirty years and has received several professional awards. Dr. Jenkins is the author of X-ray Fluorescence Spectrometry, An Introduction to X-ray Spectrometry, and six other books, as well as numerous papers and audio courses. He also wrote the section on X-ray technology in Kirk-Othmer Encyclo-pedia of Chemical Technology.<br> <br> L. Snyder is Professor of Ceramic Science at New York State College of Ceramics at Alfred University, and Director of the university's Institute for Ceramic Superconduc-tivity. A Fellow of the American Ceramic Society, Professor Snyder is the author of two previous books and more than 200 published papers. He is active in numerous professional organizations and speaks frequently at conferences.

Table of Contents

PREFACE	xvii	(2)
CUMULATIVE LISTING OF VOLUMES IN SERIES	xix
CHAPTER 1. CHARACTERISTICS OF X-RADIATION	1	(22)
1.1. Early Development of X-ray Diffraction	1	(1)
1.2. Origin of X-radiation	2	(1)
1.3. Continuous Radiation	3	(2)
1.4. Characteristic Radiation	5	(9)
1.4.1. The Photoelectric Effect	5	(1)
1.4.2. The Auger Effect	5	(2)
1.4.3. Fluorescent Yield	7	(1)
1.4.4. Selection Rules	7	(4)
1.4.5. Nondiagram Lines	11	(1)
1.4.6. Practical Form of the Copper K Spectrum	12	(2)
1.5. Scattering of X-rays	14	(2)
1.5.1. Coherent Scatter	15	(1)
1.5.2. Compton Scatter	15	(1)
1.6. Absorption of X-rays	16	(3)
1.7. Safety Considerations	19	(2)
References	21	(2)
CHAPTER 2. THE CRYSTALLINE STATE	23	(24)
2.1. Introduction to the Crystalline State	23	(3)
2.2. Crystallographic Symmetry	26	(9)
2.2.1. Point Groups and Crystal Systems	28	(2)
2.2.2. The Unit Cell and Bravais Lattices	30	(1)
2.2.3. Reduced Cells	31	(3)
2.2.4. Space Groups	34	(1)
2.3. Space Group Notation	35	(6)
2.3.1. The Triclinic or Anorthic Crystal System	35	(1)
2.3.2. The Monoclinic Crystal System	35	(2)
2.3.3. The Orthorhombic Crystal System	37	(1)
2.3.4. The Tetragonal Crystal System	37	(1)
2.3.5. The Hexagonal and Trigonal Crystal Systems	38	(1)
2.3.6. The Cubic Crystal System	38	(1)
2.3.7. Equivalent Positions	39	(1)
2.3.8. Special Positions and Site Multiplicity	40	(1)
2.4. Space Group Theory	41	(2)
2.5. Crystallographic Planes and Miller Indices	43	(1)
References	44	(3)
CHAPTER 3. DIFFRACTION THEORY	47	(50)
3.1. Diffraction of X-rays	47	(2)
3.2. The Reciprocal Lattice	49	(5)
3.3. The Ewald Sphere of Reflection	54	(3)
3.4. Origin of the Diffraction Pattern	57	(3)
3.4.1. Single Crystal Diffraction	57	(1)
3.4.2. The Powder Diffraction Pattern	58	(2)
3.5. The Location of Diffraction Peaks	60	(4)
3.6. Intensity of Diffraction Peaks	64	(11)
3.6.1. Electron Scattering	64	(1)
3.6.2. The Atomic Scattering Factor	65	(2)
3.6.3. Anomalous Scattering	67	(1)
3.6.4. Thermal Motion	68	(2)
3.6.5. Scattering of X-rays by a Crystal: The Structure Factor	70	(5)
3.7. The Calculated Diffraction Pattern	75	(7)
3.7.1. Factors Affecting the Relative Intensity of Bragg Reflections	76	(4)
3.7.2. The Intensity Equation	80	(2)
