Introduction to X-Ray Powder Diffractometry E-Book

Ron Jenkins

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications
• Sprache: Englisch

Seitenzahl: 563

Veröffentlichungsjahr: 2012

Beschreibung

When bombarded with X-rays, solid materials produce distinct scattering patterns similar to fingerprints. X-ray powder diffraction is a technique used to fingerprint solid samples, which are then identified and cataloged for future use-much the way the FBI keeps fingerprints on file. The current database of some 70,000 material prints has been put to a broad range of uses, from the analysis of moon rocks to testing drugs for purity.

Introduction to X-ray Powder Diffractometry fully updates the achievements in the field over the past fifteen years and provides a much-needed explanation of the state-of-the-art techniques involved in characterizing materials. It covers the latest instruments and methods, with an emphasis on the fundamentals of the diffractometer, its components, alignment, calibration, and automation.

The first three chapters outline diffraction theory in clear language, accessible to both students and professionals in chemistry, physics, geology, and materials science. The book's middle chapters describe the instrumentation and procedures used in X-ray diffraction, including X-ray sources, X-ray detection, and production of monochromatic radiation. The chapter devoted to instrument design and calibration is followed by an examination of specimen preparation methods, data collection, and reduction. The final two chapters provide in-depth discussions of qualitative and quantitative analysis.

While the material is presented in an orderly progression, beginning with basic concepts and moving on to more complex material, each chapter stands on its own and can be studied independently or used as a professional reference. More than 230 illustrations and tables demonstrate techniques and clarify complex material.

Self-contained, timely, and user-friendly, Introduction to X-ray Powder Diffractometry is an enormously useful text and professional reference for analytical chemists, physicists, geologists and materials scientists, and upper-level undergraduate and graduate students in materials science and analytical chemistry.

X-ray powder diffraction-a technique that has matured significantly in recent years-is used to identify solid samples and determine their composition by analyzing the so-called "fingerprints" they generate when X-rayed. This unique volume fulfills two major roles: it is the first textbook devoted solely to X-ray powder diffractometry, and the first up-to-date treatment of the subject in 20 years.

This timely, authoritative volume features:
* Clear, concise descriptions of both theory and practice-including fundamentals of diffraction theory and all aspects of the diffractometer
* A treatment that reflects current trends toward automation, covering the newest instrumentation and automation techniques
* Coverage of all the most common applications, with special emphasis on qualitative and quantitative analysis
* An accessible presentation appropriate for both students and professionals
* More than 230 tables and illustrations

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.

Leseprobe

CONTENTS

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Cumulative Listing of Volumes in Series

Chapter 1: Characteristics of X-Radiation

1.1. Early Development of X-Ray Diffraction

1.2. Origin of X-Radiation

1.3. Continuous Radiation

1.4. Characteristic Radiation

1.5. Scattering of X-Rays

1.6. Absorption of X-Rays

1.7. Safety Considerations

References

Chapter 2: The Crystalline State

2.1. Introduction to the Crystalline State

2.2. Crystallographic Symmetry

2.3. Space Group Notation

2.4. Space Group Theory

2.5. Crystallographic Planes and Miller Indices

References

Chapter 3: Diffraction Theory

3.1. Diffraction of X-Rays

3.2. The Reciprocal Lattice

3.3. The Ewald Sphere of Reflection

3.4. Origin of the Diffraction Pattern

3.5. The Location of Diffraction Peaks

3.6. Intensity of Diffraction Peaks

3.7. The Calculated Diffraction Pattern

3.8. Calculation of the Powder Diffraction Pattern of KCl

3.9. Anisotropic Distortions of the Diffraction Pattern

References

Chapter 4: Sources for the Generation of X-Radiation

4.1. Components of the X-Ray Source

4.2. The Line-Voltage Supply

4.3. The High-Voltage Generator

4.4. The Sealed X-Ray Tube

4.5. Effective Line Width

4.6. Spectral Contamination

4.7. The Rotating Anode X-Ray Tube

References

Chapter 5: Detectors and Detection Electronics

5.1. X-Ray Detectors

5.2. Desired Properties of an X-Ray Detector

5.3. Types of Detector

5.4. Pulse Height Selection

5.5. Counting Circuits

5.6. Counting Statistics

5.7. Two-Dimensional Detectors

References

Chapter 6: Production of Monochromatic Radiation

6.1. Introduction

6.2. Angular Dispersion

6.3. Makeup of a Diffractogram

6.4. The β-Filter

6.5. The Proportional Detector and Pulse Height Selection

6.6. Use of Solid State Detectors

6.7. Use of Monochromators

6.8. Comparison of Monochromatization Methods

References

Chapter 7: Instruments for the Measurement of Powder Patterns

7.1. Camera Methods

7.2. The Powder Diffractometer

7.3. The Seemann-Bohlin Diffractometer

7.4. The Bragg-Brentano Diffractometer

7.5. Systematic Aberrations

7.6. Selection of Goniometer Slits

References

Chapter 8: Alignment and Maintenance of Powder Diffractometers

8.1. Principles of Alignment

8.2. Routine Alignment Checks

8.3. Evaluation of the Quality of Alignment

8.4. Troubleshooting

References

Chapter 9: Specimen Preparation

9.1. General Considerations

9.2. Compositional Variations Between Sample and Specimen

9.3. Absorption Problems

9.4. Problems in Obtaining a Random Specimen

9.5. Particle Separation and Size Reduction Methods

9.6. Specimen Preparation Procedures

9.7. Measurement of the Prepared Specimen

References

Chapter 10: Acquisition of Diffraction Data

10.1. Introduction

10.2. Steps in Data Acquisition

10.3. Typical Data Quality

10.4. Selection of the d-Spacing Range of the Pattern

10.5. Manual Powder Diffractometers

10.6. Automated Powder Diffractometers

10.7. Use of Calibration Standards

References

Chapter 11: Reduction of Data From Automated Powder Diffractometers

11.1. Data Reduction Procedures

11.2. Range of Experimental Data to be Treated

11.3. Steps in Data Treatment

11.4. Conversion Errors

11.5. Calibration Methods

11.6. Evaluation of Data Quality

References

Chapter 12: Qualitative Analysis

12.1. Phase Identification By X-Ray Diffraction

12.2. Databases

12.3. Media on Which ICDD Databases are Supplied

12.4. Manual Search/Matching Methods

12.5. Limitations with the Use Of Paper Search Manuals

12.6 Boolean Search Methods

12.7. Fully Automated Search Methods

12.8. Effectiveness of Search/Matching Using the Computer

References

Chapter 13: Quantitative Analysis

13.1. Historical Development of Quantitative Phase Analysis

13.2. Measurement of Line Intensities

13.3. Foundation of Quantitative Phase Analysis

13.4. The Absorption-Diffraction Method

13.5. Method of Standard Additions

13.6. The Internal Standard Method of Quantitative Analysis

13.7. Quantitative Phase Analysis Using Crystal Structure Constraints

13.8. Quantitative Methods Based on Use of the Total Pattern

13.9. Detection of Low Concentrations

References

Appendices

Appendix A: Common X-Ray Wavelengths

Appendix B: Mass Attenuation Coefficients

Appendix C: Atomic Weights and Densities

Appendix D: Crystallographic Classification of the 230 Space Groups

Index

Introduction to X-ray Powder Diffractometry

Copyright © 1996 by John Wiley & Sons, Inc.

