Handbook of Modern Coating Technologies: Applications and Development 0444632379, 9780444632371

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Handbook of Modern Coating Technologies

Handbook of Modern Coating Technologies Advanced Characterization Methods Volume 2 Edited by

Mahmood Aliofkhazraei University of South Florida, United States

Nasar Ali The NANOSMAT Society, United Kingdom

Mircea Chipara University of Texas Rio Grande Valley, United States

Nadhira Bensaada Laidani Center for Materials and Microsystems, Bruno Kessler Foundation, Trento, Italy

Jeff Th.M. De Hosson University of Groningen, Netherlands

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2021 Elsevier B.V. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-444-63239-5 For Information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Susan Dennis Acquisitions Editor: Kostas KI Marinakis Editorial Project Manager: Grace Lander Production Project Manager: Kumar Anbazhagan Cover Designer: Christian J. Bilbow Typeset by MPS Limited, Chennai, India

Contents List of contributors

ix

About the editors

xi

Preface 1.

Application of the scanning vibrating electrode technique to the characterization of modern coatings

xiii

1

A.C. BASTOS AND M.G.S. FERREIRA

2.

1.1 Introduction

1

1.2 Metals and corrosion

2

1.3 Corrosion protection and coatings

3

1.4 The scanning vibrating electrode technique

6

1.5 Application of the scanning vibrating electrode technique to characterize modern coatings

17

1.6 Review of published work using the scanning vibrating electrode technique to characterize coatings performance

23

1.7 Critical account on the application of the scanning vibrating electrode technique to study coatings

26

1.8 Other localized techniques

29

1.9 Conclusions

33

References

34

Spectroscopic ellipsometry

45

LINGJIE LI, JINGLEI LEI, LIANGLIU WU AND FUSHENG PAN

2.1 Introduction

45

2.2 Basic principles of ellipsometry

47 v

vi

Contents

3.

2.3 Data analysis procedure

49

2.4 Extracting information of coatings

51

2.5 Spectroscopic ellipsometry application examples in coatings

63

2.6 Summary and perspectives

74

Acknowledgment

75

References

75

X-ray diffraction

85

B.S. SAINI AND RAMINDER KAUR

4.

3.1 Introduction

85

3.2 Application areas of various X-ray techniques

86

3.3 Production and characteristics of X-rays

88

3.4 Milestones

92

3.5 Crystalline materials

92

3.6 Interaction of X-rays with crystalline materials

104

3.7 Specimen preparation

111

3.8 X-ray diffraction methods

112

3.9 Powder diffractometer geometry

115

3.10 Powder diffraction measurements

118

3.11 Concluding remarks

134

Acknowledgments

135

References

135

Neutron reflectivity for the investigation of coatings and functional layers

143

MAX WOLFF AND PHILIPP GUTFREUND

4.1 Reflection and refraction of neutrons at interfaces

143

4.2 Instrumentation

153

Contents vii

5.

4.3 Experimental results

155

References

168

Application of micro- and nanoprobes to the analysis of small-sized 2D and 3D materials, nanocomposites, and nanoobjects

177

A.D. POGREBNJAK, V.M. BERESNEV, O.M. IVASISHIN, V.M. ROGOZ AND A.A. GONCHAROV

6.

5.1 Introduction

177

5.2 Scanning nuclear microprobe

179

5.3 Local microanalysis with the use of a scanning nuclear microprobe

193

5.4 Modification of materials for the creation of small-sized 3D structures

199

5.5 The use of slow positrons for diagnostics of materials

203

5.6 Near-field microwave diagnostics of materials and media

221

5.7 Application of nano- and microprobes for the analysis of nanomaterials and nanocomposites, including nitrides of high-entropy alloys

232

Acknowledgments

249

References

249

Application of fluorescence technique for understanding film formation from polymer latexes and composites

263

˘ SAZIYE ¸ UGUR AND ÖNDER PEKCAN

6.1 Introduction

263

6.2 Theoretical considerations

270

6.3 Experimental results

274

viii

Contents

7.

6.4 Film formation of polymer composites

312

6.5 Conclusions

349

References

349

Stress in physical vapor deposited thin films: Measurement methods and selected examples

359

G. ABADIAS AND R. DANIEL

8.

7.1 Introduction

359

7.2 Sources of residual stress in thin films

361

7.3 Stress evaluation methods

362

7.4 Selected examples

406

7.5 Conclusions and outlooks

423

Acknowledgment

423

References

423

Spatially resolved electrochemical tools: micropotentiometry and scanning vibrating electrode technique to detail localized corrosion problems in coated parts

437

MARYNA TARYBA, SVIATLANA LAMAKA AND FÁTIMA MONTEMOR

Index

8.1 Introduction

437

8.2 Scanning vibrating electrode technique and scanning ion-selective electrode technique applied to the study of different corrosion cases

442

8.3 Overview and final remarks

463

Acknowledgments

464

List of Abbreviations

464

References

464

469

List of contributors G. Abadias

Institut Pprime, Department of Physics and Mechanics of Materials, Université de Poitiers—CNRS—ENSMA, TSA, Poitiers Cedex 9, France

A.C. Bastos DEMaC—Department of Materials and Ceramic Engineering, CICECO—Aveiro Institute of Materials, University of Aveiro, Aveiro, Portugal V.M. Beresnev

Kharkov National University, Kharkov, Ukraine

R. Daniel

Chair of Functional Materials and Materials Systems, Department of Materials Science, Montanuniversität Leoben, Leoben, Austria

M.G.S. Ferreira DEMaC—Department of Materials and Ceramic Engineering, CICECO—Aveiro Institute of Materials, University of Aveiro, Aveiro, Portugal A.A. Goncharov

Sumy State University, Sumy, Ukraine

Philipp Gutfreund

Institut Laue-Langevin, Grenoble, France

O.M. Ivasishin G.V. Kurdyumov Institute for Metal Physics of the NAS of Ukraine, Kiev, Ukraine Raminder Kaur

Department of Basic & Applied Sciences, Punjabi University,

Patiala, India

Sviatlana Lamaka

Magnesium Innovation Centre MagIC, Institute of Materials Research, Helmholtz-Zentrum Geesthacht, Germany

Jinglei Lei

School of Chemistry and Chemical Engineering, Chongqing University, Chongqing, P.R. China

Lingjie Li School of Chemistry and Chemical Engineering, Chongqing University, Chongqing, P.R. China

Fátima Montemor

Centro de Quimica Estrutural, Department of Chemical Engineering, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, Lisbon, Portugal

ix

x

List of contributors

Fusheng Pan

School of Materials Science and Engineering, Chongqing University, Chongqing, P.R. China

Önder Pekcan

Faculty of Arts and Science, Kadir Has University, Istanbul,

Turkey

A.D. Pogrebnjak V.M. Rogoz

Sumy State University, Sumy, Ukraine

Sumy State University, Sumy, Ukraine

B.S. Saini Department of Mechanical Engineering, Punjabi University, Patiala, India

Maryna Taryba

Centro de Quimica Estrutural, Department of Chemical Engineering, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, Lisbon, Portugal

S¸ aziye U˘gur

Department of Physics, Istanbul Technical University, Istanbul,

Turkey

Max Wolff

Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden

Liangliu Wu

School of Chemistry and Chemical Engineering, Chongqing University, Chongqing, P.R. China

About the editors Dr. Mahmood Aliofkhazraei is an expert in corrosion, coatings, and surface engineering (University of South Florida). His research interests include nanotechnology and its use in surface and corrosion science. His main interests are multilayered electrodeposition and plasma electrolysis, and he has published more than 180 papers and 7 books in related subjects. He has presented invited lectures and keynotes in several countries. His works have been recognized by the Khwarizmi award, IMES medal, and INIC award. He is on the advisory editorial board of several materials science and nanotechnology journals. He is also a member of the International Association of Corrosion Engineers (NACE International) and the Materials Research Society (MRS). Dr. Nasar Ali is currently the scientific director of NANOSMAT Global, an international organization involved with nanoscience and nanotechnology. Further, he is the founder and chair of Young Professionals Society (www.ypsociety.uk)—a global organization helping young people with personal and professional development. His research interests are in carbon-based nano/microscale materials, such as polycrystalline diamond, diamond-like carbon, carbon nanotubes, and carbon-based nanocomposite materials. He has published over 100 papers, book chapters, and books in peer-reviewed journals and conference proceedings. He was the recipient of the prestigious 2002 Bunshah prize for presenting his work on the novel time-modulated chemical vapor deposition (CVD) process used for depositing CVD diamond thin films at the ICMCTF in San Diego, United States. He has served in the past as the Fellow of the Institute of Nanotechnology (United Kingdom). Mircea Chipara obtained the BS from the University of Bucharest (Romania), Faculty of Physics, and completed a master’s degree in Polymer Physics within the same faculty. He received a PhD in Solid State Physics from the Institute for Atomic Physics (Bucharest Romania) with a thesis on “Hyperfine Interaction in Solids” (1996). After receiving the master’s degree, he was hired as a researcher by the National Institute for Materials Physics, Bucharest, Romania. He accepted a postdoctoral position in 1999 at the University of Nebraska (Lincoln) in nanomaterials. He was a scientist at the Indiana University Cyclotron Facility and Indiana University Bloomington (Chemistry Department) before accepting a position of Assistant Professor in Physics at the University of Texas-Pan American (Edinburg campus), in 2006. He is now Professor at the University of Texas Rio Grande Valley (Edinburg campus), within the Physics and Astronomy department. His research is focused on nanomaterials, with emphasis on polymer-based nanocomposites and polymer nanofibers. He was involved in the organization of some symposia to Materials Research Society, the organization of NANOSMAT-USA conferences, and guest editor to some professional journals. He is acting editor for Surfaces and Interfaces. xi

xii

About the editors

Dr. Nadhira Bensaada Laidani is Senior Researcher at Fondazione Bruno Kessler (FBK). She received her degree in Petrochemistry Engineering from the “Hydrocarbons and Chemistry National Institute” (Algeria) and her PhD in Plasma Chemistry at Pierre and Marie Curie University (Paris, France). Her expertise includes low-pressure plasma thin film deposition and surface treatment; atomic layer deposition; nanocomposite films and multinanolayers; chemical structural characterization with X-ray photoelectron spectroscopy; FT-IR spectroscopy; and optical, electrical, and mechanical characterization of thin films and surfaces. Her recent research interests cover materials science for energy applications (photon converters and transparent electrodes), protective coatings, and catalysis. Prof. Jeff Th.M. De Hosson holds a PhD in Physics from the University of Groningen, the Netherlands (with honors and highest distinction), and after his postdoctoral years in the United States (Northwestern University and UC-Berkeley), he was appointed in 1977 by the Crown. His passion is to carry out innovative and precompetitive research in the field of nanoscience with particular emphasis on advances in in situ electron microscopy, nanostructured coatings, coatings on elastomers (rubbers), high-entropy alloys, nanofoams, and highpower lasers for applications in transportation, communications, and data processing. He published more than 1000 scientific papers and so far he supervised 87 PhD theses. He is elected member of the Royal Netherlands Academy of Sciences, Academia Europaea, Royal Holland Society of Sciences and Humanities, editor of two international journals, member of editorial boards of numerous journals, and Elected Fellow of various foreign scientific societies, including TMS-USA and ASM-USA. He acts as Honorary Professor of Tsinghua University-Beijing, UST-Beijing, and Nelson Mandela Metropolitan University (formerly University of Port Elizabeth), Port Elisabeth, South Africa. He holds several patents and received a number of prestigious international awards, including the European Materials Gold Medal in 2005, the Nanostructured Materials Prize, and NANOSMAT Prize 2009. In 2019 he was knighted by the Crown of the Netherlands (Knighthood Netherlands Lion).

Preface Coating technology is an emerging field that is constantly evolving due to the development in advanced materials, in particular due to recent achievements in nanoscience and nanotechnology. Smart coatings can respond to environmental factors, for example, external and internal stress state, gradients in temperature, pH, biomarkers, and radiation. Modern coatings open new avenues of applications such as waterproof systems, self-cleaning, and selfhealing systems. New coatings are developed for biological and medical applications, with emphasize on antibacterial features. The progress affects also coating manufacturing and related technologies. In addition to modern coating fabrication technologies, new methods for their analysis and characterization of materials are introduced which increase our abilities to better study their micro and nanostructure including different properties at various length and time scales. It is worth noting here that wear/corrosion resistance and therefore the coating performance is a property, not an intrinsic of materials, but of systems and the responses to the extrinsic factors should be understood in detail. Demands for coatings increase continuously as new applications require stringent constraints (e.g., in microelectronics industry). Smart phones and other electronic devices also require self-shielding and self-healing coatings. Alongside there are investments in R&D that will lead to market growth in the near future. There are several types of coatings currently on the market, including wear/corrosion resistant coatings, self-cleaning coatings, and biomedical coatings. Industries dedicated to personal health, aerospace, food packaging, home appliances, automotive, and information technology will have the largest impact onto the market. The global paints and coatings market are anticipated to reach around $286 billion by 2026. It is expected to grow significantly over the forecast period from 2020 onward due to numerous advancements that are driven by a strong rebound in worldwide building, construction, and manufacturing primarily in Western Europe, North America, and Japan. In addition, new coating methods are introduced everyday with higher efficiencies and clean processes. The overall importance and progress of coatings make it necessary to provide a reference book for coating technologies. Hence we have prepared this collection with the input of well-known researchers both from academic and industrial centers. We like to appreciate all of the contributions to this collection and thank them for their high-quality manuscripts. We wish that the publication will benefit all researchers and may act as a source of inspiration to this sparkling and sprightly field of research.

M. Aliofkhazraei, N. Ali, N. Laidani, M. Chipara, J.Th.M. DeHosson

xiii

1

Application of the scanning vibrating electrode technique to the characterization of modern coatings A.C. Bastos, M.G.S. Ferreira DEMAC —DEPARTMENT OF MATERIALS AND CE RAMIC E NGINEERING, CICECO—AVEIRO INSTITUTE OF MATERIALS, UNIVERSITY OF AVEIRO, AVEIRO, PORTUGAL

1.1 Introduction The scanning vibrating electrode technique (SVET) uses a vibrating microelectrode to sense the electric field in an electrolyte solution associated with the ionic currents flowing therein. When this is done close to a surface it is possible to identify the points where oxidation reactions occur (anodic regions) and where reductions take place (cathodic regions). The SVET is a noninvasive and nondestructive technique and is well suited for corrosion studies because it makes available in a single map the global picture of the corrosion process occurring at the surface, displaying the spatial distribution of the regions where oxidation and reductions take place, and their local current density magnitudes. The corrosion evolution of the sample can be described by a succession of maps acquired over time. In the context of coatings, which is the focus of this chapter, SVET can detect porosity and defects on a protective film, identify self-healing properties of responsive layers, or characterize the activity of an electrocatalytic surface. In spite of being around for a few decades, SVET use is still scarce and remains an exotic and unexplored technique. Taking this into account, this chapter covers a list of matters that should be of interest to those who never had a contact with the technique and should also benefit all others that already work with it. The chapter starts with an introduction to metals and corrosion, followed by a short description of coatings for corrosion protection, their modes of action, and forms of degradation. This provides the background and justification for the application of SVET. Then, the principles of the technique, experimental details, and examples of use with the different types of coatings are presented. It continues with a literature assessment of works using SVET to characterize coatings applied on metals, followed by a discussion about the capabilities and limitations. The chapter ends with a comparative description of alternative localized techniques that can be used to analyze modern coatings.

Handbook of Modern Coating Technologies. DOI: https://doi.org/10.1016/B978-0-444-63239-5.00001-9 © 2021 Elsevier B.V. All rights reserved.

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Handbook of Modern Coating Technologies

1.2 Metals and corrosion Modern civilization is based on metals as the main building blocks in all areas of human activity, including tools, instruments and infrastructures, in industry, construction, transportation, and communications [1]. The great importance of metals comes from their availability on Earth’s crust and the unparalleled set of properties, such as castability, machinability, recyclability, electrical, and thermal conductivities, together with the outstanding range of mechanical properties, encompassing strength, hardness, ductility, toughness, and resilience [2]. The main drawback is their tendency to corrode, that is, the natural predisposition to react with the environment and change the chemical state from the metallic (reduced) form to their original (oxidized) state in nature. Through corrosion, metals lose their properties, putting in danger the function of the structures and equipment they are part. In the crust of the Earth most metals exist in the oxidized state, as ores, and energy is necessary to bring them to the reduced form. As soon as metals are produced, they are ready to spontaneously return to the native state and this readiness is proportional to the energy spent in transforming them. The corrosion process is an electrochemical phenomenon that can be split in the metal oxidation and in the reduction of chemical species in the adjacent environment. The metal (M) oxidation is usually written as MðsÞ ! Mn1 ðaqÞ 1 ne2

(1.i)

In acidic media the main reduction is 2H1 ðaqÞ 1 2e2 ! H2 ðgÞ

(1.ii)

In neutral or basic media the dominant reduction is O2 ðgÞ 1 2H2 OðlÞ 1 4e2 ! 4OH2 ðaqÞ

(1.iii)

The electrochemical half-reactions take place at the same rate but separated in space. Fig. 11 shows an idealization of a corrosion cell together with a sketch of the corresponding A)

B) Neutral and alkaline

Acidic media H+

Mn+

H2

OH– O2 H2O

Cathode

Cathode e–

e– Anode

Current lines Equipotential surfaces

FIGURE 1–1 (A) Representation of a corrosion cell with the main cathodic reactions in acid and in neutral or alkaline media and (B) current lines between anode and cathodes and corresponding equipotential surfaces.

Chapter 1 • Application of the scanning vibrating electrode technique

3

current lines and electric field in solution, which will be important for understanding the measuring principle of SVET. The oxidation and reduction currents must be balanced. In fact, the current is the same, just named differently and having opposite sign when associated with anodes or cathodes. Often the rate of corrosion is controlled by the cathodic process. This is because the metal is there ready to oxidize but the actual velocity and extension of the reaction are dependent on the availability of chemical species able to accept the electrons, the most common being O2 and H2O. In normal conditions, the oxygen dissolved in water (B2.5 3 1024 M or 8 mg/L [3]) determines the corrosion rate but in acidic conditions the concentration of H1(aq) is much larger and corrosion increases exponentially with the decrease in pH. After the initial electrochemical half-reactions, the process continues with the formation of solid corrosion products by chemical reaction involving the products of (1.i)(1.iii), Mn1 ðaqÞ 1 nOH2 ðaqÞ ! MðOHÞn ðsÞ

(1.iv)

xMn1 ðaqÞ 1 yH2 OðlÞ ! Mx Oy ðsÞ 1 2yH1 ðaqÞ

(1.v)

Many other reactions with chemical species existing in the environment are possible. Common corrosion products include oxides, hydroxides, chlorides, sulfates, and carbonates. An impressive figure to retain is the cost of corrosion, estimated to lie between 3% and 5% of the gross domestic product [4,5]. Given the enormous economic impact of metallic corrosion, a great effort has been undertaken in the past century to understand this phenomenon and control it.

1.3 Corrosion protection and coatings 1.3.1 Strategies of corrosion control Corrosion is a thermodynamic inevitability and the question is not whether the metal corrodes but how long will it take until it does. Fortunately it is possible to significantly slow down the process. The procedures for control corrosion (1) act over the metal, (2) or act over the environment, or (3) separate the metal from the environment [6]. Acting over the metal can be done during the product design by selecting more corrosion resistant alloys or even nonmetallic materials. In service, the action on the metal takes place by changing its electric potential. A potential shift in the positive direction might form a passive layer on the metal surface protecting it from corrosion (anodic protection). A shift in the negative direction turns the metal into a cathode (cathodic protection) and the potential can be placed at values where the metal oxidation is thermodynamically impossible. It is then said to be immune to corrosion. Acting over the environment includes controlling room temperature and humidity, elimination of aggressive species (e.g., Cl2 and SO422), purging dissolved oxygen from aqueous solution, and the use of corrosion inhibitors. Separating the metal from the environment can be achieved by applying coatings to the surfaces. The coating hides the surface for the redox reactions and blocks

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the ionic paths between anodes and cathodes, interrupting the electric circuit of the corrosion cell. Most objects are coated and corrosion protection is only one of the functionalities. Other functions are decoration, reflection, adhesion, wettability, wear resistance, chemical resistance, thermal shielding, electrical conductivity, catalysis, etc. Such functionalities are obtained with coatings chemically very distinct, applied in many different ways, with very diverse forms of film formation, resulting in films morphologically and structurally very different. These coatings are usually classified as metallic, inorganic, and organic.

1.3.2 Metallic coatings Metallic layers are applied to the surfaces for various reasons including corrosion resistance, appearance, brightness, smoothness, hardness, wear resistance, thermal resistance, and electrical contact. For corrosion protection, the thicknesses range from 400 nm (tin in tinplate) to 0.5 mm or even more (zinc or aluminum coats on large steel structures). The coatings can be applied in various ways being electrodeposition, immersion in molten metal bath, thermal spraying, and cladding, the most common ones. The primary mechanism of protection is the shielding (or barrier) effect, which isolates the substrate from the aggressive environment. This mechanism is common to all coatings. The applied metallic films are more resistant to corrosion than the underlying metal. Corrosion still occurs but the durability of the coated material is significantly extended, principally if the coating is intact and covers completely the base material. When the two metals become exposed to the environment, at defects, pores, or cutedges, a galvanic corrosion process starts with the metal of more negative potential being oxidized, protecting the other metal from corrosion. If the coating is more negative, it will provide cathodic protection to the substrate preventing its corrosion (a zinc layer on steel is a typical example). Conversely if the potential of the base metal is more negative than that of the coating (e.g., chromium-plated steel), it will corrode at the points open to the environment with an increased rate, owing to the large cathodic area of the nobler coating.

1.3.3 Inorganic coatings Inorganic coatings for corrosion protection comprise vitreous (porcelain) enamels for decoration and protection, ceramic thermal barrier coatings for high-temperature applications, phosphate layers as base for paints, chromate conversion coatings for metal finishing or paint pretreatment, and anodized layers for finishing and base for paint. These coatings provide a barrier to the environment and higher protection may be attained by impregnating them with corrosion inhibitive compounds. Inorganic coatings are inert and their degradation usually occurs by mechanical damage or extreme acidbase conditions.