3.8. Calculation of the Powder Diffraction Pattern of KCI	82	(3)
3.9. Anisotropic Distortions of the Diffraction Pattern	85	(9)
3.9.1. Preferred Orientation	85	(4)
3.9.2. Crystallite Size	89	(2)
3.9.3. Residual Stress and Strain	91	(3)
References	94	(3)
CHAPTER 4. SOURCES FOR THE GENERATION OF X-RADIATION	97	(24)
4.1. Components of the X-ray Source	97	(1)
4.2. The Line-Voltage Supply	98	(1)
4.3. The High-Voltage Generator	99	(6)
4.3.1. Selection of Operating Conditions	102	(2)
4.3.2. Source Stability	104	(1)
4.4. The Sealed X-ray Tube	105	(9)
4.4.1. Typical X-ray Tube Configuration	106	(3)
4.4.2. Specific Loading	109	(4)
4.4.3. Care of the X-ray Tube	113	(1)
4.5. Effective Line Width	114	(2)
4.6. Spectral Contamination	116	(2)
4.6.1. X-ray Tube Life	117	(1)
4.7. The Rotating Anode X-ray Tube	118	(2)
References	120	(1)
CHAPTER 5. DETECTORS AND DETECTION ELECTRONICS	121	(30)
5.1. X-ray Detectors	121	(1)
5.2. Desired Properties of an X-ray Detector	122	(5)
5.2.1. Quantum-Counting Efficiency	122	(1)
5.2.2. Linearity	123	(2)
5.2.3. Energy Proportionality	125	(1)
5.2.4. Resolution	126	(1)
5.3. Types of Detector	127	(9)
5.3.1. The Gas Proportional Counter	128	(2)
5.3.2. Position-Sensitive Detectors	130	(1)
5.3.3. The Scintillation Detector	131	(1)
5.3.4. The Si(Li) Detector	132	(3)
5.3.5. Other X-ray Detectors	135	(1)
5.4. Pulse Height Selection	136	(2)
5.5. Counting Circuits	138	(2)
5.5.1. The Ratemeter	139	(1)
5.6. Counting Statistics	140	(2)
5.7. Two-Dimensional Detectors	142	(6)
References	148	(3)
CHAPTER 6. PRODUCTION OF MONOCHROMATIC RADIATION	151	(22)
6.1. Introduction	151	(2)
6.2. Angular Dispersion	153	(1)
6.3. Makeup of a Diffractogram	154	(4)
6.3.1. Additional Lines in the Diffractogram	155	(2)
6.3.2. Reduction of Background	157	(1)
6.4. The Beta-Filter	158	(4)
6.4.1. Thickness of the Beta-Filter	159	(1)
6.4.2. Use of Pulse Height Selection to Supplement the Beta-Filter	160	(2)
6.4.3. Placement of the Beta-Filter	162	(1)
6.5. The Proportional Detector and Pulse Height Selection	162	(1)
6.6. Use of Solid State Detectors	163	(1)
6.7. Use of Monochromators	164	(6)
6.7.1. The Diffracted-Beam Monochromator	167	(3)
6.7.2. The Primary-Beam Monochromator	170	(1)
6.8. Comparison of Monochromatization Methods	170	(2)
References	172	(1)
CHAPTER 7. INSTRUMENTS FOR THE MEASUREMENT OF POWDER PATTERNS	173	(32)
7.1. Camera Methods	173	(5)
7.1.1. The Debye-Scherrer/Hull Method	173	(1)
7.1.2. The Gandolfi Camera	174	(3)
7.1.3. The Guinier Camera	177	(1)
7.2. The Powder Diffractometer	178	(2)
7.3. The Seemann-Bohlin Diffractometer	180	(1)
7.4. The Bragg-Brentano Diffractometer	180	(7)
7.5. Systematic Aberrations	187	(8)
7.5.1. The Axial-Divergence Error	187	(4)
7.5.2. The Flat-Specimen Error	191	(2)
7.5.3. Error Due to Specimen Transparency	193	(1)
7.5.4. Error Due to Specimen Displacement	194	(1)
7.6. Selection of Goniometer Slits	195	(7)
7.6.1. Effect of Receiving Slit Width	195	(2)