All rights reserved. Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone]. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone].

Library of Congress Cataloging in Publication Data

Jenkins, Ron, 1932- Introduction to X-ray powder diffractometry / Ron Jenkins and Robert L. Snyder. p. cm.—(Chemical analysis ; v. 138) “A Wiley-Interscience publication.” Includes index. ISBN 0-471-51339-3 (cloth: alk. paper) 1. X-rays—Diffraction—Technique. 2. X-ray diffractometer. 3. Powders—Optical properties—Measurement. I. Snyder, R. L. (Robert L.), 1941- II. Title. III. Series. QC482.D5J46   1996 548’.83—dc20 96-12039 CIP

Dedicated to

J. L. de VriesandW. Parrish

PREFACE

The purpose of this book is to act as an introductory text for users of X-ray powder diffractometers and diffractometry. We have worked to supply the fundamental information on the diffractometer, including consideration of its components, alignment, calibration, and automation. Much of this information is being presented in textbook form for the first time here. The goal of this book is to act as an introduction to students of materials science, mineralogy, chemistry, and physics. This volume contains all of the fundamentals required to appreciate the theory and practice of powder diffraction, with a strong emphasis on the two most important applications: qualitative and quantitative analysis. The treatment of advanced applications of powder diffraction would have both distracted the introductory user and more than doubled the size of this volume. Therefore we decided to develop Applications of Powder Diffraction as a companion volume to this one. The pair of books are designed to bring an introductory user to appreciate all of the applications at the current state of the art. A reader content to understand and use the most common applications should find everything required in the present volume.

A book such as this can never be considered simply the work of two people. Science is a discipline that is built on the inspiration of a few and the mistakes of many. The X-ray powder diffraction field is certainly no exception to this general rule. To this extent we would both like to thank not just the few that have inspired us but also the many who have accepted our mistakes and shortcomings. We are especially grateful to those who have taken time from their busy schedules to review the manuscript at the various stages of its preparation. In this context we are especially indebted to Tom Blanton, Greg Hamill, Jim Kaduk, Greg McCarthy, and Paul Predecki. Special thanks go to Chan Park for his painstaking help in preparing some of the difficult figures. We are pleased to acknowledge the help of those who patiently read the final manuscript: Mario Fornoff, Paden Dismore, Chan Park, and Mike Haluska. Our special thanks also go to Leo Zwell and Zhouhui Yang, who provided invaluable help in locating some of the more obscure original references. We would also like to thank a full generation of graduate students of the New York State College of Ceramics at Alfred University, who have contributed ideas that have helped simplify the explanations of various sections of this book. Anything that does not strike the reader as brilliantly clear, however, may safely be blamed on the authors. The two women whose judgment of human nature was so poor as to marry each of us also need to be acknowledged. Our marriages have survived the first volume of this endeavor; perhaps a bit of time in Cancún will get us through the companion volume!

We have chosen to dedicate this book to two people who have made a dramatic impact on our professional lives, Dr. J. L. (Hans) de Vries and Dr. W. (Bill) Parrish (now deceased). These two men did more than any others to promote the budding field of X-ray powder diffractometry in the early 1950s when the two of us were still in the salad days of our youth. We have learned much at the feet of our masters and gratefully acknowledge their patience and understanding.

RON JENKINSROBERT L. SNYDER

Newtown Square, PennsylvaniaAlfred, New YorkMay 1996

CHEMICAL ANALYSIS

A SERIES OF MONOGRAPHS ON ANALYTICAL CHEMISTRY AND ITS APPLICATIONS

J. D. Winefordner, Series Editor

Vol.

1.

The Analytical Chemistry of Industrial Poisons, Hazards, and Solvents.

Second Edition.

By the late Morris B. Jacobs

Vol.

2.

Chromatographic Adsorption Analysis.

By Harold H. Strain (

out of print

)

Vol.

3.

Photometric Determination of Traces of Metals.

Fourth Edition

Part I: General Aspects. By E. B. Sandell and Hiroshi OnishiPart IIA: Individual Metals, Aluminum to Lithium. By Hiroshi OnishiPart IIB: Individual Metals, Magnesium to Zirconium. By Hiroshi Onishi

Vol.

4.

Organic Reagents Used in Gravimetric and Volumetric Analysis.

By John F. Flagg (

out of print

)

Vol.

5.

Aquametry: A Treatise on Methods for the Determination of Water.

Second Edition

(

in three parts

). By John Mitchell, Jr. and Donald Milton Smith

Vol.

6.

Analysis of Insecticides and Acaricides.

By Francis A. Gunther and Roger C. Blinn (

out of print

)

Vol.

7.

Chemical Analysis of Industrial Solvents.

By the late Morris B. Jacobs and Leopold Schetlan

Vol.

8.

Colorimetric Determination of Nonmetals.

Second Edition.

By the late David F. Boltz and James A. Howell

Vol.

9.

Analytical Chemistry of Titanium Metals and Compounds.

By Maurice Codell

Vol.

10.

The Chemical Analysis of Air Pollutants.

By the late Morris B. Jacobs

Vol.

11.

X-Ray Spectrochemical Analysis.

Second Edition.

By L. S. Birks

Vol.

12.

Systematic Analysis of Surface-Active Agents.

Second Edition.

By Milton J. Rosen and Henry A. Goldsmith

Vol.

13.

Alternating Current Polarography and Tensammetry.

By B. Breyer and H. H. Bauer

Vol.

14.

Flame Photometry.

By R. Herrmann and J. Alkemade

Vol.

15.

The Titration of Organic Compounds

(

in two parts

). By M. R. F. Ashworth

Vol.

16.

Complexation in Analytical Chemistry: A Guide for the Critical Selection of Analytical Methods Based on Complexation Reactions.

By the late Anders Ringbom

Vol.

17.

Electron Probe Microanalysis.

Second Edition.

By L. S. Birks

Vol.

18.

Organic Complexing Reagents: Structure, Behavior, and Application to Inorganic Analysis.

By D. D. Perrin

Vol.

19.

Thermal Analysis.

Third Edition.

By Wesley Wm. Wendlandt

Vol.

20.

Amperometric Titrations.

By John T. Stock

Vol.

21.

Reflectance Spectroscopy.

By Wesley Wm. Wendlandt and Harry G. Hecht

Vol.

22.

The Analytical Toxicology of Industrial Inorganic Poisons.

By the late Morris B. Jacobs

Vol.

23.

The Formation and Properties of Precipitates.

By Alan G. Walton

Vol.

24.

Kinetics in Analytical Chemistry.

By Harry B. Mark, Jr. and Garry A. Rechnitz

Vol.

25.

Atomic Absorption Spectroscopy.

Second Edition.

