Preface

1  Spheres, Clusters and Packing of Spheres

  1.1  Introduction

  1.2  Geometry of Spheres

    1.2.1  A Sphere and Its Neighbours

    1.2.2  Neighbours by Touching

    1.2.3  Hard and Soft Spheres

  1.3  Geometry of Clusters

    1.3.1  Regular Clusters

    1.3.2  Irregular Clusters

    1.3.3  Coordination of (1+k) Clusters

    1.3.3.1  Blocking Model for Cluster Formation

    1.3.3.2  Furth Model for Cluster Formation

    1.3.4  Configuration of (1+k) Clusters

    1.3.4.1  Regular Clusters

    1.3.4.2  Irregular Clusters

    1.3.4.3  Closing Vector Based on Radial Vector Polygon

    1.3.4.4  Physical Meaning of the Closing Vector,

    1.3.4.5  Spherical Harmonics

  1.4  Geometry of Sphere Packings

    1.4.1  Fixed and Loose Packings

    1.4.2  Ordered Packing

    1.4.3  Disordered Packing

    1.4.4  Random Packing

    1.4.5  Random Sequential Addition of Hard Spheres

    1.4.6  Random Closed Packing of Spheres

    1.4.7  Neighbours by Voronoi Tessellation

    1.4.8  Neighbours by Coordination Shell

    1.4.8.1  Pair Distribution Function

    1.4.8.2  The Probability of Contacts

    1.4.8.3  Contact Configuration Function

    1.9.4  Short and Medium Range Order

  References

    Books on Crystallography

    Books on Glasses

    Books on Random Walks

    Books on Sphere Packings

    Books on Crystal Imperfections

2  Characteristics of Sphere Packings

  2.1  Geometrical Properties

    2.1.1  The Coordination Distribution Function, ~P(k)

    2.1.2  Tetrahedricity

    2.1.3  Voronoi Polyhedra Notation

    2.1.4  Topology of Clusters

    2.1.4.1  Ordered Clusters

    2.1.4.2  Irregular Clusters

    2.1.5  The Configuration Distribution Function, Φk(ζ)

    2.1.6  The Volume Fraction

    2.1.6.1  Regular Polyhedra

    2.1.6.2  Irregular Polyhedra

    2.1.7  The Packing Fraction

    2.1.7.1  The Average Packing Fraction for the Round Cell

    2.1.7.2  The Local Packing Fraction

    2.1.7.3  The Limits of Packing Fraction

    2.1.8  Representative Volume Element

    2.1.9  Density of Single Phase

    2.1.9.1  Density of Crystalline Solid

    2.1.9.2  Density of Amorphous Solid

    2.1.10  Density of a Composite

    2.1.11  Solidity of Packing

  2.2  X-ray Scattering

    2.2.1  Introduction

    2.2.2  Geometry of Diffraction and Scattering

    2.2.3  Intensity of a Scattered Wave

    2.2.3.1  Amorphous Solid

    2.2.3.2  Ehrenfest Formula

    2.2.3.3  Polyatomic Solid

    2.2.4  Factors Affecting Integrated Scattered Intensity

    2.2.4.1  Integrated Intensity of Powder Pattern Lines from Crystalline Body

    2.2.4.2  Integrated Scattered Intensity from Monoatomic Body

  2.3  Glass Transition Measured by Calorimetry

  References

3  Glassy Materials and Ideal Amorphous Solids

  3.1  Introduction

    3.1.1  Solidification

    3.1.1.1  Solidification by Means of Crystallization

    3.1.1.2  Solidification through Vitrification

    3.1.2  Cognate Groups of Amorphous Materials (Glasses)

    3.1.2.1  Metallic Glasses

    3.1.2.2  Inorganic Glasses

    3.1.2.3  Organic Glasses

    3.1.2.4  Amorphous Thin Films

  3.2  Summary of Models of Amorphous Solids

    3.2.1  Lattice with Atomic Disorder

    3.2.2  Disordered Clusters on Lattice

    3.2.3  Geometric Models for Amorphous Networks

    3.2.4  Packing of Regular but Incongruent Clusters

    3.2.5  Irregular Clusters - Random Packing

    3.2.6  Molecular Dynamics

    3.2.7  Monte Carlo Method

  3.3  IAS Model of a-Argon

    3.3.1  IAS Parameters

    3.3.2  Round Cell Simulation and Analysis

    3.3.2.1  Coordination Distribution Function

    3.3.2.2  Voronoi Volume and Configuration Distribution Functions

    3.3.2.3  Radial Distribution Function

    3.3.2.4  X-ray Scattering from the IAS Model

    3.3.2.5  Crystalline and Amorphous Cluster

    3.3.3  Summary of a-Ar IAS Structure

  3.4  IAS Model of a-NiNb Alloy

    3.4.1  Introduction

    3.4.2  IAS Model of a-NiNb Alloy

    3.4.2.1