7.6.2. Effect of the Divergence Slit	197	(5)
References	202	(3)
CHAPTER 8. ALIGNMENT AND MAINTENANCE OF POWDER DIFFRACTOMETERS	205	(26)
8.1. Principles of Alignment	205	(11)
8.1.1. The Rough xyz Alignment	206	(2)
8.1.2. Setting the Takeoff Angle	208	(2)
8.1.3. Setting the Mechanical Zero	210	(2)
8.1.4. Setting the 2:1	212	(1)
8.1.5. Aligning of the Divergence Slit	213	(1)
8.1.6. Tuning of the Monochromator	214	(2)
8.2. Routine Alignment Checks	216	(6)
8.3. Evaluation of the Quality of Alignment	222	(4)
8.4. Troubleshooting	226	(3)
References	229	(2)
CHAPTER 9. SPECIMEN PREPARATION	231	(30)
9.1. General Considerations	231	(2)
9.2. Compositional Variations Between Sample and Specimen	233	(1)
9.3. Absorption Problems	234	(1)
9.4. Problems in Obtaining a Random Specimen	235	(9)
9.4.1. Particle Inhomogeneity	235	(1)
9.4.2. Crystal Habit and Preferred Orientation	236	(4)
9.4.3. Particle Statistics	240	(4)
9.5. Particle Separation and Size Reduction Methods	244	(1)
9.6. Specimen Preparation Procedures	244	(10)
9.6.1. Use of Standard Mounts	246	(1)
9.6.2. Back and Side Loading	247	(2)
9.6.3. Top Loading	249	(1)
9.6.4. The Zero Background Holder Method	249	(2)
9.6.5. Spray-Drying	251	(2)
9.6.6. Use of Aerosols	253	(1)
9.7. Measurement of the Prepared Specimen	254	(4)
9.7.1. Specimen Displacement	254	(1)
9.7.2. Mechanical Methods for Randomizing	255	(2)
9.7.3. Handling of Small Samples	257	(1)
9.7.4. Special Samples	257	(1)
References	258	(3)
CHAPTER 10. ACQUISITION OF DIFFRACTION DATA	261	(26)
10.1. Introduction	261	(1)
10.2. Steps in Data Acquisition	261	(3)
10.3. Typical Data Quality	264	(1)
10.4. Selection of the d-Spacing Range of the Pattern	265	(5)
10.4.1. Choice of the 20 Range	266	(1)
10.4.2. Choice of Wavelength	266	(4)
10.5. Manual Powder Diffractometers	270	(4)
10.5.1. Synchronous Scanning	270	(1)
10.5.2. Use of Ratemeters	270	(2)
10.5.3. Step Scanning	272	(2)
10.6. Automated Powder Diffractometers	274	(7)
10.6.1. Step Scanning with the Computer	277	(2)
10.6.2. Choice of Step Width	279	(1)
10.6.3. Open-Loop and Absolute Encoders	280	(1)
10.7. Use of Calibration Standards	281	(4)
10.7.1. External 20 Standards	282	(1)
10.7.2. Internal 20 and d-Spacing Standards	283	(1)
10.7.3. Quantitative Analysis Standards	283	(1)
10.7.4. Sensitivity Standards	284	(1)
10.7.5. Line Profile Standards	285	(1)
References	285	(2)
CHAPTER 11. REDUCTION OF DATA FROM AUTOMATED POWDER DIFFRACTOMETERS	287	(32)
11.1. Data Reduction Procedures	287	(1)
11.2. Range of Experimental Data to Be Treated	287	(4)
11.2.1. Computer Reduction of Data	288	(3)
11.3. Steps in Data Treatment	291	(14)
11.3.1. Use of Data Smoothing	292	(5)
11.3.2. Background Subtraction	297	(2)
11.3.3. Treatment of the Alpha(2)	299	(1)
11.3.4. Peak Location Methods	300	(5)
11.4. Conversion Errors	305	(3)
11.5. Calibration Methods	308	(2)
11.5.1. 20 Correction Using an External Standard	308	(1)
11.5.2. 20 and d-Spacing Correction Using an Internal Standard	309	(1)