By Morris Slavin

Vol.

26.

Characterization of Organometallic Compounds

(

in two parts

). Edited by Minoru Tsutsui

Vol.

27.

Rock and Mineral Analysis.

Second Edition.

By Wesley M. Johnson and John A. Maxwell

Vol.

28.

The Analytical Chemistry of Nitrogen and Its Compounds

(

in two parts

). Edited by C. A. Streuli and Philip R. Averell

Vol.

29.

The Analytical Chemistry of Sulfur and Its Compounds

(

in three parts

). By J. H. Karchmer

Vol.

30.

Ultramicro Elemental Analysis.

By Günther Tölg

Vol.

31.

Photometric Organic Analysis

(

in two parts

). By Eugene Sawicki

Vol.

32.

Determination of Organic Compounds: Methods and Procedures.

By Frederick T. Weiss

Vol.

33.

Masking and Demasking of Chemical Reactions.

By D. D. Perrin

Vol.

34.

Neutron Activation Analysis.

By D. De Soete, R. Gijbels, and J. Hoste

Vol.

35.

Laser Raman Spectroscopy.

By Marvin C. Tobin

Vol.

36.

Emission Spectrochemical Analysis.

By Morris Slavin

Vol.

37.

Analytical Chemistry of Phosphorus Compounds.

Edited by M. Halmann

Vol.

38.

Luminescence Spectrometry in Analytical Chemistry.

By J. D. Winefordner, S. G. Schulman and T. C. O’Haver

Vol.

39.

Activation Analysis with Neutron Generators.

By Sam S. Nargolwalla and Edwin P. Przybylowicz

Vol.

40.

Determination of Gaseous Elements in Metals.

Edited by Lynn L. Lewis, Laben M. Melnick, and Ben D. Holt

Vol.

41.

Analysis of Silicones.

Edited by A. Lee Smith

Vol.

42.

Foundations of Ultracentrifugal Analysis.

By H. Fujita

Vol.

43.

Chemical Infrared Fourier Transform Spectroscopy.

By Peter R. Griffiths

Vol.

44.

Microscale Manipulations in Chemistry.

By T. S. Ma and V. Horak

Vol.

45.

Thermometric Titrations.

By J. Barthel

Vol.

46.

Trace Analysis: Spectroscopic Methods for Elements.

Edited by J. D. Winefordner

Vol.

47.

Contamination Control in Trace Element Analysis.

By Morris Zief and James W. Mitchell

Vol.

48.

Analytical Applications of NMR.

By D. E. Leyden and R. H. Cox

Vol.

49.

Measurement of Dissolved Oxygen.

By Michael L. Hitchman

Vol.

50.

Analytical Laser Spectroscopy.

Edited by Nicolò Omenetto

Vol.

51.

Trace Element Analysis of Geological Materials.

By Roger D. Reeves and Robert R. Brooks

Vol.

52.

Chemical Analysis by Microwave Rotational Spectroscopy.

By Ravi Varma and Lawrence W. Hrubesh

Vol.

53.

Information Theory As Applied to Chemical Analysis.

By Karel Eckschlager and Vladimir Štpánek

Vol.

54.

Applied Infrared Spectroscopy; Fundamentals, Techniques, and Analytical Problemsolving.

By A. Lee Smith

Vol.

55.

Archaeological Chemistry.

By Zvi Goffer

Vol.

56.

Immobilized Enzymes in Analytical and Clinical Chemistry.

By P. W. Carr and L. D. Bowers

Vol.

57.

Photoacoustics and Photoacoustic Spectroscopy.

By Allan Rosencwaig

Vol.

58.

Analysis of Pesticide Residues.

Edited by H. Anson Moye

Vol.

59.

Affinity Chromatography.

By William H. Scouten

Vol.

60.

Quality Control in Analytical Chemistry.

Second Edition.

By G. Kateman and L. Buydens

Vol.

61.

Direct Characterization of Fineparticles.

By Brian H. Kaye

Vol.

62.

Flow Injection Analysis.

By J. Ruzicka and E. H. Hansen

Vol.

63.

Applied Electron Spectroscopy for Chemical Analysis.

Edited by Hassan Windawi and Floyd Ho

Vol.

64.

Analytical Aspects of Environmental Chemistry.

Edited by David F. S. Natusch and Philip K. Hopke

Vol.

65.

The Interpretation of Analytical Chemical Data by the Use of Cluster Analysis.

By D. Luc Massart and Leonard Kaufman

Vol.

66.

Solid Phase Biochemistry: Analytical and Synthetic Aspects.

Edited by William H. Scouten

Vol.

67.

An Introduction to Photoelectron Spectroscopy.

By Pradip K. Ghosh

Vol.

68.

Room Temperature Phosphorimetry for Chemical Analysis.

By Tuan Vo-Dinh

Vol.

69.

Potentiometry and Potentiometric Titrations.

By E. P. Serjeant

Vol.

70.

Design and Application of Process Analyzer Systems.

By Paul E. Mix

Vol.

71.

Analysis of Organic and Biological Surfaces.

Edited by Patrick Echlin

Vol.

72.

Small Bore Liquid Chromatography Columns: Their Properties and Uses.

Edited by Raymond P. W. Scott

Vol.

73.

Modern Methods of Particle Size Analysis.

Edited by Howard G. Barth

Vol.

74.

Auger Electron Spectroscopy.

By Michael Thompson, M. D. Baker, Alec Christie, and J. F. Tyson

Vol.

75.

Spot Test Analysis: Clinical, Environmental, Forensic and Geochemical Applications.

By Ervin Jungreis

Vol.

76.

Receptor Modeling in Environmental Chemistry.

By Philip K. Hopke

Vol.

77.

Molecular Luminescence Spectroscopy: Methods and Applications

(

in three parts

). Edited by Stephen G. Schulman

Vol.

78.

Inorganic Chromatographic Analysis.

By John C. MacDonald

Vol.

79.

Analytical Solution Calorimetry.

Edited by J. K. Grime

Vol.

80.

Selected Methods of Trace Metal Analysis: Biological and Environmental Samples.

By Jon C. Van Loon

Vol.

81.

The Analysis of Extraterrestrial Materials.

By Isidore Adler

Vol.

82.

Chemometrics.

By Muhammad A. Sharaf, Deborah L. Illman, and Bruce R. Kowalski

Vol.

83.

Fourier Transform Infrared Spectrometry.

By Peter R. Griffiths and James A. de Haseth

Vol.

84.

Trace Analysis: Spectroscopic Methods for Molecules.

Edited by Gary Christian and James B. Callis

Vol.

85.

Ultratrace Analysis of Pharmaceuticals and Other Compounds of Interest.

By S. Ahuja

Vol.

86.

Secondary Ion Mass Spectrometry: Basic Concepts, Instrumental Aspects, Applications and Trends.

By A. Benninghoven, F. G. Rüdenauer, and H. W. Werner

Vol.

87.

Analytical Applications of Lasers.

Edited by Edward H. Piepmeier

Vol.

88.

Applied Geochemical Analysis.

