Elements of X-Ray Diffraction . A Volume in Addison-Wesley Series in Metallurgy and Materials.

519 Pages·1959·32.88 MB·English

by  B.D. Cullity

ELEMENTS OF
X-RAY DIFFRACTION
ADDISON-WESLEY METALLURGY SERIES
MORRIS COHEN, ConsultingEditor
Cidlity ELEMENTS OF X-RAY DIFFRACTION
Guy ELEMENTS OF PHYSICAL METALLURGY
Norton ELEMENTS OF CERAMICS
Schuhmann METALLURGICAL ENGINEERING
VOL. I: ENGINEERING PRINCIPLES
Wagner THERMODYNAMICS OF ALLOYS
ELEMENTS OF
X-RAY DIFFRACTION
by
B. D. CULLITY
AssociateProfessorofMetallurgy
UniversityofNotre Dame
ADDISON-WESLEY PUBLISHING COMPANY, INC.
READING, MASSACHUSETTS
Copyright 1956
ADD1SON-WESLEY PUBLISHING COMPANY, Inc.
Printed ni the United States ofAmerica
ALL RIGHTS RESERVED. THIS BOOK, OR PARTS THERE-
OF, MAY NOT BE REI'RODlCED IN ANY FORM WITHOUT
WRITTEN PERMISSION OF THE PUBLISHERS
Library ofCongress Catalog No 56-10137
PREFACE
X-ray diffraction is a tool for the investigation of the fine structure of
matter. This technique had its beginnings in von Laue's discovery in 1912
that crystals diffract x-rays, the manner of the diffraction revealing the
structure of the crystal. At first, x-ray diffraction was used only for the
determination of crystal structure. Later on, however, other uses were
developed, and today the method is applied, not only to structure deter-
mination, but to such diverse problems as chemical analysis and stress
measurement, to the study of phase equilibria and the measurement of
particle size, to the determination of the orientation of one crystal or the
ensemble of orientations in a polycrystalline aggregate.
The purpose of this book is to acquaint the reader who has no previous
knowledge of the subject with the theory of x-ray diffraction, the experi-
mental methods involved, and the main applications. Because the author
is a metallurgist, the majority of these applications are described in terms
of metals and alloys. However, little or no modification of experimental
method is required for the examinatiorrof nonmetallic materials, inasmuch
as the physical principles involved do not depend on the material investi-
gated. This book should therefore be useful to metallurgists, chemists,
physicists, ceramists,mineralogists,etc.,namely,toallwhousex-raydiffrac-
tion purely as alaboratory tool for the sort of problems alreadymentioned.
Members of this group, unlike x-ray crystallographers, are not normally
concerned with the determination of complex crystal structures. For this
reason the rotating-crystal method and space-group theory, the two chief
tools in the solution of such structures, are described only briefly.
This is a book of principles and methods intended for the student, and
not a reference book for the advanced research worker. Thus no metal-
lurgical data are given beyond those necessary to illustrate the diffraction
methods involved. For example, the theory and practice of determining
preferred orientation are treated in detail, but the reasons for preferred
orientation, the conditions affecting its development, and actual orien-
tations found in specific metals and alloys are not described, because these
topics are adequately covered in existing books. In short, x-ray diffrac-
tion is stressed rather than metallurgy.
The book is divided into three main parts: fundamentals, experimental
methods, and applications. The subject of crystal structure is approached
through, and based on, the concept of the point lattice (Bravais lattice),
because the point lattice of a substance is so closely related to its diffrac-
VI PREFACE
tion pattern. The entire book is written in terms of the Bragg law and
can be read without any knowledge of the reciprocal lattice. (However, a
brieftreatment ofreciprocal-lattice theory isgiven in an appendixfor those
who wish to pursue the subject further.) The methods of calculating the
intensities of diffracted beams are introduced early in the book and used
throughout. Since a rigorous derivation of many of the equations for dif-
fracted intensity is too lengthy and complex a matter for a book of this
kind, I have preferred asemiquantitative approachwhich, although it does
not furnish a rigorous proof of the final result, at least makes it physically
reasonable. This preference is based on my conviction that it is better
for a student to grasp the physical reality behind a mathematical equation
than to be able to glibly reproduce an involved mathematical derivation
of whose physical meaning he is only dimly aware.
Chapters on chemical analysis by diffraction and fluorescence have been
included because of the present industrial importance of these analytical
methods. In Chapter 7 the diffractometer, the newest instrument for dif-
fraction experiments, is described in some detail here the material on the
;
various kinds of counters and their associated circuits should be useful,
not only to those engaged in diffraction work, but also to those working
with radioactive tracers or similar substances who wish to know how their
measuring instruments operate.
Each chapter includes a set of problems. Many of these have been
chosen to amplify and extend particular topics discussed in the text, and
as such they form an integral part of the book.
Chapter 18 contains an annotatedlist ofbooks suitable forfurtherstudy.
The reader should become familiar with at least a few of these, as he pro-
gresses through this book, in order that he may know where to turn for
additional information.
Like any author of a technical book, I am greatly indebted to previous
writers on this and allied subjects. I must also acknowledge my gratitude
totwoofmyformerteachersat theMassachusetts InstituteofTechnology,
Professor B. E. Warren and Professor John T. Norton: they will find many
an echo of their own lectures in these pages. Professor Warren has kindly
allowed me to use many problems of his devising, and the advice and
encouragement of Professor Norton has been invaluable. My colleague at
Notre Dame, Professor G. C. Kuczynski, has read the entire book as it was
written, and his constructive criticisms have been most helpful. I would
also like to thank the following, each of whom has read one or more chap-
ters and offered valuable suggestions: Paul A. Beck, Herbert Friedman,
S. S. Hsu, Lawrence Lee, Walter C. Miller, William Parrish, Howard
Pickett, and Bernard Waldman. I am also indebted to C. G. Dunn for
the loan of illustrative material and to many graduate students, August
PREFACE Vll
Freda in particular, who have helped with the preparation of diffraction
patterns. Finally butnot perfunctorily, I wish to thank Miss Rose Kunkle
for her patience and diligence in preparing the typed manuscript.
B. D. CULLITY
Notre Dame, Indiana
March, 1956

