9780201610918

Intended to acquaint the reader with the theory of x-ray diffraction, the experimental methods involved, and the main applications. The book is a collection of principles and methods stressing X-ray diffraction rather than metallurgy.The book is written entirely in terms of the Bragg law and can be read without any knowledge of the reciprocal lattice. It is divided into three main partsFundamentals; experimental methods; and applications.Designed for beginners, not as a reference tool for the advanced reader.

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Preface

xvii

Properties of X-Rays

1

(30)

Introduction

1

(1)

Electromagnetic Radiation

2

(2)

The Continuous Spectrum

4

(3)

The Characteristic Spectrum

7

(4)

Absorption

11

(7)

Filters

18

(1)

Production of X-Rays

19

(8)

Gas Tubes

20

(1)

Filament Tubes

20

(2)

Focal Spot

22

(1)

Power Rating

23

(1)

Rotating-Anode Tubes

23

(1)

Microfocus Tubes

23

(1)

Pulsed (Or Flash) Tubes

24

(1)

Miniature Tubes

24

(1)

High Voltage Tubes and Linear Accelerators

24

(1)

Synchrotron Radiation

24

(3)

Detection of X-Rays

27

(1)

Safety Precautions

27

(4)

Electric Shock

27

(1)

Radiation Hazard

27

(1)

Problems

28

(3)

Geometry of Crystals

31

(58)

Introduction

31

(1)

Lattices

31

(4)

Designation of Points, Lines, and Planes

35

(3)

Reciprocal Lattice

38

(2)

Symmetry

40

(3)

Crystal Systems

43

(4)

Primitive and Nonprimitive Cells

47

(4)

Indexing in the Hexagonal System

51

(1)

Crystal Structure

52

(11)

Atom Sizes and Coordination

63

(2)

Crystal Shape

65

(1)

Crystal Defects

66

(4)

Annealing Twins

67

(2)

Deformation Twins

69

(1)

General

70

(1)

The Stereographic Projection

70

(19)

Problems

85

(4)

Diffraction I: Geometry

89

(34)

Introduction

89

(1)

Diffraction

90

(5)

Bragg's Law

95

(1)

Laue's Equations

96

(2)

Reciprocal Lattice and Diffraction

98

(3)

Diffraction Directions

101

(2)

X-Ray Spectroscopy

103

(3)

Diffraction Methods

106

(12)

Laue Method

107

(6)

Powder Method

113

(5)

Experimental Visualization of the Reciprocal Lattice

118

(2)

Diffraction Under Nonideal Conditions

120

(3)

Problems

122

(1)

Diffraction II: Intensities Diffraction II: Intensities

123

(44)

Introduction

123

(1)

Scattering by an Electron

124

(4)

Scattering by an Atom

128

(3)

Scattering by a Unit Cell

131

(6)

Some Useful Relations

137

(1)

Structure-Factor Calculations

138

(6)

Application To Polycrystal Diffraction

144

(1)

Multiplicity Factor

145

(1)

Lorentz Factor

145

(5)

Absorption Factor

150

(4)

Hull/Debye-Scherrer Camera

150

(2)

Diffractometer

152

(2)

Temperature Factor

154

(3)

Intensities of Diffraction Peaks From Polycrystalline Samples

157

(2)

Hull/Debye-Scherrer Camera

157

(1)

Diffractometer

158

(1)

Qualifications

158

(1)

Examples of Intensity Calculations

159

(3)

Reciprocal Space and Diffracted Intensities

162

(2)

Measurement of X-Ray Intensity

164

(3)

Problems

165

(2)

Diffraction III: Real Samples

167

(18)

Introduction

167

(1)

Crystallite Size

167

(4)

Interference Function

171

(3)

Strain

174

(3)

Perfect Crystals

177

(5)

Amorphous and Partially Crystalline Samples

182

(3)

Problems

183

(2)

Diffractometer Measurements

185

(50)

Introduction

185

(1)

General Features

186

(8)

X-Ray Optics

194

(4)

Detectors (General)

198

(4)

Counting Losses

198

(2)

Counting Efficiency

200

(1)

Energy Resolution

201

(1)

Proportional Counters

202

(4)

Geiger Counters

206

(1)

Scintillation Detectors

207

(1)

Semiconductor Detectors

208

(3)

Pulse-Height Analysis

211

(4)

Pulse-Height Discriminator

212

(1)

Single-Channel Pulse-Height Analyzer

213

(2)

Multichannel Pulse-Height Analyzer

215

(1)

Special Kinds of Diffractometry

215

(3)

