LOGARITHMICALLY PERIODIC SOLIDS

LOGARITHMICALLY PERIODIC SOLIDS

CONTENTS

PREFACE

INTRODUCTION

Chapter 1 LOGARITHMIC PERIODICITY – PROPERTIES, TESTS AND UNCERTAINTIES

ABSTRACT

1.1. INTRODUCTION

1.2. MODEL

1.3. PROPERTIES

1.3.1.

1.3.2.

1.3.3.

1.3.4.

1.3.5.

1.3.6.

1.4. CONSEQUENCES

1.4.1. Indexation

1.4.2. The Compromise Spacing Effect

1.4.3. Dimensions

1.4.4. Enthalpy, the Driving Force

1.4.5. Angular Filtering

1.4.6. Double Diffraction

1.4.7. Electronic States

1.5. EVIDENCE

1.5.1. Simplicity, Symmetry, and Sharpness

1.5.2. Ranking of Beam Intensities and Calculated ‘Structure Factors’

1.5.2.1. Logarithmic Periodicity

1.5.2.2. Double Diffraction in CBED

1.5.2.3. Diffraction Anomaly in the 2-Fold Pattern

1.5.2.4. 2-Fold Pattern Orientation Anomaly

1.5.3. Diffraction Due to Clusters

1.5.4. HREM Images of Clusters and Superclusters

1.5.4.1. ‘Structure Factor’ for the HREM Model Structure

1.5.4.2. The Tripartite Cluster Center in the 5-Fold Pattern

1.6. UNCERTAINTIES

1.6.1 Extension

1.6.2. Defects

1.6.2.1. The Aperiodic Cluster ‘Hole’

1.6.2.2. The ‘Hole’ in Supercluster Order 1

1.6.2.3. The ‘Hole’ in Superclusters of Higher Order

1.6.2.4. Glassy Structures

1.6.3. Limitation to Binary Systems

1.6.4. Quasicrystal Growth Mechanisms

1.7. CONCLUSION

APPENDIX 1. QUASI BRAGG DIFFRACTION

APPENDIX 2. LEMMAS, PROOFS AND COROLLARIES

REFERENCES

Chapter 2 INDEXED SCATTERING POWERS IN A LOGARITHMICALLY PERIODIC SOLID

ABSTRACT

2.1. INTRODUCTION

2.2. QUASI BRAGG DIFFRACTION

2.3. CLUSTER OF CLUSTERS SIMULATION

2.4. LOGARITHMIC INDEXATION

2.5. EXPLANATION FOR THE COMPROMISE SPACING EFFECT

2.6. CONCLUSION

REFERENCES

Chapter 3 SIMULATION FOR THE LOCAL TRIPARTITE CENTER IN THE PERIODIC FIVE-FOLD DIFFRACTION PATTERN OF ICOSAHEDRAL Al6Mn

ABSTRACT

3.1. INTRODUCTION

3.2. LOGARITHMICALLY PERIODIC CLUSTERS

REFERENCES

BIBLIOGRAPHY

INDEX