2nd Edition

Foundations of Crystallography with Computer Applications

ISBN 9780429097393
Published October 3, 2014 by CRC Press
680 Pages

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Book Description

Taking a straightforward, logical approach that emphasizes symmetry and crystal relationships, Foundations of Crystallography with Computer Applications, Second Edition provides a thorough explanation of the topic for students studying the solid 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 part of crystallography, and computer-based exercises are integrated into this book. 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.

See What’s New in the Second Edition:

  • Eight new chapters that give detailed crystallographic analyses of one crystal chosen for each crystal system
  • Numerous molecular examples and suggestions for student projects
  • Coverage of special topics that naturally arise in the treatment of the crystals
  • Suggestions for student projects with date that can be found in the free Teaching Subset of the Cambridge Structural Database
  • Point group and space group diagrams have been color coded using a new scheme devised by the author to emphasize the change of handedness of the symmetry operations
  • All the Starter Programs have been rewritten and improved, and a new one has been added in Chapter 6 on the graphing of intensity vs. 2θ for powder diffraction data
  • New appendices contain detailed information about the 32 three-dimensional point groups and the 10 two-dimensional point groups

The book explains the individual entities, such as symmetry operations, and also explains how they fit together in a larger context. Coverage includes lattices, symmetry operations, metric matrices, point groups, space groups, reciprocal lattices, properties of x-rays, and electron density maps, all leading to a formal description of the crystal structures and an interpretation of the published crystallographic data. The author connects general properties such as the piezoelectric effect, compressibility, thermal expansion, and Mosely’s relationship in ordering the elements of the periodic table giving students a thorough foundation in the subject.

Print Versions of this book also include access to the ebook version.

Table of Contents

Chapter Objectives
Two-Dimensional Lattices
Two-Dimensional Basis Vectors and Unit Cells
Two-Dimensional Transformations between Sets of Basis Vectors
Three-Dimensional Basis Vectors, Unit Cells, and Lattice Transformations
Conversion into Cartesian Coordinates
A Crystal: Hexamethylbenzene
A Crystal: Anhydrous Alum
Effects of Temperature and Pressure on the Lattice Parameters
MATLAB Code: Starter Program for Chapter 1: Graphic of triclinic unit cell

Unit Cell Calculations
Chapter Objectives
Fractional Coordinates
Plotting Atoms in the Unit Cell
Calculation of Interatomic Bond Distances
Calculation of Interatomic Bond Angles
Area and Volume of the Unit Cell
Summary of Metric Matrix Calculations
Quartz Example
Transformation Matrices
HMB Example
Crystallographic Directions
Crystallographic Planes and Miller Indices
Revisiting Thermal Expansion and Isothermal Compressibility
MATLAB Code: Starter Program for Chapter 2: Graphic of HMB projection

Point Groups
Chapter Objectives
Group Theory
Symmetry Operations
Crystallographic Rotations
Summary of the Two-Dimensional Crystallographic Operations
Two-Dimensional Crystallographic Point Groups
Two-Dimensional Crystal Systems
Two-Dimensional Point Group Tree
Part II: Three Dimensions
Three-Dimensional Point Groups
Three-Dimensional Crystal Systems
Examples of Three-Dimensional Point Groups with Multiple Generators
Three-Dimensional Point Group Trees
Point Group Symmetry and Some Physical Properties of Crystals
MATLAB Code: Starter Program for Chapter 3: Point Group
Multiplication Table 1

Space Groups
Chapter Objectives
Part I: Two Dimensions
Two-Dimensional Bravais Lattices
Crystal Systems and the G Matrices
Two-Dimensional Sp ace Groups
Color Coding and Overview of the Two-Dimensional Symbol Diagrams
Recipe for Analyzing a Periodic Pattern
Primitive Cells for cm and c2mm
Two-Dimensional Space Group Tree
Summary of Two-Dimensional Space Groups
Part II: Three Dimensions
Three-Dimensional Bravais Lattices
Three-Dimensional Space Groups
HMB and Space Group No. 2, P1
AA and Space Group No. 150, P321
Caffeine Monohydrate and Two Effective Tools for Relating Symmetry and Structure
MATLAB Code: Starter Program for Chapter 4: Graphic of populated unit cell and projections

The Reciprocal Lattice
Chapter Objectives
The Reciprocal Lattice
Relationships between Direct and Reciprocal Lattices
Reciprocal Lattice Calculations for Three Crystals
Relationships between Transformation Matrices
Diffraction Pattern and the Reciprocal Lattice
Three Applications of the Reciprocal Lattice
MATLAB Code: Starter Program for Chapter 5: Graphic of reciprocal cell superimposed on direct unit cell