CONTENTS
FUNDAMENTALS
CHAPTER 1 PROPERTIES OF X-RAYS 1
1-1 Introduction 1
1-2 Electromagnetic radiation 1
1-3 The continuous spectrum . 4
1-4 The characteristic spectrum 6
1-5 Absorption . 10
1-6 Filters 16
1-7 Production of x-rays 17
1-8 Detection of x-rays 23
1 9 Safety precautions . 25
CHAPTER 2 THE GEOMETRY OF CRYSTALS 29
^2-1 Introduction 29
.
J2-2 Lattices 29
.
2-3 Crystal systems 30
^2-4 Symmetry 34
2-5 Primitive and nonprimitive cells 36
2-6 Lattice directions and planes * . 37
J
2-7 Crystal structure 42
2-8 Atom sizes and coordination 52
2-9 Crystal shape 54
2-10 Twinned crystals . 55
2-11 The stereographic projection . . 60
CHAPTER 3 DIFFRACTION I: THE DIRECTIONS OF DIFFRACTED BEAMS 78
.78
3-1 Introduction
.
3-2 Diffraction f. 79
^3-3 The Bragg law * ' . 84
3-4 X-ray spectroscopy 85
3-5 Diffraction directions - 88
3-6 Diffraction methods 89
.
3-7 Diffraction under nonideal conditions 96
.
CHAPTER 4 DIFFRACTION II: THE INTENSITIES OF DIFFRACTED BEAMS . 104
4-1 Introduction 104
4-2 Scattering by an electrons . . 105
4-3 Scattering by an atom >, . / 108
4-4 Scattering bya unit cell */ . Ill
CONTENTS
4-5 Some useful relations .^ 118
4-6 Structure-factor calculations 118
4-7 Application to powder method ' 123
4-8 Multiplicity factor 124
4-9 Lorentz factor 124
1-10 Absorption factor 129
4-11 Temperature factor 130
4-12 Intensities of powder pattern lines 132
4-13 Examples of intensity calculations 132
4-14 Measurement of x-ray intensity 136
EXPERIMENTAL METHODS
LPTER 5 LAUE PHOTOGRAPHS 138
5-1 Introduction 138
5-2 Cameras 138
.
5-3 Specimen holders .141443
5-4 Collimators
.
5-5 The shapes of Laue spots . 146
kPTER 6 POWDER PHOTOGRAPHS .149
.
6-1 Introduction . .... 149
6-2 Debye-Scherrer method . 149
6-3 Specimen preparation 153
6-4 Film loading . . 154
6-5 Cameras for high an.d l.ow.temperatures . 156
6-6 Focusing cameras . 156
6-7 Seemann-Bohlin camera . 157
.160
6-8 Back-reflection focusing cameras . .
6-9 Pinhole photographs . 163
.165
6-10 Choice of radiation .
6-11 Background radiation . 166
6-12 Crystal monochromators . 168
6-13 Measurement of line position 173
6-14 Measurement of line intensity . 173
VPTER 7 DlFFRACTOMETER MEASUREMENTS 177
....
7-1 Introduction . . . 177
7-2 General features 177
7-3 X-ray optics . . . - ... 184
7-4 Intensity calculations . 188
7-5 Proportional counters . . ... . .. 191930
7-6 Geiger counters . .
7-7 Scintillation counters... . .... .- 220021
7-8 Sealers
.
7-9 Ratemeters . - 206
7-10 Use of monochromators 211