By C. O. Ingamells and F. F. Pitard

Vol.

89.

Detectors for Liquid Chromatography.

Edited by Edward S. Yeung

Vol.

90.

Inductively Coupled Plasma Emission Spectroscopy: Part I: Methodology, Instrumentation, and Performance; Part II: Applications and Fundamentals.

Edited by J. M. Boumans

Vol.

91.

Applications of New Mass Spectrometry Techniques in Pesticide Chemistry.

Edited by Joseph Rosen

Vol.

92.

X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS, and XANES.

Edited by D. C. Konnigsberger

Vol.

93.

Quantitative Structure-Chromatographic Retention Relationships.

Edited by Roman Kaliszan

Vol.

94.

Laser Remote Chemical Analysis.

Edited by Raymond M. Measures

Vol.

95.

Inorganic Mass Spectrometry.

Edited by F. Adams, R. Gijbels, and R. Van Grieken

Vol.

96.

Kinetic Aspects of Analytical Chemistry.

By Horacio A. Mottola

Vol.

97.

Two-Dimensional NMR Spectroscopy.

By Jan Schraml and Jon M. Bellama

Vol.

98.

High Performance Liquid Chromatography.

Edited by Phyllis R. Brown and Richard A. Hartwick

Vol.

99.

X-Ray Fluorescence Spectrometry.

By Ron Jenkins

Vol.

100.

Analytical Aspects of Drug Testing.

Edited by Dale G. Deutsch

Vol.

101.

Chemical Analysis of Polycyclic Aromatic Compounds.

Edited by Tuan Vo-Dinh

Vol.

102.

Quadrupole Storage Mass Spectrometry.

By Raymond E. March and Richard J. Hughes

Vol.

103.

Determination of Molecular Weight.

Edited by Anthony R. Cooper

Vol.

104.

Selectivity and Detectability Optimizations in HPLC.

By Satinder Ahuja

Vol.

105.

Laser Microanalysis.

By Lieselotte Moenke-Blankenburg

Vol.

106.

Clinical Chemistry.

Edited by E. Howard Taylor

Vol.

107.

Multielement Detection Systems for Spectrochemical Analysis.

By Kenneth W. Busch and Marianna A. Busch

Vol.

108.

Planar Chromatography in the Life Sciences.

Edited by Joseph C. Touchstone

Vol.

109.

Fluorometric Analysis in Biomedical Chemistry: Trends and Techniques Including HPLC Applications.

By Norio Ichinose, George Schwedt, Frank Michael Schnepel, and Kyoko Adochi

Vol.

110.

An Introduction to Laboratory Automation.

By Victor Cerdá and Guillermo Ramis

Vol.

111.

Gas Chromatography: Biochemical, Biomedical, and Clinical Applications.

Edited by Ray E. Clement

Vol.

112.

The Analytical Chemistry of Silicones.

Edited by A. Lee Smith

Vol.

113.

Modern Methods of Polymer Characterization.

Edited by Howard G. Barth and Jimmy W. Mays

Vol.

114.

Analytical Raman Spectroscopy.

Edited by Jeannette Graselli and Bernard J. Bulkin

Vol.

115.

Trace and Ultratrace Analysis by HPLC.

By Satinder Ahuja

Vol.

116.

Radiochemistry and Nuclear Methods of Analysis.

By William D. Ehmann and Diane E. Vance

Vol.

117.

Applications of Fluorescence in Immunoassays.

By Ilkka Hemmila

Vol.

118.

Principles and Practice of Spectroscopic Calibration.

By Howard Mark

Vol.

119.

Activation Spectrometry in Chemical Analysis.

By S. J. Parry

Vol.

120.

Remote Sensing by Fourier Transform Spectrometry.

By Reinhard Beer

Vol.

121.

Detectors for Capillary Chromatography.

Edited by Herbert H. Hill and Dennis McMinn

Vol.

122.

Photochemical Vapor Deposition.

By J. G. Eden

Vol.

123.

Statistical Methods in Analytical Chemistry.

By Peter C. Meier and Richard Zund

Vol.

124.

Laser Ionization Mass Analysis.

Edited by Akos Vertes, Renaat Gijbels, and Fred Adams

Vol.

125.

Physics and Chemistry of Solid State Sensor Devices.

By Andreas Mandelis and Constantinos Christofides

Vol.

126.

Electroanalytical Stripping Methods.

By Khjena Z. Brainina and E. Neyman

Vol.

127.

Air Monitoring by Spectroscopic Techniques.

Edited by Markus W. Sigrist

Vol.

128.

Information Theory in Analytical Chemistry.

By Karel Eckschlager and Klaus Danzer

Vol.

129.

Flame Chemiluminescence Analysis by Molecular Emission Cavity Detection.

Edited by David Stiles, Anthony Calokerinos, and Alan Townshend

Vol.

130.

Hydride Generation Atomic Absorption Spectrometry.

Edited by Jiri Dedina and Dimiter L. Tsalev

Vol.

131.

Selective Detectors: Environmental, Industrial, and Biomedical Applications.

Edited by Robert E. Sievers

Vol.

132.

High-Speed Countercurrent Chromatography.

Edited by Yoichiro Ito and Walter D. Conway

Vol.

133.

Particle-Induced X-Ray Emission Spectrometry.

By Sven A. E. Johansson, John L. Campbell, and Klass G. Malmqvist

Vol.

134.

Photothermal Spectroscopy Methods for Chemical Analysis.

By Stephen Bialkowski

Vol.

135.

Element Speciation in Bioinorganic Chemistry.

Edited by Sergio Caroli

Vol.

136.

Laser-Enhanced Ionization and Spectrometry.

Edited by John C. Travis and Gregory C. Turk

Vol.

137.

Fluorescence Imaging Spectroscopy and Microscopy.

Edited by Xue Feng Wang and Brian Herman

Vol.

138.

Introduction to X-ray Powder Diffractometry.

By Ron Jenkins and Robert L. Snyder

CHAPTER 1

CHARACTERISTICS OF X-RADIATION

1.1. EARLY DEVELOPMENT OF X-RAY DIFFRACTION

Following the discovery of X-rays by W. C. Röntgen in 1895, three major branches of science have developed from the use of this radiation. The first and oldest of these is X-ray radiography, which makes use of the fact that the relative absorption of X-rays by matter is a function of the average atomic number and density of the matter concerned. From this has developed the whole range of diagnostic methods for medical and industrial use. Early attempts to confirm the dual nature of X-rays, i.e., their particle and wave character, were frustrated by experimental difficulties involved with the handling of the very short wavelengths in question. Not until the classic work of Max von Laue in 1912 was the wave character confirmed by diffraction experiments from a single crystal. From this single experiment has developed the field of X-ray crystallography, of which X-ray powder diffractometry is one important member. X-ray crystallography, using single crystals or powder, is mainly concerned with structure analysis. The third technique, X-ray spectrometry, also has its fundamental roots in the early part of this century, but routine application of X-ray fluorescence spectrometry has only developed over the last 20 to 30 years.