11.5.3. Sensitivity Correction Using an External Intensity Standard	309	(1)
11.6. Evaluation of Data Quality	310	(7)
11.6.1. Use of Figures of Merit	310	(2)
11.6.2. Use of Figures of Merit for Instrument Performance Evaluation	312	(1)
11.6.3. Use of Figures of Merit for Data Quality Evaluation	313	(3)
11.6.4. Use of Figures of Merit in Indexing of Powder Patterns	316	(1)
References	317	(2)
CHAPTER 12. QUALITATIVE ANALYSIS	319	(36)
12.1. Phase Identification by X-ray Diffraction	319	(4)
12.1.1. Quality of Experiment Data	322	(1)
12.2. Databases	323	(6)
12.2.1. The Powder Diffraction File	324	(2)
12.2.2. The Crystal Data File	326	(1)
12.2.3. The Elemental and Interplanar Spacing Index (EISI)	327	(1)
12.2.4. The Metals and Alloys Index	328	(1)
12.3. Media on Which ICDD Databases Are Supplied	329	(3)
12.3.1. Historical Evolution of Database Media	329	(1)
12.3.2. Computer-Readable Products	330	(1)
12.3.3. The CD-ROM System	331	(1)
12.4. Manual Search/Matching Methods	332	(12)
12.4.1. The Alphabetic Method	333	(2)
12.4.2. The Hanawalt Search Method	335	(4)
12.4.3. The Fink Search Method	339	(5)
12.5. Limitations with the Use of Paper Search Manuals	344	(1)
12.6. Boolean Search Methods	345	(2)
12.7. Fully Automated Search Methods	347	(3)
12.7.1. First-Generation Programs	347	(1)
12.7.2. Second-Generation Search/Match Algorithms	348	(1)
12.7.3. Commercial Search/Match Programs	348	(1)
12.7.4. Third-Generation Search/Match Algorithms	349	(1)
12.8. Effectiveness of Search/Matching Using the Computer	350	(1)
References	351	(4)
CHAPTER 13. QUANTITATIVE ANALYSIS	355	(34)
13.1. Historical Development of Quantitative Phase Analysis	355	(1)
13.2. Measurement of Line Intensities	356	(5)
13.3. Foundation of Quantitative Phase Analysis	361	(1)
13.4. The Absorption-Diffraction Method	362	(7)
13.4.1. Use of Klug's Equation	365	(2)
13.4.2. Use of Measured Mass Attenuation Coefficients	367	(1)
13.4.3. Use of Mass Attenuation Coefficients Derived from Elemental Chemistry	368	(1)
13.5. Method of Standard Additions	369	(1)
13.6. The Internal Standard Method of Quantitative Analysis	370	(6)
13.6.1. I/I(corundum) and the Reference Intensity Ratio Method	372	(1)
13.6.2. The Generalized Reference Intensity Ratio	372	(1)
13.6.3. Quantitative Analysis with RIRs	373	(1)
13.6.4. The Normalized RIR Method	373	(1)
13.6.5. Constrained XRD Phase Analysis: Generalized Internal Standard Method	374	(2)
13.7. Quantitative Phase Analysis Using Crystal Structure Constraints	376	(2)
13.8. Quantitative Methods Based on Use of the Total Pattern	378	(6)
13.8.1. The Rietveld Method	378	(5)
13.8.2. Full-Pattern Fitting with Experimental Patterns	383	(1)
13.9. Detection of Low Concentrations	384	(2)
References	386	(3)
APPENDIX A: COMMON X-RAY WAVELENGTHS	389	(1)
APPENDIX B: MASS ATTENUATION COEFFICIENTS	390	(1)
APPENDIX C: ATOMIC WEIGHTS AND DENSITIES	391	(1)
APPENDIX D: CRYSTALLOGRAPHIC CLASSIFICATION OF THE 230 SPACE GROUPS	392	(5)
INDEX	397