Table Of ContentQuantitative X-Ray Diffractometry
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Lev S. Zevin Giora Kimmel
Quantitative X-Ray
Diffractometry
Edited by Inez Mureinik
With 70 Illustrations
, Springer
Lev S. Zevin (deceased) Giora Kimmel
The Institutes for Applied Research and Department of Materials Engineering
Department of Materials Engineering Ben-Gurion University of the Negev
Ben-Gurion University of the Negev Beer-Sheva 84105, Israel
Beer-Sheva 84105, Israel
Edited by
Inez Mureinik
The Institutes for Applied Research
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
Library of Congress Cataloging-in-Publication Data
Zevin, Lev S.
Quantitative X-ray diffractometry / Lev S. Zevin, Giora Kimmel;
edited by Inez Mureinik.
p. cm.
Includes bibliographical references and index.
ISBN-13:978-1-4613-9537-9 e-ISBN-13:978-1-4613-9535-5
DOl: 10.1007/978-1-4613-9535-5
1. X-rays-Diffraction. 2. X-rays-Diffraction-Industrial
applications. -I. Kimmel, Giora. II. Mureinik, Inez. III. Title.
QC482.D5Z48 1995
545'.81-dc20 95-19428
Printed on acid-free paper.
© 1995 Springer-Verlag New York, Inc.
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Production managed by Hal Henglein; manufacturing supervised by Jeffrey Taub.
Camera-ready copy prepared from the editor's Microsoft Word files.
987654321
ISBN-13 :978-1-4613-9537-9
Preface
The first book dealing with quantitative analysis in powder mixtures
(if only in one chapter) was that of Klug and Alexander, X-ray
Diffraction Procedures, which was published in 1954. The only work
dedicated entirely to quantitative X-ray powder diffraction (QXRD)
that has appeared since that time is the 200-page monograph of Davis,
Reference Intensity Method of QXRD Analysis. However, this publica
tion, which appeared in 1988, was devoted only to a single aspect of
QXRD, as reflected in its title. On the other hand, most books on the
characterization of materials by X-ray powder diffraction do include a
section or a chapter on QXRD. In contrast to structure determination, in
which single crystal methods are favored, quantitative analysis of
phases is specific to the powder method, and the lack of a special book
dealing with QXRD analysis is inexplicable. The aim of the present
book is to fill this void.
Since the terminology pertaining to QXRD is not always standard
ized in the literature, the reader should pay special attention to
descriptions of the particular methodology and to the formulation of
each method in order to compare similar procedures described under
different names by other workers.
The book is divided into six chapters. The first chapter is introduc
tory, giving the history of X-ray powder diffraction and comparing
QXRD to other analytical methods. The second chapter deals with the
physical background of X-ray powder diffraction in general and with
its application to QXRD, with special emphasis on the attenuation of
X-rays and microabsorption. The third chapter is devoted to instrumen
tation, with particular reference to the Bragg-Brentano diffractometer.
Other powder facilities are also reviewed in detail.
The methodology of QXRD is given in the fourth chapter, which
constitutes the core of the book. A variety of problems and solutions in
the field of quantitative phase analysis are given. The chapter starts
with the general case, in which all absorption coefficients are known,
and then continues with the internal standard method (including the
addition methods of doping and dilution); full-phase analysis
(external standard); the reference intensity ratio method; the full
diffraction pattern approach; standardl ess methods; combination of
v
vi Preface
X-ray diffraction with chemical analysis; crystallinity of polymers;
and analysis of low-mass samples.
The fifth chapter is devoted to practical aspects of QXRD: optimal
data collection; hints for sample preparation; intensity measurement;
absorption; analytical standards; pattern treatment and simulation;
correction of preferred orientation; and errors and limitations. The
section on preferred orientation was kindly edited by Prof. Matti
Jarvinen. The final ~hapter addresses some applications, most of them
industrial.
The unique quality of this book lies in the fact that it brings together
between one set of covers all the aspects of the multifaceted discipline
of QXRD, and we thus trust that it will make a major contribution to
promoting QXRD in a wide spectrum of applications.