1.3.4 Organic coatings Organic coatings (or paints) are the most common, universal, and economic method for corrosion control. They are applied with many different objectives, from protection and decoration

Chapter 1 • Application of the scanning vibrating electrode technique

5

to sanitation and visibility [7,8]. A paint formulation contains constituents from five families: binder, pigments, fillers, solvents, and additives. The binder (nowadays predominantly synthetic resins) is responsible for the adhesion to the substrate, is the medium that keeps together all other constituents, and determines most of the coating properties; pigments are added for color and opacity; fillers (extenders) are included to reduce price by partly replacing the more expensive binder and pigments; solvents are necessary for adjusting the viscosity during manufacture and application; and additives are important to aid pigment dispersion and for special purposes (dispersants, wetting agents, defoamers, thickeners, rheology modifiers, driers, flash-rust inhibitors, and antiskin agents) [911]. A typical paint scheme is composed by at least one layer of primer, to insure good adhesion and to level surface roughness, and by a topcoat for color, gloss, and weather resistance. The protection against corrosion is obtained by (1) a barrier to oxygen, water, and ions, (2) incorporation of anticorrosive pigments, and (3) adhesion to the substrate [1214]. A polymeric film with high ionic resistance and good adhesion to the substrate represents an extremely difficult path for the flow of electric current between anodes and cathodes needed to close the corrosion circuit. The durability of paint schemes is limited and even the best systems rarely last more than 15 years without repainting [15]. The degradation is originated by abrasion, mechanical impact, ultraviolet (UV) radiation, cracking, hydrolysis, and oxidation reactions [16]. The corrosion of the metal underneath the paint appears in different forms: blistering, cathodic delamination, anodic undermining, filiform corrosion, and flash-rusting [8,12,13].

1.3.5 Techniques for assessing coating degradation Taking into account the plethora of coatings, functionalities, fields of application, and environments of service, it is clear that the mechanisms of degradation and the techniques and parameters for estimating the deterioration and predict service life can be very different. The most common testing conditions are natural weathering and accelerated tests in UV light, humidity, or corrosion chambers. The degradation state can be assessed simply by visual inspection (sometimes comparing with reference images) or by spectroscopic and surface analysis methods, such as gloss and color measurements, infrared spectroscopy, and scanning electron microscopy. Often, the tests follow international standards so that academia, industry, and end users have a common ground of understanding. By following normalized tests, anyone will know how they were performed and understand the results, independently on when or where they were produced. Corrosion testing is frequently done using electrochemical methods, such as open circuit potential monitoring, linear sweep voltammetry (polarization curves), and electrochemical impedance spectroscopy (EIS) [17]. For nonconducting films such as organic coatings, due to the high resistance, and consequent high ohmic drop, DC techniques should not be used [18,19] and EIS is the technique of choice [2023]. These methods give the average response of the sample but lack spatial resolution which is important to fully describe the degradation process. For this, localized techniques are needed. Among the several techniques available (see Section 1.8), the SVET stands out because it has the advantage of offering the global picture of the corrosion process,

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identifying the places where oxidation and reduction take place, their magnitudes, and evolution in time [24,25]. The technique was first used in biology [2628] and its application to the corrosion field was pioneered by Hugh Isaacs in the 1980s [29,30].

1.4 The scanning vibrating electrode technique 1.4.1 The principle The SVET provides the localization of the anodic, cathodic, and inactive areas on electroactive surfaces. Fig. 11B shows current lines and the electrical field in solution related to the corrosion at the surface. In a SVET measurement, a vibrating microelectrode is brought close to the surface (typical distances are from 50 to 200 μm) where it measures the potential difference in solution, @V, between the ends of the vibration, @r (1040 μm are typical values). The local potential gradient in solution, rΦ, in point (x, y, x) is given by, rΦ 5

@Vy @Vx @Vz i1 j1 k @rx @ry @rz

(1.1)

where i, j, and k are the standard unit vectors in the directions of the x, y, and z coordinates, respectively. The electric field in solution in each point of measurement is ~ E 5 2 rΦ

(1.2)

which multiplied by the solution conductivity, κ, gives the local current density, ~i 5 κ~ E

(1.3)

Most SVET systems only measure the field in a single direction, usually the normal to the surface, thus providing the component of the current density that flows perpendicularly to the sample surface, iz 5 2 κ

@Vz @rz

(1.4)

For imaging purposes this is the most important current component because the positive and negative currents can be related to the anodes and cathodes, respectively. Naturally quantitative information is limited since the X and Y components are unknown. The potential difference can also be measured with two microelectrodes placed at distance @r [31,32] in an arrangement called scanning reference electrode technique (SRET) [33]. The advantage of the vibration is that it modulates the signal allowing its amplification and filtering, thus significantly increasing the signal-to-noise ratio. In practice, instead of Eq. (1.4) a calibration routine allows the system to immediately give the current density from the measured potential [2628,34].

Chapter 1 • Application of the scanning vibrating electrode technique

7

SVET has been used to analyze many corrosion systems, such as galvanic corrosion [3539], pitting corrosion [4043], crevice corrosion [44], stress corrosion cracking [45], microbiologically influenced corrosion [4648], corrosion inhibitors [4954], and corrosion of weldments [5557]. Regarding coated systems it was used to characterize metallic coatings [36,58,59], inorganic coatings [60,61], organic coatings [6268], conducting polymers [6974], and more recently, self-healing properties of protective coatings [7579]. Revisions of published work can be found in Refs. [8083].

1.4.2 Experimental set-up A few designs of SVET equipment have been described in the literature [26,27,34,8489]. Fig. 12 shows the photographs of the equipment produced by Applicable Electronics [85]. The set-up exists basically to place a vibrating electrode at known positions in space, make it vibrate and record the potential difference between the ends of vibration. A collection of such points gives a SVET line or a SVET map. The oscilloscope (a) is used to check the quality of the probe tip response. The light source (b) and the camera (h) help placing the electrode in the desired position and allow monitoring the corroding sample. The motion control interface (c) controls the motors (f) which govern the position of the vibrating electrode in the three directions in space with micrometer resolution. The camera is also moved with a motor (not shown). Signals from two lock-in amplifiers (d) actuate piezoelectric benders inside a metallic

a)

b)

l)

m) n)

k) g) c)

h)

d)

1 cm i)

j) o)

e) f)

5 cm

10 µm

p)

FIGURE 1–2 Photographs of the SVET model used by the authors: (a) oscilloscope, (b) light source (with infrared filter and optical fiber to lamp), (c) motion control interface, (d) lock-in amplifiers, (e) computer with ASET software, (f) side of Faraday cage on the top of air table, (g) motors, (h) preamplifier, (i) ring lamp around a zoom scope connected to CCD camera, (j) metal box with 2 piezoelectric benders inside, (k) sample holder, (l) vibrating electrode, (m) sample, (n) ground electrode, (o) pseudoreference electrode, (p) vibrating electrode tip with platinum black deposit, and (q) electrode vibrating. SVET, Scanning vibrating electrode technique.

8

Handbook of Modern Coating Technologies

box (i), which are glued to a plastic arm with the vibrating probe connected at the end. Each piezoelectric bender transmits X and Z movement to the electrode, making it vibrate in the two directions with respect to the surface. Usually the vibrating electrode (k) is a 1.5-cm long Pt80Ir20 metal wire of 225 μm diameter, thinned at the end, and insulated with parylene C polymer except the B5 μm tip [90]. A small cathodic current is applied to produce a 10- to 40μm platinum black deposit at the electrode tip (o), which increases the surface area and consequently decreases the tip impedance [91]. The vibration frequency can be chosen in a range between 40 and 1000 Hz and the vibration amplitude (p) is usually between 5 and 10 μm (resulting in 20 μm between the ends of probe vibration for a 10-μm tip with 5-μm vibration amplitude). During the measurements the probe vibrates at the selected frequencies (triggered by signals from the lock-in amplifiers to the piezoelectric benders). The potential difference between the vibrating probe and a platinum black pseudoreference electrode (n) is measured with a dual n-channel field effect transistor inside a preamplifier (g), and sent back to the lockin amplifiers. The amplification can be up to 50,000 3 . A second Pt black electrode (m) is connected to the ground of the equipment. The typical electrochemical cell comprises the sample (l), glued to a nonconductive holder of 3 cm in diameter with tape around it to make the walls of the solution container. The ASET software (e) developed by Science Wares, Inc. (USA) [92] controls the measurement sequence. Best results are obtained using a Faraday cage, an antivibration table, and an uninterruptible power source, to minimize noise, ground loops, and external power peaks. Other SVET systems have only the Z vibration, bigger electrodes, larger volumes of solution, and no camera on the top of the sample [34,88,89]. Eq. (1.4) converts the potential between the ends of the vibration into local current density. In practice, the correlation between the two quantities is done directly by the system after a prior calibration. Different ways have been reported in the literature [2628,34]. For the system being described, the calibration consists of a routine in which the SVET probe is placed at a certain distance (e.g., 150 μm) from a point source that injects a known current, I (e.g., 60 nA). The current density i at the distance r from the source is given by [26,27,93], i5

I 4 π r2

(1.5)

A brief explanation is given in the SVET manual from Applicable Electronics [85] and Science Wares [92]. The system acquires two voltage signals for each vibration. As an example for the X vibration, the two signals are the voltage in phase (XPh 5 Vx sin A) and voltage in quadrature (XQ 5 Vx cos A), where Vx is the voltage amplitude (potential difference) and A is the phase angle determined from the relative amplitude of the signals in the sin and cos channels, A 5 arctan XQ/XPh. Assuming the phase angle stays constant (true for well-made probes, in a properly operating linkage and a calibration near the depth of the measurements), it is possible to determine the proportionality constant K relating the measured voltages to the actual current density. In the X vibration (1D) case,
 ix 5 Kx XPh cosA 1 XQ sinA

(1.6)

Chapter 1 • Application of the scanning vibrating electrode technique

9

The calibration determines A and Kx, and during scans the computer reads XPh and XQ from the lock-in outputs and uses them to calculate ix. For 2D measurements, the system acquires four voltage signals, X sin A, X cos A, Z sin B, and Z cos B, at two known points (chosen along the coordinate axes of vibration) with known current densities. The 2D case involves a calibration matrix that is designed to take into account the possibility of nonperpendicular axes of vibration. The mathematical statement is more complex than the 1D case but the principle is the same. The calibration is valid for other solutions provided the system is updated with the new testing conductivity. No electrochemical reactions take place at the tip of the microelectrode because no electrical currents pass through due to the high impedance of the preamplifier (1015 Ω). In addition, the vibration mixes the solution around the probe nullifying the concentration gradients that could otherwise be sensed and added to the SVET signal [94,95].

1.4.3 Common measurements Fig. 13 illustrates the sequence of steps to obtain a SVET map. The sample for this example is presented in Fig. 13A. It consists of a zinc foil of 50 μm thickness and a 900-μm thick iron sheet, mounted side by side in nonconductive polymeric matrix, and connected electrically at the back. This simulates the cut edge of galvanized steel with a better perception of the process in each metal due to the spatial separation between them. The area to be mapped by SVET is indicated in Fig. 13A. The part of the sample that will not be scanned is insulated with varnish to insure the active area is entirely scanned. This area is shown in more detail in Fig. 13B with the position of the measured points (50 3 50). The probe scans in a plane parallel to the surface at a height of 200 μm and in each point the probe waits 0.1 s and acquires the signal for 0.1 s. The total scanning time was 25 min for this map. Details about experimental parameters are given in the next section. In each point the probe vibrates in two directions, sensing the potential in the X and Z directions. Each vibration originates an alternating current (AC) potential signal that is amplified and filtered in a lock-in amplifier, as described earlier. Fig. 13C shows the maps of potential (difference between the ends of amplitude vibration) that are actually measured by SVET. Some SVET systems only provide this information. More important is the current density flowing in solution in the plane of measurement. This is obtained by the calibration using Eq. (1.6). The X and Z components of the current density are presented in Fig. 13D. The most common way of presenting SVET results is the map of the Z component (normal to the surface) because it gives a good picture of the positive (anodic) and negative (cathodic) areas of the corroding surface. Alone the X component (only accessible by one equipment) is not so insightful for corrosion studies but it is certainly helpful for a more complete description of the processes that are taking place. Maps with vectors of each component of the current density are possible (Fig. 13E) and maps of 2D vectors offer a nice visualization of the current flowing in solution from anodes to cathodes. Measurements in the three directions are not presently possible but have been reported in the past [84,86]. The SVET results can be presented in many ways. The maps of the current density in Fig. 13D can also be presented in a sort of 3D plot as in Fig. 14B. A different way is the

10

Handbook of Modern Coating Technologies

A)

Zn 50 µm

Fe 900 µm

Scanned area with measured points

B)

Scanned area

1 cm

Epoxy mount

1 mm

Zn

Fe

Differential potentiometer and lock-in amplifier

C)

Z vibration

X vibration µV

µV

36 28 20 12 4 –4 –12 –20 –28 –36

40 20 0 –20 –40 –60 –80 –100

1 mm Calibration

X component

Z component µA/cm2

Anodes

µA/cm2 50 40 30 20 10 0 –10 –20 –30 –40

Cathode

D)

Calibration

140 120 100 80 60 40 20 0 –20 –40

1 mm

E)

X vectors

Z vectors 2D vectors

1 mm

FIGURE 1–3 Sequence of steps in the most common SVET measurement (map acquired in a plane parallel to the surface at a specified height): (A) sample in the epoxy matrix with indication of the scanned area, (B) detail of the scanned area with the points of measurement, (C) maps of the potential difference measured between the ends of each vibration, (D) maps of X and Z components of the current density; and (E) vector maps of the current density (X, Z, and 2D). SVET, Scanning vibrating electrode technique.

Chapter 1 • Application of the scanning vibrating electrode technique

A)

Zn (50 µm)

Fe (900 µm)

11

B) Anodes 217 µA/cm2

Local anodes on zinc

Cathode –79

1 mm

D)

Scale vectors: 75 µA cm–2

C)

Zinc corrosion products

FIGURE 1–4 Various ways of plotting the SVET results: (A) detail of the measured surface, (B) 3D map of the Z current (normal to the surface), (C) contour lines of the Z current density, and (D) 2D vectors superimposed to the image of the sample surface. SVET, Scanning vibrating electrode technique.

superimposition of contour lines or current vectors to an image of the surface, as shown in Fig. 14C and D, respectively. Plots with vectors are produced by the ASET program from Science Wares. For other plots, the experimental results can be exported to files easily readable by any plotting program. Most of the figures in this chapter were made with the Quikgrid program written by John Coulthard (Canada) [96]. SVET maps show the “instant” activity on the sample during the period of measurement, whereas the optical images display the total corrosion accumulated from the beginning of immersion. Apart from maps parallel to the surface, other measurements are sketched in Fig. 15A. A map in the plane normal to the surface (XZ map) (Fig. 15B) can be interesting in some studies because it shows the regions inside the solution that are affected by the interfacial

12

Handbook of Modern Coating Technologies

B) Height (mm)

3

A)

XZ map

2 20 µA/cm2 1

40 60

0.1

XZ map

(d)

i (mA/cm2)

(c)

Z lines X lines Zn

Zn

(b)

C)

150 125 100 75 50 25

Above Fe

i (mA/cm2)

500

300 250 200 150 100 50 0 –50 –100

i (mA/cm2)

1000 1500 2000 Distance to surface (µm)

2500

3000

X line

Zn

–3000

E)

Z lines

0

0

D)

Fe

Above Zn

–25 –50

Fe

–20

–2000

Fe

–1000 0 1000 x distance (µm)

2000

3000

150 Fixed point 100

Accelerator

50

Inhibitor added to solution

0 0

300 600 900 1200 1500 1800 2100 2400 2700 3000 3300 3600 Time (min)

FIGURE 1–5 Other SVET measurements: (A) sketch of the sample surface with the position of sampled regions, (B) map in a plane normal to surface, (C) lines normal to the surface, (D) line parallel to the surface, and (E) measurement in a fixed position over time. SVET, Scanning vibrating electrode technique.

processes. Alternatively lines in the Z-axis can provide similar information, with the advantage that lines for various times or different conditions can be overlaid in the same plot. The lines in Fig. 15C show current density particularly intense close to the surface and a rapid decay until a height of 12 mm, where the bulk of the solution is reached. Lines parallel to the surface can be chosen to highlight superficial differences, as in Fig. 15D. Several lines can be plotted in the same graph to reveal the effect of time or changes in the system. Another way to continuously monitor changes in the kinetics of the processes at the surface is to place the probe at a point of interest (pit, defect, inclusion, intermetallic, active spot, etc.) and measure the response over time after variations have been introduced in the system (O2 concentration, pH, Cl2 concentration, corrosion inhibitors, etc.). It is important at this time to refer the type of samples that can be studied and how the electrochemical cells can be assembled. Fig. 16 shows various examples. Bulk materials

Chapter 1 • Application of the scanning vibrating electrode technique

A)

B)

1 cm

D)

1 cm

13

C)

1 mm

E)

F)

1 cm

FIGURE 1–6 Examples of samples preparation for SVET analysis: (A) metal sample embedded in polymeric matrix (the tape around the mount delimits the solution reservoir), (B) sample glued to the polymer mount and isolated with scotch tape except for the area to be measured, (C) sample insulated with beeswax 1 colophony (3:1 mass ratio), (D) larger painted metal sample glued to a Petri dish and the sides isolated with a varnish, (E) thick metal plate in a larger solution reservoir, and (F) cross section of metal sheet. SVET, Scanning vibrating electrode technique.

can be embedded in polymeric matrix and, after the test, be abraded and polished for reuse in subsequent measurements. Coated samples cannot be processed in the same way and must be glued to the epoxy mount. The samples must be isolated except the area to be measured. This can be done with adhesive tape, beeswax, varnish, etc. If polarization of the sample is desired, an electrical wire through the epoxy mount provides the connection to a potentiostat. In general, tape around the epoxy mount makes the reservoir for the testing solution. A volume around 5 cm3 is usual. The small volume can be a problem for measurements prolonged for more than a few hours because solvent evaporation or very active samples can change the solution concentration and pH, leading to alteration in the system kinetics. A variation in solution conductivity by solvent evaporation leads to incorrect current estimation. Different procedures can be applied to overcome this problem. The simplest is to perform experiments for just a few hours, renew the solution from time to time, or add water to the initial level to compensate for the evaporation. More elaborate measures involve electrochemical cells of larger volume, communicating vessels, or even solution recirculation between the small cell and a larger pool. Most of the SVET systems use larger solution vessels. The reduced size in the Applicable Electronics system comes from the original development for biological applications where small volumes are sufficient and easier to handle.

14

Handbook of Modern Coating Technologies

1.4.4 Experimental parameters When performing SVET measurements it is important to be aware of the most important experimental parameters and how they influence the results. 1. Electrode tip size. In Applicable Electronics equipment the electrode tip ranges typically from 10 to 40 μm in diameter. Other systems have bigger tips, of the order of 100500 μm. 2. Amplitude of vibration. Values between 5 μm [25] and 30 μm [34] are reported in the literature. Usually this parameter is not changed. If it does recalibration is needed. Higher amplitudes can lead to better sensitivity but may also stir the solution increasing the transport of O2 to the active surface [97]. The electric field is overestimated when the vibration amplitude is 0.25 times higher than the distance to the surface [98]. 3. Frequency of vibration. Any can be used. Recalibration is needed if changed. 4. Acquisition rules. SVET measurements can be performed point by point or continuously while the probe scans the surface. The scan rate, time constant, and gain play a decisive role in the data quality. For the Applicable Electronics system, which measures point by point, the most important parameters are the wait and average times. The first is the time the probe waits in a point before starting measuring, the second is the time given for acquiring signal. Typical values vary from 0.02 1 0.02 to 1 1 1 s in each point. The optimal combination for fast measurements keeping low noise depends on the system under study and should be checked before measurements. 5. Height of measurement. Common values are 50, 100, and 200 μm above the surface. The probe-surface distance is an important parameter in determining the spatial resolution. Isaacs determined the FWHM to be 1.533 times the height of the probe [99]. Therefore the closer the better for spatial resolution. However, close distances increase the risk of collision with the surface or touching corrosion products. Additionally, distances shorter than 4 times the vibration amplitude may lead to an overestimation of the electric field measured by SVET [98]. 6. Number of points. SVET systems measure the electric field either continuously or point by point. The Applicable Electronics equipment measures only point by point. Typical maps range from 10 3 10 to 100 3 100 points and the most common are between 20 3 20 and 50 3 50 (for sample areas ranging from 1 3 1 to 10 3 10 mm2). More points usually mean better map definition but there is no advantage for spatial resolution in having points closer than the distance to the surface. The parameters of the maps presented in this chapter were probes between 10 and 30 μm in tip diameter, frequencies between 70 and 400 Hz, vibration amplitude of 510 μm, distances to surface of 100 or 200 μm (sometimes 50 μm), and testing solutions from 0.005 to 0.1 M NaCl. The conditions used for each SVET map presented in this chapter are given in Annex. The proper selection of the experimental parameters, along with the quality of the equipment, is decisive for two important figures of merit, the sensitivity and the spatial resolution.

Chapter 1 • Application of the scanning vibrating electrode technique

15

1.4.4.1 Sensitivity The sensitivity corresponds to the smallest currents that can be measured above noise. For a discussion about the types of noise and their sources in SVET measurements see Ref. [91]. The noise level in a solution of interest is easily obtained from the measurements in that solution without any current source present. The noise level is dependent on the solution conductivity, decreasing as it increases. Limits of detection in 0.005, 0.05, and 0.5 M NaCl have been found to be, respectively, 0.1, 1, and 7.5 μA/cm2 [25]. Using these values in the following equation: ΔV 5  i ρΔr

(1.7)

where i is the minimum detectable current density, ρ is the solution resistivity, and Δr is the peak to peak amplitude (here taken as 10 μm), leads to ΔV 5 165180 nV, which can be considered the limit of the equipment.

1.4.4.2 Spatial resolution Spatial resolution depends on the distance to surface, tip size, and vibration amplitude. In normal operation, the distance to surface is the most important parameter. The FWHM 5 1.533h (h is the distance to the source) [99] means that higher spatial resolution is achieved when the probe is closer to the surface. It also means that there is no advantage for spatial resolution in having a SVET tip much smaller than the scan height. In other words, no improvement in spatial resolution is obtained with points closer than the distance to the surface.

