ALL 24 CHAPTERS COVERED
Solution Sets for Editions 1 and 2
SOLUTIONS MANUAL
,Structure of Materials:
An Introduction to
Crystallography,
Diffraction, and
Symmetry
Solution Sets for
Editions 1 and 2
Marc De Graef
Carnegie Mellon University, Pittsburgh
Michael E. McHenry
Carnegie Mellon University, Pittsburgh
This version contains complete solutions for chapters 1 through 17 of both
the first and second editions as well as partial solutions for chapters 18 and
beyond. This file (created on September 25, 2012) will be updated throughout
the Fall of 2012 until all solutions are completed.
,Problems and Solutions for the First Edition
This PDF file contains all the problems and their solutions for the first edition
of our book. To preserve continuity, we have kept the original section number-
ing of the first edition intact.
Note that Chapter 14 does not have an associated Problem set.
While we have done our best to provide correct solutions to (nearly) all the
problems, it is of course possible that errors have slipped between the cracks;
if you find an error, we would appreciate it if you would let us know by email.
Problems and Solutions for the Second Edition
This PDF file also contains all the problems and their solutions for the second
edition of our book. For each chapter, you will find first the four problems
that are listed in the book, along with their solutions. This is then followed by
supplemental problems and solutions. For continuity reasons, the sections in
this solution manual are numbered according to the corresponding sections in
the second edition.
Note that the solution set for each chapter of the second edition can be found
immediately following the solution set for the corresponding chapter in the
first edition.
Much more information can be found on the book’s web site,
http://som.web.cmu.edu/.
, CHAPTER
1 Materials and materials
properties
1.8 Problems
(i) Electron diffraction and the de Broglie wave length: Consider electrons
with kinetic energies of 1 eV; 100 eV; and 10 keV.
(a) Find the de Broglie wave length in each case, and consider whether
the electron would be appropriate for use in electron diffraction
determinations of crystal structures. (Ignore relativistic corrections.)
(b) Calculate m0 c2 for an electron and the size of the relativistic correc-
tion for the case of 100 keV electrons.
Answer:
(a) Ignoring relativistic corrections because they are small. For 1 eV:
h h 1.22639
λ= =√ = √ = 1.26639 nm
p 2m0 eV V
For 100 eV we find:
λ = 0.122639 nm,
and for 10 keV:
λ = 0.0122639 nm.
100 eV and 10 keV electrons have sufficiently small wavelengths for
electron diffraction. However, higher energy electrons penetrate fur-
ther in transmission experiments, so 100 keV to 1 MeV are more
appropriate. In those cases, we must use the relativistically corrected
expression for the wave length.
(b) m0 c2 for an electron is:
( )2
9.1 × 10−31 kg × 3.0 × 108 m/s
m0 c2 = = 512 keV.
1.6 × 10−19 J/eV
1
Solution Sets for Editions 1 and 2
SOLUTIONS MANUAL
,Structure of Materials:
An Introduction to
Crystallography,
Diffraction, and
Symmetry
Solution Sets for
Editions 1 and 2
Marc De Graef
Carnegie Mellon University, Pittsburgh
Michael E. McHenry
Carnegie Mellon University, Pittsburgh
This version contains complete solutions for chapters 1 through 17 of both
the first and second editions as well as partial solutions for chapters 18 and
beyond. This file (created on September 25, 2012) will be updated throughout
the Fall of 2012 until all solutions are completed.
,Problems and Solutions for the First Edition
This PDF file contains all the problems and their solutions for the first edition
of our book. To preserve continuity, we have kept the original section number-
ing of the first edition intact.
Note that Chapter 14 does not have an associated Problem set.
While we have done our best to provide correct solutions to (nearly) all the
problems, it is of course possible that errors have slipped between the cracks;
if you find an error, we would appreciate it if you would let us know by email.
Problems and Solutions for the Second Edition
This PDF file also contains all the problems and their solutions for the second
edition of our book. For each chapter, you will find first the four problems
that are listed in the book, along with their solutions. This is then followed by
supplemental problems and solutions. For continuity reasons, the sections in
this solution manual are numbered according to the corresponding sections in
the second edition.
Note that the solution set for each chapter of the second edition can be found
immediately following the solution set for the corresponding chapter in the
first edition.
Much more information can be found on the book’s web site,
http://som.web.cmu.edu/.
, CHAPTER
1 Materials and materials
properties
1.8 Problems
(i) Electron diffraction and the de Broglie wave length: Consider electrons
with kinetic energies of 1 eV; 100 eV; and 10 keV.
(a) Find the de Broglie wave length in each case, and consider whether
the electron would be appropriate for use in electron diffraction
determinations of crystal structures. (Ignore relativistic corrections.)
(b) Calculate m0 c2 for an electron and the size of the relativistic correc-
tion for the case of 100 keV electrons.
Answer:
(a) Ignoring relativistic corrections because they are small. For 1 eV:
h h 1.22639
λ= =√ = √ = 1.26639 nm
p 2m0 eV V
For 100 eV we find:
λ = 0.122639 nm,
and for 10 keV:
λ = 0.0122639 nm.
100 eV and 10 keV electrons have sufficiently small wavelengths for
electron diffraction. However, higher energy electrons penetrate fur-
ther in transmission experiments, so 100 keV to 1 MeV are more
appropriate. In those cases, we must use the relativistically corrected
expression for the wave length.
(b) m0 c2 for an electron is:
( )2
9.1 × 10−31 kg × 3.0 × 108 m/s
m0 c2 = = 512 keV.
1.6 × 10−19 J/eV
1
