Surface structure determination by LEED and X-rays / Wolfgang Moritz, Michel A. Van Hove.

Format:

Book

Author/Creator:

Moritz, Wolfgang, 1943- author.

Van Hove, M. A. (Michael A.), 1947- author.

Language:

English

Subjects (All):

Surface chemistry.

Surfaces (Technology)--Analysis.

Surfaces (Technology).

Low energy electron diffraction.

X-ray diffraction imaging.

Chemical structure.

Physical Description:

1 online resource (xxxiii, 440 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge ; New York, NY, USA : Cambridge University Press, 2022.

Summary:

This timely text covers the theory and practice of surface and nanostructure determination by low-energy electron diffraction (LEED) and surface X-ray diffraction (SXRD): it is the first book on such quantitative structure analysis in over 30 years. It provides a detailed description of the theory, including cutting-edge developments and tested experimental methods. The focus is on quantitative techniques, while the qualitative interpretation of the LEED pattern without quantitative I(V) analysis is also included. Topics covered include the future study of nanoparticles, quasicrystals, thermal parameters, disorder and modulations of surfaces with LEED, with introductory sections enabling the non-specialist to follow all the concepts and applications discussed. With numerous colour figures throughout, this text is ideal for undergraduate and graduate students and researchers, whether experimentalists or theorists, in the fields of surface science, nanoscience and related technologies. It can serve as a textbook for graduate-level courses of one or two semesters.

Contents:

Cover

Half-title

Title page

Copyright information

Contents

Preface

List of Abbreviations

List of Major Symbols

Glossary

1 Introduction

1.1 Brief Historical Background

1.2 Physical Basis of LEED and SXRD

1.3 Organisation of This Book

1.4 Comparison of Some Surface Structure Techniques

2 Basic Elements

2.1 Surface Geometry

2.1.1 3-D Lattices

2.1.1.1 Symmetry Operations

2.1.2 Bravais Lattices

2.1.3 Miller Indices

2.1.4 2-Dimensional Lattices

2.1.5 Reciprocal Lattice

2.1.6 2-D Space Groups

2.1.7 Atomic Positions

2.1.8 Symmetry Operators in 2-D Space Groups

2.1.9 Lattice Transformations

2.1.10 Transformation of Reflection Indices

2.1.11 Description of Superlattices

2.1.12 Stepped Surfaces

2.1.12.1 Direction of Step Edges

2.1.12.2 Determination of Step Microfacets

2.1.12.3 Determination of Step-to-Step Translation Vectors

2.2 Diffraction from Surfaces

2.2.1 Kinematic Theory of Diffraction

2.2.2 X-ray Diffraction

2.2.3 Electron Diffraction

2.2.4 Ewald Construction for Diffraction from Surfaces

3 LEED Experiment

3.1 Experimental Setup

3.2 Diffraction Geometry

3.3 Measurement of LEED Intensities

3.3.1 Sample Preparation

3.3.2 Accurate Alignment

3.3.3 Measurement of LEED Intensities with a Video System

3.4 Instrumental Response Function

3.5 Brief Overview of Types of Available LEED Systems

3.6 High-Resolution Instruments

3.6.1 Spot Profile Analysis LEED (SPA-LEED)

3.6.2 Low-Energy Electron Microscopy (LEEM)

3.7 Some Developments for Special Applications

3.7.1 In-situ Observation of Adsorption Processes

3.7.2 Nanostructures

3.7.3 Convergent Beam LEED

3.7.4 Ultrafast Measurements

4 Interpretation of the Diffraction Pattern

4.1 Symmetry and Orientation of the Unit Cell.

4.1.1 Domains due to Different Substrate Terminations

4.1.2 Twin Domains in Structures with Superlattices

4.1.3 Glide Planes

4.2 Determination of the Lattice Constant

4.3 Correction of the Incidence Angle

4.4 Stepped Surfaces

4.5 Faceted Surfaces

4.6 Antiphase Boundaries

4.7 Modulated Layers

5 LEED Theory: Basic Formalisms

5.1 Diffraction Geometry

5.2 Scattering Theory

5.2.1 Atomic Scattering: Phase Shifts

5.2.2 Multiple Scattering: Plane Waves and Spherical Waves

5.2.3 Multiple Scattering in a Cluster of Atoms

5.2.4 Multiple Scattering in Nanoparticles: NanoLEED

5.2.4.1 The Sparse-Matrix Canonical Grid Method

5.2.4.2 The UV Method

5.2.4.3 NanoLEED for Nanoparticles

5.2.4.4 NanoLEED with Matrix Inversion in Subclusters

5.2.5 Multiple Scattering in Atomic Layers

5.2.5.1 A Periodic Plane of Atoms

5.2.5.2 Several Periodic Planes of Atoms

5.2.5.3 Diffraction Matrices for a Bravais-Lattice Layer

5.2.5.4 Diffraction Matrices for a Layer with N Periodic Atomic Planes

5.2.5.5 Layer Reflection and Transmission Matrices

5.2.6 Layer Stacking

5.2.6.1 Bloch Wave and Transfer Matrix Methods

5.2.6.2 Layer-by-Layer Stacking

5.2.6.3 Layer Doubling

5.2.6.4 Renormalised Forward Scattering (RFS)

5.2.6.5 The Case of Stepped Surfaces

5.2.6.6 Beam Subsets Independent in the Bulk

5.3 Symmetry in Calculations

5.3.1 Symmetry in Reciprocal Space

5.3.2 Symmetry in Angular Momentum Space

5.4 Approximations

5.4.1 Tensor LEED Approximation

5.4.2 Frozen LEED Approximation

5.4.3 Diffuse LEED for Disordered Surfaces

5.5 Thermal Effects

5.5.1 Thermal Vibration in the Kinematic Theory of Diffraction

5.5.2 Thermal Parameters

5.5.3 Harmonic Vibrations

5.5.4 Anharmonic Vibrations

5.5.5 Multiple Scattering Theory of Thermal Effects.

5.5.6 Multipole Expansion Coefficients for Harmonic Vibrations

5.5.7 Multipole Expansion Coefficients for Anharmonic Vibrations

5.5.8 Example: Cu(110)

5.5.9 Example: Ru(0001)+(x)R30?CO

5.6 From Calculated Amplitudes to Intensities

6 LEED Theory: Applications

6.1 Quantitative Structure Analysis

6.1.1 Approaches to Obtain Structural Information Directly from LEED Intensities

6.1.1.1 Averaging Methods and the Patterson Function

6.1.1.2 Holography

6.1.1.3 Further Approaches

6.1.2 Comparison of Measured and Calculated I(V) Curves

6.1.3 Error Estimates

6.1.4 Optimum Energy Range

6.1.5 Structure Analysis Methods

6.1.5.1 Local Optimisation Methods

Least-Squares Refinement

Simplex Method

Direction-Set Method

Rosenbrook Method

Hooke-Jeeves Method

Bounded Optimisation by Quadratic Approximation (BOBYQA)