1.4.5 Quantitative information The greatest benefit of SVET is the qualitative imaging of the corrosion process, revealing active (anodic and cathodic) and inactive areas. Alone, this capability is already of utmost importance because it is not matched by any other technique. Nevertheless, quantitative information is often reported [34,43,100109] and the approaches to correlate the current density that is measured in solution by SVET with the current at the surface (current source) include (1) treating local spots as point sources, (2) integrating the currents of the SVET map, and (3) using numerical simulation and modeling [95,106110]. 1. The simplest equation to be used when analyzing the data is I 5 2iz πh2

(1.8)

which gives the current I, emerging from a point source at the surface, that originates the current density iz, measured at a height h directly above the source. This may be used in cases of localized activity, if all active sites are well identified and separated and admitting that they can be treated as point sources.

16

Handbook of Modern Coating Technologies

2. The most common approach is to integrate the currents of the map. Eq. (1.9) gives the total anodic current, Ia, in a map of area A, by integrating the currents of all positive points (iz . 0) [34,102,104], Ia 5 A i a $

ðx ðy 0

½ iz ðx; yÞ . 0 dx dy

(1.9)

0

Alternatively when the data are discrete (e.g., collection of points in a table), the total anodic current can be determined by summing the small currents that flow in the positive points of the map. This corresponds to the summation of the local current densities of all positive points (above noise level) multiplied by the area related to a single point (obtained dividing the map area A by the number of points in the map N), as shown in Eq. (1.10), Ia 5

Nð1Þ AX ðin . jinoise jÞ N n51

(1.10)

where N( 1 ) is the number of positive point in the map, in is the current density of the nth positive point, and inoise is the noise level of the experimental conditions. It is advisable to have the area of the map A coincident with the area of the sample. In Eqs. (1.9) and (1.10) the calculation is presented for the anodic current (i . 0) but it could be similarly done for the cathodic current (i , 0). 3. In any case, the best approach, leading to more accurate results, is to use modeling and simulation tools to analyze the SVET data. This can overcome most of the limitations inherent to the experimental results, as discussed in the next section.

1.4.6 Limitations It is difficult to achieve quantitative and accurate results with Eqs. (1.8)(1.10). In fact, only underestimations are usually obtained for the following reasons: 1. the probe scans at a certain height above the surface and the current that flows below is missed; 2. the current outside the mapped area is not measured, 3. currents below the noise level will not be detected; and 4. only one (or two at the most) component of the current density is measured by SVET, leading to an underestimation of the total current density. These reasons explain why calculations from SVET should always be considered with great care. This is also why many times the anodic and cathodic currents in a map do not cancel. Since SVET gives a partial picture of the current flowing in the system, the best approach is to use numerical modeling tools to reconstitute the missing information. Nowadays this is done using the finite elements method with models using the Laplace

Chapter 1 • Application of the scanning vibrating electrode technique

17

equation [106,109,111113] and models analyzing the transport and reaction of chemical species in the system under analysis [95,107,108,110].

1.4.7 Main sources of artifacts and errors The difficulties in using SVET as a truly quantitative technique were described. In addition, there are errors and artifacts easy to occur, with strong impact on the results. Fortunately they are easy to detect.

1.4.7.1 Electrode platinization The active area of the SVET microelectrode needs to be substantially increased, to lower the impedance and decrease noise. This is done by plating platinum black (hair-like threads) at the tip. If the tip is not well “platinized,” maps will be noisy and, in the limit, no coherent signals will be detected. A routine exists to check the quality of the tip response [91,114]. SVET systems using large electrodes do not require platinization.

1.4.7.2 Bad calibration The calibration relates the potential difference measured by SVET to the current density flowing in that point in space. It is performed in a medium with a known conductivity and remains valid for other solutions if their conductivities are updated in the software. Moreover, a similar probe size and the same frequency and vibration amplitude must be used. If any of these change, the calibration must be repeated in the new conditions.

1.4.7.3 Wrong conductivity As referred in the last point, wrong conductivity leads to erroneous current values. If the conductivity of the new solutions is higher and not updated, the currents will be lower than the true ones. The wrong current densities can be corrected using the following equation: itrue 5 iwrong

κtrue κwrong

(1.11)

1.4.7.4 Unknown distance to source Since the current density varies with the inverse square of the distance to the source (Eqs. 1.5 and 1.8), measurements performed at different heights will give different current values and cannot be directly compared. If the distance to the surface is unknown, the value of the measurements is very limited.

1.5 Application of the scanning vibrating electrode technique to characterize modern coatings SVET measures ionic currents in an electrolyte solution; therefore, it is especially suited for analyzing active coatings or pores and defects in inert coatings applied to active substrates.

18

Handbook of Modern Coating Technologies

Different cases are summarized in Table 11 and sketched in Fig. 17. The first case corresponds to nonconductive coatings applied on nonconductive substrates as, for example, a paint on plastic, wood, paper, glass, or ceramic. No currents are developed in these systems; therefore, SVET does not provide any results of interest. Case 2 refers to conductive coatings applied on nonconductive substrates, for example, a metallic film on the substrates of the previous case. The results will be that of the metal film, similar to the bulk metal. The opposite case is a nonconductive coating applied on a conductive substrate. The coating can be organic (paint or varnish) or inorganic (chromate conversion film, anodized layer, phosphate layer, and vitreous enamel), and three cases are possible: intact coatings with no activity to be detected by SVET (Case 3); coatings with small pores or blisters, which may or may not be detected by SVET (Case 4); and large pores or defects, easily measured by SVET (Case 5). The last four cases concern conductive coatings on conductive substrates. It is important to distinguish two situations: coating anodic to the substrate (e.g., zinc on steel) and coating cathodic to the substrate (e.g., chromium on steel). For each situation it is also necessary to Table 1–1

Types of coated systems that can be measured by SVET.

Case no.

Substrate

Coating

1 2 3 4 5 6 7 8 9

N

N C N

C

C (anodic) C (cathodic)

Condition

Corrosion

SVET

Intact Pores/blistering Defect Intact Defect Intact Defect

N N/Y N Y Y N/Y Y N/Y Y

✕ ✕ü ✕ ✕ü ü ✕ü ü ✕ü ü

References

[68] [51,6062,65,67,115118] [59,100,106] [58,60,61]

C, Conductive; N, nonconductive; SVET, scanning vibrating electrode technique; ü, signals can be sensed by SVET; ✕, no signals to be detected by SVET.

1

2

6

7

4

3

8

5

9

FIGURE 1–7 Schematic representation of the coated systems in Table 11. Current lines indicate the cases where corrosion occurs.

Chapter 1 • Application of the scanning vibrating electrode technique

19

consider intact and defective coatings. Thus Cases 6 and 7 are for, respectively, intact and defective coatings anodic to the substrate and Cases 8 and 9 for, respectively, intact and defective coatings cathodic to the substrate. Examples of the application of SVET for each case are now presented.

1.5.1 Systems with inert coating or inert substrate (Cases 13) Case 1 corresponds to nonconductive materials in both coating and substrate. No ionic currents are produced to be detected by SVET. Case 2 is for conductive coatings on inert substrates. The response is the same as that of the metal constituting the coating. It may be a noble or passive layer, without activity at the surface to be measured. If it is an active metal (hardly chosen as coating material), it will be simply a case of metallic corrosion and will not be presented here. Case 3 refers to a conductive substrate with an intact nonconducting coating. The substrate is isolated from the environment, consequently it does not react and no signals exist to be detected by SVET. Two examples are presented here. Fig. 18A shows a sample of the aluminum alloy 2024-T3 with a thin layer (2 μm) of an organicinorganic film applied by the solgel method. No activity was found even after 1 month of immersion in 0.05 M NaCl. Another example—Fig. 18B—is a layer of Al2O3 applied by plasma deposition on LM24 [119] cast aluminum alloy. After 1 h in 0.1 M NaCl no currents were measured. The maps show an absence of anodic or cathodic currents. The values are not zero, but very A1)

A2)

A3) µA/cm2

1 µA/cm2

0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1

B1)

B2)

B3) µA/cm2

2 µA/cm2

2.6 1.9 1.2 0.5 –0.2 –0.9 –1.6 –2.3 –3

FIGURE 1–8 Example of coated systems with no signals detected by SVET (Case 3 in Table 11): (A) 2024-T3 aluminum alloy coated with 2 μm thick hybrid organicinorganic solgel film after 1 month of immersion in 0.05 M NaCl and (B) LM24 cast aluminum alloy with alumina layer applied by plasma deposition after 1 h of immersion in 0.1 M NaCl. The numbers 1, 2, and 3 represent, respectively, an optical image of the sample with the indication of the scanned area (dashed lines), 2D current density map measured by SVET, and the same map in 3D. SVET, Scanning vibrating electrode technique.

20

Handbook of Modern Coating Technologies

small (between 6 1 and 2 μA/cm2), at the noise level of the solution. The values could be taken as the manifestation of many anodes and cathodes (small positive and negative current sources) randomly distributed. To confirm that the signals are indeed noise and not very small currents emanating from the surface, measurements can be repeated closer to the surface. If no activity exists, the same noise will be measured in any place of the cell, close or far from the surface. Conversely if currents truly exist, their magnitudes will increase as the maps are acquired closer to the surface. In addition, when corrosion is actually taking place, the activity will continue in subsequent maps, and the cumulative degradation will be visible at later times.

1.5.2 Coatings with pores or small defects (Case 4) The absence of signal from SVET in coated active metals (metals with tendency to corrode) is a proof of high-quality coatings. Porosity, or small defects, is enough for the metal/environment interaction and for corrosion initiation. Examples are now given using the same systems presented for Case 3. This time the solgel film was cured for a shorter period (80 min at 120 C compared with 17 h in the previous example), rendering a not completely cured film and consequently not perfectly continuous, permitting the solution to easily reach the substrate. In just 2 days of immersion, one anodic spot was detected and several cathodic regions were developed at the surface of the sample, coincident with the dark regions in the optical picture—Fig. 19A. The maps in Fig. 19B correspond to the LM24 aluminum alloy A1)

A2)

A3) µA/cm2 10 8 6 4 2 0 –2 –4 –6 –8

B1)

B2)

8

B3) µA/cm2

16

2.6 1.9 1.2 0.5 –0.2 –0.9 –1.6 –2.3 –3

FIGURE 1–9 Examples of the same coatings in Fig. 18, this time with pores or small defects (Case 4 in Table 11): (A) solgel film with incomplete curing, after 2 days of immersion in 0.05 M NaCl and (b) LM24 cast aluminum alloy with alumina layer after 6 h of immersion. The numbers 1, 2, and 3 represent, respectively, an optical image of the sample with the indication of the scanned area (dashed lines), 2D current density map measured by SVET, and the same map in 3D. SVET, Scanning vibrating electrode technique.

Chapter 1 • Application of the scanning vibrating electrode technique

21

coated with Al2O3 layer, where currents were detected after 6 h of immersion in localized points, coincident with the pores in the coating.

1.5.3 Coatings with macroscopic defects (Case 5) Along with pores and small defects, coatings may have much larger defects, either appearing in the course of the service life or deliberately produced to accelerate the degradation of very good coated systems, where changes would take months or years to be noticed. Fig. 110 shows artificial defects (scribes) produced in an organic coating (polyurethane) applied to 2024-T3 aluminum alloy. They were chosen to demonstrate that it is possible to have defects with no activity detected by SVET (Fig. 110A), or defects with both anodic and cathodic activities, (Fig. 110B), or even with just anodic (Fig. 110C) or cathodic activity (Fig. 110D). In the last two cases, cathodic activity (Fig. 110C) and anodic activity (Fig. 110D) exist but most likely occur under the paint (blisters are observed in some of the optical pictures) and are not detected. The mismatch between anodic and cathodic currents, as well as the not detection of currents that should be there, are examples of the limitations presented in Section 1.4. When various defects are present, they are often galvanically coupled. This is easily perceived in systems with only two defects. While it could be expected that the two worked independently, each one with both anodic and cathodic activities, in practice it has been found a separation of the anodic and cathodic activities in different defects [51,115,120]. A)

B)

–1

1 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1

1 mm

0 2.5

10

1 mm

C)

10 9 8 7 6 5 4 3 2 1 0 –1 –2

D) –1

15 10 0

1 mm

–1

5

20 18 16 14 12 10 8 6 4 2 0 –2

–2

1 mm

2 1.5 1 0.5 0 –0.5 –1 –1.5 –2

FIGURE 1–10 Four examples of the currents that can be measured by SVET above a defect (scribe) on organic coating (Cases 4 and 5 in Table 11): (A) no currents, (B) both positive and negative currents, (C) only positive currents, and (D) only negative currents. Dashed lines indicate the mapped areas. The units in the scales are μA/cm2. SVET, Scanning vibrating electrode technique.

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One example is shown in Fig. 111 with 2024-T3 aluminum alloy coated by a solgel film and exposed to 0.05 M NaCl. The film protects the alloy from corrosion except at the defects, and one is positive and the other negative. The same spatial separation of both activities has been found in samples with more defects [116].

1.5.4 Coatings anodic to the substrate (Cases 6 and 7) A very common example of metallic coating anodic with respect to the substrate is galvanized steel. Zinc has higher tendency to corrosion than steel but it corrodes at a slower rate due to the formation of an oxide/hydroxide/carbonate deposit on its surface. As a consequence, the zinc coating on steel without defects will corrode slowly and increase the lifetime of the whole material. When the steel substrate is exposed in defects, it will still be protected through cathodic protection conferred by the zinc, which oxidizes preferentially. The way this process takes place can be followed by SVET. Fig. 112 shows steel coated with a zinc layer of 7 μm, immersed in 0.1 M NaCl. This corresponds to Case 6. The corrosion of the zinc layer occurs in a localized manner (Fig. 112A) and the ferrous substrate is rapidly reached. In 1 day, steel is exposed in well-defined round spots, but not corroding (no yellow, orange, or brown iron corrosion products) because it is galvanically protected (Fig. 112B). The sample becomes an example of Case 7 (anodic coating with defects). During 1 week, zinc continued dissolving, increasing the exposed substrate area but steel was still protected from corrosion. Eventually zinc will run out and steel will start corroding. Fig. 112D shows the microscopic aspect of the zinc crystals and Fig. 112E gives a detail of one corrosion spot, after 24 h of immersion, with the zinc layer, the exposed steel and corrosion products in the center of the spots. The SVET can be used to monitor a coated system over time, compare different systems, or study the influence of environment conditions.

20 15

5

500 µm

Y (µm)

0

iz (µA/cm2)

10

–5

600 300 0 –300 –600

–10 250 –750 –500 –250 0 X (µm)

500

–15

FIGURE 1–11 Example of a typical SVET measurement on a coated sample with two defects: one becomes anodic and the other cathodic. SVET, Scanning vibrating electrode technique.

Chapter 1 • Application of the scanning vibrating electrode technique

A)

B)

C)

D)

µA/cm2 120 100 80 60 40 20 0 –20 –40

1 mm

23

1 mm

10 µm

E)

Zinc

Steel

Corrosion products 30 µm

FIGURE 1–12 Corrosion of electrogalvanized steel. Example of an anodic coating applied to a cathodic substrate intact and with defects (Cases 5 and 6 in Table 11). (AC) show the condition of the surface after 1 h, 1 day, and 1 week of immersion in 0.1 M NaCl; (D) microscopic surface of the zinc electrodeposit; and (E) close look of the border of one corroded pit after 1 day of immersion, with the zinc layer, the steel substrate, and corrosion products.

1.5.5 Coatings cathodic to the substrate (Cases 8 and 9) A final case is that of a coating cathodic to the substrate. The chosen example is carbon steel with a TiN layer deposited by physical vapor deposition (PVD). This coating is electroactive but passive to corrosion in this medium, therefore no currents are generated at the surface to be detected. Fig. 113A shows the system with intact coating after 4 days immersed in 0.05 M NaCl and no significant currents are detected by SVET. This is an example of Case 8. Fig. 113B depicts a similar system but with defects on the TiN film (Case 9). The electrolyte solution is able to contact the ferrous substrate in the defects, leading to localized corrosion. The SVET maps show two intense anodic spots. The remaining area presents negative currents, indicating that the TiN layer is electrochemically active and able to support reduction reactions. The high cathode to anode area ratio leads to high anodic current densities, fast corrosion, and easy visualization of corrosion products in just a few hours.

1.6 Review of published work using the scanning vibrating electrode technique to characterize coatings performance After an overview of the responses that can be found by SVET with the various types of coatings, a short review of the literature is now presented. The first published study with SVET and coatings dates from 1987, in which Isaacs described the use of the vibrating probe technique to detect the presence of defects in ion vapordeposited aluminum on steel [58].

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Handbook of Modern Coating Technologies

A1)

A2)

A3) 1 µA/cm2

µA/cm2 2.5 2 1.5 1 0.5 0 –0.5 –1 –1.5 –2

B1)

B2)

314

B3) µA/cm2 210 180 150 120 90 60 30 0 –30

250

–28 –28

FIGURE 1–13 Corrosion of steel coated with TiN. Example of a cathodic coating applied to an anodic substrate intact and with defects (Cases 8 and 9 in Table 11). (A) Steel sheet coated with 2 μm thick TiN layer deposited by PVD, after 4 days of immersion in 0.05 M NaCl. (B) Same coated system with defects in the TiN layer. The numbers 1, 2, and 3 represent, respectively, an optical image of the sample with the indication of the scanned area (dashed lines), 2D current density map measured by SVET, and the same map in 3D. PVD, Physical vapor deposition; SVET, scanning vibrating electrode technique.

A nonaggressive borate solution was chosen to prevent any significant damage to the coating during defect location. The experimental set-up involved polarization measurements on specific areas of the surface. The results showed that the defects were not from the exposed steel but were caused by the presence of inclusions in the coating. Worsley et al. combined SVET and micrographic analysis to study the mechanisms of corrosion on the surface and on the edges of hot dip galvanized steel and also the effect of the cooling rate and gauge on total zinc loss and anodes lifetimes [59]. The defects induced by mechanical forming of galvanized steel was also analyzed by SVET [60,61]. Another subject with intensive study using SVET was the corrosion at cut-edges [36,106108,111,121127]. Of all types of coatings, organic coatings (paints) are the largest group with many different compositions and possible responses. They were also studied by SVET. One of the first studies with organic coatings was reported by Isaacs [62], where the technique was used to detect defects of a 20-μm thick epoxy paint applied on phosphated zincplated steel or pure zinc sheet, immersed in 10 mM sodium chloride or sodium sulfate. A deconvolution method was used for obtaining the current densities at the metal surface. Not long after, Sekine and coworkers [63,64] used SVET to study several coating systems (epoxy, polyurethane, polyester, polyvinyl chloride, and alkyds) and found a linear correlation between the current density measured by SVET, the film resistance measured by EIS, and the coating lifetime (the higher the current density, the shorter was the coating lifetime). They also found that the current density for the same coating system depended on the testing solution, increasing in the order

Chapter 1 • Application of the scanning vibrating electrode technique

25

NaCl , Na2SO4 , K2CO3 , H3PO4 , HCOOH. Later, SVET was used to study chromate-epoxy primers applied on steel and aluminum [65] and contributed to the elucidation of the sacrificial effect of magnesium rich primers developed as replacement to chromate based pigments [6567]. Another study involved weldable primers (very thin films incorporating conductive particles to provide electrical continuity through the coating) for welding of coated metal panels in the automotive industry [68]. Conductive polymers have been investigated for corrosion control, directly as pretreatments or as modifiers of fillers and pigments in paints. Several works used SVET to characterize the action of conductive polymers, principally in defective areas [6974].

1.6.1 Self-healing coatings A new line of investigation in coatings research is the search for self-healing systems [7579,128135]. “Self-healing” can be defined as the autonomous recuperation of the initial properties of a coating that were lost after a negative interaction with the surrounding environment (corrosion, pH change, mechanical impact, thermal shock, chemical attack, UV irradiation, water ingress, etc.). “Smart” is a related term applied to a coating capable of sensing alterations in the environment and able to respond in a preestablished manner. It may be the self-recovery of properties lost after an external aggression (self-healing) or the indication (change in color for example) that a critical threshold (temperature, humidity, radiation, pressure, etc.) has been reached (in the coating or in the environment), prompting human action to fix the problem. In the field of coatings for corrosion protection, self-healing is currently being implemented either by responsive prepaint layers or by formulations containing self-sealing components or incorporating micro/nanoreservoirs of corrosion inhibitors for later release [128135]. The loading of corrosion inhibitors into micro/nanoreservoirs and their incorporation in paint formulations as additives or replacement of pigments is the most common approach. The reservoirs are dispersed in the coating and the inhibitor stays inside until an external stimulus activates the liberation of inhibitors, and, sometimes, the capture of aggressive species like chloride ions. The stimulus can be the level of moisture, temperature, UV radiation, mechanical impact, change in local pH (at anodes or cathodes), rise of ionic strength, or increase in the concentration of metallic ions (from metal oxidation) or of aggressive ions (e.g., Cl2). SVET can monitor the self-healing capability of surface coatings by means of maps, lines, or measurements on a single point above artificial defects. If indeed self-healing is operating, after an initial increase, the corrosion current should decrease until the degradation process is stopped. The possible responses of current versus time are typified in Fig. 114. In a normal situation corrosion will start at the defect and grow in size with an increasing current over time (Fig. 114a). Alternatively the current will stabilize at a certain level or it may decrease (Fig. 114b and c). This is sometimes considered an indication of self-healing because the system is able to prevent the progress of corrosion or even minimize its effect. The ideal situation is represented in Fig. 114d with the complete suppression of corrosion and the ability to keep healing whenever further defects are made.

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Handbook of Modern Coating Technologies

SVET current

Defect formation: a)

b)

c)

d)

Time FIGURE 1–14 Possible evolution of SVET current after a defect is produced in an organic coating without and with self-healing capability. SVET, Scanning vibrating electrode technique.

