2nd Edition

Foundations of Crystallography with Computer Applications

By Maureen M. Julian Copyright 2015
    680 Pages 601 Color Illustrations
    by CRC Press

    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.

    Lattices
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 1: Graphic of triclinic unit cell

    Unit Cell Calculations
    Chapter Objectives
    Introduction
    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
    Density
    Revisiting Thermal Expansion and Isothermal Compressibility
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 2: Graphic of HMB projection

    Point Groups
    Chapter Objectives
    PART I: TWO DIMENSIONS
    Introduction
    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
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 3: Point Group
    Multiplication Table 1

    Space Groups
    Chapter Objectives
    Part I: Two Dimensions
    Introduction
    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
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 4: Graphic of populated unit cell and projections

    The Reciprocal Lattice
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 5: Graphic of reciprocal cell superimposed on direct unit cell

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

    Electron Density Maps
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises
    MATLAB Code: Starter Program for Chapter 7: Graphic of atomic scattering curve

    Introduction to the Seven Crystals Exemplifying the Seven Crystal Systems
    Chapter Objectives
    Introduction
    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
    Introduction
    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
    Definitions
    Exercises

    Monoclinic System: Sucrose
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises

    Orthorhombic Crystal System: Polyethylene
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises

    Tetragonal System: α-Cristobalite
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises

    Trigonal Crystal System: H12B12-2, 3K+, Br-
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises

    Hexagonal System: Magnesium
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises

    Cubic System: Acetylene
    Chapter Objectives
    Introduction
    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
    Definitions
    Exercises
    References,
    Appendix 1: Definitions,
    Appendix 2: The Ten Two-Dimensional Point Groups,
    Appendix 3: The Thirty-Two Three-Dimensional Point Groups,
    Index

    Biography

    Maureen M. Julian earned an AB from Hunter College, New York City, with a double major in physics and mathematics, and a PhD from Cornell University in physical chemistry with a thesis in crystallography. She was a research fellow at University College, London, with Professor Dame Kathleen Lonsdale, a founder of the International Tables for Crystallography. The author has given several series of crystallography workshops for undergraduate and graduate students in various departments, including chemistry, geology, and materials science. Her interests include ab initio calculations, molecular bonding, and group theory.