Properties of X-Rays
Chapter Objectives
The Discovery of X-rays
Properties of Waves
X-Ray Spectrum
The X-Ray Tube
X -Ray Diffraction
Synchrotron X-Rays
MATLAB Code: Starter Program for Chapter 6: Graphic of powder diffraction file

Electron Density Maps
Chapter Objectives
Scattering by an Electron
Scattering by an Atom
Scattering by a Crystal
Some Mathematical Identities
Structure Factors for Some Crystals
Structure Factors for Centrosymmetric and Noncentrosymmetric Crystals
Electron Density Maps
Major Uses of Structure Factors
MATLAB Code: Starter Program for Chapter 7: Graphic of atomic scattering curve

Introduction to the Seven Crystals Exemplifying the Seven Crystal Systems
Chapter Objectives
Crystallographic Data for the Seven Crystal Examples
Presentation of Crystals in Chapters 9 through 15
Color-Coding Point Group and Space Group Diagrams
Crystal Selection Criteria
Student Projects
Distribution of Crystal Structures among Space Groups and Crystal Systems

Triclinic Crystal System: DL-Leucine
Chapter Objectives
DL-Leucine: Point Group Properties
DL-Leucine: Sp ace Group Properties
DL-Leucine: Direct and Reciprocal Lattices
DL-Leucine: Fractional Coordinates and Other Data for the Crystal Structure
DL-Leucine: Crystal Structure
DL-Leucine: Reciprocal Lattice and d-Spacings
DL-Leucine: Atomic Scattering Curves
DL-Leucine: Structure Factor

Monoclinic System: Sucrose
Chapter Objectives
Sucrose: Point Group Properties
Sucrose: Sp ace Group Properties
Sucrose: Direct and Reciprocal Lattices
Sucrose: Fractional Coordinates and Other Data for the Crystal Structure
Sucrose: Crystal Structure
Sucrose: Atomic Scattering Curves
Sucrose: Structure Factor

Orthorhombic Crystal System: Polyethylene
Chapter Objectives
Polyethylene: Point Group Properties
Polyethylene: Space Group Properties
Polyethylene: Direct and Reciprocal Lattices
Polyethylene: Fractional Coordinates and Other Data for the Crystal Structure
Polyethylene: Crystal Structure
Polyethylene: Reciprocal Lattice and d-Spacings
Polyethylene: Atomic Scattering Curves
Polyethylene: Structure Factor

Tetragonal System: α-Cristobalite
Chapter Objectives
α-Cristobalite: Point Group Properties
α-Cristobalite: Sp ace Group Properties
α-Cristobalite: Direct and Reciprocal Lattices
α-Cristobalite: Fractional Coordinates and Other Data for the Crystal Structure
α-Cristobalite: Crystal Structure
α-Cristobalite: Reciprocal Lattice and d-Spacings
α-Cristobalite: Atomic Scattering Curves
α-Cristobalite: Structure Factor

Trigonal Crystal System: H12B12-2, 3K+, Br-
Chapter Objectives
H12B12-2,3K+,Br-: Point Group Properties
H12B12-2,3K+,Br-: Space Group Properties
H12B12-2,3K+,Br-: Direct and Reciprocal Lattices
H12B12-2,3K+,Br-: Fractional Coordinates and Other Data for the Crystal Structure
Special Topic: Boron Icosahedron
H12B12-2,3K+,Br-: Crystal Structure
H12B12-2,3K+,Br-: Reciprocal Lattice and d-Sp acings
H12B12-2,3K+,Br-: Atomic Scattering Curves
H12B12-2,3K+,Br-: Structure Factor
Special Topic: H12B12-2,3K+,Br- Isotypic Crystal Structures

Hexagonal System: Magnesium
Chapter Objectives
Magnesium: Point Group Properties
Magnesium: Space Group Properties
Magnesium: Direct and Reciprocal Lattices
Magnesium: Fractional Coordinates and Other Data for the Crystal Structure
Magnesium: Crystal Structure
Magnesium: Reciprocal Lattice and d-Spacings
Magnesium: Atomic Scattering Curve
Magnesium: Structure Factor

Cubic System: Acetylene
Chapter Objectives
Acetylene: Point Group Properties
Acetylene: Space Group Properties
Acetylene: Direct and Reciprocal Lattices
Acetylene: Fractional Coordinates and Other Data for the Crystal Structure
Acetylene: Crystal Structure
Acetylene: Reciprocal Lattice and d-Spacings
Acetylene: Atomic Scattering Curves
Acetylene: Structure Factor
Appendix 1: Definitions,
Appendix 2: The Ten Two-Dimensional Point Groups,
Appendix 3: The Thirty-Two Three-Dimensional Point Groups,

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