For this type of investigation it is necessary to discard other reasons for the decrease in SVET signal before concluding for self-healing: (1) the defects can be covered by corrosion products which may hinder or deviate the current pathway; (2) corrosion might move from the defect to areas below the coating or out of the scanned area, not measurable by SVET; and (3) the anodic and cathodic areas may become so small and uniformly distributed that the current lines between them flow close to the surface and below the plane of measurement. In all these cases, corrosion exists but is not sensed by SVET. A few examples from the literature are now presented. In 2004 Khramov et al. [75] studied a 2024-T3 aluminum alloy covered by a hybrid organoinorganic film containing corrosion inhibitors. Films as thin as 1 μm thick were able to heal the localized corrosion on artificial defects. With mercaptobenzimidazole corrosion was not detected during the testing period, while with mercaptobenzothiazole the current measured by SVET increased at the beginning but then it declined to values that remained negligible during the rest of the testing period. Healing was also detected when the inhibitors were loaded into nanocontainers dispersed in the solgel film [77]. EIS showed evidences of healing but the corrosion suppression was better visualized by SVET. In another study nanoparticles with a layered double hydroxide structure incorporating benzotriazole (BTA) were mixed in epoxy coating together with nanosized bentonite clay with Ce31 [79]. The coating was applied to 6061 aluminum alloy in contact with carbon fiberreinforced plastic (CFRP). To accelerate the degradation one defect was produced on the metal part and another one on the CFRP part. The degradation was followed by SVET. Oxidation appeared on the defect in aluminum, and reduction on the defect in the conductive plastic. The SVET currents were noticeably smaller in these samples compared with samples coated with the epoxy without nanocontainers (reference system). The decrease in corrosion was attributed to the synergistic action of BTA and Ce31, the former mainly at the anode and the later at the cathode.

1.7 Critical account on the application of the scanning vibrating electrode technique to study coatings The examples presented in the last section show the application of SVET to a great number of coated systems. This was possible, despite the limitations discussed in Section 1.4.6. A

Chapter 1 • Application of the scanning vibrating electrode technique

27

coating brings further limitations. It is a barrier between electrode and electrolyte solution, blocking the current path. Often, only part of the actual processes taking place at the surface is accessible to SVET. It is very important to be aware of these limitations when studying organic coatings. Fig. 115 summarizes the most common problems. The first example is a thick coating. Fig. 115A shows 1-mm thick silanebased clear coat, applied on AZ31 magnesium alloy, after 20 days of immersion. The sample is still not much attacked, just a dark area adjacent to the scribe. The small current involved in the corrosion process is not strong enough to be detected by SVET so far from the surface. Similarly a large blister (Fig. 115B) also does not show any signals detectable by SVET. The large distance to surface and the blocking effect of the polymeric film makes difficult the detection of any current. Smaller blisters will also not be well resolved, as demonstrated in Fig. 115C. In this case, two defects were produced on an epoxy clear coat applied on pure zinc sheet. Due to an incompatibility of this coating formulation with the substrate, it rapidly delaminated from the surface, in the form of many blisters. The purple color inside the blisters is due to phenolphthalein (pH indicator) added to solution, permitting to identify the alkalinization associated with the cathodic reactions and evidencing a case of cathodic delamination [13]. The activity at the defects was easily detected by SVET but not the currents at the blisters. The map shows small cathodic currents that may be assumed to be emanating from the blisters. However, given the small magnitude, those signals can be just noise. In any case, the level of blistering in the sample (number, size, and shape of blisters) could not be resolved. A last case selected to show the limits of SVET with organic coatings, is a scribe on epoxy clear coat applied to electrogalvanized steel (Fig. 115D). In this example, SVET only detects positive currents at the defect. The coating is transparent making possible to see the degradation of the sample, with a large area of zinc layer dissolved and the dissolution front well away from the defect. It is evident that the degradation of the sample was not properly characterized by the SVET. The currents were flowing mainly below the paint film, not crossing it to be detected by the probe. The corrosion of the substrate beneath a metallic coating may also be not well characterized by SVET. Fig. 116 shows an aluminum alloy coated with Inconel 625 (corrosion resistant NiCr-based alloy) applied by HVOF, after 6 days immersed in 0.1 M NaCl. A single point of strong anodic activity dominates the SVET map. In the optical picture it coincides with a crack on the Inconel layer. The crack is surrounded by a reddish color, attributed to a copper deposit formed by reduction of copper ions that come from the oxidation of the aluminum alloy (which contains 2% of copper). The Inconel does not corrode and the current is due to the dissolution of the aluminum alloy taking place beneath it. The extent of the attack is only visible after removal of the Inconel layer (Fig. 116C), which reveals that corrosion progressed in depth and laterally, even outside the mapped area. SVET (or any other technique) is unable to anticipate the morphology of the substrate dissolution beneath the metallic coating. However, the volume of lost metal could have been predicted by monitoring the peak current, then use Eq. (1.8) to relate the current in solution measured by SVET with the current emanating from the crack and, finally, using the Faraday laws of electrolysis to obtain the mass loss. From the mass, knowing the density, the corresponding volume is obtained.

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Handbook of Modern Coating Technologies

A)

µA/cm2 1.6 1.2 0.8 0.4 0 –0.4 –0.8 –1.2 –1.6 –2

B)

4.6 3.9 3.2 2.5 1.8 1.1 0.4 –0.3 –1

C)

38 33 28 23 18 13 8 3 –2

D) µA/cm2 71 63 55 47 39 31 23 15 7 –1

FIGURE 1–15 Limitations of the SVET with organic coatings. (A) No response detected above defects on thick coatings (B1 mm), (B) large blister without signs of current, (C) delaminated epoxy clear coating with blistering but activity detected only above two artificial defects, and (D) activity beneath the paint film not resolved by SVET. SVET, Scanning vibrating electrode technique.

Chapter 1 • Application of the scanning vibrating electrode technique

A)

B)

29

C) µA/cm2

1 mm

300 260 220 180 140 100 60 20 –20 –60 –100

Mapped area 0.5 cm

FIGURE 1–16 Cast LM24 aluminum alloy coated with a layer of Inconel 625, after 6 days of immersion in 0.1 M NaCl, with evidences of anodic undermining: (A) optical picture, (B) SVET map, and (C) aluminum substrate after removal of Inconel layer (white line shows the limit of the SVET map). SVET, Scanning vibrating electrode technique.

SVET is normally used with active samples, where the spontaneous redox reactions of the corrosion process originate the currents to be measured. For conductive substrates or coatings, when no spontaneous currents are generated (because corrosion is not likely to occur), it is still possible to pass current through the sample and monitor the response by SVET. By this way it is possible to identify conductive regions, especially pores and defects in a nonconductive coating, and the electroactive ability of the conductive surface (substrate and/or coating) to sustain electrochemical processes. Fig. 117A shows the surface of coated tinplate (steel sheet with a very thin—400 nm—layer of tin covered by B1 μm hybrid silane film) after 48 h of immersion in 0.05 M NaCl. Steel is corroding in a few points, identified as brown spots in Fig. 117A. When a positive or negative current of 2 μA is applied to the sample (in an organic solvent—absolute ethanol saturated with NaCl—to avoid the corrosive effect of aqueous solutions), more active points are visible in the SVET maps. Many points are common in maps (C) and (D) but some are only active for the cathodic or for the anodic processes, which might give indication about the electroactivity of those points. Fig. 117E and F shows a similar approach to reveal the porosity of an Al2O3 layer applied on an aluminum alloy (same system presented in Figs. 18B and 19B). The objective was to rapidly detect the porosity of the sample without promoting the corrosion of the substrate [117]. Instead of organic solvents, this analysis could have been done in aqueous solutions of low corrosivity, for example, buffered borate solutions [58].

1.8 Other localized techniques In this last section other localized techniques are briefly presented and put in perspective with SVET.

1.8.1 Scanning reference electrode technique The SRET is the predecessor of SVET. A reference electrode scans the solution close to the metal surface and measures the potential referred to another reference electrode placed in a

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Handbook of Modern Coating Technologies

A)

B)

1 mm

1 mm

OCP; I = 0 A

7 5 3 1 –1 –3 –5 –7

D)

C)

1 mm

E)

I = –2 µA

12 9 6 3 0 –3 –6 –9 –12

1 mm

I = 2 µA

12 9 6 3 0 –3 –6 –9 –12

F) 2 µA/cm2

µA/cm2 2 1.5 1 0.5 0 –0.5 –1 –1.5 –2

1 mm X / 7.3 mm

Y / 6.5 mm

FIGURE 1–17 Detection of defects and porosity using organic solvents and applying current: (A) silane film on tinplate after 2 days of immersion in 0.05 M NaCl, (B) SVET response in 0.05 M NaCl, (C) response in ethanol saturated with NaCl and a current of 22 μA and (D) with a current of 2 μA passing in the cell, (E) Al2O3 layer on LM24 aluminum alloy, and (F) porosity revealed by passing a current of 2 μA through the sample in ethanol saturated with NaCl. SVET, Scanning vibrating electrode technique.

stationary position. In some designs the two reference electrodes are mounted with fixed distance between them and scan together the area of interest. The local difference in potential is related to the local current density by Eq. (1.4). The results can be presented either as

Chapter 1 • Application of the scanning vibrating electrode technique

31

maps of potential or maps of current density. Compared with SRET, SVET brought noise reduction and higher sensitivity. SRET has been used to analyze many corrosion problems [33], including coated systems [136].

1.8.2 Potentiometric microelectrodes SVET and SRET do not identify the chemical species involved in the measured potentials and currents. For this, potentiometric microelectrodes can be used, detecting and quantifying important chemical species involved in the corrosion process, such as the metal cations originated in the oxidation half-reaction, corrosion inhibitors, and electrolyte ions. These microelectrodes are not new. Ammann refers the existence of pH microelectrodes already in (1927) [137] and their use in the life sciences has several decades of experience [138140]. However, nowadays they are often presented as an application of scanning electrochemical microcopy (SECM) [141143]. Examples in corrosion research can be found in reviews [83,144,145] and many times they appear together with SVET [51,95,115,116,118,120,127, 146,147].

1.8.3 Voltammetric/amperometric microelectrodes Similarly to potentiometric microprobes, inert microelectrodes (Pt and Au) can be used as voltammetric or amperometric sensors for species relevant to corrosion, like reactants (O2 [51,148]) or products (metal cations from the substrate oxidation [148] or H2 generated in the cathodic process of magnesium alloys corrosion [149,150]). The inert electrode is polarized at a potential where the species of interest is oxidized or reduced and the measured current (positive or negative) is proportional to the concentration of the species.

1.8.4 Scanning electrochemical microscopy This technique appeared at the end of the 1980 decade [151,152] and since then was applied in many areas of research [153]. SECM in its original form is an imaging technique with a bipotentiostat to independently control the potential of the substrate and the potential of the tip, with a reversible redox mediator in between. For corrosion and coatings characterization the most important mode of operation is the substrate generation/tip collection mode, in which the microelectrode works as a sensor, like the potentiometric and amperometric microelectrodes described above. SECM has the advantage of high (micrometer) resolution and has been applied to many corrosion studies [83,144,145].

1.8.5 Localized electrochemical impedance spectroscopy Another powerful technique with still high potential ahead is localized electrochemical impedance spectroscopy (LEIS) [154,155]. It measures local ionic currents while a small AC potential stimulation is applied to the substrate. The AC potential signal divided by the local AC current gives the impedance response of that local point of the sample. Often, the areas where the impedance is lower correspond to the areas of higher current density in SVET

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Handbook of Modern Coating Technologies

maps. One of the most striking features to expect from LEIS is the ability to acquire separate kinetic parameters of the oxidation and reduction reactions involved in the corrosion process. An important related breakthrough would be the capability to analyze and spatially resolve the individual reactions occurring underneath polymeric paints.

1.8.6 Alternate current scanning electrochemical microscopy A different experimental approach for LEIS is the alternating current-scanning electrochemical microscopy (AC-SECM), where the AC potential perturbation is applied to the SECM tip and no mediator is added to solution [156158]. A lock-in amplifier determines the tip current magnitude and its phase shift with respect to the AC potential. AC-SECM acquires topographic images and collects local electrochemical information of the substrate. A recent modification is the scanning electrochemical impedance microscopy [159162] where local impedance spectra are acquired through multifrequency AC-SECM in each point of measurement. The technique has been employed to study the action of corrosion inhibitors [163165], defects [166], and blistering [167] in coatings and localized corrosion processes [149,159,168,169].

1.8.7 Scanning Kelvin microscopy One of the few techniques able to give substantial information about the processes beneath organic coatings is the scanning Kelvin probe (SKP) [170,171], which was first applied to corrosion by Stratmann in 1987 [172]. SKP measures the volta potential difference between the metallic probe and the conductive substrate through insulating media (air or polymer film). The volta potential difference is usually considered to be proportional to the corrosion potential [170,171].

1.8.8 Scanning Kelvin probe force microscopy The resolution of SKP can be improved by applying the concept to atomic force microscopy (AFM) devices, in an arrangement called scanning Kelvin probe force microscopy (SKPFM). Similar to SKP, SKPFM provides topographic and potential maps on a sample surface [170,173175]. The higher spatial resolution is due to the smaller probe size and the shorter distance to the surface. A resolution of 100 nm is possible, which allows studying samples with heterogeneous microstructure. On the other hand, AFM scanners are typically limited to 100 μm and many relevant processes in corrosion take place on a larger scale.

1.8.9 Microcapillary and microdroplet cells A different methodology to obtain localized information is by delimiting very small areas of the working electrode with the so called microdroplet or microcapillary cells [176,177]. Areas of 10100 μm in diameter can be analyzed. Different grains of a metal or alloy can be studied separately without being short-circuited by the electrolyte solution. The main drawback is the small cell size leading to high uncompensated resistance, fast contamination of the

Chapter 1 • Application of the scanning vibrating electrode technique

33

solution, and blockage by corrosion products and gas bubbles. The problems were overcome by redesigning the cell to allow recirculation of solution. These microcells are not so suited to study organic coatings (exceptionally at defects) but they can be used to study cut-edges, surface treatments and metallic coatings, being of particular interest if different phases and other heterogeneities are present at the surface.

1.8.10 Wire beam electrodes Another way to analyze the electrochemical response of small areas is to use small electrodes assembled together to imitate a large electrode. This is called wire beam electrode and was developed by Tan [178]. Typically 4100 wires are assembled in a beam. The electrochemical response (open circuit potential, polarization curves, electrochemical noise, EIS, etc.) can be obtained for the entire beam of selected wires. Examples of application to coatings can be found in Ref. [179]. The high resolution attained by several techniques (SECM, AFM, and SKPFM) is not always an advantage. It requires small-sized maps (50100 μm side or less) and the probe close to the surface (10 μm or less). This is good for grain boundaries, intermetallic particles, inclusions, and small pits but cannot be applied with large, rough, or very active surfaces. The samples analyzed in this chapter would not be satisfactorily characterized by SECM, AFM, or SKPFM (at least taking the advantage of the high resolution) because of their size and the rapid formation of corrosion products. SECM, and amperometric or potentiometric sensors in general, show the distribution of a single chemical species, evidencing part of the corrosion process that is taking place. SVET, on the other hand, gives the distribution of the whole electrochemical process, which cannot be provided by any other technique. The localized techniques in this section are more complements than competitors, since they provide, not the same type of data, but different pieces of information which, together, offer a more complete picture of the system under analysis. The combination of various techniques is possible, desirable and, in fact, often reported. These localized techniques and their methods are continuously under development, with improvements in resolution, sensitivity, selectivity, and response time. Future will bring an increasing compatibility between techniques, with different sensors scanning together the same target. Progress in dedicated computer analysis and modeling will expand the information that can be extracted from the experimental data.

1.9 Conclusions This chapter presented an overview of SVET and its application to coatings characterization. The SVET shows the global view of the electrochemical activity at the metal surface in a single image. No other technique is able to provide such information. SVET has been applied to the study of many coating systems, being well suited to detect pores and defects on nonconductive coatings, characterize the corrosion of metallic coatings, and study the electrochemical activity of any conductive surface. Examples were presented to highlight both the capabilities and the limitations of the technique in the characterization of modern coatings.

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References [1] R. Raymond, Out of the Fiery Furnace: The Impact of Metals on the History of Mankind, Penn State University Press, 1986. [2] J.R. Davis (Ed.), Metals Handbook Desk Edition, second ed., ASM International, 1998. [3] M. Hitchman, Measurements of Dissolved Oxygen, Vol. 49 of Chemical Analysis: A Series of Monographs on Analytical Chemistry and its Applications, John Wiley and Sons, 1978. [4] G.H. Koch, P.H. Brongers, N.G. Thompson, Y.P. Virmani, J.H. Payer, Corrosion Costs and Preventive Strategies in the United States, Report FHWA-RD-01-156, Washington, 2002. [5] J. Kruger, Cost of metallic corrosion, in: R.W. Revie (Ed.), Uhlig’s Corrosion Handbook, third ed., John Wiley and Sons, 2011, pp. 1520. [6] G. Wranglen, An Introduction to Corrosion and Protection of Metals, second ed., Chapman and Hall, 1985. [7] S. Paul, Surface Coatings Science and Technology, John Wiley & Sons, Chichester, 1986. [8] C.J. Munger, Corrosion Prevention by Protective Coatings, NACE, Houston, TX, 1986. [9] Oil and Colour Chemists’ Association, Surface Coatings Vol. 1  Raw Materials and Their Usage, Springer, 1993. [10] Z.W. Wicks, F.N. Jones, S.P. Papas, D.A. Wicks (Eds.), Organic Coatings Science and Technology, third ed., Wiley, 2007. [11] G.P.A. Turner, Introduction to Paint chemistry and Principles of Paint Technology, third ed., Chapman and Hall, London, 1988. [12] A. Forsgren, Corrosion Control Through Organic Coatings, CRC, Taylor and Francis Group LLC, 2006. [13] H. Leidheiser, Coatings, in: F. Mansfeld (Ed.), Corrosion Mechanisms, Chem. Ind. 28, Marcel Dekker Inc., New York, 1987, pp. 165210. [14] G.W. Walter, A critical review of the protection of metals by paints, Corros. Sci. 26 (1986) 27. [15] ISO 12944-5:2007, Paints and Varnishes  Corrosion Protection of Steel Structures by Protective Paint Systems  Part 5 Protective paint systems, International Organization for Standardization, 2007. [16] E.V. Schmid, Exterior Durability of Organic Coatings, FMJ, Surrey, 1988. [17] R. Baboian (Ed.), Electrochemical Techniques for Corrosion Engineering, NACE, Houston, TX, 1986. [18] J. Wolstenholme, Electrochemical methods of assessing the corrosion of painted metals  a review, Corros. Sci. 13 (1973) 521. [19] G.W. Walter, A critical review of d.c. electrochemical tests for painted metals, Corros. Sci. 26 (1986) 39. [20] J.N. Murray, Electrochemical test methods for evaluating organic coatings on metals: an update. Part I. Introduction and generalities regarding electrochemical testing on organic coatings, Prog. Org. Coat. 30 (1997) 225. [21] J.N. Murray, Electrochemical test methods for evaluating organic coatings on metals: an update. Part II. Single test parameter measurements, Prog. Org. Coat. 31 (1997) 255. [22] J.N. Murray, Electrochemical test methods for evaluating organic coatings on metals: an update. Part III. Multiple test parameter measurements, Prog. Org. Coat. 31 (1997) 375. [23] A. Lasia, Electrochemical Impedance Spectroscopy and Its Applications, Springer, 2014. [24] V. Upadhyay, D. Battocchi, Localized electrochemical characterization of organic coatings: a brief review, Prog. Org. Coat. 99 (2016) 365. [25] A.C. Bastos, M.V. Quevedo, O.V. Karavai, M.G.S. Ferreira, Review  on the application of the scanning vibrating electrode technique (SVET) to corrosion research, J. Electrochem. Soc. 164 (2017) C973.

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[151] R.C. Engstrom, M. Weber, D.J. Wunder, R. Burgess, S. Winquist, Measurements within the diffusion layer using a microelectrode probe, Anal. Chem. 58 (1986) 844. [152] A.J. Bard, F.F. Fan, J. Kwak, O. Lev, Scanning electrochemical microscopy. Introduction and principles, Anal. Chem 61 (1989) 132. [153] A.J. Bard, M.V. Mirkin (Eds.), Scanning Electrochemical Microscopy, second ed., CRC, Taylor and Francis Group LLC, Boca Raton, FL, 2012. [154] R.S. Lillard, P.J. Moran, H.S. Isaacs, A novel method for generating quantitative local electrochemical impedance spectroscopy, J. Electrochem. Soc. 139 (1992) 1007. [155] V.M. Huang, S.L. Wu, M.E. Orazem, N. Pébère, B. Tribollet, V. Vivier, Local electrochemical impedance spectroscopy: a review and some recent developments, Electrochim. Acta 56 (2011) 8048. [156] B.B. Katemann, A. Schulte, E.J. Calvo, M. Koudelka-Hep, W. Schuhmann, Localized electrochemical impedance spectroscopy with high lateral resolution by means of alternating current scanning electrochemical microscopy, Electrochem. Commun 4 (2002) 134. [157] M. Etienne, A. Schulte, W. Schuhmann, High resolution constant-distance mode alternating current scanning electrochemical microscopy (AC-SECM), Electrochem. Commun. 6 (2004) 288. [158] K. Eckhard, W. Schuhmann, Alternating current techniques in scanning electrochemical microscopy (AC-SECM), Analyst 133 (2008) 1486. [159] V. Kuznetsov, A. Maljusch, R.M. Souto, A.S. Bandarenka, W. Schuhmann, Characterisation of localised corrosion processes using scanning electrochemical impedance microscopy, Electrochem. Commun. 44 (2014) 38. [160] A.S. Bandarenka, K. Eckhard, A. Maljusch, W. Schuhmann, Localized electrochemical impedance spectroscopy: visualization of spatial distributions of the key parameters describing solid/liquid interfaces, Anal. Chem. 85 (2013) 2443. [161] A. Estrada-Vargas, A. Bandarenka, V. Kuznetsov, W. Schuhmann, In situ characterization of ultrathin films by scanning electrochemical impedance microscopy, Anal. Chem. 88 (2016) 3354. [162] A.S. Bandarenka, A. Maljusch, V. Kuznetsov, K. Eckhard, W. Schuhmann, Localized impedance measurements for electrochemical surface science, J. Chem. Phys. C 118 (2014) 8952. [163] R.M. Souto, B. Socas, J. Izquierdo, J.J. Santana, S. González, New opportunities for the study of organic films applied on metals for corrosion protection by means of alternating current scanning electrochemical microscopy, Prog. Org. Coat. 74 (2012) 371. [164] J.J. Santana, M. Pähler, W. Schuhmann, R.M. Souto, Investigation of copper corrosion inhibition with frequency-dependent alternating-current scanning electrochemical microscopy, ChemPlusChem 77 (2012) 707. [165] M. Pähler, J.J. Santana, W. Schuhmann, R.M. Souto, Application of AC-SECM in corrosion science: local visualisation of inhibitor films on active metals for corrosion protection, Chem. Eur. J. 17 (2011) 905. [166] B.B. Katemann, C.G. Inchauspe, P.A. Castro, A. Schulte, E.J. Calvo, W. Schuhmann, Precursor sites for localised corrosion on lacquered tinplates visualised by means of alternating current scanning electrochemical microscopy, Electrochim. Acta 48 (2003) 1115. [167] J.J. Santana, M. Pähler, R.M. Souto, W. Schuhmann, Direct evidence of early blister formation in polymer-coated metals from exposure to chloride-containing electrolytes by alternating-current scanning electrochemical microscopy, Electrochim. Acta 77 (2012) 60. [168] K. Eckhard, M. Etienne, A. Schulte, W. Schuhmann, Constant-distance mode AC-SECM for the visualisation of corrosion pits, Electrochem. Commun. 9 (2007) 1793. [169] K. Eckhard, T. Erichsen, M. Stratmann, W. Schuhmann, Frequency-dependent alternating-current scanning electrochemical microscopy (4D AC-SECM) for local visualisation of corrosion sites, Chem. Eur. J. 14 (2008) 3968.

