Preface_1977_Diffraction-from-Materials

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Preface 
The atomic arrangement in condensed matter plays an important role in many 
areas of science and technology* materials science and engineering, chemistry, 
biology, physics, and electrical, civil, mechanical, and chemical engineering. 
Many of the exciting discoveries in these fields in the twentieth century stem 
from studies of atomic arrangements using the tools of diffraction: the nature of 
the structure and, hence, the functions of D N A and other biological molecules; 
the crystalline nature of metals, semiconductors, and insulators, and the links 
between these structures, their defects and the materials' properties; the elec­
tronic structure of atoms; what little we know of the structure of liquids and 
amorphous solids such as water and glass; surfaces and their interaction with the 
environment; particle sizes in catalysts and fine adsorbates; chemical analysis, 
stresses in materials, and so on. 
The broad interdisciplinary character of diffraction studies makes them par­
ticularly exciting. With the development of new tools such as the high-resolution 
electron microscope, high-intensity sources of radiation, new detectors, and the 
new spectroscopic techniques (x-ray, photoelectron, Auger, etc.), the horizon of 
problems that can be examined has greatly expanded. However, within each field 
diffraction and crystal structure is only one specialty and it is all too easy for this 
area to be developed in such a narrow way within a specific field that one loses 
sight of the basic principles and broad possibilities. This has indeed happened, 
for example, with chemsits trained only to work on structure determinations, and 
materials scientists who know how to take pictures on an electron microscope, 
but who often do not possess the basic knowledge about diffraction necessary to 
use or advance the theory pertinent to their particular device. 
It is our hope that this book will help bridge these gaps between different fields 
and place diffraction methods in proper perspective right from the start. The 
book is intended for use in the senior or first graduate year in a university. The 
first five chapters contain the basic information concerning crystal symmetry, 
kinematical scattering theory, and the physical properties of χ rays, electrons, 
and neutrons. The last three chapters develop in more detail three major topics: 
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xii PREFACE 
structure determination, defects in condensed matter, and dynamical scattering. 
We have tried to provide a suitable introduction to all these areas, and the major 
mathematical topics associated with them, including Fourier series and transform 
space, reciprocal lattice vectors, and convolution theory. 
4 4
Diffraction from Materials" evolved over a fifteen-year period and was 
tested in its present form in the classroom at Northwestern University for three 
years with three different instructors, and once at another university. Revisions, 
extensions, and deletions were carried out each time as a result of these tests; as 
painful as this sometimes was, we believe that the result is a text that can be used 
with some confidence. In addition, we have tried to present the information in a 
form that will be useful as a continuing reference for workers in this field. 
The first five chapters and perhaps the first few pages of Chapter 6 are suitable 
for a one-semester course at the level indicated, provided that the instructor 
chooses one or two radiations and eliminates the material on the other(s), or 
seriously condenses the material in Chapter 1. If less than a semester is available, 
say 10-11 weeks (the quarter employed in many U.S . universities), this conden­
sation is essential. As well as dealing with only one radiation, one might even 
think of teaching Chapters 1 and 2 as parts of other courses. In a full year all of 
Chapters 1-5 can readily be covered and one other chapter (say Chapter 6 on 
structures) can be used and expanded upon, or two of the remaining three chap­
ters can be covered. 
Of course, laboratory sessions are an integral part of a course in this area. 
Many problems in the text include original films or data for those cases where 
equipment is not readily available for a particular topic. As an example of a 
sequence of laboratories for such a course in which x-ray diffraction is em­
phasized, the instructor might consider the following: 
First Session drawing two-dimensional lattices, point groups, and space groups 
and identifying symmetry elements. (Escher's drawings are wonderful for 
the latter and a suitable reference is "Symmetry Aspects of M . C . Escher's 
Periodic Drawings" by C . H. MaGillavry, A . Oosthoek's Uitgeversmaat 
Schappij. NV. Utrecht, 1965.) 
Second Session examining models of real structures in detail and checking 
atom coordinates versus space group coordinates in the International Ta­
bles. 
Third Session stereographic projections. 
Fourth and Fifth Sessions the diffractometer and its electronics. 
Sixth Session chemical analysis using x-ray fluorescence. 
Seventh Session Laue pattern analysis. 
Eighth Session powder pattern analysis. 
Alternatively, the formal laboratory might stop after the fifth or sixth session 
and small groups might be given a project such as an unknown crystal and the 
freedom of the laboratory to determine its system, lattice, and space group, and 
PREFACE xiii 
as much as reasonable of the atom coordinates. While this route requires consid­
erable effort of the students, it is much more fun than the weekly " s e t " labora­
tory and perhaps more useful in the long run. In a year-long course, we believe 
such a project in some area of diffraction to be essential in at least the second 
half. 
Solutions for most of the problems are given, but the reader is advised to use 
these only as a last resort, after first expending considerable effort to solve the 
problems. It is, after all, the development of the thought process in an area that is 
its key. The reader is unlikely to see a problem later on identical to the one he is 
solving, so that learning the solution alone is not enough. 
Parts of this work are based on a textbook, now out of print, written by one 
of the authors (Cohen) and entitled, "Diffraction Methods in Materials Science," 
Macmillan, New York, 1966.