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Underneath the Bragg Peaks - 2nd Edition - ISBN: 9780080971339, 9780080971414

Underneath the Bragg Peaks, Volume 16

2nd Edition

Structural Analysis of Complex Materials

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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 Function

7.5 Effect of Inelastic Scattering on the PDF


Chapter 8. Local Structure of Well-Ordered Crystals and Systems with Competing Interactions

8.1 Structure of Well-Ordered Crystals

8.2 Quasicrystals

8.3 Competing Interactions in Complex Oxides

8.4 Local Correlations and Phase Transitions

8.5 Phase Transition in Systems with Competing Interaction: Lithium-Nickelate


Chapter 9. Defects in Crystals and Crystallographically Challenged Materials

9.1 Introduction

9.2 Defective Crystals

9.3 Chemical Short-Range Order

9.4 In Situ and In Operando Studies


Chapter 10. Nanoparticles and Clusters

10.1 Introduction

10.2 Information in the PDFs of Nanoparticles

10.3 Clusters Suspended in a Solvent

10.4 Clusters and Molecules Intercalated in Nanoporous Solids


Chapter 11. Local Packing in Molecular Materials

11.1 Introduction

11.2 Fingerprinting

11.3 Sensitivity Dependence on Qmax

11.4 Modeling Molecular Systems


Chapter 12. Structure of Amorphous Materials

12.1 PDF Analysis of Amorphous Materials

12.2 Structure of Multicomponent Glasses

12.3 Structural Changes due to Structural Relaxation

12.4 Structural Changes due to Mechanical Deformation


Chapter 13. Concluding Remarks



Underneath the Bragg Peaks: Structural Analysis of Complex Materials 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


No. of pages:
© Pergamon 2012
22nd November 2012
Hardcover ISBN:
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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

Ratings and Reviews

About the Authors

Takeshi Egami

Affiliations and Expertise

University ofTennessee, Knoxville, USA

Simon Billinge

Affiliations and Expertise

Columbia University, New York, NY, USA