The Laue Method - 1st Edition - ISBN: 9780120574506, 9780323140768

The Laue Method

1st Edition

Authors: J.L. Amoros
eBook ISBN: 9780323140768
Imprint: Academic Press
Published Date: 28th January 1975
Page Count: 388
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Description

The Laue Method demonstrates why and how the Laue method provides an easy vehicle for identification of crystalline species. The more important aspects of classical crystal theory and projection methods (such as the stereographic, gnomonic and stereognomonic projections) are discussed. The subject matter of this book falls into two parts. After a brief historical introduction that considers early interpretation of Laue photographs and Laue's theory of diffraction by crystals, the first part provides, at an elementary level, a simple and compact treatment of the Laue method and the background needed to make use of it. The stereographic projection, gnomonic projection, stereognomonic projection, and crystallochemical analysis are covered here. The chapters that follow examine the Laue method on a higher level, paying particular attention to the polychromatic component, the cross ratio and its application in crystallography, and the indexing of Laue photographs. The reader is also introduced to the optics of the Laue method and the application of Laue photographs to the study of diffuse scattering. The book concludes with a very simple new interpretation of the Laue method. This book should appeal to both students and specialists who study crystals.

Table of Contents


Preface

Chapter 1 Prologue

Historical Background

Early Interpretation of Laue Photographs

Laue's Theory of Diffraction by Crystals

Deduction of the Bragg Equation from the Laue Equations

Importance, Peculiarities, and Applications of the Laue Method

Significant Literature

Chapter 2 The Stereographic Projection

Projections in General

Perspective Projections

Basic Properties of the Stereographic Projection

Some Features of Crystallographic Problems

Basic Constructions

Aids to Using the Stereographic Projection

Example of the Use of the Stereographic Projection

Crystal Drawing

Summary

Notes on History

Significant Literature

Chapter 3 The Gnomonic Projection

Nature of the Gnomonic Projection

Indexing

Relation to the Reciprocal Lattice

Basic Constructions

Aids in Using the Gnomonic Projection

Crystal Drawing

Some Relations between the Gnomonic and Stereographic Projections

Summary

History

Significant Literature

Chapter 4 The Stereognomonic Projection

Background

Transformation between Stereographic and Gnomonic Projections

The Combination of Stereographic and Gnomonic Projections

Significant Literature

Chapter 5 The Conventional Laue Method

Experimental Conditions

Reflection Characteristics

General Geometry

Interpretation of Reflections

Determination of the Reciprocal Lattice

Application to the Study of Thermal Motion

Appraisal of the Laue Method

Notes on History

Significant Literature

Chapter 6 Symmetry Determination with the Aid of Laue Photographs

Friedel Symmetry

The Symmetry of the Laue Photograph

The Symmetry of the Cylindrical Laue Photograph

Significant Literature

Chapter 7 Crystallochemical Analysis

Background

Appraisal of the Powder Method

Single-Crystal X-Ray Methods of Identification

Advantages of Using the Laue Method as a Source of Data for Crystallochemical Analysis

Data Furnished by the Laue Method

Identification

Significant Literature

Chapter 8 Planes and Zones

Basic Crystallographic Relations

The Normal Pattern of the Projection

Interpretation of the Symmetry from Certain Features of a Laue Photograph

Axial Ratio and the Crystal Lattice

Classical Treatment of the Crystal Systems

Significant Literature

Chapter 9 The Polychromatic Component

Crystal Goniometry

The Spherical Projection

The Reflection Sphere

Coordinate Settings

Relation between Coordinates in the Pole Sphere and in the Reflection Sphere for Setting 1

Transformation Equations between Film and Pole Coordinates in Setting 1

Cylindrical Laue Photographs

Flat Laue Photographs

Relation between Coordinates on the Pole Sphere and on the Reflection Sphere for Settings 2 and 3

Transformation Equations between the Film and Pole Coordinates in Setting 2

Other Coordinate Settings

The Projection of the Polychromatic Component

The Stereographic Projection of the Laue Photograph

Gnomonic Projection of a Laue Photograph

Stereognomonic Projection of a Laue Photograph

Significant Literature

Chapter 10 the Cross Ratio and Its Application in Crystallography

Geometrical Background

Applications in Crystallography

Summary

Notes on History

Significant Literature

Chapter 11 the Indexing of Laue Photographs

Indexing by Zone-Cone Intersections

Indexing Through the Gnomonic Projection

Indexing Through Stereographic Projection

Determination of Crystal Orientation: Standard Projections

Direct Indexing of the Laue Spots

Significant Literature

Chapter 12 The Characteristic Component of Laue Photographs and Its Application to the Study of Diffuse Scattering

Bragg Spots in Laue Photographs

Background of Laue Photographs

The Nature of Diffuse Scattering as Deduced from the Study of Laue Photographs

Interpretation of the Characteristic Component of the Laue Photograph

The Relations between Reciprocal-Space Coordinates and Film Coordinates

The Bernal Charts

The Systematic Laue Method

Significant Literature

Chapter 13 the Optics of the Laue Method

The Shapes of Laue Spots

The Basic Components of a Laue Spot

The Six Types of Laue Diagrams

The Optics of the Conventional Laue Method

Geometry of Laue-Spot Formation with Only One Circular Aperture

The Distribution of Intensity in a Laue Spot

Significant Literature

Chapter 14 Epilogue: Graphical Interpretation of the Laue Method

Polychromatic and Monochromatic Laue Reflections

Blank Areas

General Equation of the Laue Method

Angular Range of a Laue Reflection

Range of Wavelengths for a Laue Reflection

Number of Orders of Reflection in a Laue Spot

Temperature Factor and Zone Development

Author Index

Subject Index


Details

No. of pages:
388
Language:
English
Copyright:
© Academic Press 1975
Published:
Imprint:
Academic Press
eBook ISBN:
9780323140768

About the Author

J.L. Amoros