The purpose of this work is to discuss X-ray powder diffractometry. Powder diffractometry is mainly used for the identification of compounds by their diffraction patterns. The first X-ray powder diffractometer was developed in 1935 by Le Galley [1], but, due mainly to the lack of parafocusing conditions, the instrument gave relatively poor intensities. In 1945 Parrish and Gordon [2] developed a Geiger-counter spectrometer1 for the precision cutting of quartz oscillator plates used in frequency control for military communication equipment. At the same time, Friedman [3] was working on X-ray spectrometer techniques at the U.S. Naval Research Laboratory in Washington, DC. The modern parafocusing X-ray powder diffractometer was based on these ideas, and the first commercial equipment was introduced by North American Philips in 1947. The latest versions of the powder diffractometer differ little in their construction and geometry, but considerable advances have been made in detection and counting systems, automation, and in the X-ray tubes themselves.

1.2. ORIGIN OF X-RADIATION

X-rays are relatively short-wavelength, high-energy beams of electromagnetic radiation. When an X-ray beam is viewed as a wave, one can think of it as a sinusoidal oscillating electric field with, at right angles to it, a similarly varying magnetic field changing with time. Another description of X-rays is as particles of energy called photons. All electromagnetic radiation is characterized either by its wave character using its wavelength λ (i.e., the distance between peaks) or its frequency v (the number of peaks that pass a point in unit time) or by means of its photon energy E. The following equations represent the relationships between these quantities:

(1.1)

(1.2)

(1.3)

Insertion of the appropriate values for the fundamental constants gives

(1.4)

or

(1.5)

where E is in keV and λ in angstroms. As an example the Cu Kα1, Kα2 doublet has an energy of about 8.05 keV, corresponding to a wavelength of 12.398/8.046= 1.541 Å.

1.3. CONTINUOUS RADIATION

X-radiation arises when matter is irradiated with a beam of high-energy charged particles or photons. When an element is bombarded with electrons the spectrum obtained is similar to that shown in Figure 1.1. The figure illustrates the main features of the spectrum that would be obtained from a copper anode (target) X-ray tube, operated at 8.5, 25, and 50 kV, respectively. It will be seen that the spectrum consists of a broad band of continuous radiation (bremsstrahlung, or white radiation) superimposed on which are discrete wavelengths of varying intensity. The continuous radiation is produced as the impinging high-energy electrons are decelerated by the atomic electrons of the target element. The continuum is typified by a minimum wavelength, λmin, which is related to the maximum accelerating potential V of the electrons. Thus, as follows from Equation 1.5,

Figure 1.1. Continuous and characteristic radiation for copper.

(1.6)

Note from Figure 1.1 that as the operating voltage is increased from 8.5 to 25 to 50 kV, the λmin value shifts to shorter wavelengths and the intensity of the continuum increases. The intensity distribution of the continuum reaches a maximum intensity at a wavelength of about 1.5 to 2 times λmin. The wavelength distribution of the continuum can be expressed quantitatively in terms of the excitation conditions by means of Kramers’ formula [4]:

(1.7)

Kramers’ formula relates the intensity I(λ) from an infinitely thick target of atomic number Z with the applied current i where K is a constant. This expression does not correct for self-absorption by the target, which in practice leads to some modification of the intensity distribution.

It will also be seen from Figure 1.1 that somewhere between X-ray tube potentials of 8.5 and 25 kV sharp lines appear, superimposed on the continuum. These lines were shown by Moseley [5] to be characteristic wavelengths since their values differ for each unique target element. These characteristic lines will only appear when their equivalent excitation potential value V is exceeded. While the wavelengths of these characteristic lines are completely independent of the X-ray tube conditions, the intensities of the lines are very much dependent on the X-ray tube current i and voltage V; see Section 4.3.

1.4. CHARACTERISTIC RADIATION

1.4.1. The Photoelectric Effect

The processes whereby characteristic radiation is produced in an X-ray tube are based on interactions between the atomic electrons of the target and the incident particles. In the case described in Figure 1.2, the incident particles are high-voltage electrons. The incident particle can also be an X-ray photon, a γ-ray, or a proton. Each will produce similar effects if the energy of the particle is greater than the energy binding the electron to the nucleus. The atomic electron may be removed from its original atomic position leaving the atom in an ionized state. The free electron, called a photoelectron, will leave the atom with a kinetic energy E — ϕe, i.e., equal to the difference between the energy E of the incident photon and the binding energy ϕe of the electron.

Figure 1.2. The Auger and photoelectric effects.

From R. Jenkins, R. W. Gould, and D. Gedcke, Quantitative X-Ray Spectrometry, p. 16, Fig. 2-9. Dekker, New York, 1981. Reprinted by courtesy of Marcel Dekker Inc.

Figure 1.2 shows the basic processes involved in a photoelectric interaction. Figure 1.2a shows an atom with its various energy levels ϕK, ϕL, ϕM, etc., and incident upon it is a photon of energy E. Figure 1.2b shows the ejected photoelectron leaving the atom with an energy equal to E — ϕK. Note that this process creates a vacancy in the atom, in this instance, with an equivalent energy of ϕK. One of the processes by which this vacancy can be filled is by transferring an outer orbital electron to fill its place. Such a transference is shown in Figure 1.2c, where an electron from the L level is transferred to the K vacancy. Associated with this electron transfer (and subsequent lowering of the ionized energy of the atom) will be the production of a fluorescent X-ray photon with an energy Ex-ray equal to ϕK — ϕL. As will be shown later, this photon is called a Kα photon.

1.4.2. The Auger Effect

An alternative deexcitation process, called the Auger effect, can also occur, and this effect is illustrated in Figure 1.2d. It may happen that the ionization of an inner shell electron produces a photon that in turn gets absorbed by an outer shell electron. Thus, the incident X-ray is absorbed by, for example, a K shell electron that leaves the atom. Next, an electron falls into the K shell, producing a Kα photon. The Kα photon, in turn, may be absorbed by an M electron, causing its ionization as an Auger electron. The kinetic energy of the emitted Auger electron is not just dependent on the energy of the initial X-ray photon (or particle) that ionized the K electron. Any incident particle with sufficient energy to create the initial vacancy can be responsible for the subsequent production of an Auger electron of unique energy. Study of the energy and intensities of Auger electrons, called Auger spectroscopy, allows measurement of the precise energy of the chemical bonds that involve the valence electrons.

1.4.3. Fluorescent Yield

It is apparent from the foregoing that there are two competing processes by which an ionized atom can regain its initial, or ground, state, these processes being the fluorescence of an X-ray photon and the Auger effect. The efficiency of the production of characteristic X-rays will be dependent upon the relative effectiveness of these two processes in a given atom. As the atomic number decreases, the production of Auger electrons becomes more probable and thus the production of K radiation falls off at low Z. The efficiency of a particular element producing fluorescent X-rays is quantified by the fluorescent yield ω. The fluorescent yield is the ratio of the number of photons produced from a given atomic shell to the number of equivalent shell vacancies created. For the production of K radiation from a specimen,

(1.8)

The probability of the production of an Auger electron is 1 — ω. Fluorescent yield values vary as the fourth power of atomic number and range from almost unity, for high atomic number elements, to 0.001, for low atomic numbers. For the wavelengths typically employed in powder diffraction, the K fluorescent yield values are about 0.5.