Energy-Dispersive Diffractometry

216

(1)

Position-Sensitive Diffractometry

217

(1)

Scalers

218

(4)

Ratemeters

222

(3)

Monochromatic Operation

225

(6)

Monochromating Crystal

225

(4)

Balanced Filters

229

(2)

Determination of Diffraction Peak Positions

231

(4)

Problems

234

(1)

Powder Photographs

235

(28)

Introduction

235

(1)

Hull/Debye-Scherrer Method

236

(3)

Specimen Preparation

239

(1)

Film and Other Detection Media

240

(3)

Fluorescent Screens

240

(1)

Photographic Film

241

(1)

Image Plates

241

(2)

Film Loading

243

(2)

Cameras For Special Conditions

245

(1)

High-Temperature Cameras

245

(1)

Low-Temperature Cameras

246

(1)

High-Pressure Cameras

246

(1)

Seemann-Bohlin Camera

246

(2)

Back-Reflection Focusing Cameras

248

(3)

Pinhole Photographs

251

(4)

Microbeams and Microcameras

255

(1)

Choice of Radiation

255

(1)

Background Radiation

256

(2)

Crystal Monochromators

258

(1)

Guinier Cameras [G.13, G.17]

258

(1)

Measurement of Line Position

259

(1)

Measurement of Line Intensity

260

(3)

Problems

261

(2)

Laue Photographs

263

(12)

Introduction

263

(1)

Cameras

264

(4)

Transmission Camera

264

(1)

Back-Reflection Camera

265

(1)

General

266

(2)

Specimens and Holders

268

(2)

Collimators

270

(2)

The Shapes of Laue Spots

272

(3)

Problems

273

(2)

Phase Identification By X-Ray Diffraction

275

(20)

Introduction

275

(1)

Basic Principles

276

(1)

Powder Diffraction File

276

(3)

Hanawalt Method

277

(2)

Fink Method

279

(1)

Procedure

279

(1)

Identification of Single Phase Samples

280

(2)

Identification of Phases in Mixtures

282

(6)

Computerized Search-Match

288

(3)

Practical Difficulties

291

(4)

Problems

293

(2)

Determination of Crystal Structure

295

(36)

Introduction

295

(2)

Preliminary Treatment of Data

297

(2)

Indexing Patterns of Cubic Crystals

299

(3)

Indexing Patterns of Noncubic Crystals

302

(4)

Tetragonal System

303

(1)

Hexagonal System

303

(2)

Orthorhombic System

305

(1)

Monoclinic and Triclinic Systems

306

(1)

General

306

(1)

The Effect of Cell Distortion on the Powder Pattern

306

(2)

Determination of the Number of Atoms in a Unit Cell

308

(1)

Determination of Atom Positions

309

(2)

Example of Structure Determination

311

(4)

Order-Disorder Determination

315

(1)

Long-Range Order

315

(11)

Short-Range Order and Clustering

326

(5)

Problems

328

(3)

Phase-Diagram Determination

331

(16)

Introduction

331

(1)

General Principles

332

(5)

Solid Solutions

337

(3)

Determination of Solvus Curves (Disappearing-Phase Method)

340

(2)

Determination of Solvus Curves (Parametric Method)

342

(5)

Problems

345

(2)

Quantitative Phase Analysis

347

(16)

Introduction

347

(1)

Chemical Analysis by Parameter Measurement

347

(1)

Basic Principles of Multiphase Quantitative Analysis

348

(1)

External Standard Method

349

(2)

Direct Comparison Method

351

(4)

Internal Standard Method

355

(3)

Other Methods

358

(1)

Practical Difficulties

359

(4)

Problems

361

(2)

Precise Parameter Measurements

363

(22)

Introduction

363

(2)

Diffractometers

365

(4)

Hull/Debye-Scherrer Cameras

369

(5)

Back-Reflection Focusing Cameras

374

(1)

Pinhole Cameras

374

(1)

Example

375

(1)

Cohen's Method

376

(6)

Cubic System

377

(5)

General

382

(3)

Problems

383

(2)

Structure of Polycrystalline Aggregates

385

(50)

Introduction

385

(1)

Crystal Size and Quality

386

(1)

Grain Size

386

(2)

Crystallite Size

388

(2)

Crystal Quality (Microstrain)

390

(6)

Depth of X-Ray Penetration

396

(3)

Size and Strain Separation

399

(3)

Crystal Orientation

402

(1)

General

402

(5)

Fiber Texture

403

(1)

Sheet Texture

404

(1)

Pole Figures

404

(3)

The Texture of Wire (Area Detector Method)