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Handbook of Modern Coating Technologies

[170] M. Rohwerder, M. Stratmann, P. Leblanc, G.S. Frankel, Application of scanning Kelvin probe in corrosion science, in: F. Mansfeld, P. Marcus (Eds.), Analytical Methods in Corrosion Science and Engineering, CRC, Taylor and Francis Group, Boca Raton, FL, 2006, pp. 133168. [171] A. Leng, H. Streckel, M. Stratmann, The delamination of polymeric coatings from steel. Part 1: calibration of the Kelvinprobe and basic delamination mechanism, Corros. Sci. 41 (1999) 547578. [172] M. Stratmann, The investigation of the corrosion properties of metals, covered with adsorbed electrolyte layers - a new technique, Corros. Sci. 27 (1987) 869. [173] P. Schmutz, G.S. Frankel, Characterization of AA2024-T3 by scanning Kelvin probe force microscopy, J. Electrochem. Soc. 145 (1998) 2285. [174] H. Jacobs, P. Leuchtmann, O. Homan, A. Stemmer, Resolution and contrast in Kelvin probe force microscopy, J. Appl. Phys. 84 (1998) 1168. [175] M. Rohwerder, F. Turcu, High-resolution Kelvin probe microscopy in corrosion science: scanning Kelvin probe force microscopy (SKPFM) versus classical scanning Kelvin probe (SKP), Electrochim. Acta 53 (2007) 290. [176] T. Suter, H. Böhni, Microelectrodes for corrosion studies in microsystems, Electrochim. Acta 47 (2001) 191. [177] M. Lohrengel, A. Moehring, M. Pilaski, Capillary-based droplet cells: limits and new aspects, Electrochim. Acta 47 (2001) 137. [178] Y.J. Tan, Wire beam electrode: a new tool for studying localised corrosion and other heterogeneous electrochemical processes, Corros. Sci. 41 (1998) 229. [179] Y.J. Tan, An overview of techniques for characterizing inhomogeneities in organic surface films and underfilm localized corrosion, Prog. Org. Coat. 76 (2013) 791.

Chapter 1 • Application of the scanning vibrating electrode technique

ANNEX—

Experimental details of the SVET maps in the chapter.

Figures Tipe size (µm)

3 and 4 5B 5C 5D 8A 8B 9A 9B 10AD 11

15 15 15 15 10 15 10 15 10 1020

12 13A 13B 15A 15B 15C 15D 16B 17BD 17F

15 20 20 15 30 15 25 13 20 20

a

Vibration

Distance to surface (µm)

N points

Amplitude (µm)

Frequency (Hz)

5 (25 ptp)a 5 (25 ptp) 5 (25 ptp) 5 (25 ptp) 5 (20 ptp) 5 (25 ptp) 5 (20 ptp) 5 (25 ptp) 5 (20 ptp) 5 (2030 ptp) 5 (25 ptp) 5 (30 ptp) 5 (30 ptp) 5 (25 ptp) 5 (40 ptp) 5 (25 ptp) 5 (35 ptp) 5 (23 ptp) 5 (30 ptp) 5 (30 ptp)

X 5 97; Z 5 134 134 134 134 397 244 397 244 397 162

200 3000100 3000100 200 100 200 200 200 100 100

244 397 397 69 432 69 432 244 69 69

200 200 200 1050b ? 100 200 200 100 100

ptp, peak to peak. 50 μm above a 1000 μm thick film.

b

43

Sampling rules

Scanning time (min)

Wait (s)

Average (s)

50 3 50 96 3 29 29 50 50 3 50 40 3 40 100 3 50 40 3 40 50 3 50 40 3 40

0.1 0.2 0.1 0.1 0.2 0.02 0.2 0.02 0.1 0.2

0.1 0.3 0.1 0.1 0.3 0.03 0.3 0.03 0.2 0.3

25 30 0.4 0.5 30 12 60 12 20 18

50 3 50 20 3 20 50 3 50 50 3 50 21 3 21 50 3 50 30 3 30 40 3 40 30 3 30 50 3 50

0.2 0.1 0.2 0.1 0.02 0.1 0.2 0.02 0.2 0.2

0.3 0.2 0.3 0.2 0.03 0.3 0.2 0.03 0.2 0.2

28 5 23 28 6 23 5 12 12 28

Spectroscopic ellipsometry

2

Lingjie Li1, Jinglei Lei1, Liangliu Wu1, Fusheng Pan2 1

SCHOOL OF CHEMISTRY AND CH EMICAL ENGINEERING, CH ONGQING UNIVERSITY,

C HO NG Q I N G , P . R . CH I N A 2 SCHOOL OF MA TERIALS SCIENCE AND ENGINEERING, CHONGQING UNIVERSITY, C HONG QING, P.R. CHINA

2.1 Introduction Ellipsometry is a century-old optical measurement technique based on analyzing the change in the polarization state when a beam of polarized light was reflected from the surface or interfaces of coatings, which can be used to extract the thickness, optical properties, and composition of the coatings. Before Rothen named this technique as “ellipsometry” in 1945 [1], the basic theory of ellipsometry was established by Drude in 1887 [2]. Drude also conducted the first ellipsometric experimental measurement in 1890 to determine the optical properties of some metals [3]. Although ellipsometry has long history, it developed slowly, especially in the early stage. The ellipsometer with a single wavelength dominated the ellipsometry field for a long time because of the complex of multiwavelength ellipsometer and the difficulty of the data analysis processes. Moreover, the ellipsometers in the initial stage were too slow to be used to investigate the change of dynamic systems. Till approximately 1970s, benefitting from the implementation of photometric instruments (such as light sources and detectors) and the availability of minicomputers, the ellipsometry developed rapidly. The wavelength range, measurement precision, and speed were improved significantly. Those developments have been reviewed by Hauge [4], Vedam [5], and Aspnes [6,7]. The first ellipsometric spectrum which covered 300
400 nm was described by Jasperson and Schnatterly [8], indicating spectroscopic ellipsometry (SE) was really established. Comparing with the single-wavelength ellipsometry, SE can deconvolute multiwavelength ellipsometric data with complicated optical models, which is helpful to obtain abundant, precise, and reliable information about the samples. At present, with the advanced optical components being introduced into the ellipsometers, the attainable wavelength range has been extended deeper into the Terahertz and vacuum ultraviolet, thus some extra information about the samples such as their compositions could be extracted reliably [9]. Besides broadening the spectral range, there are also many kinds of SE techniques developed. For example, variable angle spectroscopic ellipsometry (VASE) carries out the ellipsometric measurements at several incidence angles, which helps to improve the reliability of results of data deconvolution. Mueller matrix spectroscopic ellipsometry is an effective tool to extract Handbook of Modern Coating Technologies. DOI: https://doi.org/10.1016/B978-0-444-63239-5.00002-0 © 2021 Elsevier B.V. All rights reserved.

45

46

Handbook of Modern Coating Technologies

the information on anisotropic materials and complex systems by interpreting the SE data with the Mueller
Jones formalism [4,10]. While the wavelength range of ellipsometers enlarged, the spectrum acquisition time of ellipsometers shorten continuously. In 1984 it was reported by Muller et al. [11] that the first rapid-scanning spectroscopic ellipsometer which provided 114 nm/s scanning rate within the wavelength range of 370
720 nm. Later, with utilizing multichannel detection systems, the acquisition time was reduced significantly. This kind of the multichannel detector spectroscopic ellipsometer makes the in situ real-time SE (RTSE) very powerful for characterizing the dynamic evolution of the optical properties or the structure of films [12,13], so that it has been used widely to monitor the growth or damage processes of coatings. Furthermore multiple-technology coupling is another trend of SE development. Infrared (IR) spectroscopic ellipsometry (IRSE) is a method that combines ellipsometer with a Fourier transform spectrometer, by which not only the thicknesses but also the composition of the films can be determined [14
17]. Internal reflection ellipsometry is based on the measurement of reflective light beam which penetrates a prism, so it could be applied in the ambient with strong absorption [18,19]. Especially while internal reflective ellipsometry combines with surface plasmon resonance (SPR), the new method is called total internal reflection ellipsometry (TIRE) and has much higher sensitivity than traditional ellipsometry [20,21]. Imaging ellipsometry (IE) is a technique using a charge
coupled device (CCD) camera as the detector in an ellipsometric configuration and it scans the sample surface point by point with a high spatial resolution, which is capable of visualization and quantification of thinfilm thickness distributions [22,23]. IE has been gained significant interest and used in lots of fields such as biotechnology and semiconductor metrology. With the rapid development of ellipsometry, many comprehensive reviews have appeared. Table 2
1 lists some monographs on ellipsometry. The first classic monograph was published by Azzam and Bashara [24], then other monographs were published gradually. For example, a brief user’s guide by Tompkins [25], the treatise of IR ellipsometry by Schubert [26], the comprehensive book written by Fujiwara [27], two collections of monographs edited by Tompkins and Irene [9] and Losurdo and Hingerl [28], respectively. At the same time, as an important characterization method, ellipsometry has also been introduced in the chapters about the topics of thin films, surface, and interfaces. Some chapters are listed in Table 2
2. Table 2–1

Monographs on ellipsometry.

No.

Monographs

1 2 3 4 5 6

Ellipsometry and Polarized Light [24] A User’s Guide to Ellipsometry [25] Infrared Ellipsometry on Semiconductor Layer Structures [26] Handbook of Ellipsometry [9] Spectroscopic Ellipsometry—Principles and Applications [27] Ellipsometry at the Nanoscale [28]

Published year 1977 1993 2004 2005 2007 2013

Chapter 2 • Spectroscopic ellipsometry

Table 2–2

47

SE related chapters in books.

No.

Book

Related chapters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Comprehensive Chemical Kinetics [29] Plasma Diagnostics [30] Physics of Thin Films [31] Physics of Thin Films [32] Physics of Thin Films [33] Physics of Thin Films [34] Physics of Thin Films [35] Handbook of Optical Constants of Solids [36] Handbook of Optical Constants of Solids [37] Progress in Optics [38] Studies in Interface Science [39] Handbook of Surfaces and Interfaces of Materials [40] Encyclopedia of Materials: Sciences and Technology [41] Handbook of Thin Films [42] Handbook of Thin Films [43] Surfaces and Interfaces for Biomaterials [44] In Situ Characterization of Thin Film Growth [45] Encyclopedia of Spectroscopy and Spectrometry [46]

Volume 29, pages 427
452 Volume 2, pages 67
108 Volume 19, pages 49
125 Volume 19, pages 127
189 Volume 19, pages 191
247 Volume 19, pages 249
278 Volume 19, pages 279
314 Volume I, pages 89
112 Volume II, pages 213
246 Volume 41, pages 181
282 Volume 11, pages 1
42 Volume 4, pages 335
367 Pages 2753
2761 Volume 2, pages 277
330 Volume 2, pages 331
372 Pages 271
298 Pages 99
151 Pages 482
489

Coatings play an important role in various fields, and their characterization techniques are indispensable for the preparation of high-quality coatings. Due to the advantages of high precision and nondestructive operation, ellipsometry has been widely used in vacuum, gas, or liquid ambient to extract the information of coatings, such as the thickness, optical constants, and other related properties. This chapter will introduce the principle of ellipsometry, discuss the data analysis procedures, address the analytical information, and sum up the common applications in coating characterization.

2.2 Basic principles of ellipsometry The Fresnel reflection and transmission equations for polarized light are the foundation for the analysis of ellipsometric data. As shown in Fig. 2
1, the incident light is often linearly polarized, whose electric-field components orient parallel (p-) and perpendicular (s-) to the plane of incidence. When this linearly polarized light is reflected by a planar
layered specimen at an oblique incidence, it encounters actually multiple interferences in the specimen, which change the amplitudes and phases of the s- and p-components of the light. The ellipsometer measures those changes. The change in amplitudes between the s- and p-components in the reflected light is named as the ellipsometric parameter ψ, and the difference in the phases as another ellipsometric parameter W. In brief, these two ellipsometric parameters (ψ, W) are defined by [27]: ρ 5 tanψ eiΔ

(2.1)

48

Handbook of Modern Coating Technologies

Film on substrate S 0

p E

Eis

Ers  0

Eip

Erp

Ambient (0) 

d

1

Film (1)

Linearly polarized light 2

Substrate (2)

Elliptically polarized light

FIGURE 2–1 Schematic of ellipsometry [27,47].

where ρ is complex reflectance ratio, that is the ratio of complex reflection coefficients for the parallel (Rp) and perpendicular (Rs) polarizations according to the following equations [24]: ρ5

Rp Rs



r01;p 1 r12;p e2i2β Rp 5
Rp
eiΔp 5 1 1 r01;p r12;p e2i2β Rs 5 jRs jeiΔs 5

r01;s 1 r12;s e2i2β 1 1 r01;s r12;s e2i2β

(2.2)

(2.3)

(2.4)

where r01,p, r12,p, r01,s, and r12 are the Fresnel reflection coefficients at the ambient-film (0
1) and film-substrate (1
2) interfaces for p- and s-polarized lights. Here three media (ambient, film, and substrate) are indicated by the subscript of 0, 1, and 2, respectively. And the phase angle β expresses the phase difference between the two boundaries of the film. According to the Snell’s law and the Fresnel equation, the following relationships can be deduced [24]: r01;p 5

N1 cosθ0 2 N0 cosθ1 N1 cosθ0 1 N0 cosθ1

(2.5)

r01;s 5

N0 cosθ0 2 N1 cosθ1 N0 cosθ0 1 N1 cosθ1

(2.6)

r12;p 5

N2 cosθ1 2 N1 cosθ2 N2 cosθ1 1 N1 cosθ2

(2.7)

Chapter 2 • Spectroscopic ellipsometry

r12;s 5 β5

N1 cosθ1 2 N2 cosθ2 N1 cosθ1 1 N2 cosθ2

2πd 2πd 2 N1 cosθ1 5 ðN1 2N02 sin2 θ0 Þ1=2 λ λ

49

(2.8)

(2.9)

where N0, N1, and N2 are the complex optical constants (optical indices or complex refractive indices) of the ambient, film, and substrate, respectively. The complex refractive index is normally written as N 5 n 1 ik, where n and k are called the refractive index and extinction coefficient. In some literature, the dielectric functions ε appear in the above equations because of the relationship ε 5 N2. From the abovementioned equations, we can express the fundamental equation of ellipsometry as follows [24]: ρ 5 tanψeiΔ 5

r01;p 1 r12;p e2i2β 1 1 r01;s r12;s e2i2β 3 2i2β 1 1 r01;p r12;p e r01;s 1 r12;s e2i2β

(2.10)

According to Eqs. (2.1)
(2.4), it is easy to derive that: tanψ 5




R p
jRs j

Δ 5 Δp 2 Δs

(2.11) (2.12)

Thus the ellipsometric parameters (ψ, W) are functions of the optical properties of the ambient-film-substrate system (since only one film is involved here, this model is called single-layer model), including the complex refractive indices of the ambient (N0), film (N1), substrate (N2), as well as the film thickness (d), the vacuum wavelength (λ) of the ellipsometer light beam and the incidence angle (θ0). The functional dependence of ψ and W on these optical properties can be symbolically expressed briefly as: tanψ eiΔ 5 f ðN0 ; N1 ; N2 ; d; θ0 ; λÞ

(2.13)

If the values of N0, N2, θ0, and λ are known in advance from experiments or references, the optical constants (N1) and thickness (d) of the thin film can be determined using the above relationship. Especially for the most common situation, the ellipsometric experiments are carried out in the air, the system becomes air-film-substrate and the complex refractive index of air is always treated as N0 5 1, which makes data analysis easier.

2.3 Data analysis procedure The ellipsometric parameters (ψ, W) are collected within given spectral range and incident angles by using an ellipsometer. However, the measured data (ψ and Δ) do not give direct

50

Handbook of Modern Coating Technologies

information about the properties of the sample. To extract meaningful physical information about the sample, it is necessary to perform a data analysis procedure. Usually the data analysis procedure includes the following steps [9,27,45,48], as outlined in Fig. 2
2. The first step is to construct a felicitous optical model to describe the sample system. Usually each material in the system, including the substrate, bulk material, ambient and so on, are always looked as a “layer” and the model is built layer by layer. There are also possible interface layers (gradual transition area between two materials) and surface roughness layer (gradual transition area between the top material and ambient) should be considered. In this step, the number of layers and basic structure concerning the contents of each layer must be assigned so that an optical model is built. A reasonable optical model must represent an approximated structure of the real sample system very well. Additionally some essential information about the real sample, such as the compositions and morphologies, is very helpful for building a “good” model. For example, for an unknown sample, various complementary characterization techniques including X-ray photoelectron spectroscopy (XPS),

Surface roughness Bulk layer

Construction of a stratified model

Interface layer Substrate Modeling of optical functions

 = 1 + i2 Model fit Exp Ψ Exp Δ

Generation of theoretical data

N 1 MSE = Σ 2N – M 1–1

imod – iexp exp ,i

2

÷

Δimod – Δiexp exp ,i

2

Results evaluation Yes

Results: the film thicknesses, optical constants (n, k)... FIGURE 2–2 Flowchart of the SE data analysis [27]. SE, Spectroscopic ellipsometry.

No

Chapter 2 • Spectroscopic ellipsometry

51

atomic force microscopy (AFM) and scanning electron microscopy (SEM) could be used to obtain the exact information about the compositions, roughness and morphologies of the sample. On the other hand, it must be remembered that the construction of the optical model follows the “simple-better” rule, which means that the best sample description is often the matched curve produced by the simplest model. After the optical model is constructed, the optical constants N (or the dielectric functions ε, ε 5 N2) of each layer in the model should be assigned. For the simplex situation, the optical constants are a real “constant,” which likes the optical constant of the air is always given as Nair 5 1. However, for the most materials, the optical constants are not a “constant” and they always change with the wavelength, that is, the optical constants N are the function of the wavelength λ. To describe the function relationship, many models such as Drude [49], Cauchy [50], Sellmeier [51], Lorentz [52], Tauc-Lorentz [53], and so on, have been developed. In addition, to model the mixing layer which contains two or more kinds of materials, effective medium approximation (EMA) [27] model is introduced. A typical example of EMA layer is the surface roughness, which could be looked as the mixture of the top layer material and the air (or void). The optical constants of the EMA layer are the average values of the optical constants of each component. For instance, the optical constants of a classical EMA layer, Bruggeman EMA [54] layer, can be calculated with Eq. (2.14), where εa and εb are the dielectric functions of two components a and b, V is the volume fraction of the first component (component a) and εeff is the average dielectric functions of the EMA layer. Choosing a felicitous N
λ model based on the optical properties of every layer of the sample, is the second step for analyzing the ellipsometric data. V

εb 2 εeff εa 2 εeff 1 ð1 2 V Þ 50 εb 1 2εeff εa 1 2εeff

(2.14)

Generating theoretical data according to the optical model and the optical constants of every layer and comparing them with the measured data are the third step in the SE data analysis process. Because Eqs. (2.3)
(2.12) are so complex that we cannot solve them directly, data fitting is necessary. Data fitting is the process to search the optimal values of some parameters by adjusting other model parameters, and the Marquardt
Levenberg regression algorithm is the most common one for data fitting. In this algorithm, the mean square error (MSE) is introduced to evaluate the fitting effect. MSE is the sum of the squares of the differences between the measured and generated data [9]. Usually a small MSE value (usually is given as less than 3) describes a good fit because it means that the generated data are very close to the measured data. For the ellipsometric data analysis, if the MSE value is great, it means that the data fitting results are not good and the data analysis procedure must be repeated all over again by adjusting model or assigning new optical constants or dielectric functions.

2.4 Extracting information of coatings SE offers sensitive, nondestructive, fast and precise measurements for films, so it has been widely used in characterization of coatings by extracting diverse valuable information, such

52

Handbook of Modern Coating Technologies

as the thickness, roughness, optical indices, energy band gap, anisotropy, and compositions. If in situ SE is used, the growth kinetics of coating is even could be investigated.

2.4.1 Ex situ measurements 2.4.1.1 Thickness/roughness characterization Thickness characterization is the most important and common usage of ellipsometry. After a reliable stratified model is constructed based on the structure and composition information of the sample, and the optical constants of the layers are known, the thickness of each layer can be extracted accurately and facilely. Walsh et al. [55] used two-wavelength ellipsometry with a simple two-layer model (shown in Fig. 2
3) for characterizing the thickness of spin
coated poly(methyl methacrylate) (PMMA) films. The results showed that the PMMA film thicknesses (ranging from 0.08 to 2.0 μm) were linear related to c1.33ω20.50, where c is the initial polymer concentration in solution (1.0
7.5 wt.%) and ω is the spin speed (1000
4000 rev/min) for preparing the films. SE has been a well-known characterization tool to evaluate the surface quality of coatings. Bhattacharyya et al. [56] prepared metallic films with sputter deposition method and determined the surface roughness with SE. They treated the surface layer as the mixture of bulk material and air so that Bruggeman EMA was introduced. It was found that the increase in surface roughness of the films followed the increase in thickness. The same conclusion was also drawn based on AFM and grazing-incidence X-ray reflectivity (GIXR) measurements. Mendoza-Galván et al. [57] also used SE to determine simultaneously the roughness and thicknesses of CuCdTeO thin films prepared by using reactive cosputtering technique. SE can also be used to determine the thicknesses of an interface layer. As shown in Fig. 2
4, a two-layer optical model (ambient-bulk layer-interface layer-substrate) was built to fit the SE data and extract the thickness of the bis-1,2-(triethoxysilyl)ethane (BTSE) films [58], which were prepared by dipping the Al substrates into BTSE solutions. The results shown in Table 2
3 indicates that the thickness of the films increased with the BTSE bath concentration and the curing condition had significant influence on the film quality. The SE results were consistent with these of Auger electron spectroscopy and transmission electron microscopy (TEM) measurements.