1.4.4. Selection Rules

Table 1.1. Binding Energies for the K, L, and M Levels of Copper

Level

Binding Energy (keV)

K

8.978

L

II

0.953

L

III

0.933

M

II

0.078

M

III

0.075

Table 1.2. Siegbahn and IUPAC Notation for the K Series

Table 1.3. Construction of Transition Groups and Number of Electrons Allowed in Each State (Multiplicity)

Figure 1.3 shows the usual transitions for the K spectrum of copper, giving both transition groups and quantum numbers. It will be seen that the copper K spectrum is quite simple, consisting of two α lines (called a doublet) from 2p1/2 → 1s and 2p3/2 → 1s transitions, and two β lines from 3p1/2 → 1s and 3p3/2 → 1s transitions. Since in the case of both doublets the energy difference between the lines in each pair is simply that due to the spin quantum number, the relative energy difference is very small. As will be seen in later sections, the energy difference between α1 and α2 being very small causes only partial separation of the two wavelengths to generally occur in diffraction. In practice the β1, β3 doublet is never resolved, but the α1, α2 is resolved at moderate-to-high diffraction angles. It should be noted that since copper does not have electrons in the 4p level the 4p → 1s transition (the β3 doublet) is absent. In the case of higher atomic numbers such as silver (47) and molybdenum (42) the β2 doublet is observed as an unresolved line. The relative intensities of the characteristic wavelengths are determined by the appropriate quantum mechanical transition probabilities. It is evident that a K shell with a missing electron represents a higher energy state than a similar hole in the corresponding L shell. The transition probability is a rather complex function of the difference in energy of the two levels concerned.

Figure 1.3. The copper Kα spectrum.

The relative intensity ratio of possible lines for an element is constant but may differ from one element to another. The greater the energy difference, the less probable the transition becomes and the less intense is the resulting line. Consequently the intensity of Kα1, Kα2 > Kβ1, β3 > Kβ2. For a copper anode the ratio is about 5:1:0, and for molybdenum about 3:1:0.3. The relative intensity of α1, α2 (and also Kβ1, β3) is much simpler to predict since for these line pairs the Burger-Dorgelo rule [6] holds, stating that the intensity ratio is equal to the number of electrons that may make the transition. In the case of the Kα1:Kα2 ratio, there are four p3/2 electrons (as shown in Table 1.3) giving rise to the Kα1 line and two p1/2 electrons giving rise to the Kα2 line. Thus, the intensity ratio is 4:2 or 2:1.

The original nomenclature system for X-ray wavelengths was proposed by K. M. G. Siegbahn in the 1920s and is properly called the Siegbahn notation. Since the introduction of the Siegbahn notation a number of lines have been observed that have not been classified within the Siegbahn nomenclature, particularly for the M and N series. A further complication is that the Siegbahn notation is unsystematic and consequently rather difficult to learn. In recent years this problem has been addressed by the IUPAC, with the result that a new IUPAC notation has been recommended [7]. At the time of the publication of this book, the acceptance of the new IUPAC nomenclature among the X-ray community is still uncertain. However, for information, Tables 1.2 and 1.4 list typical Siegbahn and IUPAC equivalents.

Table 1.4. Nomenclature for the Copper K Series Wavelengths

Transition

Siegbahn

IUPAC

2

p

3/2

→ 1

s

K

α

1

KL3

2

p

1/2

→ 1

s

K

α

2

KL2

3

p

3/2

→ 1

s

K

β

1

KM3

3

p

1/2

→ 1

s

K

β

3

KM2

2

p

3/2

(2

p

-1

) → 1

s

K

α

3

KL3,3

2

p

1/2

(2

p

-1

) → 1

s

K

α

4

KL2,3

2

p

3/2

(2

s

-1

) → 1

s

K

α

5

KL3,1

2

p

3/2

(2

s

-1

) → 1

s

K

α

6

KL2,1

1.4.5. Nondiagram Lines

Not all observed characteristic X-ray lines can be satisfactorily described by the selection rules just outlined. Other lines occur following special conditions of ionization that generally fit into one of two categories—forbidden transitions and satellites. The origin of forbidden transitions is rather complex, but, in simple terms, forbidden transitions arise because outer orbital electrons are typically not distributed in absolutely unique and well-separated orbitals. For example, there is much hybridization of outer orbitals, meaning that an 5 electron may tend to show the character of a p electron and so on. Thus, transitions may occur that are close to obeying the selection rules, but in which-the electron being transferred acts as if it had a different angular quantum number than expected. As an example, in the Cu K spectrum a weak Kβ5 occurs from a 3d → Is transition. Since such a line corresponds to a Δl of 2 it is forbidden by the selection rules for normal lines.

Satellite lines occur from transitions involving removal of more than one electron from a target atom (dual ionization). Although the excitation/deexcitation process is fast (10-12s), it is finite, and there is a probability that a second electron may be removed before the first vacancy is filled. Figure 1.4 shows the origin of the Kα satellites in the Cu K spectrum. The left-hand diagram shows the usual situation with a K vacancy being filled by a 2p3/2 → 1s and a 2p1/2 → 1s transition, giving the Kα1 and Kα2 lines, respectively. The center, diagram shows similar transitions, except that now there are two atomic vacancies, one in the K shell and one in the LIII level. Removal of the LIII electron decreases the total electron charge of the atom and the attraction of the charge by the nucleus of the atom. There is a consequent widening of the energy gap between the K and L levels. Hence, the two transitions give a pair of lines similar to the Kα1 and Kα2, but of shorter wavelength. These lines are called the α3 and α4. The right-hand diagram shows a similar circumstance in which the second vacancy is in the L1 level, which gives rise to the α5 and α6 lines. Thus, each of the Kα1 and Kα2 lines is actually a triplet, and there are actually six lines (i.e., two triplets) in what is usually called the Kα1, Kα2 doublet. A major difference between the satellites and the forbidden transitions is that the satellites occur close to the α1, α2 doublet, and even though they are not resolved by the normal monochromatization devices, they do play some part [8] in the profile-fitting process.

Figure 1.4. Origin of the copper Kα. satellite lines from doubly ionized atoms.

