Diffraction From Materials

Diffraction from Materials provides the basic information concerning crystal symmetry, the kinematic scattering theory, as well as the physical properties of x-rays, electrons, and neurons. This book explores the crystalline nature of metals, semiconductors, and insulators. Organized into eight chapters, this volume starts with an overview of the basic ideas associated with the arrangements of atoms in crystals to help readers understand why diffraction studies are useful in learning about crystals. This book considers the analytical and geometrical methods to represent the symmetry relationships for the atoms in crystals. Other chapters examine the production of radiation suitable for diffraction from materials. The final chapter examines the various techniques for x-ray topography, including the Schulz technique, the Guinier and Tennevin technique, and the Berg–Barret method. This book is a valuable resource for electrical, civil, mechanical, and chemical engineers. This text will also be useful to materials scientists, chemists, biologists, and physicists.

Preface

Acknowledgments

Chapter 1 Principles of Crystallography

1.1 Introduction

1.2 One-Dimensional Symmetry

1.3 Two-Dimensional Symmetry—Point Groups

1.4 Two-Dimensional Symmetry—Lattices

1.5 Two-Dimensional Symmetry—Space Groups

1.6 Three-Dimensional Symmetry

1.7 Some Real Crystal Structures

References

Problems

Chapter 2 Geometrical Representations of Crystals

2.1 Naming Planes, Points, and Directions

2.2 Analytical Calculations in Crystallography

2.3 Graphical Methods in Crystallography

2.4 Practical Applications of Graphical Methods

References

Problems

Chapter 3 The Nature of Diffraction

3.1 Diffraction from a Grating

3.2 Diffraction from Planes of Atoms—Bragg's Law

3.3 Diffraction from a Row of Atoms

3.4 Diffraction from a Three-Dimensional Crystal

3.5 Calculation of the Structure Factor

3.6 Summary

References

Problems

Chapter 4 Properties of Radiation Useful for Studying the Structure of Materials

4.1 Production of Radiation—X Rays

4.2 Production of Radiation—Neutrons

4.3 Production of Radiation—Electrons

4.4 The Interaction of X Rays with Matter

4.5 The Interaction of Electrons with Matter

4.6 The Interaction of Neutrons with Matter

4.7 The Absorption of X Rays in Matter

4.8 The Absorption of Neutrons in Matter

4.9 Refraction of Radiation by Matter

4.10 Detection of Radiation—Film Techniques

4.11 Detection of Radiation—Counters and Associated Electronic Components

References

Problems

Chapter 5 Recording the Diffraction Pattern

5.1 Introduction

5.2 Using a Range of Wavelengths—Laue Patterns

5.3 The Rotating Crystal Method

5.4 The Weissenberg Method

5.5 The Precession Method

5.6 Orienting a Crystal for One Diffraction Spot

5.7 The Powder Method

5.8 Patterns with Very Short Wavelength Radiation

References

Problems

Chapter 6 Determination of Crystal Structures

6.1 Introduction

6.2 Obtaining FF* from Measured Intensities

6.3 Some Simple Crystal Structures

6.4 Refinement by Least Squares

6.5 Applications of Fourier Analysis to Diffraction

6.6 Electron Density Mapping

6.7 The Patterson Function

6.8 Heavy Atom Techniques

6.9 Intensity Statistics and Inequalities

6.10 Difference Techniques

6.11 Helical Structures

References

Problems

Chapter 7 What Else Can We Learn from a Diffraction Experiment besides the Average Structure?

7.1 Introduction

7.2 Thermal-Diffuse Scattering

7.3 Distortion and Mosaic Size

7.4 Slit Corrections

7.5 Stacking Disorder

7.6 Local Ordering and Clustering

7.7 Small-Angle Scattering

7.8 Liquids and Amorphous Solids

References

Problems

Chapter 8 The Dynamical Theory of Diffraction

8.1 Introduction

8.2 The Dielectric Constant in a Crystal

8.3 Waves That Satisfy Bragg's Law and Maxwell's Equations inside a Crystal

8.4 Boundary Conditions

8.5 Field Amplitudes

8.6 Poynting's Vector and Energy Flow in a Crystal

8.7 Absorption in More Detail

8.8 Physical Interpretation of Anomalous Absorption

8.9 Exit Beams Again

8.10 Intensity in Bragg Reflections

8.11 X-Ray Topography

References

Problems

Appendix A Location of Useful Information in International Tables for Crystallography

Appendix Β Crystallographic Classification of the 230 Space Groups

Appendix C Determination of the Power of the Direct Beam in X-Ray Diffraction

Answers to Selected Problems

Index