Ambient PMMA Silicon oxide Silicon

φ0 φ0

n0 φ1

n0,d1 φ2

n2,d2 N3 = n3 – ik3

FIGURE 2–3 Schematic of an idealized two-layer system used for the ellipsometric analysis of thin, spin
coated polymer films on thermal oxides of silicon [55].

Chapter 2 • Spectroscopic ellipsometry

53

Cauchy dispersion relation Thickness (nm) Non uniformity (%)

Silane coating

EMA (cauchy + x% Al) Thickness (nm)

Al2O3

AI (pseudo constantants n and k

AI

Optical model

Presumed structure

FIGURE 2–4 Two-layer optical model used for deconvoluting the SE data to determine the silane layer optical constants, film thickness, and nonuniformity [58]. SE, Spectroscopic ellipsometry.

Table 2–3

Comparable thickness of silane films determined by SE [58]. Oven
cured silane film (200 C, 5 min)

Silane films left to dry at room temperature

BTSE bath concentration (%)

Bulk layer (nm)

Interface layer (nm)

Bulk layer (nm)

Interface layer (nm)

2 4 6 8 10

27.1 90.0 105.4 239.8 482.5

2.1 18.8 20.2 18.5 18.2

26.9 88.1 174.9 213.7 344.6


17.7 32.1 20.7 17.9

BTSE, bis-1,2-(triethoxysilyl)ethane; SE, spectroscopic ellipsometry.

Surface roughness

W -Ti-O film SiO2(interface) Si substrate

FIGURE 2–5 Stack model of the Ti
doped WO3 constructed for ellipsometry data analysis [59].

SE can be applied to extract the thickness information about the interface layer and surface roughness simultaneously. Ramana et al. [59] reported the SE results on the radio frequency (RF) magnetron sputtered Ti
doped WO3 films. As shown in Fig. 2
5, a three-layer optical model was built, in which the surface roughness and interface layer were considered simultaneously to accurately deconvolute the experimental data. Both the surface roughness and interface thickness determined were very thin, and the growth temperature almost had no influence on the film thickness. As shown in Fig. 2
6, the film thicknesses obtained from SE and observed by SEM were in good agreement with each other.

54

Handbook of Modern Coating Technologies

120

80 3

SEM data SE data

60 40

Roughness (nm)

Thickness (nm)

100

2 1 0

20

0

200 400 600 Deposition temperature (°C)

0 0

100

200

300

400

500

Deposition temperature (°C) FIGURE 2–6 Thickness of Ti
doped WO3 films grown at various temperatures. Insert shows the variation in surface roughness of the films with growth temperature [59].

Glue

Layer 2

Layer 3 a - Si

Layer 4

Layer 5

SiN

Layer 6

10 nm

FIGURE 2–7 TEM image of the a-Si/SiN multilayer sample [60]. TEM, Transmission electron microscopy.

Moreover, SE can measure the thicknesses (including the total thickness and the thickness of each layer) of a multilayer sample based on a complex optical model. As a typical example, the structure of an amorphous silicon
silicon nitride multilayer sample is shown in Fig. 2
7 [60].

Chapter 2 • Spectroscopic ellipsometry

55

Table 2–4 Thickness values for the a-Si/SiN multilayer sample determined by SE and TEM [60]. Thickness (nm) Sample structure

SE

TEM

1. Surface oxide 2. a-Si 3. SiN 4. a-Si 5. SiN 6. a-Si buffer c-Si substrate

0.5 6 0.9 4.6 6 0.3 7.7 6 0.6 4.6 6 0.3 7.7 6 0.6 119 6 2 —

— 5.4 6 0.3 7.1 6 0.3 5.3 6 0.3 7.1 6 0.3 115 6 3 —

SE, Spectroscopic ellipsometry; TEM, transmission electron microscopy.

SE provided detailed quantitative information about that system. Both the Tauc-Lorentz oscillator and Cauchy dispersion models were used to describe the dielectric functions of amorphous silicon and silicon nitride, respectively. The thickness values were obtained by analyzing SE data, which were in accord with those measured results by TEM, as shown in Table 2
4. These typical applications of SE to measure the thickness or roughness of coatings are listed in Table 2
5.

2.4.1.2 Optical and electric properties characterization By using SE, the complex optical constants N (or dielectric functions ε) of layers can be determined, then their optical and electric properties such as the energy band gap, free carriers concentration, can be derived. Therefore SE has been developed as an important method to measure the optical and electric properties of coatings. Shaaban et al. [61] used SE to study the changes of the optical properties with the thickness for ZnSe films. They found that the refractive index of ZnSe film increases when the thickness increases within the used wavelength range. Fig. 2
8 shows this change tendency of the optical constants (including both refractive indices and extinction coefficients) with thicknesses. Optical anisotropic materials have special properties and are very important in the field of optics. This kind of material has two sets optical indices No (no and ko) and Ne (ne and ke), here the subscripts o (means ordinary) and e (means extraordinary) express the directions are parallel or perpendicular to the substrate, respectively. SE also could be applied to study the optical anisotropic materials. Yokoyama et al. [62,63] demonstrated the application of VASE for characterization of the optical anisotropy organic amorphous films. To deconvolute SE data, uniaxial anisotropic models were introduced. Results showed the molecular structure affects significantly the optical properties of the films, the longer the molecular length was, the larger the differences of ordinary and extraordinary optical constants became, which was shown in Fig. 2
9.

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Table 2–5 Brief summary of SE applications for the thickness/roughness characterization. Ellipsometric experimental conditions

No. Systems 1

2

3

PMMA on Si VASE, wavelengths Two-layer model at 4050 and 6328 Mo/Si/Mo or Phase
modulated, Two-layer model wavelength W/Si/W range on c-Si 300
1200 nm Two-layer model CdTeOx and Photon energy range of CuCdTeO 1.5
5 eV on glass

4

BTSE on Al

5

Ti
doped Wavelength range WO3 on 250
1350 nm Si a-Si and SiN VASE, wavelength on Si range 250
820 nm

6

Optical model

VASE, wavelength range 250
1700 nm

N
λ relation used

Parameters extracted by SE

Cauchy dispersion equation

Thickness and refractive index

[55]

Bruggeman EMA

Thicknesses of total film, compact layer, surface layers, and volume fraction Film thickness, roughness, dielectric functions, and volume fractions Thickness, optical constants, and nonuniformity

[56]

Thickness, optical constants, and relative density Tauc-Lorentz and Thicknesses of total film Cauchy models and each layer and and Bruggeman refractive index EMA

[59]

Lorentz harmonic oscillator and Bruggeman EMA Cauchy dispersion equation and Bruggeman EMA

Single-layer model and two-layer model with nonuniform top layer Three-layer model

Tauc-Lorentz model

Multilayer model

Refs.

[57]

[58]

[60]

BTSE, bis-1,2-(Triethoxysilyl)ethane; EMA, effective medium approximation; PMMA, poly(methyl methacrylate); SE, spectroscopic ellipsometry; VASE, variable angle spectroscopic ellipsometry.

1.0 5.0

Refractive index

4.0

Extinction coefficient

ZnSe d = 275.2 nm d = 402.5 nm d = 533.5 nm d = 676.8 nm

4.5

3.5 3.0 2.5

0.8

ZnSe d = 275.2 nm d = 402.5 nm d = 533.5 nm d = 676.8 nm

0.6 0.4 0.2

2.0 200

400

600

800

Wavelenght (nm)

1000

1200

0.0 300 350 400 450 500 550 600 650 Wavelenght (nm)

FIGURE 2–8 The spectral dependence of refractive index n and extinction coefficient k of ZnSe films with different thicknesses [61].

Chapter 2 • Spectroscopic ellipsometry

57

FIGURE 2–9 Dependence of ordinary and extraordinary refractive indices and extinction coefficients on molecular length (a) 4,40 -bis(N-carbazole)biphenyl; (b), (c) The derivatives of (a); (d) 4,40 -bis[(N-carbazole)styryl]biphenyl [62].

The related optical properties, such as the complex refractive index (optical constants, N), absorption coefficient (α), normal incidence reflectivity (R), and dielectric constant (ε) can also be detected by the following formulas [64
66]: N 5 n 1 ik 4πk λ

(2.16)

½n212 1 k 2 ½n112 1 k 2

(2.17)

α5 R5

(2.15)

ε 5 ðn1ikÞ2 5 ε1 1 iε2

(2.18)

ε1 5 n2 2 k 2

(2.19)

where

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Table 2–6

The bandgap with different thickness from SE and UV
vis [68].

Thickness (nm)

Eg ellipso (eV)

Eg UV
vis (eV)

153.5 156.5 167.2 177.9 186.9 204.9

3.0984 3.0966 3.0031 2.8241 2.7758 2.5627

3.18 3.10 3.08 2.90 2.71 2.54

SE, Spectroscopic ellipsometry.

ε2 5 2nk

(2.20)

After the N
λ or ε
λ relationship is obtained, the other physical properties of the material which is relevant to the absorption of the light, such as their energy band gap of semiconductors, could be calculated further with Forouhi
Bloomer (FB) dispersion relations. FB dispersion relations are expressed as follows [67,68]: kðEÞ 5

X Ai ðE2Eg Þ2 E 2 2 Bi E 1 Ci i

nðEÞ 5 nN 1

X B0i E 1 C0i E 2 2 Bi E 1 Ci i

(2.21)

(2.22)

where B0i 5

Ai B2 ð2 i 1 Eg Bi 2 Eg2 1 Ci Þ Qi 2

(2.23)

Ai B2 ððEg2 1 Ci Þ i 2 2Eg Ci Þ Qi 2

(2.24)

1 Qi 5 ð4Ci 2B2i Þ1=2 2

(2.25)

C0i 5

in which Ai, Bi, Ci, Eg, and nN are fitting parameters. Das et al. [68] used FB relations to obtained the optical gap of the nanocrystalline CdS thin films successfully. The energy band gap of CdS thin films with different thicknesses is listed in Table 2
6, and the values extracted by SE are in accordance with those from UV
vis measurements. The optical band gap also can be calculated from the optical absorption coefficient (α), which could be determined experimentally by using Eq. (2.16) [69,70] and the values of the known wavelength (λ) as well as the extinction coefficient (k) measured by SE: α5

4πk λ

(2.16)

Chapter 2 • Spectroscopic ellipsometry

(b) 800

Sample A (MoS2 1.99 nm)

(αhν)1/2 (cm–1 eV)1/2

(αhν)1/2 (cm–1 eV)1/2

(a)

59

600 400 200 Eg = 1.61 eV 0 1.2

1.4

1.6

1.8

2.0

2.2

800

Sample D (MoS2 9.83 nm)

600 400 200 Eg = 1.36 eV 0 1.2

2.4

hν (eV)

1.4

1.6

1.8

2.0

2.2

2.4

hν (eV)

FIGURE 2–10 Plot of (αhυ)1/2 versus hυ for MoS2 thin films. (a) Thickness of the MoS2 thin film is 1.99 nm. (b) Thickness of the MoS2 thin film is 9.83 nm [69].

At the same time, the relationship of the absorption coefficient and the photon energy can be described as: α5

K ðhν2Eg Þm hν

(2.26)

where K is a constant, hυ is the incident photon energy, Eg is the optical band gap, and m is a number characterizing the transition process, respectively. It should be noted that the value of m is determined by the band gap transition type, m equals 1/2 for a direct transition, and m equals 2 for an indirect transition. Based on these equations, the value of Eg could be calculated easily by fitting the linear part of the plot and then extrapolating to (αhυ)1/m 5 0, where hυ 5 Eg. Fig. 2
10 demonstrates the calculation procedure with a typical example, which involves the measurement of optical band gap of MoS2 thin films [69]. Chung et al. [71] also studied the direct optical band gap, electronic structure and lattice dynamics of Li2Ni(WO4)2 with SE and Raman scattering measurements. SE could be used to extract the information about charge carriers in metals or semiconductors (such as the carrier concentration). Usually the light energy could be absorbed by the free carriers in metals and semiconductors and the dielectric functions of the materials would be changed, which could be described by Drude model very well. The Drude model is expressed as [49,72]: ε1 ðωÞ 5 εN 2

ε2 ðωÞ 5

ω2p ω2 2 ω2τ

ω2p ωτ ωðω2 2 ω2τ Þ

(2.27)

(2.28)

where εN, ωp, and ωτ are the permittivity, plasma frequency, and scattering frequency, respectively. Then, the charge carrier concentration Nc and the mobility μ can be calculated with the relations [73]:

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Handbook of Modern Coating Technologies

Nc 5 μ5

ω2p ε0 m

(2.29)

e2 e ωτ m

(2.30)

where ε0 is the free-space permittivity, e is the electronic charge, and m is the effective mass of the carriers. Using this approach, Jing et al. [74] found that in Ga
doped ZnO (GZO) thin films, the accurate electron effective mass (me ) is more impactful than the optical band gap shift for analyzing the electrical transport behavior. IRSE was used by Nakano et al. [75] to determine the carrier concentration of n-type GaAs epitaxial layers. The results derived from the IR ellipsometry and from the electrochemical capacitance
voltage (C
V) measurements were consistent very well, as shown in Table 2
7. The difference of the carrier concentrations obtained by these two methods was no more than 19%. Morino et al. [76] used terahertz time-domain spectroscopic ellipsometry to study the electric properties of an InN epilayer and found that the electric properties of the films were improved with the increase in the film thickness. Table 2
8 summarizes the main applications of SE to measure optical and electric properties mentioned above.

2.4.1.3 Other properties characterization As we introduced above, when a layer is the mixture of two or more components, EMA model is a good approach to obtain the average optical constants or dielectric functions based on equations [27] such as Eq. (2.14). In those equations, the volume fractions (V) of each component of the layer are involved and can be calculated, then the density and porosity could be derived. Schubert et al. [77] used IRSE to characterize a mixed-phase BN thin film, which was the mixture of isotropically h-BN and c-BN. By using the Bruggeman EMA [54] to describe the Table 2–7

Comparison of Nc extracted by SE and C
V methods [75]. Nc (cm23)

Sample 1 2 3 4 5 6 7 8 9 C
V, Capacitance
voltage; SE, spectroscopic ellipsometry.

SE

C
V

5.0 3 1018 2.1 3 1018 3.9 3 1018 1.1 3 1018 5.6 3 1017 1.0 3 1018 8.7 3 1017 4.9 3 1017 7.4 3 1017

6.2 3 1018 2.5 3 1018 4.7 3 1018 1.1 3 1018 5.1 3 1017 1.1 3 1018 8.7 3 1017 5.3 3 1017 7.7 3 1017

Chapter 2 • Spectroscopic ellipsometry

61

Table 2–8 Brief summary of SE applications for optical and electric properties characterization.

No. Systems

Ellipsometric experimental conditions

N
λ relation used

Parameters extracted by SE

Three-layer model

Not mentioned

[61]

Drude and Tauc-Lorentz models Not mentioned

Optical constants, thickness and roughness, and optical bandgap Ordinary and extraordinary dielectric constants Ordinary and extraordinary dielectric constants, and thicknesses of layers Thickness, refractive indices, extinction coefficient, and optical band gap Optical constants, thickness, and optical bandgap Optical bandgap

[71]

Optical properties, effective mass, and optical bandgap Thickness, optical constants, and carrier concentration

[74]

Thickness, optical constants, carrier density, and mobility

[76]

1

ZnSe on glass

2

VASE, wavelength Organic range amorphous 245
1000 nm films on Si Organic VASE, in situ real-time amorphous SE, wavelength films range on Si 245
1000 nm CdS on glass Wavelength range or Si 248
825 nm

Single-layer model with a uniaxial anisotropic layer Single-layer and twolayer models with a uniaxial anisotropic layer Not mentioned

MoS2 on fused quartz or SiO2 Li2Ni(WO4)2 pellet

Wavelength range 380
900 nm

Three-layer model

Tauc-Lorentz model

VASE, photon energy range of 0.73
6.42 eV Photon energy range of 0.7
4.14 eV

Substrate only

Lorentz model, Bruggeman EMA Drude and Lorentz models

3

4

5

6

Wavelength range 300
1100 nm

Optical model

7

GZO on glass

8

GaAs epitaxial FTIR layer phase
modulated SE, photon energy range of 11.7
2.9 InN epilayer THz-TESE, frequency on GaN/ range of sapphire 1.4
3.2 THz

9

Not mentioned

Forouhi
Bloomer relations

Single-layer model or two-layer model

Drude model

Three-layer model

Drude model

Refs.

[62]

[63]

[68]

[69]

[75]

EMA, Effective medium approximation; GZO, Ga
doped ZnO; SE, spectroscopic ellipsometry; VASE, variable angle spectroscopic ellipsometry.

dielectric functions of the mixed-phase BN thin film, the volume fraction of c-BN in the film was estimated. Vargas et al. [78] reported the relative density (which is the ratio of film density to that of the bulk material) of films can be determined according to the following Lorentz
Lorentz relation: " # ρf ðnf 21Þ2 ðnb 11Þ2 5 U ρb ðnf 11Þ2 ðnb 21Þ2

(2.31)

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Handbook of Modern Coating Technologies

where ρf, ρb, nf, and nb are the density of the film and the bulk material, the refractive index of the film, and the bulk material, respectively. SE was used to determine the “n” values in Eq. (2.31) and the relative density was calculated further.

2.4.2 In situ measurement It is well known that the ellipsometry measurement is fast and nondistractive, so many processes can be monitored by in situ SE in real-time. Not only the growth rates were obtained, but also the growth kinetics and mechanisms were elucidated. An important application of in situ SE is to study the initial growth stages of films because of the high sensitivity of SE. Fig. 2
11 shows the deposition process of RF magnetron sputtered molybdenum thin film which was obtained by using in situ RTSE [79]. The variations of the Mo bulk layer thickness and surface roughness thickness under three Ar pressures were obvious different, which revealed the mechanisms of the Ar pressure affects the nucleation and growth for the molybdenum thin film. Lyon et al. [80] prepared Hg12xCdxTe alloys with x . 0.5 by using molecular beam epitaxy method and determined its real-time composition with SE. SE possesses sufficient sensitivity (can distinguish the tiny composition different about WxB0.0002) as well as very good runto-run stability (WxB0.0012), so it could be applied in the feedback-control system. In situ SE could be employed to track and measure the film growth process not only in the vacuum environment, but also in the solution environment. Therefore in situ SE has been applied widely in chemical studies in which solutions are involved. Dardona et al. [81] prepared trivalent Cr process (TCP) conversion coatings on Al substrates and studied the formation process by using in situ SE within the spectral region of 1.3
4.3 eV. They used Cauchy dispersion relation to describe the film optical constant and then calculated the film thickness. The results showed that the film thickness is related to the immersion time, and

14 4 mTorr 12 mTorr 20 mTorr

800

12 10

600

8

400

6 4

200

2

Surface roughness thickness (nm)

Bulk layer thickness (nm)

1000

0

0 0

10

20 30 Time (min)

40

FIGURE 2–11 Surface roughness and bulk layer thicknesses versus deposition time obtained by RTSE for Mo depositions at three Ar pressures [79]. RTSE, Real-time spectroscopic ellipsometry.

Chapter 2 • Spectroscopic ellipsometry

63

the initial stages of film formation included three stages, that is, the chemical thinning of the native oxide layer, formation of a very thin initiation layer, and the subsequent rapid formation of the TCP film. SE is a typical optical technique so that it does not disturb the electric measurements. Therefore SE has been a powerful tool in the field of electrochemistry to study the formation or dissolution of the films on the electrode surface. Li et al. [82] employed in situ SE to obtain detailed insights into the growth of anodic ZrO2 films in an inorganic electrolyte contained F2 ion. Three different models were constructed for the dynamic SE data analysis. Four distinguished phases were found during the initial growth stage of anodic ZrO2 film, namely, formation of compact barrier layer, formation of pores, pore evolution to nanotubes and the nanotube steady-growth. Moreover, in those different phases, the thickness of porous layer increased linearly with the anodization time and the rate was 25.6 nm/s. Similarly Lei et al. [83] studied the initial stages of anodization of aluminum in H2SO4. In Table 2
9, the typical applications of in situ SE in several environments (vacuum, solution, and electrochemical cell) are summarized.

2.5 Spectroscopic ellipsometry application examples in coatings In this part, the applications of SE to characterize various coatings, such as photovoltaic films, display coatings, protective coatings, films of biological molecules as well as films of two-dimensional (2D) materials are illustrated. The huge potential of SE in characterizing coatings and thus yielding insight into the coating’s nature and formation mechanism is demonstrated (Fig. 2
12).

2.5.1 Photovoltaic films Photovoltaic cells are developed rapidly in the past decades because of their advantages of environmental-friendly and economical harvesting of solar energy. Most photovoltaic researches are focused on the effects of the compositions, microstructure as well as optical properties of photovoltaic thin films on the energy conversion efficiency. In these investigations, the SE measurements were commonly carried out to obtain the fundamental characteristics of photovoltaic thin films fabricated by various technique, such as the optical properties, thickness and roughness, and even to understand the growth mechanism of the films. Cu2ZnSn(S, Se)4 (CZTSSe) is a prospective material to prepare the absorber layer in thin-film solar cells. Caballero et al. [84] prepared CZTSSe thin film by chemical vapor transport technique and used SE to research its bandgap engineering. They found that the fundamental band gap E0 was within the range of 1.59
1.94 eV when the Ge content was within the range of 0.1
0.5. SE measurements were also carried out by Hermann et al. [85,86] to extract the surface roughness and optical properties of large area Cu(In, Ga)Se2 (CIGS) thin films grown with sequential sputtering method. To deconvolute SE data, the Gaussian broadened polynomial superposition parametric relationship was introduced to describe the

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Table 2–9

Brief summary of applications in situ SE in various environments.