1.4.6. Practical Form of the Copper K Spectrum

From the foregoing discussion it will be clear that the characteristic α radiation emission from copper is much more complex than the simple α-doublet and β-doublet model generally employed in classical powder diffractometry. The relative intensities of the satellite lines in each line within each triplet differ somewhat in the α1 and α2 sets, which probably accounts for the higher degree of asymmetry of the α2 relative to the α1 typically observed. The largest energy gap within any of the triplets is only about 2.5 eV. Since the absolute energy resolution of the powder diffractometer using Cu Kα radiation ranges from about 200 eV at 10° 2θ to about 2.5 eV at 140° 2θ, the fine structure of the triplets is not resolved. However, as indicated in Figure 1.5, asymmetry is introduced in the α2, which starts to become apparent at very high 2θ values. Even more important, where profile-fitting methods are employed, the effective “fitting resolution” is probably on the order of a few electronvolts, and here allowance must be made for wavelengths other than the α1 and α2 if accurate (<2% or so) fitting is required. For most practical purposes, however, in powder diffractometry, the copper K spectrum is considered to consist simply of two pairs of lines, the Kα1, Kα2 doublet occurring from 2p → 1s transitions; and the Kβ1, β3 doublet from 3p → 1s transitions. In most experimental work the β doublet intensity is typically reduced to less than a few percent of the α-doublet intensity by use of filtration or is removed by use of a crystal monochromator or an Si(Li) energy-resolving detector. In each case, what remains is essentially bichromatic radiation.

Figure 1.5. Full spectrum for copper K radiation.

The most commonly used values for the wavelengths of Cu Kα1 and Cu Kα2 are 1.54056 and 1.54439 Å, respectively. These values were reported by Bearden [9] and have been recommended in the International Union of Crystallography (IUCr) publication International Critical Tables [10]. The values are generally given in terms of a unit length in angstrom units, based on the energy of the W Kα line of 59.31821 keV. There is a degree of uncertainty that arises because of the conversion of × units (Xu) to angstrom units. Bearden uses a value of 1.002056 for this conversion factor. Because of this uncertainty, minor differences will be found in other tables. As an example, Cauchois and Senemaud [11] list a value of 1537.400 Xu with a conversion factor of 1.0020802 to give 1.540598 Å. This value has also been used by the National Bureau of Standards (NBS; now the National Institute of Standards and Technology, NIST) and has been widely used in the powder diffraction community for the last 15 years. The NBS value is based on the techniques used by Deslattes et al. [12]. There is clearly some inconsistency between these values, and Bearden et al. [13] have suggested a new value of 1537.370 Xu for Cu Kα. Most recently Härtwig et al. [14] have suggested 1.54059292 Å. These minor variations will not affect most X-ray powder diffraction measurements, and we recommend the use of 1.54060 Å for the Cu Kα1 line.

1.5. SCATTERING OF X-RAYS

Electromagnetic radiation is a form of energy that can be described as an oscillating electric field E with an oscillating magnetic field H at right angles to it, as shown in Figure 1.6. The magnetic field will only interact with other magnetic fields and is therefore not generally important in considering the interactions of X-rays with matter. However, the oscillating electric field will couple to the charged electrons surrounding the atoms and cause them to accelerate and decelerate. Since an electron bound to an atom has an amount of energy fixed by the laws of quantum mechanics, the extra energy imparted to it from the acceleration must be reradiated or absorbed by perhaps stimulating a vibrational mode of the lattice. The phenomenon known as scattering occurs when any of the incident energy is reradiated.

Figure 1.6. Electromagnetic radiation.

1.5.1. Coherent Scatter

Coherent scatter, or elastic scatter, can be thought of as a perfectly elastic collision between a photon and an electron. The photon changes direction after colliding with the electron but transfers none of its energy to the electron. The result is that the scattered photon leaves in a new direction but with the same phase and energy as that of the incident photon.

From the wave perspective one thinks of the incoming wave being instantaneously absorbed by an electron and reemitted (i.e., in a time interval short enough to fall within the uncertainty principle) as spherical waves. Thus, each electron on a scattering atom in a material will act as a Huygens scattering center. If the scattering atoms are arranged in an orderly manner, with a distance between each on the order of the wavelength of the radiation, then the phase relationships between scatterers will become periodic and interference diffraction effects will be observed at various angles of view (see Section 3.1).

1.5.2. Compton Scatter

It can also happen that the X-ray photon loses part of its energy in the collision process, especially where the electron is only loosely bound. In this case the scatter is said to be incoherent (Compton scatter) and the wavelength of the incoherently scattered photons will be longer than the coherently scattered wavelength. Compton scatter amounts to an inelastic collision between a photon and an electron. Part of the energy of the incident photon is absorbed by an electron, and the electron is ionized. However, instead of all of the remaining energy of the original photon converting to kinetic energy of the ionized photoelectron, some of it is reemitted as an X-ray photon of lower energy. Not only has the energy of this Compton photon been lowered, but it loses any phase relationship to the incident photon. For this reason the process is often called incoherent scatter. Since the Compton (phase) modified photons are emitted in arbitrary directions very few of them will reach the detector and, therefore, this is also a source of absorption. Compton scatter decreases in importance as the atomic number of the scatterer increases.

The total scatter σ is made up of both coherent and incoherent terms:

(1.9)

The first term is the coherent term, and the second is the incoherent term; f is called the atomic scattering factor and will be discussed in Section 3.6.2.

1.6. ABSORPTION OF X-RAYS

When a beam of X-radiation falls onto an absorber, a number of different processes may occur. The more important of these are illustrated in Figure 1.7. In this example, a monochromatic beam of radiation of wavelength λ and intensity I0 is incident on an absorber of thickness t (with differential thickness dt) and density ρ. A certain portion, I, of the radiation may pass through the absorber. Where this happens the wavelength of the transmitted beam is unchanged and the intensity of this transmitted beam I(λ) is given by

(1.10)

Figure 1.7. Absorption processes for X-rays.

where μ/ρ is the mass attenuation coefficient of the absorber for the wavelength λ and the density ρ. Equation 1.10 is very general and is called the mass-absorption law. In other parts of the spectrum the same equation will be called the Lambert-Beer law. The value of the X-ray mass attenuation coefficient μ/ρ in Equation 1.10 is a function both of the photoelectric absorption τ and the scatter σ:

(1.11)

The scatter term contains contributions from coherent and incoherent scatter. However, τ is generally large in comparison with σ and generally μ/ρ f(τ). For this reason, the mass attenuation coefficient is often referred to as the mass absorption coefficient. The mass attenuation coefficient is independent of the physical state of a material (i.e., solid, liquid or gas) and depends only on the wavelength of the incident radiation. The wavelength dependence is roughly proportional to the cube of λ. However, since no one has found an exact theoretical relationship for the wavelength dependence, we must resort to measuring μ/ρ for all of the commonly used wavelengths and tabulating them. An empirical relationship,

(1.12)

known as the Bragg-Pierce law, has been established, where Z is the atomic number and K is an empirical constant that is different on each side of each of the absorption edges shown in Figure 1.8.

Figure 1.8. The absorption curve for barium.

The difference between I and I0 for a fixed wavelength is dependent on the thickness of the absorber and on the linear absorption coefficient μ, which is a constant related to the absorbing material. Since all of the absorption processes shown in Figure 1.7 ultimately depend on the presence of electrons, clearly the ability of a material to absorb electromagnetic radiation is related to the density of electrons. In turn, the electron density of a material is determined by the types of atoms composing the material and the closeness of their packing. The linear absorption coefficient of a material, therefore, depends on the types of atoms present and the density of the material. However, with the elimination of the functional dependence on density, which is determined by the type and strength of the chemical bonds in a material, a true constant for each type of element is obtained. Thus, μ/ρ is characteristic of each element at any specified wavelength. The absorption coefficients of the elements are listed in Appendix B.

