Table Of ContentMATERIALS SCIENCE
FOUNDATIONS of CRYSTALLOGRAPHY
with Computer Applications WITH VITALSOURCE®
EBOOK
SECOND EDITION
Taking a straightforward, logical approach that emphasizes symmetry and crystal re- Julian
lationships, Foundations of Crystallography with Computer Applications, Second
Edition provides a thorough explanation of the topic for students studying the solid
w F
state in chemistry, physics, materials science, geological sciences, and engineering. It
is also written for scientists who want to teach themselves. Computers are an essential i O
t
part of crystallography, and computer-based exercises are integrated into this book. h U
The material is presented with the goal of creating an understanding of how atoms are
arranged in crystals and how crystal systems are related to each other. CN
oD
See What’S NeW iN the SecoNd editioN:
m
• Eight new chapters that give first an overview and then detailed crystallographic A
analyses of one crystal chosen for each of the seven crystal systems pT
• Numerous examples of molecules illustrating point and space group
uI
symmetries O
t
• Coverage of special topics that naturally arise in the treatment of the crystals
e
N
• Suggestions for student projects with data that can be found in the free r
Teaching Subset of the Cambridge Structural Database S
A
• Point group and space group diagrams have been color coded using a new
po
scheme devised by the author to emphasize the change of handedness of the
f
symmetry operations p
• All the Starter Programs have been rewritten and improved, and a new one lC
i
has been added in Chapter 6 on the graphing of intensity vs. 2€ for powder cR
diffraction data a
Y
• New appendices contain detailed information about the 32 three-dimensional t
point groups and the 10 two-dimensional point groups iS
o
T
The book explains the individual entities, such as symmetry operations, and also ex- n
A
plains how they fit together in a larger context. Coverage includes lattices, symmetry s
operations, metric matrices, point groups, space groups, reciprocal lattices, properties L
of x-rays, and electron density maps, all leading to a formal description of the crystal L
structures and an interpretation of the published crystallographic data. The author O
connects general properties such as the piezoelectric effect, compressibility, thermal
expansion, and Mosely’s relationship in ordering the elements of the periodic table, G
giving students a thorough foundation in the subject.
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SECOND
EDITION
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Foundations
of
Crystallography
with
Computer applications
sECond Edition
Foundations
of
Crystallography
with
Computer applications
sECond Edition
Maureen M. Julian
Department of Materials Science and Engineering
Virginia Tech, USA
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20140227
International Standard Book Number-13: 978-1-4665-5292-0 (eBook - PDF)
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Visit the Taylor & Francis Web site at
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This book is dedicated to the future of all young
people, particularly my grandchildren
Carla Itzel Julian
Isaac Batian Mikanatha
Jonathan Rey Julian
and all the students who have taken, or will take,
the crystallography journey with me.
Preface
This book presents the fundamentals of crystallography to university and college students
in biology, chemistry, engineering, geological sciences, materials science, and physics. It is
also appropriate for scientists who want to teach themselves.
The chapters are
• Chapter 1: Lattices
• Chapter 2: Unit Cell Calculations
• Chapter 3: Point Groups
• Chapter 4: Space Groups
• Chapter 5: Reciprocal Lattice
• Chapter 6: Properties of X-rays
• Chapter 7: Electron Density Maps
• Chapter 8: Introduction to the Seven Crystals Exemplifying the Seven Crystal Systems
• Chapter 9: Triclinic System: DL Leucine
• Chapter 10: Monoclinic System: Sucrose
• Chapter 11: Orthorhombic System: Polyethylene
• Chapter 12: Tetragonal System: α-Cristobalite
• Chapter 13: Trigonal System: H B −2,3K+,Br−
12 12
• Chapter 14: Hexagonal System: Magnesium
• Chapter 15: Cubic System: Acetylene
This second edition includes new material on the color coding of the symbol and gen-
eral position diagrams. In the first seven chapters many more molecular examples have been
added, including a detailed description of a third model crystal—caffeine monohydrate. There
are eight new chapters. In seven of these chapters, one for each crystal system, the reader is
introduced to a detailed crystallographic analysis of a crystal illustrating its crystal system.
Many new topics have been added, such as neutron diffraction. A new appendix on point
vii
viii ◾ Preface
groups gives detailed information including a representative matrix for each symmetry opera-
tion and the color-coded stereographic projections. The Brief Teaching Edition of Volume A of
the International Tables for Crystallography is the companion book from which almost all the
examples and exercises are based as is appropriate. The Starter Programs have been updated.
GOALS OF THE BOOK
The goal of this book is to describe the symmetry tools used to interpret the crystal struc-
ture, that is, the spatial arrangement of atoms in a crystal.
The material is given in a logical order with an emphasis on how crystal systems are
related to each other. The ideas proceed from simple to complex. The theoretical material is
developed extensively in two dimensions and then extended to three dimensions.
An emphasis is on crystallographic interrelationships. For example, many point group
trees have been drawn, not only with their point group names, but also with the general
position and symbol stereographic projection icons.
This book aims to communicate an understanding of how to read reports on the
arrangement of atoms in any crystal that may be of interest. Once a crystallographer has
analyzed the arrangement of atoms, the results are reported in a code that is published in
the International Tables for Crystallography. The code is terse, but it captures the essence
of a body of theory that deals with all the ways atoms can be arranged in a crystal.
Finally, topics are included to show how crystallography can be applied. For example,
thermal expansion, compressibility, and piezoelectricity are discussed.
MATHEMATICS PREREQUISITES AND COMPUTERS
The mathematics prerequisite for this book is an introductory knowledge of linear algebra
including matrices and determinants, although these matters are explained and illustrated
in the course of this book.
Linear algebra allows exploitation of the power of the metric matrix. The metric matrix
incorporates the information for the lattice—the lattice constants a, b, c, α, β, and γ—into
a single matrix. All the crystal systems from triclinic to cubic are accommodated in one
technique. This allows easy computation of important crystallographic quantities, such
as bond lengths, bond angles, unit cell volumes, reciprocal lattice constants, interplanar
angles, and d-spacings in all crystal systems.
Computers are an essential part of crystallography, and appropriate computer-based
exercises are integrated into this book. The computing requirement is a familiarity with
an advanced computer language like MATLAB. However, Starter Programs are supplied
to help considerably with the details of the MATLAB language. Videos are on the book
website https://sites.google.com/a/vt.edu/foundations_of_crystallography/.
TEACHING WITH COLOR CODING OF SYMMETRY DIAGRAMS
This second edition includes new material on the color coding of the symbol and general
position diagrams. In the first edition of this book many diagrams were colored to dis-
tinguish crystallographically distinct graphical symbols, such as the four crystallographi-
cally distinct rotations in p2. Colors were also used to distinguish guidelines from the more
