Properties of Crystalline Materials by X-ray Diffraction Methods and Symmetry Groups A Practical Approach

Foreword

Preface

Acknowledgments

Introduction  

Physical Foundations of X-rays

The discovery of X-rays

Continuous spectrum

Line spectrum

X-ray diffraction

X-ray diffraction by a diffraction grating

Compton effect          

X-ray diffraction methods

Bibliography

Symmetry Groups – Crystallography  

Introduction

Geometry of crystals

Point symmetry operations

Point symmetry groups and Laue class

Group theory

Symmetry Space Groups

Bibliography

Introduction to Tensor Analysis

Introduction

Notation and tensor transformations

Second- and higher order

Tensor algebra

Cartesian tensors

Principal values and directions of second-order symmetric tensors

Hamilton-Cayley equation

Tensor fields

Quadratic transformation forms

Bibliography

Introduction to Elasticity Theory

Introduction

Stress tensor

Strain tensor

Fundamental laws and equations

Linear elasticity

Bibliography

Material Properties from the Symmetry Group

Equilibrium tensor properties of solids

Pyroelectric effect

Electrocaloric effect

Bibliography

Determination of Crystal Structure and Fundamentals of Rietveld Refinement

Scattering by a single electron

Scattering by a single atom

Scattering by a unit cell

Estimation of X-ray diffraction intensity from a polycrystalline sample

General formula of the intensity of diffracted X-rays for powder crystalline samples

Crystal structure determination

Data processing (Profiling reduction)

Quantitative analysis methods by XRD

Bibliography

Appendix 1. X-ray Diffraction Applications Using PANalytical X’Pert HighScore

Appendix 2. Methods for the Elimination of the Kalpha2 Peak

Appendix 3. Preferred Orientation

Appendix 4. Material Properties from the Symmetry Group

Index

Biography

John Fernando Zapata Mesa has a B.Sc. in theoretical physics, an M.Sc. in elementary particle physics, and a Ph.D. in materials engineering. He completed his postdoctoral stay in quantum mechanics, addressing the problem of quantum confinement in semiconductor heterostructures. He obtained all degrees at the University of Antioquia, Medellín, Colombia. He has been working at the University of Envigado for 17 years and is a full professor attached to the Faculty of Engineering.

His most recent research deals with the characterization of cementitious materials, the study of confinement in semiconductor heterostructures, and the modeling and simulation of physical phenomena at the macro and microstructure level and at the quantum level. Now he focuses on the study of the properties of materials from the study of their symmetries in the case of crystalline materials and methods of quantification of the amorphous phase in non-crystalline materials. For this purpose, he uses artificial intelligence tools, and tools such as the modified Rietveld method, FTIR modeling and Raman spectroscopy complemented with thermal analysis methods such as DSC and TGA techniques.