Characterisation Methods in Solid State and Materials Science

340 Pages·2019·59.762 MB·English

by  Kelly Morrison

Characterisation Methods in Solid
State and Materials Science

Characterisation Methods in Solid
State and Materials Science
Kelly Morrison
Physics Department, Loughborough University, Leicestershire, UK
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2019
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ISBN 978-0-7503-1383-4(ebook)
ISBN 978-0-7503-1384-1(print)
ISBN 978-0-7503-1385-8(mobi)
DOI 10.1088/2053-2563/ab2df5
Version:20191001
IOPExpandingPhysics
ISSN2053-2563(online)
ISSN2054-7315(print)
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fromtheBritishLibrary.
PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London
IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK
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To the students who inspired me to bring all this information together in one place,
and to Rob, whose unique combination of patience and impatience helped drag me
over the finish line.

Contents
Author biography xv
1 Introduction 1-1
1.1 Overview 1-1
1.2 Microscopy, spectroscopy and diffraction 1-3
1.3 Introductory optics 1-6
1.3.1 Definitions of a wave 1-6
1.3.2 Refraction, reflection, retardation 1-8
1.3.3 Diffraction 1-9
1.3.4 Resolution 1-11
1.3.5 Lenses 1-12
1.4 Introduction to atomic physics 1-16
1.4.1 The periodic table 1-16
1.4.2 The photoelectric effect 1-17
1.4.3 The atomic model, and energy levels 1-20
1.5 Introductory solid state physics 1-24
1.5.1 The crystal lattice 1-24
1.5.2 Translation vectors 1-26
1.5.3 Miller indices and notation 1-27
1.5.4 Wyckoff sites and space groups 1-28
References 1-32
2 Fourier series, transforms and their relevance in diffraction 2-1
and microscopy
2.1 Introduction 2-1
2.2 Fourier series 2-2
2.3 The Fourier transform 2-3
2.4 Key functions and their Fourier transforms 2-4
2.4.1 The aperture function (single slit of finite width) 2-4
2.4.2 The Dirac delta function (infinitely narrow slit) 2-5
2.4.3 The Lorentzian and Gaussian functions 2-6
2.5 The convolution theorem 2-7
2.6 Classic examples of diffraction patterns 2-8
2.6.1 Young’s double slit 2-8
2.6.2 The diffraction grating 2-10
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CharacterisationMethodsinSolidStateandMaterialsScience
2.7 Autocorrelation and the loss of phase information in measurements 2-10
2.8 Aside: some useful theorems 2-11
2.8.1 Linearity theorem 2-12
2.8.2 Scaling theorem 2-12
2.8.3 Shifting theorem 2-12
2.8.4 Parseval’s theorem 2-12
2.8.5 Correlation theorem 2-12
2.8.6 Convolution theorem 2-12
2.9 Questions 2-13
2.9.1 Some standard Fourier transforms 2-13
2.9.2 Normalisation of the Fourier transform pair 2-14
2.9.3 Further questions 2-15
References 2-16
3 Diffraction techniques 3-1
3.1 Elastic scattering 3-1
3.1.1 X-rays versus neutrons 3-4
3.1.2 Nuclear scattering length and form factors 3-5
3.1.3 Scattering cross-section 3-7
3.1.4 Some final notes 3-9
3.2 Methods 3-9
3.2.1 X-ray sources 3-9
3.2.2 Neutron sources 3-12
3.2.3 Time of flight 3-13
3.2.4 Detectors 3-13
3.3 Diffraction: Rietveld refinement 3-19
3.3.1 Least squares refinement 3-20
3.3.2 General equation 3-20
3.3.3 Structure factor 3-21
3.3.4 Profile function 3-22
3.3.5 Basic refinement strategy 3-23
3.3.6 Figures of merit 3-23
3.3.7 Single crystal diffraction 3-24
3.3.8 Magnetic contrast 3-25
3.4 Grazing incidence diffraction 3-26
3.5 X-ray and neutron reflectivity (XRR & NR) 3-26
3.5.1 Overview 3-26
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CharacterisationMethodsinSolidStateandMaterialsScience
3.5.2 Fourier derivation of the reflectivity curve 3-27
3.5.3 Classic examples of reflectivity profiles 3-30
3.5.4 X-rays versus neutrons 3-33
3.5.5 Polarised neutron reflectivity (PNR) 3-33
3.6 Examples of diffraction techniques in the literature 3-34
3.6.1 In ‘Strain in nanoscale germanium hut clusters on Si(001) 3-34
studied by x-ray diffraction’
3.6.2 In ‘Neutron-diffraction study of the Jahn–Teller transition 3-34
in stoichiometric LaMnO ’
3
3.6.3 In ‘Neutron-diffraction measurements of magnetic order 3-35
and a structural transition in the parent BaFe As
2 2
compound of FeAs-based high temperature superconductors’
3.6.4 In ‘Unconventional magnetic order on the hyperhoneycomb 3-35
Kitaev lattice in β-Li IrO : full solution via magnetic
2 3
resonant x-ray diffraction’
3.7 Questions 3-36
3.7.1 Structure factor and reflection rules 3-36
3.7.2 Extracting key information from x-ray diffraction data 3-38
3.7.3 Space groups 3-40
3.7.4 Identifying key information in XRR data 3-41
3.7.5 Computer aided problems 3-42
3.7.6 Calibrating detectors—some basic geometry 3-45
References 3-46
4 Microscopy techniques 4-1
4.1 Optical microscopy 4-1
4.1.1 The optical microscope 4-1
4.1.2 Use of polarised light 4-3
4.1.3 Phase contrast imaging 4-5
4.1.4 Interference contrast microscopy 4-6
4.2 Electron microscopy 4-7
4.2.1 Scanning electron microscopy (SEM) 4-7
4.2.2 Sources 4-11
4.2.3 SEM resolution and contrast 4-12
4.2.4 Sample preparation and beam damage 4-13
4.2.5 Transmission electron microscopy (TEM) 4-14
4.3 Profilometry 4-17
4.3.1 Optical profilometry 4-17
4.3.2 Scanning tunnelling microscope (STM) 4-19
ix