Foundations of Crystallography with Computer Applications: 2nd Edition (Hardback) book cover

Foundations of Crystallography with Computer Applications

2nd Edition

By Maureen M. Julian

CRC Press

680 pages | 601 Color Illus.

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Hardback: 9781466552913
pub: 2014-10-03
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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,


Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / General
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Solid State Physics