Underneath the Bragg Peaks, Volume 16

2nd Edition

Structural Analysis of Complex Materials

Authors: Takeshi Egami Simon Billinge
Hardcover ISBN: 9780080971339
eBook ISBN: 9780080971414
Imprint: Pergamon
Published Date: 22nd November 2012
Page Count: 422
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Table of Contents

Pergamon Materials Series


Preface to the first edition

Chapter 1. Structure of Complex Materials

1.1 Crystallography and Beyond

1.2 The Power of Total Scattering and PDF Methods

1.3 Resources for Learning Total Scattering and PDF Methods


Further reading

Chapter 2. Crystallographic Analysis of Complex Materials

2.1 Theoretical Background

2.2 Crystallographic Analysis

2.3 Crystallographic Methods and Disorder: Limitations of Crystallographic Methods


General Texts on Electron Diffraction

Chapter 3. The Method of Total Scattering and Atomic Pair Distribution Function Analysis

3.1 Total Scattering and the PDF

3.2 Compositionally Resolved Partial PDF

3.3 Magnetic Correlation Functions

3.4 The PDF in Higher Dimensions

3.5 Error Analysis for the PDF

3.6 Information Content in the PDF and the Nyquist–Shannon Sampling Theorem


Chapter 4. Total Scattering Experiments

4.1 General Considerations

4.2 The Neutron Scattering Experiment

4.3 The X-ray Scattering Experiment

4.4 The Electron PDF Experiment


4.5 Selected Bibliography

Chapter 5. Data Collection Analysis

5.1 Introduction

5.2 Data Analysis Overview

5.3 Obtaining S(Q) in Practice

5.4 Real-World Data Analysis


Selected Bibliography

Chapter 6. Extracting Structural Information from the PDF

6.1 Introduction

6.2 Direct Information

6.3 Modeling the PDF

6.4 Ab Initio Nanostructure Solution from PDF Data


Chapter 7. Dynamics of the Local Structure

7.1 Measurement of Inelastic Scattering

7.2 Dynamic Structure Factor

7.3 Correlated Dynamics and the PDF

7.4 Dynamic Pair-Density Functio


This book focuses on the structural determination of crystalline solids with extensive disorder. Well-established methods exist for characterizing the structure of fully crystalline solids or fully disordered materials such as liquids and glasses, but there is a dearth of techniques for the cases in-between, crystalline solids with internal atomic and nanometer scale disorder. Egami and Billinge discuss how to fill the gap using modern tools of structural characterization. This problem is encountered in the structural characterization of a surprisingly wide range of complex materials of interest to modern technology and is becoming increasingly important.

Takeshi Egami received the 2003 Eugene Bertram Warren Diffraction Physics Award for the work described in the book.

The authors received 2010 J. D. Hanawalt Award from the International Union of Crystallography largely based on the success of this book.

Key Features

  • Introduces a unique method to study the atomic structure of nanomaterials
  • Lays out the basic theory and methods of this important emerging technique
  • The first edition is considered the seminal text on the subject


Academics and Professionals working in materials science


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"Egami…and Billings…have updated this second edition on nanostructures substantially, using new materials drawn from the past ten years. They begin with general remarks on the structure of complex materials, then go on to examine crystallographic analysis of complex materials, the method of total scattering and pair distribution function (PDF) analysis, total scattering experiments, data collection analysis, exacting structural information on the PDF,…" --Reference and Research Book News, December 2013

Praise for the first edition:
"Egami and Billinge are experts in the application of PDF analysis and their writing is both clear and insightful. The organisation of the book is also excellent, with illuminating examples provided throughout. ...If you have an interest in atomic structure of materials, and local structural details in particular, PDF methods can be profoundly useful. I would heartily recommend this book as a starting point if you are considering using PDF analysis in your own work. For more experienced practitioners, this text is a useful reference." --Materials Today

About the Authors

Takeshi Egami Author

Affiliations and Expertise

University ofTennessee, Knoxville, USA

Simon Billinge Author

Affiliations and Expertise

Columbia University, New York, NY, USA