Giora Kimmel
Editor's preface
It might seem strange to dedicate a book to the author himself, but this
book is dedicated to the memory of Lev Zevin, who sadly did not live to
see its completion. Zevin, as he was known affectionately to those of us
who worked with him at Ben-Gurion University of the Negev, was an
outstanding diffractionist-the range of his knowledge and experience
is reflected in the scope and depth of this work. Indeed, the concept of
the book-of bringing together all the facets of quantitative X-ray
analysis, both theoretical and applied-evolved during many years of
teaching, research and analytical work, first in the former USSR and
later in Israel. I sincerely hope that what stands on these pages will be
a fitting tribute to a scientist of his caliber.
Inez Mureinik
vii
Acknowledgments
Prof. Lev Zevin dedicated his life to scientific research. He was a
hard-working, active, and creative personality who never hesitated to
share his knowledge and inexhaustible sources of original ideas with
all who came into contact with him-researchers in different fields,
colleagues, and especially the students who were so important to him.
We hope that this book will contribute to progress in the field of
quantitative X-ray diffractometry. The methods of QXRD analysis
outlined in this book will be of use to researchers and scientists at
universities and industrial laboratories who are investigating
compounds with special technological properties; to chemists and
physicists working on the synthesis and properties of new materials; to
geologists studying natural deposits; and to specialists dealing with ore
beneficiation. These methods also have important applications in the
routine technological processes of the cement industry. If this book will
serve as an everyday working manual for all these fields, it will be the
best way to preserve the memory of Prof. Zevin.
Prof. Zevin started working on this book a few years before his
death. At the time he passed away, the book was almost completely
written, except for the last few sections of Chapter 6. The final editing
and completion of the book were accomplished after his death. Before
he died, Prof. Zevin asked his colleague and friend, Prof. Giora
Kimmel, to see the book through to completion. We thank him for his
part.
The publication of the book was made possible due to the efforts of
the highly qualified and professional editor, Ms. Inez Mureinik. We
would like to express our deepest gratitude to her.
Special thanks are due to Prof. M. Jarvinen of Lappeenranta
University of Technology, Finland, who read and edited the sections on
crystallite orientation.
We would also like to thank Ms. Shula Rabinovitz for her highly
professional illustrations; Ms. Marion Milner for typing the manuscript;
and Ms. Dorot Imber for her understanding and encouragement.
Finally, we would like to thank Dr. Thomas von Foerster, Springer
Verlag's Senior Editor for Physics and Mathematics, for his
sympathetic attitude and patience, and the Production staff at
ix
x Acknowledgments
Springer-Verlag, for their investment of time and effort in the
production aspects of the book.
If we-his wife and children-have inadvertently omitted any of
Prof. Zevin's colleagues who were involved in the writing of this book,
we apologize and thank them.
Isabella, Shaul, and Miriam Zevin
Contents
Preface. ........................................................................................... v
EdI' tor' s pre ace .......f..................................."............................... VII
Acknowledgments ..................................................................... ix
1 Introduction .............................................................................. 1
1.1 Phase analysis-when and why ............................................. 1
1.2 Phase analysis as an analytical method ................................. 2
1.2.1 Direct methods of phase analysis ............................... 2
1.2.2 Indirect methods of phase analysis ............................. 3
1.2.3 General approach to phase quantification ................. .4
1.3 History of quantitative X-ray phase analysis ......................... 5
1.3.1 Quantification techniques .......................................... 5
1.3.2 Instrumentation .......................................................... 8
2 Physical basis .......................................................................... 10
2.1 Interaction of X-rays with materiaL .................................... 10
2.1.1 Scattering of X-rays ................................................. 11
2.1.2 Absorption of X-rays ................................................ 15
2.1.3 Various forms of absorption coefficients .................... 16
2.2 Intensity in powder diffraction ............................................. 18
2.2.1 General expression derived from the kinematic
theory of diffraction ................................................ 19
2.2.2 Polarization factor in X-ray diffractometry .............. 21
2.2.3 Extinction of X-rays .................................................. 22
2.3 Background-angle variation and intensity .......................... 24
2.3.1 Introduction ............................................................. 24
2.3.2 Scattering of continuous radiation ............................. 25
2.3.3 Scattering of characteristic radiation ....................... 26
2.4 X-ray diffraction by nonhomogeneous polycrystalline
materials ............................................................................. 29
2.4.1 Introduction ............................................................. 29
xi