Photoelectric absorption occurs at each of the energy levels of the atom, and the total photoelectric absorption τ(total) is determined by the sum of each of the individual absorptions. Thus,

(1.13)

where τ(n) represents the outermost level of the atom containing electrons. It is apparent that all radiation produced as a result of electron transitions following ejection of orbital electrons must have a wavelength longer than that of the source which stimulated the excited state. Also, not all of the radiation produced is X-radiation; hence the photoelectric effect must be giving rise to X-radiation (λ) from the absorber and other photons.

The various contributions to the total absorption from the different energy levels is illustrated in Figure 1.9, which shows the absorption curve for barium. As is seen in the figure, the value of the mass attenuation coefficient increases steadily with wavelength in accord with the Bragg-Pierce law (Equation 1.12); also the curve has very sharp discontinuities, called absorption edges, indicated as K, LI, LII, LIII, etc. These absorption edges correspond to the binding energy of electrons in the appropriate levels. Where the absorbed wavelength is shorter than the wavelength of one of the edges, an electron from the corresponding level can be excited. For instance, in Figure 1.9 an absorbed wavelength of 0.3 Å is shorter than the K absorption edge of barium (0.332 Å) and hence photoelectric absorption in the K level can occur. For an absorbed wavelength of 0.4 Å, however, photoelectric absorption in the K level certainly cannot occur. Thus, in general terms, each time the wavelength increases to a value in excess of a certain absorption edge, one of the terms in Equation 1.13 drops out with a corresponding decrease in the value of the total absorption term. Mass attenuation coefficients are well documented for most of the X-ray region, and the data are readily available in tabular form [15, 16]. Where the specimen is made up of n elements, the total mass attenuation coefficient of the specimen μs is given by

Figure 1.9. The absorption curve for barium, plotted on a log/log scale showing the contributions of the different levels.

From R. Jenkins, X-Ray Fluorescence Spectrometry, p. 10, Fig. 1-4.

Copyright © 1988, John Wiley & Sons, Inc. Reprinted by permission of the publisher.

(1.14)

where wi is the weight fraction of element i.

1.7. SAFETY CONSIDERATIONS

It has been shown that X-rays are beams of energetic electromagnetic radiation that ionize matter with which they interact by ejecting electrons from their atoms. The extent of the ionization, absorption, and even molecular change of the material depends on the quantity (radiation flux and intensity) and the quality (the spectral distribution of the photon energy) of the radiation. Living organisms that are exposed to various doses of X-radiation can be injured by such exposures, and death may result if the exposure is particularly severe (see Figure 1.11). The amount of damage done to the body by the radiation is often difficult to estimate, but Figure 1.10 gives typical effects of various levels of exposure to human beings. The extent of the damage depends on the energy of the radiation, the total dose received, the type of tissue exposed, the dose rate, and the volume of the body exposed. It is thus vitally imperative that all operators of X-ray instruments be knowledgeable in their use to protect themselves and others from injury [17–19].

Figure 1.10. Units for the measure of radiation exposure.

Figure 1.11. Effects of radiation exposure.

REFERENCES

1. Le Galley, D. P. A type of Geiger-Muller counter suitable for the measurement of diffracted Mo K X-rays. Rev. Sci. Instrum.6, 279–283 (1935).

2. Parrish, W., and Gordon, S. G. Precise angular control of quartz-cutting by X-rays. Am. Mineral.30, 326–346 (1945).

3. Friedman, H. A Geiger counter spectrometer for industrial research. Electronics April (1945).

4. Kramers, H. A. On the theory of X-ray absorption and of the continuous X-ray spectrum. Philos. Mag. [6]. 46, 836–871 (1923).

5. Moseley, H. G. J. The high frequency spectra of the elements. Philos. Mag. [6] 26, 1024–1034 (1912); 27, 703–714 (1913).

6. Dorgelo, H. B. Photographic photometry of line spectra. Phys. Z.26, 756–793 (1925).

7. Jenkins, R., Manne, R., Robin, J., and Senemaud, C. Nomenclature, symbols, units and their usage in spectrochemical analysis. VIII. Nomenclature system for X-ray spectroscopy. Pure Appl. Chem.63, 736–746 (1991).

8. Snyder, R. L. Analytical profile fitting of X-ray powder diffraction profiles in Rietveld analysis. In The Rietveld Method (R. A. Young, ed.), Chapter 7, pp. 111–131. Oxford Univ. Press, Oxford, 1993.

9. Bearden, J. A. X-ray wavelengths. Rev. Mod. Phys.39, 78–124 (1967).

10. International Critical Tables for X-ray Crystallography, Vol. IV: Revised and Supplementary Tables. Kynoch Press; Birmingham, England, 1974.

11. Cauchois, Y., and Senemaud, C. International Tables of Selected Constants, Vol. 18: Wavelengths of X-ray Emission Lines and Absorption Edges. Pergamon, Oxford, 1978.

12. Deslattes, R. D., Henins, A., and Kessler, E. G., Jr. Accuracy in X-ray wavelengths. In Accuracy in Powder Diffraction, NBS Spec. Publ. 567. U.S. Dept. of Commerce, National Bureau of Standards, Gaithersburg, MD, 1980.

13. Bearden, J. A., Henins, A., Marzolf, J. G., Sauder, W. C., and Thomsen, J. S. Precision determination of standard reference wavelengths for X-ray spectroscopy. Phys. Rev. A135, 899–910 (1964).

14. Härtwig, J., Hölzer, G., Wolf, J., and Förster, M. Remeasurement of the profile of characteristic Cu Kα emission line with high precision and accuracy. J. Appl. Crystallogr.26, 539–548 (1993).

15. Leroux, J., and Thinh, T. P. Revised Tables of X-ray Mass Attenuation Coefficients. Corporation Scientifique Claisse Inc., Sainte-Foy, Quebec, Canada, 1984.

16. Wilson, A. J. C., ed. International Tables for Crystallography, Vol. C: Mathematical, Physical and Chemical Tables. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.

17. Jenkins, R., and Haas, D. J. Hazards in the use of X-ray analytical instrumentation. X-Ray Spectrom.2, 135–141 (1973).

18. Jenkins, R., and Haas, D. J. Incidence, detection and monitoring from X-ray analytical instrumentation. X-Ray Spectrom.4, 33–42 (1975).

19. Upton, A. C., Health effects of low-level ionizing radiation. Phys. Today, August pp. 34–39 (1991).

1Confusion may occur in the study of early papers in this field since the term X-ray spectrometer referred to a system incorporating a crystal diffracting medium. The modern term spectrometer refers to an instrument employing a crystal or grating to separate a polychromatic beam of radiation into its constituent wavelengths. A diffractometer utilizes a monochromatic beam of radiation to yield information about d-spacings and intensities from a single crystal or crystalline powder.

CHAPTER 2