6.1.5.2 Global Search Methods

Simulated Annealing

Genetic or Evolutionary Algorithms

Discrete Variables and Generalised Pattern Search

6.1.6 Influence of Non-structural Parameters on the Structure Determined by LEED

6.1.6.1 The Conventional Muffin-Tin Model

6.1.6.2 An Improved Muffin-Tin Model

6.1.6.3 A New Step-Free Overlapping Muffin-Tin Potential

Overlap Parameter

Energy Dependence of the Exchange-Correlation Potential

6.1.6.4 Energy Dependence of the Inner Potential

6.1.6.5 Inelastic Mean Free Path (IMFP)

6.2 Quasicrystals

6.2.1 Quasicrystalline Order

6.2.2 Structural Principles of Quasicrystals

6.2.3 Diffraction from Quasicrystalline Surfaces

6.2.4 Quantitative Analysis of Quasicrystalline Surfaces

6.3 Modulated Surfaces

6.3.1 Principles of Modulated Structures

6.3.2 Examples of Modulated Surfaces

6.3.3 Identification of Modulated Lattices from STM Images

6.3.4 Reflection Indexing

6.3.5 Modulation Functions.

6.3.6 Symmetry Restrictions of the Modulation

6.3.7 Diffraction from Modulated Surfaces

6.3.8 Multiple Scattering Effects in LEED from Modulated Structures

7 Surface X-ray Diffraction

7.1 X-ray Diffraction Methods

7.1.1 General Properties of X-ray Scattering

7.1.2 Reflection and Transmission of X-rays

7.1.3 Reflection and Transmission Coefficients near the Critical Angle

7.1.4 X-ray Diffraction at Grazing Incidence

7.2 Experimental Setup

7.2.1 Diffractometer Types

7.2.2 Measurement

Point Detector

Area Detector

Further Techniques

7.2.3 Examples of Surface X-ray Diffractometers at Synchrotron Sources

APS (Advanced Photon Source, Argonne National Laboratory, USA)

NSLS (National Synchrotron Light Source, Upton, New York, USA)

ESRF (European Synchrotron Radiation Facility, Grenoble, France): Surface diffraction beam line ID03

ESRF (European Synchrotron Radiation Facility, Grenoble, France): Spanish Beam Line SPLINE, BM25

ESRF (European Synchrotron Radiation Facility, Grenoble, France): French beam line, BM 32

PETRA III, DESY (Deutsches Elektronen Synchrotron, Hamburg, Germany)

Diamond Light Source (Harwell Science and Innovation Campus, Oxfordshire, UK)

SOLEIL (Gif-sur-Yvette, France)

SPring-8 (Sayo, Japan)

7.2.4 Examples of Surface X-ray Diffractometers for Use as Laboratory Sources

Laboratory Sources

7.2.5 Synchrotron Radiation Facilities

7.3 Data Analysis

7.3.1 Patterson Function

7.3.2 Direct Methods for Surface Structure Analysis

7.3.3 Coherent Bragg Rod Analysis (COBRA)

7.3.4 Modulus Sum Function (MSF)

7.3.5 Phase and Amplitude Recovery and Diffraction Image Generation Method (PARADIGM)

Outline placeholder

Iteration Scheme for a Single Domain

Iteration Scheme for Multiple Domains.

7.3.6 Difference Map Using the Constraints of Atomicity and Film Shift (DCAF)

7.3.7 Perturbation Method of Analysis of Density Profiles from Crystal Truncation Rod Data

7.3.8 Further Methods for Experimental Phase Determination

Appendix A Lists of Books Related to Surface Science

A.1 General Books and Proceedings

A.2 Books and Proceedings on Phenomena

A.3 Books and Proceedings on Techniques

Appendix B Lists of Surface Science Websites, LEED Codes and Related Data

B.1 General Websites

B.2 Website Related to Surface Structures

B.3 Websites Related to Techniques

B.4 LEED Codes and Related Data

B.4.1 Structure Determination from LEED Intensities

B.4.2 Experimental I(V) Curve Generation from LEED Patterns

B.4.3 LEED I(V) Data

B.4.4 Surface Structure Data

B.4.5 LEED Pattern Simulation

B.4.6 Visualisation Software for Surface Structures

Appendix C Vector Calculation in Oblique Lattices

Appendix D Distance between Neighbouring Lattice Planes in the Bravais Lattices

Appendix E Lattice Transformations

E.1 The (111) Surface of the fcc Lattice

E.2 The (111) Surface of the bcc Lattice

E.3 Hexagonal to Rhombohedral Transformation

E.4 Rhombohedral to Hexagonal Transformation

Appendix F Calculation of Translation Vectors for Stepped Surfaces

F.1 Example 1

F.2 Example 2

Appendix G Symmetry Use in the Calculation of Reflection and Transmission Matrices

Appendix H Symmetry Use in Tensor LEED

Appendix I Atomic Displacement Parameters

I.1 Isotropic Displacements and Gaussian Distributions

I.2 Anisotropic Displacements and Gaussian Distributions

I.2.1 Anisotropic Displacement Parameter ?ij

I.2.2 Anisotropic Displacement Parameter Uij

I.2.3 Anisotropic Displacement Parameters in Cartesian Coordinates

I.2.4 Relation between Uij and ?ij.

I.2.5 Relation between Uij and.

Notes:

Title from publisher's bibliographic system (viewed on 18 Aug 2022).

Includes bibliographical references and index.

ISBN:

1-108-30771-X

1-108-28457-4

OCLC:

1293917727