Basic Elements of Crystallography

An impeccable, authoritative, yet refreshingly lucid work on the development of nanocrystalline materials, this book is the first definitive step to understanding the relationship between the properties of nanomaterials and their microstructure. Thousands of papers have been published that concentrate on the comprehension of the strength and ductility of such materials in order to maximize both. Moving beyond reiterating just the strength, toughness, and stability of these materials, this compendium provides much analysis to better understand the crystal grain and grain boundary bases that determine property behaviors over a range of temperatures and applied loading rates. The original relation that connects grain size and strength, known as the Hall-Petch relation, is studied in the nanometer grain size region. The breakdown of such a relation is a challenge. Why and how to overcome it? Is the dislocation mechanism still operating when the grain size is very small, approaching the amorphous limit? How do we go from the microstructure information to the continuum description of mechanical properties? The book effectively answers these questions, besides many others that have made nanocrystalline materials an object of unprecedented interest of late. Publisher's note Copyright......Page 5 PREFACE......Page 6 CONTENTS ......Page 8 ABBREVIATIONS......Page 12 2. One-Dimensional Crystal Structures......Page 13 3. Two-Dimensional Crystal Structures......Page 16 4. Problems......Page 25 2. Examples of Symmetry Axes of Three-Dimensional Figures......Page 29 3. Symmetry Axes of a Cube......Page 32 4. Symmetry Axes of a Set of Points......Page 34 5. Crystal Systems......Page 36 6. Conventional Cell for the Trigonal System......Page 39 7.1. Introduction......Page 40 7.3. The Monoclinic System......Page 41 7.4. The Orthorhombic System......Page 44 7.6. The Cubic System......Page 46 7.8. Symbols for Bravais Lattices......Page 47 7.9. Conclusions......Page 48 8. Coordination Number......Page 50 9. Body Centered Cubic Lattice......Page 51 10. Face Centered Cubic Lattice......Page 54 11.1. Rhombohedral Unit Cell of the sc Lattice......Page 58 11.2. Simple Cubic Crystal Structure......Page 60 11.3. Interpretation of Data for As, Sb, Bi, and Hg......Page 61 12. Trigonal Lattice......Page 62 13. Triple Hexagonal Cell R in a Cubic Lattice......Page 67 14.2. The Wigner-Seitz Cell of the bcc Lattice......Page 68 15. Problems......Page 70 1. Introduction......Page 79 2. Pearson Notation and Prototype Structure......Page 80 4. Simple Cubic Structure......Page 81 5. Body Centered Cubic Structure......Page 83 6. Face Centered Cubic Structure......Page 85 7. Close-Packed Structures......Page 87 8. Double Hexagonal Close-Packed Structure......Page 91 9. Samarium Type Close-Packed Structure......Page 93 10. Hexagonal Close-Packed Structure......Page 95 11. Interstices in Close-Packed Structures......Page 99 12. Diamond Structure......Page 104 13. Atomic Radius......Page 110 14. Problems......Page 114 2. The Ionic Radius Ratio and the Coordination Number......Page 119 3. Zinc Blende Structure......Page 124 4.1. Fluorite Structure......Page 126 4.2. Anti-Fluorite Structure......Page 129 5. Wurtzite Structure......Page 130 6.1. NiAs Structure......Page 136 6.2. TiAs Structure......Page 145 7. Sodium Chloride Structure......Page 146 8. Cesium Chloride Structure......Page 156 9. Problems......Page 161 2. The Concept of the Reciprocal Lattice......Page 165 3.2. Reciprocal of the Simple Cubic Lattice......Page 174 3.3. Reciprocal of the Face Centered Cubic Lattice......Page 176 4. Problems......Page 177 2. Miller Indices......Page 181 3. Application of Miller Indices......Page 187 4. Problems......Page 192 REFERENCES......Page 197 INDEX......Page 199 "An excellent primer on crystallography - a discipline necessary for everyone concerned with the solid state, overarching the fields of materials science, metallurgy, condensed matter physics, micro- and nano-technology. Abundant and clear drawings allow the authors to introduce the concepts of crystal structures and lattices in a very easy way, starting from one dimensional cases and proceeding to all 14 Bravais lattices. The book expounds on the close packed monoatomic structures as well as several important binary compounds. The ideas of the reciprocal lattice are explained in a straightforward manner. The strengths of this book are the excellent images and a large number of tabulated lattice parameters. This textbook is definitely a good starting point for learning crystallography or teaching introductory courses. I would certainly recommend this to my students, while professionals may also enjoy reading it." Boris I. Yakobson Rice University, USA "Crystals are viewed as objects of nature which can be described by a set of few vectors. The consequent restriction to elementary topics and elementary methods goes, however, hand in hand with an intuitive, explicit and very detailed presentation of the subject and experienced teachers like Professor Szwacka knows that the most important means in mastering crystallography is visualization. In the text, more than 150 well-designed figures served this purpose. The detailed description of the crystals of elements and a number of binary compounds will certainly be appreciated by undergraduates and graduates in physics as well as in other science disciplines. This fine book provides the appropriate basic knowledge of crystallography both for those who are satisfied with introductory level and those who like to go for more. The authors deserve acknowledgement for their didactic skills." Janos Hajdu Cologne University, Germany This book is a clear and comprehensive introduction to the field of crystallography. It includes an extensive discussion of the 14 Bravais lattices and its reciprocals, basic concepts of point group symmetry, the crystal structure of elements and binary compounds, and much more. The purpose of this book is to illustrate rather than just describe the structure of materials. Readers who are unfamiliar with the topic, but still interested to learn how the atoms are arranged in crystal structures, will find this book useful. The chapters are accompanied by exercises designed to encourage students to explore the crystal structures they are learning about. The entire notation in this book consistent with the International Tables for Crystallography. --Book Jacket

This book is a clear and comprehensive introduction to the field of crystallography. It includes an extensive discussion of the 14 Bravais lattices and its reciprocals, basis concepts of point group symmetry, the crystal structure of elements and binary compounds, and much more. The purpose of this book is to illustrate rather than just describe the structure of materials. Readers who are unfamiliar with the topic, but still interested to learn how the atoms are arranged in crystal structures, will find this book useful. The chapters are accompanied by exercises designed to encourage students to explore the crystal structures they are learning about. The entire notation in this book is consistent with the International Tables for Crystallography.

This book concentrates on both understanding and development of nanocrystalline materials. The original relation that connects grain size and strength, known as the Hall-Petch relation, is studied in the nanometer grain size region. The breakdown of such a relation is a challenge. Why and how to overcome it? Is the dislocation mechanism still opera Provides a complete and clear introduction to the field of crystallography. Includes an extensive discussion of the 14 Bravais lattices and the reciprocal to them, basic concepts of point group symmetry, and the crystal structure of elements and binary co Nanocrystalline materials have attracted a lot of interest lately because of the potential of making very strong and tough materials for light weight devices. This book concentrates on both understanding and development of nanocrystalline materials.