407

(4)

The Texture of Sheet (Diffractometer Methods)

411

(12)

Transmission Methods

412

(4)

Reflection Methods

416

(3)

Plotting the Pole Figure

419

(4)

The Texture of Wire (Diffractometer Method)

423

(4)

Inverse Pole Figures

427

(2)

Orientation Distribution Functions

429

(2)

Amorphous and Semi-Amorphous Solids

431

(1)

Summary

431

(4)

Problems

432

(3)

Stress Measurement

435

(36)

Introduction

435

(1)

Applied Stress and Residual Stress

436

(3)

General Principles

439

(4)

Elasticity

443

(3)

Biaxial and Triaxial Stress Analysis

446

(4)

Diffractometer Method

450

(9)

Measurement of Line Position

454

(1)

Specimen Preparation

455

(1)

Measurement of Stress as a Function of Depth

455

(1)

Variant Techniques

456

(1)

Special Diffractometers

457

(2)

Photographic or Area Detector Method

459

(4)

Calibration

463

(2)

Precision and Accuracy

465

(2)

Precision

465

(1)

Accuracy

466

(1)

Practical Difficulties

467

(4)

Large Grain Size

467

(1)

Preferred Orientation

467

(1)

Plastic Deformation

468

(1)

Problems

469

(2)

Orientation of Single Crystals

471

Introduction

471

Back-Reflection Laue Method

471

Transmission Laue Method

487

Diffractometer Method

490

Setting a Crystal in a Required Orientation

496

Problems

500

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PrefaceThis edition appears over twenty years after the Second Edition was released. That the Second Edition, without revision, continued as a popular materials text and as a reference book is a tribute to Professor Cullity's clarity and thoroughness.Instrumentation and techniques have changed considerably, however, in the intervening twenty years, engendered by the revolution in distributed computing heralded by the advent of the personal computer. In the Fall of 1973, for example, I ran BASIC programs from one of many teletypes connected to a single PDP-8 computer with 8 Bytes of memory. I recently came across loan papers from 1984 for my personal computer (256 Bytes RAM, no hard drive). Analyses which required graphical solution before computers or very astute programming in the first digital decades now can be done using spreadsheets packaged with word processing software; the earlier approaches are no longer of interest, except perhaps to historians.With changes in instruments came changes in the types of x-ray diffraction experiments a materials scientist/engineer might be required to perform (or at least to interpret). Film-based techniques for powder diffraction fell into relative obscurity while diffractometry (parafocusing geometry) with electronic detectors assumed the principle role. The Second Edition, however, followed the First Edition in treating x-ray diffraction first from the standpoint of photographic methods and second from that of diffractometry; this edition changes emphasis to diffractometry as the primary technique. Practical considerations dictate this change: any x-ray diffraction data collection/analysis that the students subsequently encounter will almost surely be diffractometry, and most instructors emphasize these experiments. If the students are to understand their laboratory sessions, which must begin early in the term, diffractometry must be pushed forward in the course. Unfortunately, this requires a progression different from the very satisfactory approach used before: a single crystal diffracting many wavelengths in all directions, a polycrystal sample diffracting one wavelength in many directions, an apparatus sampling a small section of diffraction cones along a particular direction. I predict, however, that the second decade of the new millennium will see the area detector methods regain the prominence once held by photographic methods.Yet another challenge was integrating reciprocal lattice treatment of diffraction into the text and adding reforming the material on diffraction from nearly perfect crystals. Since the Second Edition appeared, several topics have grown in importance in different segments of the materials community, diffraction from polymers and small angle scattering, and this is reflected in two new chapters. Finally, materials engineers n6ed some familiarity with transmission electron microscopy, and a couple of weeks, building on reciprocal lattice concepts developed earlier, at the end of a semester course on x-ray diffraction and crystal structure may be all that can be spared. To support this possibility, a brief summary of the high points of TEM in materials characterization is provided.This revision took a long time to be completed, and I am grateful to the various editors who helped it along: Dan Jorananstad, Rob Merino, Laura Curless and especially Michael Slaughter and Scott Disanno, and also their staffs. I am grateful to the various reviewers for their advice: Z.L. Wang, Steve Spooner and Ray Young. I apologize to those who were forced to wait for me to finish this revision, but the revision was done without taking leave from my academic duties and this delay was the result.Virtually all scholars blend research and teaching to various degrees, and I am no exception. It is difficult to imagine how this revision it might have been completed without the confidence of having a stable base of research funding pr

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Elements of X-Ray Diffraction

Elements of X-Ray Diffraction

0201610914

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