No. Systems

Ellipsometric experimental conditions

Optical model Two-layer model

N
λ relation used EMA and Drude and Lorentz models

1

Mo on glass

In situ RTSE, photon energy range of 0.75
6.5 eV, and spectra acquisition time 1.5 s

2

HgCdTe on CdZnTe (211)B

3

TCP coating on Al

4

Electrochemical anodization of Zr in solutions

Not EMA In situ RTSE, photon mentioned. energy range of 1.7
5 eV, and spectra acquisition time 16 s Single-layer Cauchy In situ SE in solutions model model and photon energy range of 1.3
4.3 eV Three-layer Bruggeman In situ SE in solutions, model EMA wavelength range of 600
800 nm, and spectra acquisition time 1.5 s

Parameters extracted by SE

Refs.

Time evolution of the thicknesses of film and roughness, optical properties, and intraband electronic relaxation time. Growth kinetics of films Time evolution of the thickness, optical properties, and composition

[79]

Time evolution of the thickness and optical properties. Film growth rate Time evolution of the thicknesses, optical properties, and volume fractions. Film growth kinetics

[81]

[80]

[82]

EMA, Effective medium approximation; RTSE, real-time SE; SE, spectroscopic ellipsometry; TCP, trivalent Cr process.

Films of biological molecules

Photovoltaic films

Coatings of 2D materials Extracting coatings information using SE, such as the thickness, optical and electric properties, etc.

Display coatings

Protective coatings

FIGURE 2–12 Typical application fields of SE for coatings characterization. SE, Spectroscopic ellipsometry.

optical properties of CIGS films. Based on the SE results, the film preparation was optimized and the photovoltaic efficiency was higher than 10%. McLaughlin and Pearce [87] used SE to investigate the influence of medium indium content on the properties of wurtzite indium

Chapter 2 • Spectroscopic ellipsometry

65

gallium nitride (InxGa12xN) thin films (0.38 , x , 0.68). They developed a Kramers
Kronig consistent parametric model to fit SE data and obtained the film thicknesses, absorption coefficients, and dielectric functions. For the tantalum oxide (TaOx or Ta2O5) tunnel barrier with the thickness of 3 nm, Tyagi [88] revealed by using SE that the extinction coefficient of TaOx was evidently larger than that of Ta2O5 and TaOx is a promising photoelectric material. This was confirmed by the fact that TaOx ultrathin film with 3 nm thickness absorbed about 12% of the energy of the incident light within the range of 400
1000 nm. Woo et al. [89] obtained the complex dielectric function of a lead halide perovskite (CH3NH3PbBr3) quantum dots, which is helpful to fabricate effective optoelectronic devices. SE was also used to optimize the parameters (thickness, porosity, dielectric constants, and distribution of the elements) of inhomogeneous layers of single-crystal silicon nanowires and Ag porous nanolayer for the better photoelectrical performance by Zharova et al. [90]. SE has been applied to study the influence of doping on the photovoltaic performance. For example, it was found that Mg doping into CdO could improve optical properties and stability of CdO films [91]. SE combined with Cauchy
Urbach model, which describes the N
λ relationship very well, were used to fit the thicknesses and refractive indices of the films. This Mg doped CdO films had enhanced photovoltaic properties and were promising photovoltaic optoelectronic materials. Undoped and Cu doped CdS films, which were prepared by Kost et al. [92] using ultrasonic spray pyrolysis method, were investigated with SE and UV/vis spectrophotometer. Cauchy model was used for fitting the SE data and then the optical constants (n and k) and thicknesses of the films were determined. The structure and values about the band gap of the films were also obtained. An important conclusion of this work was that increase in Cu dosage would probably change the conductivity type of the films from n-type to p-type, which would be applied in optoelectronic devices in the future. Leem and Yu [93] studied the influence of thermal annealing on the properties of (Sb)-doped tin oxide (SnO2) films with SE, X-ray diffraction (XRD) and SEM techniques. It was found that upon the increase in the relative void fraction, the refractive index and extinction coefficient gradually decreased for the annealed films. Organic photovoltaic thin films have been developed rapidly and SE is used to characterize the films. Liang et al. [94] prepared thin films of conjugated polymers and CdSe nanoparticles with layer-by-layer method and measured the thickness of films by using SE. It was found that the film thickness was linearly related to the number of layers. Tse et al. [95] reported the similar linear relationship existed for multilayer thin films of rhenium containing hyperbranched polymer and poly [2-(3-thienyl)ethoxy-4-butylsulfonate] (PTEBS). These reports showed that SE has been a powerful tool for organic photovoltaic thin studies. Real-time SE has been a powerful tool to track and measure the dynamic evolution of photovoltaic thin films. For example, Li et al. [96] studied the preparation, the changes of the structure, and dielectric functions of sputtered CdTe, CdS, and CdTe12xSx thin films. They first found that the deposition temperature (T) was the most important preparation condition for CdTe and CdS, and the rf power level was the most important condition for the cosputtered CdTe12xSx alloys. Then they analyzed the interdiffusion at CdS/CdTe or CdTe/CdS

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heterojunctions according to the obtained dielectric functions ε of CdTe12xSx. Moreover, they also extracted the dynamic information on the nucleation, coalescence, and structural evolution of CdS and CdTe films base on the RTSE results [97]. In situ SE and GIXS were used by Want et al. [98] to provide insights into kinetics of poly(3-hexylthiophene) and [6,6]-phenyl C61butyric acid methyl ester blend film formation process. Three stages in film drying were identified: (1) rapid solvent-evaporation, (2) moderate solvent-evaporation and rapid crystallization, and (3) slow solvent-evaporation and slow crystallization. The results would be helpful for preparing efficient photovoltaic devices and RTSE exhibits its ability as a process-control technique.

2.5.2 Display coatings Flat panel display apparatus are much lighter and smaller than the cathode ray tube apparatus, so that they have been widely used in computers, cell phones, and other electric devices. Organic light-emitting diode (OLED) technique is one of the strong competitors for the future flat panel display technique due to their outstanding nature such as flexibility, low power consumption, high luminance, and full color capability. To optimize the OLED devices, the optical characterization of organic thin films in OLEDs is required. As a nondestructive, rapid, and efficient characterization technique, SE has been widely employed to extract optical constants of organic emitters, such as 1-methyl-1,2,3,4,5-pentaphenylsilole [99], tris(2-phenylpyridine) iridium (Ir(ppy)3) [100], platinum octaethyl porphine (PtOEP) [101], N,N0 -diphenyl-N,N0 -bis(3-methyl-phenyl)-1,10 biphenyl-4,4diamine [102], tris (8hydroxy) quinolato aluminum (Alq3) [102,103], doped grapheme [104], Si(2,6-bis(benzimidazol-20 -yl)pyridine)2 (Si(bzimpy)2) [105], 4,40 bis(9-carbazolyl)-1,10 biphenyl (CBP) and 2,20 ,2v(1,3,5-benzinetriyl)-tris(1-phenly-1-H-benzimidazole) (TPBi) [106], and so on. Tsuboi et al. used a phase-modulated SE to study the optical constants of fac Ir(ppy)3 layers [100] and PtOEP layers [101] in single-layer OLED devices and on quartz plates, respectively. The results showed that the optical properties of the Ir(ppy)3 and PtOEP films as emitting layer in single-layer OLED devices were different from those of the thin films evaporated on quartz plates. Doping a few optical active molecules in emission layer is an alternative way to improve the optical device efficiency of OLED. Hartmann et al. [103] studied the doping effects of dicyanomethylene-4H-pyran (DCM) molecule on the optical indices of the Alq3 emitting layer using SE. For the Alq3 emitting layers which were doped with DCM molecules at different concentrations, their extinction coefficient (k) values corresponding to the absorption peak at around 0.55 μm increased with increasing in dopant concentration. As the comparison, the values of k corresponding to the peak located at 0.39 μm were almost not affected by the dopant concentration. Pfeiffer et al. [106] measured the refractive indices and extinction coefficients of three organic semiconductors [CBP, Ir(ppy)3, and TPBi] in a transparent OLED device [including glass, indium tin oxide (ITO), organic semiconductors, and cathode] with SE, optical transmittance, and reflectance techniques. Based on the results, they optimized the structure of the diode stack and obtained the OLEDs with an optical transmittance which was enhanced from 47% to 65%.

Chapter 2 • Spectroscopic ellipsometry

67

Thin film transistor liquid crystal display (TFT-LCD) is another kind of dominant flat panel display technology. In the TFT-LCD panels, the red, green, and blue (RGB) color filter coating is one of the main components for generating the color images. Lee et al. [107] applied SE to extract the effective thickness and refractive index of the RGB color filter coating. Considering the scattering and absorption properties of the layers as well as the roughness of the surface, they built an effective layer
included model which could be used to determine the (n, k, and d) values of the RGB color filter coatings simultaneously. SE also could be used to characterize the conductors in display devices. For example, ITO thin film is widely used as the transparent conductor in display devices. Bartella et al. [108] introduced SE to provide insight into the relationship between the optical constants n(λ) and k(λ) of ITO coating, which were obtained by SE, and the stoichiometry, film density, surface roughness, and crystalline structure. It was demonstrated that SE could serve as an effective quality-control tool for display manufacturing. Dielectric protection layer is also an important component for display devices because it can improve the firing voltage, delay time, discharge efficiency and lifetime of display devices. MgO film is the most common protection layer. To improve the discharge performance, Lee et al. [109] used an ion plating technique to prepare hydrogen
doped MgO thin films. They then monitored the changes of optical constants of the doped MgO films with the hydrogen flow rates and found that the most optimal hydrogen flow rate was 50 sccm, which corresponded to the lowest value of refractive index of the films. Lyum et al. [110] used transmission ellipsometry to characterize the ultrasmall optical anisotropy of a rubbed polyimide film for liquid crystal alignment. The ordinary refractive index (no), the extraordinary refractive index (ne), the thickness of rubbed polyimide film (d) were found to be 1.732, 1.743, and 38.8 nm, respectively. These optical properties of the film had influence on the color gamut and response time of the LCD directly, so the precise values of the optical constants were important for the LCD manufacture. Similarly Son et al. [111] compared the optical anisotropy of the ion-beam
treated polyimide layers with that of rubbed layers by using SE. The results indicated that the anisotropy of the former was much larger than that of the later because the former modified the whole polyimide layer while the latter only changed the polyimide surfaces along the rubbing direction.

2.5.3 Protective coatings Protective coatings are widely used in many fields to avoid the materials being damaged by the environment. Usually the protective coatings are thin or ultrathin, and SE with high sensitivity is very suitable to characterize them. Kaneko et al. [112] prepared films of Al2O3
Ta2O5, a well-known highly corrosion
resistant material and analyzed the deposition process of films with in situ SE. It was revealed that thicknesses of the films changed linearly with the deposition time (exclude the short induction periods). They also found that the increased tantalum cationic fraction would increase refractive indices of the film, and the extinction coefficients of the composite films were larger than those of single Al2O3 and Ta2O5 films.

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Titanium diboride (TiB2) is a high-performance metallic ceramic with high electrical conductivity, excellent corrosion, and wear resistance. TiB2 has been widely used in microelectronics, superconducting, and other fields. Kumar et al. [113] monitored the nucleation and growth of TiB2 films during thermal chemical vapor deposition on highly conducting n-type Si(100) substrate by using in situ SE. The SE data were deconvoluted with a multilayer model, in which a surface roughness layer was involved. The surface roughness layer was regarded as a mixture of 50% TiB2 and 50% void based on the Bruggeman EMA. The results showed the deposition temperature must be higher 170 C, and an increase in the surface roughness to 2.6 nm at the onset of film growth, indicating the nucleation phase. After nucleation, the film thickness increased linearly with the increase in the film roughness. Rahman et al. [114] studied the formation of a silica protection layer on top of the Ni and Ti silicide under three oxidation atmospheres (dry, wet, and microwave plasma) and experimental conditions (time and temperature). By using SE, XRD, and SEM techniques, they measured the properties of the silicides and oxides, including the roughness, thickness, and density, and they found that NiSi would be a promising protective material in the future and the microwave plasma oxidation would be an excellent oxidation atmosphere. The evolution of sol
gel based silicon-zirconia wear-resistant coatings during annealing process were investigated by Uhlmann et al. [115] with SE, SEM, and other modern techniques. The thickness results determined by SE were consistent with them measured by SEM when the annealing temperature was above 200 C. Moreover, when the preparation temperature is higher than 600 C, the film density would be 4.64 g/cm3 while the mean refractive index within the range of 1.88 to 1.93, which was very helpful to guide the preparation of high-quality protective coatings. To enhance the hardness of the systems, Gioti group [116] deposited ultrathin (B10 nm) protective hard optical coatings of amorphous carbon (a-C), carbon nitride (CNx), and boron nitride (BNx) on the top surface of optical systems, respectively. SE was applied to investigate the dielectric response and optical properties of those protective hard optical coatings. All the three coatings had low absorption indices in the visible energy region while the BNx and CNx film had the lowest the highest absorption, respectively. It could be concluded that films of a-C and BNx were promising candidates for protective hard optical coatings compared with CN x films. Another carbon wear
resistant coating, diamond-like carbon (DLC) film, was prepared on Ti
6Al
4V substrate and measured using VASE by Wu et al. [117]. The results showed that the thicknesses of DLC coatings were usually several-hundred nanometers and the thickness values were directly related to the hardness values but had no influence on the adhesion between the DLC coating and substrate. Moreover, SE could act as a rapid assessment technique of film quality by extracting the thickness and optical constants of film. Corbella et al. [118] found that the optical, electric and mechanical properties of DLC films could be improved by adding transition metal atoms (Mo, Nb, Ti, and W) into the DLC matrix. They used UV
vis SE to reveal the influence of the composition on the optical constants and found that optical gap increased upon the metal content reduced. Similarly the

Chapter 2 • Spectroscopic ellipsometry

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optical constants of titanium chromium nitride nanocomposite protective coatings were measured by Aouadi et al. [119] using SE. The absorption coefficient and elemental/ phase composition were correlated as the former increased with the increase of Cr content in the films. Since SE is a nondestructive and noninterfering technique, it has been employed in chemical or electrochemical environments to study the preparation and protective properties of the protecting coatings. Chromate conversion coatings (CCCs) technique is a traditional protective technique for metals and has been used for many years. Zhang et al. [120] investigated the CCCs formed on metal of zinc in Cr(VI) and Cr(III) treatment baths by SE. The results showed, for the same immersion period, the CCCs of Cr(VI) was thicker than that of Cr(III). The latter inhibited effectively the corrosion of zinc, but the inhibition effect was worse than that of the former. There were two reasons for the difference of these corrosion protection coatings: (1) the Cr(VI) coating was thicker and (2) the Cr(VI) species could repassivate the defects of the coating. However, chromate containing materials are extremely toxic, so some environmental-friendly nonchromate protection treatments are developed. Liu et al. [121] investigated the formation mechanism of nontoxic self-assembled monolayers (SAMs) on Mg surface. They measured the thicknesses of the alkylcarboxylate (CnH2n21O2Na, n 5 12, 14, and 18) SAMs with SE and found that the thickness increased upon increasing chain length of carboxylate. Organosilane pretreatment is another approach to replace hexavalent chromium conversion treatment. SE and electrochemical quartz crystal microbalance were used to elucidate the formation mechanism of organosilane film by Pen et al. [122]. In some situations, metals corrode in solutions and the products form protective film on the metal surface, which could prevent the metal from corroding further. Hara et al. [123] reported this kind of protective surface films generated on AZ91D Mg alloy in 0.1 M NaCl solution. Based on the in situ SE results, as shown in Fig. 2
13, the experimental plot moved from the theoretical curve of N2 5 1.510 2 0.010i to that of N2 5 1.415 2 0.016i within 0
25 s (the initial period of immersion), the authors inferred that the air
formed MgCO3 film changed into Mg(OH)2 film during this period. Then, the SE experimental spots moved along the theoretical curve of N2 5 1.415 2 0.016i, which meant that the Mg(OH)2 film grew homogeneously. This formed Mg(OH)2 film could passivate Mg in the NaCl solution so that it could be regarded as a protective coating. The authors also studied the thicknesses variation of surface films on AZ91D alloy and 6N
Mg with the immersion time in 0.1 M NaCl solution by using in situ SE. The results are shown in Fig. 2
14. Obviously the films grew quickly in two continuous stages: at stage I, the film thickness increased linearly with the immersion time, indicating the film grew at a constant rate; at stage II, the film growth rate decreased with the lapse of time. SE was also applied to monitor the growth of the passive film potentiostatically formed on 304 stainless steel in a 0.1-M sodium sulfate solution by Mohanmmadi et al. [124]. The results indicated that the thickness of the passive film was 2
2.6 nm. Another example of application of SE was reported by Pen et al. [125], they found that a fresh uncured organosilane film of BTSE cannot provide effective protection for aluminum substrate. Then they

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FIGURE 2–13 Experimental plot during immersion of AZ91D in 0.1 M NaCl solution and theoretical curves for growth of films with optical constants N2 5 1.415
0.016i and N2 5 1.510
0.010i [123].

Time, t / min

(a) 160

0

10

20

40

(b) Time, t / min 50

Solution : 0.1M NaCl

140 Film thickness, d / nm

30

60

160

120

100

100

80

80

60

60

40

40 Specimen : AZ91D-ThM

0

10

140

120

20

0

20

6N-Mg

0 0

1000

2000 Time, t / s

3000

0

1000 Time, t / s

FIGURE 2–14 Thickness (d) of surface films on AZ91D (a) and 6N
Mg (b) as a function of immersion time (t) in 0.1 M NaCl [123].

monitored the evolution of the film during curing with SE. The results showed that the thickness decreased and the film refractive index increased during curing, which indicates that the curing treatment could modify the structure of the BTSE film and thus enhance the protection ability. Similarly Chen et al. [126] studied 2-mercaptobenzothiazole corrosion inhibitor protective film on copper with in situ SE, IR, and Raman spectroscopies.

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2.5.4 Films of biological molecules Since SE has an excellent thickness resolution (0.01 nm or better) and could be employed in solution ambient, it is suitable for studying biological films while the resolution of SE is close to the dimensions of biological molecules and many biological reactions take place in solutions or at the solid/liquid interface. Analyzing the adsorption of proteins or macromolecules on planar solid surfaces is the most commonly investigation task and the classical application of SE. Based on the information extracted by SE, the properties, formation mechanisms, and surface dynamics of biological molecules films could be obtained, which is helpful to improve the performance of the films such as the accuracy and precision of biosensors. For the adsorption of ferritin on gold [127], SE data were deconvoluted with a four-phase model. The thicknesses of the ferritin layer, the interface layer which was treated as the mixture of protein and gold based on Bruggeman EMA, as well as the optical properties of the ferritin layer were determined simultaneously. Spaeth et al. [128] studied the change of the thickness and dispersion state of the protein multilayer during the incubation period by using SE. The Cauchy model was used to fit the SE data. The authors found that a single homogeneous protein layer after 5
15 incubations, and the refractive index nD of the layer was almost a constant of 1.384 6 0.002. The thickness and mass of protein deposition per incubation step was 18.75 nm and 4.74 ng/mm2, respectively. Preininger et al. [129] characterized anti-human immunoglobulin G (IgG) Langmuir
Blodgett films by using SE and measured accurately the mean thicknesses of an anti-IgG film on different substrates (glass, PVC-COOH, and aminopropyl sol
gel). Castilla-Casadiego et al. [130] applied IR VASE to obtain the thickness and roughness of the multilayers of heparin and collagen (COL), which was a bioactive surface coating and could enhance the response of human mesenchymal stromal cells to soluble interferongamma. The results from SE are important to optimize the preparation of the multilayers. McArthur et al. [131] used in situ SE to dynamically monitor the adsorbed protein layers on Cu12xAlx (0 # x # 1) substrate. Both fibrinogen (Fib) and albumin adsorbed preferentially onto Cu-rich surfaces. When Al content is higher than 21 at.%, the thickness of the protein adsorption layer decreased significantly. In situ SE was also used to study the adsorption mechanism of yeast cytochrome c (YCC) on SiO2/Si substrates by Toccafondi et al. [132]. Due to the variations in the Δ and Ψ spectra induced by the adsorption of proteins on the substrate were generally small, the difference spectra (δΔ and δΨ) was introduced. After the interface effect was neglected, a simple three-layer optical model, that is, solution-filmsubstrate, was built to deconvolute the experimental δΔ and δΨ spectra. Both in situ SE and the difference spectra were powerful techniques to provide the detailed insights to the protein/surface interaction mechanism. Silaghi and Zahn group [133,134] studied the optical properties of four DNA base films by using SE in the wavelength range from near IR to ultraviolet. To deconvolute the SE data, a uniaxial model was built for adenine and guanine films while an isotropic model was introduced for the thymine and cytosine films and the dielectric properties of the films were obtained, which were very helpful to design and manufacture DNA
based electronic and optoelectronic devices.

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SE and surface plasmon resonance
enhanced ellipsometry were used to measure the thickness and to quantify the molecular orientation of biological layers which were composed of single-stranded DNA [135]. In the optical model to fit the SE data, a vertical gradient was introduced to describe the optical index of the biolayer, and the thicknesses obtained by SE were identical with them obtained by AFM. Nabok et al. [20,21] presented examples of applications of the TIRE method to study the DNA hybridization and the registration of low molecular weight toxins. Their results showed that the sensitivity of TIRE is almost 10 times higher than that of conventional external reflection ellipsometry. In situ TIRE with SPR was also used by Balevicius et al. [136] to investigate the binding kinetics between an immobilized glycoprotein granulocyte colony stimulating factor (GCSF) receptor and three genetically engineered ligands [GCSF monomer (mGCSF), (GCSF)2La (GCSF-homodimer), and stem cell factor-La-GCSF]. This high sensitivity method, TIRE, provided deep insight into the mechanism of interactions between receptors and ligands. IE has become popular in biological studies [22,137] because it could be used for quantification and visualization of biomolecular interactions. Fig. 2
15 [138] shows the principle of IE schematically, in which the thickness distribution of thin layers (protein patterns) on a solid substrate was visualized by using IE. Jin et al. [137] used IE with a CCD camera to detect antigen
antibody complexes on a silicon substrate. Three types of protein layers, Fib, human serum albumin (HSA), and human IgG, adsorbed on a hydrophobic silicon substrate were studied. For the layers without incubation treatment, the results showed that the thickness of IgG layer was thinner than that of Fig layer and thicker than that of HSA layer. Then the samples were incubated in an anti-IgG serum [bovine serum albumin (BSA)] and were measured with IE again. It was found that thickness of the IgG dots increased significantly while the thicknesses of the Fib dots and HSA dots did not increase. It could be inferred that the antigen
antibody complexes of IgG formed. The images obtained from IE results distinguished clearly the distributions of the proteins. IE was also used to study the competitive adsorption of COL and BSA on chemically modified silicon substrates [139]. In noncompetitive situation, the solution only contained one protein (COL or BSA), the adsorbed amounts of Image in 3D

Image in grayscale

Complex layer

Substrate Ligand layer

FIGURE 2–15 Schematic model of bioprobe based on imaging ellipsometry [138].

