Foundations of Crystallography with Computer Applications

X-ray crystallography provides a unique opportunity to study the arrangement of atoms in a molecule. This book’s modern computer-graphics centered approach facilitates the extrapolation of these valuable observations. A unified treatment of crystal systems, the book explains how atoms are arranged in crystals using the metric matrix. Featuring two model crystal examples, the text develops theoretical concepts to point and space groups in two dimensions and then extends these ideas to three dimensions. The book interprets the International Tables for Crystallography to bridge the gap between the crystallographic literature and spatial interatomic relationships. Numerous computer-based exercises are integrated throughout the book, with MATLAB® starter programs that help reduce the minutiae of programming.

Table of Contents:
LATTICES 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 to Cartesian Coordinates A Crystal: Hexamethylbenzene A Crystal: Anhydrous Alum Effects of Temperature And Pressure On LatticeParameters UNIT CELL CALCULATIONS 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 Hexamethylbenzene Example Crystallographic Directions Crystallographic Planes and Miller Indices Density Revisiting Thermal Expansion and Isothermal Compressibility POINT GROUPS 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 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 SPACE GROUPS Two-Dimensional Bravais Lattices Crystal Systems and the G Matrices Two-Dimensional Space Groups Overview of the Asymmetric Unit Recipe for Analyzing a Periodic Pattern Primitive Cells for Cm and C2mm Two-Dimensional Space Group Tree Summary of Two-Dimensional Space Groups Three-Dimensional Bravais Lattices Three-Dimensional Space Groups Hmb and Space Group No. 2, P1 Aa and The Space Group No. 150, P321 THE RECIPROCAL LATTICE 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 PROPERTIES OF X-RAYS The Discovery of X-Rays Properties of Waves X-Ray Spectrum The X-Ray Tube X-Ray Diffraction ELECTRON DENSITY MAPS Scattering by an Electron Scattering by an Atom Scattering by a Crystal Some Mathematical Identities Structure Factors for Some Crystals Structure Factors for Centrosymmetric Crystals Electron Density Maps