Chapter 2 • Spectroscopic ellipsometry

73

COL or BSA on hydrophobic surfaces were two times more than these on the hydrophilic surfaces. In the mixed solution of BSA (1 mg/mL) and COL (0.1 mg/mL), BSA and COL would be adsorbed competitively because of their different binding affinities. The results showed that, BSA was almost 100% protein adsorbed on the substrate for the hydrophobic surface, and only 6% for the hydrophilic surface. IE directly visualized and quantified the distributions of the proteins and the results agreed with these obtained using AFM well.

2.5.5 Films of two-dimensional materials 2D materials are attractive because they possess unique and exceptional properties [140]. They have been used widely for smart or flexible electronic [141,142], optoelectronics [143,144] and energy devices [145]. For these devices, 2D materials can be used not only as the host functional coatings, but also as the protective layer or ultrasmooth substrates for other functional materials [146,147]. 2D materials have been one of the hottest research topics. Especially 2D materials coatings are ultrathin and SE which has atomic scale sensitivity is an ideal characterization tool for them. Graphene, the most widely studied 2D material, has been attracted wide attention because of the unique and excellent physical, chemical and mechanical properties [140]. The first results on the SE results of graphene flakes on dielectric substrates were reported by Kravets et al. [148]. They modeled the graphene layers as a uniaxial anisotropic material and assumed the thickness of graphene layer as 3.35 Å, and extracted the optical constants of graphene layers successfully. Then the graphene layers obtained by various methods, including CVD grapheme [149
152], exfoliated grapheme [153
156] as well as epitaxial grapheme [157
159] were characterized by using SE in near-IR
visible
ultraviolet region. To determine the optical constants and thickness of graphene flakes accurately and simultaneously by analyzing the SE data, Weber et al. [155] parameterized the optical constants with Bspline function method. The fitted thickness of graphene was 3.4 Å and this value was consistent with the interlayer spacing in graphite. Isic´ et al. [160] used SE to extract the optical properties of few-layer graphene flake. Since the size of graphene flake was smaller than that of the ellipsometric light spot (50 μm), the island-film model was introduced to deconvolute ellipsometric data. The obtained extinction coefficients for graphene were in consistent with the previously reported data [148,154,155], while the refractive index data were around 30% lower and without sharp decrease in the UV range. Matkovic´ et al. [156] employed the IE with small spot size (1 μm) to investigate the surface state of the exfoliated graphene on a Si/ SiO2 substrate in the experimental environment where some water existed. A Fano model was employed to parameterize the optical constants of graphene. Then the thickness mapping revealed that there was a water layer on the graphene sample when the sample was exposed to the experimental environment and the spatial distribution of water was obtained. To investigate the effect of the substrates on the optical properties of graphene, Wurstbauer et al. [154] used the IE to determine the shape and layer number of exfoliated graphene deposited on the flat amorphous SiO2 or crystalline GaAs substrates. Gaskell et al. [159] also employed a high spatial resolution ellipsometer to determine the thickness of exfoliated or

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epitaxial graphene films. The sensitivity to measure layer number of graphene increased when the layer number and substrate refractive index decreased. Base on IE, recently ellipsometric contrast micrography with the spatial resolution below 1 μm and atomic layer thickness resolution was developed by Hofmann et al. [161]. This technique is a powerful tool for characterizing the layer number, defects, and contamination of the 2D materials. In situ RTSE experiments were carried out by Losurdo et al. [162] to investigate the deposition process of graphene with low-pressure chemical vapor deposition approach on nickel and copper supports. As a nondestructive and nonintrusive optical method, SE was used to monitor all steps of graphene growth, including the cleaning and annealing of metal catalyst, the diffusion of carbon, covering of carbon on the surface, formation of graphene, and so on. These information provided by SE would be useful to control the graphene quality and in situ SE technique was proved to be an effective quality-control tool. Besides graphene, graphene oxide (GO) was also be studied by using SE. For example, Shen et al. [163] characterized the optical responses of GO and few layer reduced graphene oxide (FRGO) with SE in visible range. To analyze the ellipsometric data of GO and FRGO, a Lorentz oscillator model was employed. It was found that the optical responses of FRGO were very similar with these of monolayer exfoliated graphene within the visible wavelength range. Jung et al. [164] measured the optical properties and thicknesses of single and multiple layers of GO using IE with 2 μm lateral resolution and standard SE. The refractive index (n) of multiple GO layers increased while their thicknesses reduced upon the thermally treatment. To explain the change of the thicknesses, a model was proposed in which some interlamellar water was involved. The layered transition metal dichalcogenides (TMDs), whose general chemical formula could be written as MX2 (M 5 Mo, W, Ti, Zr, Ta, and Nb; X 5 S, Se, and Te), are other promising 2D materials. SE has been used to extract the optical properties of TMDs [69,70,165] and obtain the 1T/2H phase ratio [166]. IE is also applied to detect the MoS2 flakes with a lateral resolution about 1 μm [167,168]. Recently some new 2D materials such as hexagonal boron nitride, Ti2C, Nb2C, and PtSe2 were synthesized successfully and their optical and electric properties were determined precisely by using SE [169
171].

2.6 Summary and perspectives SE is a powerful tool for characterization of coatings with high precision and sensitivity. By using SE, various physical properties such as the thickness, optical, and electric properties can be obtained, which makes the application area of SE quite wide, including characterization of photovoltaic films, display coatings, protective coatings, biological films as well as 2D materials layers, etc. Moreover, SE measurement is nondestructive and very fast, so that it is easy to in situ real-time monitor the formation and change of coatings on the atomic scale. On the other hand, SE technique is an indirect characterization method. Analyzing ellipsometric data requires construction of complicated optical models, which can be considered as the greatest disadvantage of SE. To overcome this shortcoming, the complementary techniques, for example, XPS, AFM, SEM, etc., should be applied to provide enough information for building reliable models to deconvolute SE data.

Chapter 2 • Spectroscopic ellipsometry

75

In the future, SE would be developed in the following aspects: (1) enlarging spectral range so that the light beam at a given wavelength used in an ellipsometer could provide extra characteristic information about the composition or properties of samples; (2) shortening the acquisition time for in situ RTSE measurements to extract the evolution information of dynamic systems; (3) reducing the diameter of the light beam to improve the spatial resolution of ellipsometers and develop IE; (4) developing more reliable and accurate models to describe the N
λ relationships for anisotropic and complicated samples; and (5) proposing new formula system based on the optical principles to deconvolute the ellipsometric data.

Acknowledgment This work was supported by the National Natural Science Foundation of China (21773019, 21573028, and 21972012) and the Program for New Century Excellent Talents in University (NCET-12-0587 and NCET13-0633).

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3

X-ray diffraction

B.S. Saini1, Raminder Kaur2 1

DEPART ME NT OF ME CHANICAL E NGINE ERING, PUNJAB I UNIVERS ITY, PATIALA, INDIA 2

DE PARTMENT OF BASIC & APPLIED SCIENCES, PUNJAB I UNIVERS ITY, PATIALA, INDIA

3.1 Introduction The wavelength of radiation emitted by an object depends on its temperature. Hotter objects emit radiation of shorter wavelengths and so, very hot sources, such as Sun’s corona emit X-rays. Other interesting sources of X-rays in the Universe include pulsars and black-holes, while the credit for their laboratory production and detection goes to the German physicist Wilhelm Conrad Röntgen, who discovered X-rays on November 8, 1895, and was subsequently awarded the very first Nobel prize in Physics for this discovery [1]. It should however be noted that prior to their discovery and systematic study by Röntgen, many scientists working on partially evacuated discharge tubes had unknowingly produced X-rays and even found their evidence on photographic films. X-rays are high energy electromagnetic radiation, whose wavelength ranges from 10 nm for soft X-rays down to 0.01 nm on the other extreme of hard X-rays. Owing to their ability to pass through various objects otherwise opaque to visible radiation, namely, human body, wood, or even metals up to a certain thickness, X-rays could be used for radiography—a variant of photography based on transmitted radiation. As a result, they soon became a favorite diagnostic tool among physicians and engineers, even though their exact character was not known until 1912, when their diffraction by regular crystals was discovered. A new dimension to the diagnostic techniques using X-rays was added with the development of computer
assisted tomography. This innovation revolutionized the field of medical diagnostic techniques by facilitating high-contrast scanning in three dimensions. Recognizing the importance of this development, Allan Cormack and Godfrey Hounsfield were awarded the 1979 Nobel Prize in Medicine [2
6]. Although the application of conventional radiography as a diagnostic tool continues to date, the diffraction techniques are credited with many breakthroughs in the field of medicine and materials science. Study of diffraction pattern allows investigation of internal structure of materials on a much finer scale and for a much higher degree of complexity. The technique has contributed significantly to our understanding of complex molecules of life, such as proteins. On materials science front, X-ray diffraction (XRD) is an indispensable nondestructive technique for various qualitative and quantitative investigations, namely, determination of Handbook of Modern Coating Technologies. DOI: https://doi.org/10.1016/B978-0-444-63239-5.00003-2 © 2021 Elsevier B.V. All rights reserved.

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crystal structure and lattice parameters, analysis of crystal texturing, quantitative phase analysis, and estimation of residual stresses. This understanding of the application of diffraction patterns for determination of crystal structures subsequently paved the way for application of electron diffraction patterns for similar studies through transmission electron microscopy, thereby further aiding our understanding of the materials. Much of the recent technological progress in materials science, especially that in the fields of VLSI, cutting tools, and turbine vanes, has been made possible by advances in surface engineering, which involves working with thin films, whose physical, chemical, electrical, and mechanical properties are tailored to suit the given application. As the thickness of these films usually varies from just a few nanometers to a few tens of micrometers, it is generally not possible to make a sound assessment of their properties through conventional nondestructive or destructive techniques. This technological challenge has led to the development of various X-ray measurement techniques for thin films, which can be used for determining their thickness, composition, microstructure, density, residual stress, and so on. Since the quantity of material in a thin film is inherently small, its analysis using X-ray techniques poses a technological challenge and hence, often calls for specialized equipment, attachments and procedures. As a result, while XRD techniques for bulk materials had got established quite early, the advances in the field of thin films are relatively recent and have often been the result of technological push by equipment manufacturers. In view of the necessity to develop a preliminary understanding of X-rays and the nature of their interaction with matter, the discussion in the following subsections has been arranged in a logical sequence—with discussion on thin film analysis appearing towards the end. However, depending on one’s level of understanding, an individual may skip any number of sections and proceed to the section of interest. Furthermore in-line with the title of this handbook, the chapter has been written from the perspective of materials science and so, its usefulness for individuals working on biomolecules or tissues would be rather limited.

3.2 Application areas of various X-ray techniques Over the course of past few decades, various X-ray techniques have found application in diverse fields. For example, X-ray fluorescence (XRF) (refer Section 3.3.3 for a brief description of fluorescence) based Karatmeters have been finding increasing application in precious metal industry, thereby allowing speedy, reliable, and precise assessment of the composition of jewelry artifacts [7
9]. The technique also finds application in assessing food safety by detecting the presence of heavy metal contaminants [10,11]. A variant of this technique, known as total reflection XRF spectrometry, facilitates detection of trace amounts of elements in dried liquid samples such as water or milk by irradiating the sample carrier (usually quartz glass) at very small angle of incidence (B0.1 degree). The small angle of incidence (with respect to surface tangent) helps improve the signal-to-noise ratio by limiting the depth of penetration of X-rays into the underlying substrate [12], while facilitating their longer interaction with the thin layer of interest (refer Section 3.10.2.3). Different types of XRD

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87

techniques, which we shall study in subsequent sections, find application in soil characterization [13], mineralogy [14], textiles [15,16], gemology [17
19], and so on. Since XRD techniques are capable of characterizing very small samples, they are often helpful in performing forensic analysis [20]. XRD techniques had been successfully used for inferring the structure of proteins even before the structure of DNA was determined by Watson and Crick. Since then, the technique has undergone extensive refinement and is now capable of providing much more information about the structure of proteins [21,22]. Augmented by suitable computer hardware and software, the diffraction techniques are also used for analyzing other complex structures, such as those encountered in pharmaceuticals and electronics industry [23
25]. A recently developed technique benefitting VLSI fabrication is X-ray micro-CT, which is an extension over the well-developed CT scanning routinely used in medical diagnostics [26]. The application areas of various X-ray
based radiography, XRF, and XRD techniques are summarized in Fig. 3
1.

Radiography & CT scans in medicine & industry XRD in textile industry

XRD in forensic examination

XRF in elemental analysis

XRD in integrated circuits X-Ray techniques

XRD in life sciences, pharmaceuticals & drug research

XRD in mineralogy & soil analysis

XRF in food safety

XRD in gemology XRD in materials science

FIGURE 3–1 Application areas of X-ray techniques.

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While the application areas of various X-ray techniques have been constantly expanding, we shall mostly restrict our discussion in this chapter to XRD techniques, with primary focus on materials science.

3.3 Production and characteristics of X-rays The laboratory sources of X-rays include radioactive materials, X-ray tubes, and synchrotron radiation. X-rays are generally in the form of continuous spectrum radiation and characteristic radiation. Following subsections briefly describe the technique for production of X-rays, primarily from the perspective of X-ray tubes, which serve as the most common source in their laboratory production for application in the field of materials science.

3.3.1 Emission of continuous spectrum radiation Continuous spectrum or “white” X-rays are generally produced in an X-ray tube through rapid deceleration of charged particles (namely, electrons) possessing sufficient kinetic energy. For this purpose, an electron beam, accelerated to an energy level of around 5 keV is bombarded onto some metal target placed inside the X-ray tube. The radiation thus resulting from sudden deceleration of charged particles is also known as bremsstrahlung—which means “braking radiation” in German. Since only a tiny fraction of the total kinetic energy of all incident electrons gets converted into X-rays, with the remaining energy converting into heat, the target metal generally requires cooling by water for continuous operation. As various electrons hit the target atoms at different locations, they lose different fractions of their kinetic energies in each collision. As a result, the emitted X-rays comprise of a continuous spectrum of different wavelengths, whose intensity varies with wavelength and drops to zero at a limiting short wavelength (λSWL), which is independent of the target material and corresponds to conversion of entire kinetic energy to radiative energy in a single step, as described by Duane
Hunt law: K :E: 5 Ve 5

hc λSWL

As an example, the short wavelength corresponding to an accelerating voltage of 6 kV works out be around 0.2 nm, as calculated below: λSWL 5

hc 6:63 3 10234 3 3 3 108 5 2:075 3 10210 m 5 Ve 6000 3 1:6 3 10219

On increasing the tube voltage (V), the kinetic energy of bombarding electrons will also increase, thereby leading to a lower value of λSWL. The corresponding distribution of intensity over different wavelengths also shifts toward higher energy (i.e., shorter wavelength), as schematically shown in Fig. 3
2.

Chapter 3 • X-ray diffraction

100

Characteristic radiation K

Continuous radiation

24 kV

3

75

K

2

50

Absorption edge

18 kV

25

1 12 kV 6 kV

λswl

0 0.00

0.05

0.10

0.15

0.20

0.25

Mass absorption coefficient cm2/g)

X-ray intensity (relative units)

4

89

0 0.30

Wavelength (nm) FIGURE 3–2 Spectrum of X-rays emitted from molybdenum target superimposed with plot of mass absorption coefficient pertaining to a suitable β-filter.

3.3.2 Emission of characteristic radiation As the accelerating voltage is further increased, electrons in the incident beam gain sufficient energy to knock-out orbital electrons from the atoms of the target material. The vacancy thus formed is immediately filled by an electron from some neighboring shell, thereby emitting a photon of radiation, whose energy equals the difference between energy levels of the two shells. Since different pairs of shells could be involved in this process, therefore, the emitted X-rays comprise of multiple characteristic peaks, namely, Kα, Kβ, and Lα for electron transitions from L to K, M to K, and M to L shells, respectively. Thus at high accelerating voltages, the radiation will comprise of two components—first, white X-rays, which are produced as a consequence of rapid deceleration of the bombarding electrons, and second, characteristic radiation, whose wavelengths depend on energy levels of the target metal. With further increase in accelerating voltage, the intensity of characteristic radiation increases much more rapidly in comparison to that of the white radiation. The wavelengths of Kα characteristic radiation for the commonly used target metals, namely, Cr, Cu, Mo, and W are 0.229, 0.154, 0.071, and 0.021 nm, respectively, while their corresponding excitation potentials are 6, 9, 20, and 70 kV, respectively. For details concerning characteristic wavelengths of various elements, the reader can refer to Table 4.2.2.4 in Ref. [27]. Information regarding construction and operation of X-ray tubes can be found in Ref. [28].

3.3.3 Absorption and filtration of characteristic radiation The phenomenon of absorption can be understood by considering the process of interaction of X-rays with crystalline materials. The energy is removed from incident beam through two different mechanisms—first, through scattering (discussed in Section 3.6) and second through pure absorption, which includes various thermal and nonthermal processes. Nonthermal effects may

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include ionization of atoms, thereby producing β-rays, which in-turn might lead to emission of X-rays of longer wavelengths—a phenomenon known as fluorescence, commonly encountered when irradiating ferrous substrates with Cu Kα radiation. A portion of the incident energy could also be absorbed by free electrons and reemitted as radiation of longer wavelength—a phenomenon known as Compton effect. As a consequence, the transmitted beam gets reduced in intensity both due to scattering as well as absorption through the various processes described above. The term “absorption” therefore signifies reduction in residual intensity of incident beam, which happens due to cumulative effect of pure absorption, along with scattering, even though the latter phenomenon just redirects energy in some other direction. Röntgen found that the residual intensity (I) of X-rays on passing through a material of thickness t and linear absorption coefficient (μ), is progressively reduced according to the following relationship: dI 5 2 μ dx I .I 5 I0 e2μ t



I0 : Incident intensity

(3.1)

The linear absorption coefficient (μ) corresponding to a given wavelength of incident X-rays is proportional to density (ρ) of the material, regardless of its physical state. The ratio μ/ρ is a constant, known as mass absorption coefficient of the material and its values (in cm2/g) for various materials have been tabulated in Table 4.2.4.3 in Ref. [27]. The mass absorption coefficient for compound materials can be calculated as weighed averages of the coefficients of their constituent elements. The absorption of X-rays by a material decreases with decreasing wavelength (i.e., increasing energy). However, similar to the phenomenon of emission/absorption lines observed in visible spectra of various materials, there is a sudden increase in the absorption of X-rays, whenever their energy matches with some characteristic emission wavelength (namely, Kα and Kβ) of the absorbing material. Owing to the shape of its appearance on the wavelength versus absorption graph, this abrupt rise in absorption with decreasing wavelength (increasing energy) is known as absorption edge, as shown with dotted curve in Fig. 3
2. The absorption edge wavelength corresponding to a particular transition state (namely, Kα and Kβ) for different elements increases with increasing atomic number. The XRD measurements usually require an intense, collimated, and highly monochromatic beam. As a consequence, it is generally the most prominent, Kα peak that finds application in production of X-rays for application in diffraction analysis, while the neighboring Kβ peak is filtered using an absorbing thin foil (or coating) of a metal (or its compound) having atomic number one or two less than that of the target metal emitting the characteristic Kα radiation. The guiding principle for selection of the absorbing material is that its absorption edge should be located within the Kα and Kβ emission lines of the X-ray source material. For example, when the radiation originating from a Cu target is passed through 20 μm thick Ni filter, the intensity of Kα peak would get attenuated to 42% of incident intensity, while that of the Kβ peak (which is just covered by the absorption edge) will get reduced to

Chapter 3 • X-ray diffraction

91

a mere 0.63% of the original intensity, as depicted schematically in Fig. 3
3. Accordingly such filters are known as β-filters. Similarly foils of Ti and Nb act as β-filters for Kα characteristic radiation of Cr and Mo respectively. The β-filters are usually placed between the specimen and detector, so as to further improve signal-to-noise ratio by removing unwanted radiation produced by fluorescence of specimen.

3.3.4 Total external reflection of X-rays Any kind of electromagnetic radiation incident onto a surface in general undergoes a combination of specular reflection, diffuse reflection and refraction. For X-rays, the refractive index of a material is slightly less than unity. Accordingly, as the angle of incidence (θ, measured from surface tangent) of X-rays is decreased, a stage of total external reflection (similar to the familiar case of total internal reflection of light in optical fibers) is reached, wherein the incident X-rays stop penetrating into the material and begin to undergo near total specular reflection from the surface. This happens both for crystalline as well as noncrystalline materials. The angle at which this occurs is known as the critical angle (θc) for total reflection and is given (in radians) by the following expression: θc 5 λ0

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:7 3 1011 ρ

(3.2)

Absorption edge

where λ0 is the wavelength of incident monochromatic beam of X-rays in meters and ρ is the density of material in kg/m3. The phenomenon of total external reflection finds

X-ray intensity

K1 Linear absorption coefficient of  - filter material

K2 K Original emission spectrum

K1 K2

K

Spectrum after passing through  - filter

Wavelength FIGURE 3–3 Schematic showing application of β-filter for monochromatization.

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application in grazing-incidence techniques, discussed in Section 3.10.3. It is also used in fabrication of X-ray focusing equipment.

3.4 Milestones Like any other branch of science, X-ray techniques too have benefitted from developments in other streams of science and technology, ranging from materials to computing. At the forefront of technological development, this relationship has been symbiotic in nature, as the developments in X-ray techniques have in-turn provided technological push to allied fields, particularly materials science. The versatility of X-ray techniques makes it difficult to tabulate the related developments at one place. A partial timeline depicting major developments in various fields directly concerned with X-rays and allied techniques is provided in Table 3
1. The associated Nobel awards serve as testimony to the importance and versatility of the developments concerning X-ray techniques. In addition to the developments provided in Table 3
1, many more Nobel Laureates have otherwise benefitted from these developments by using the techniques in their respective areas.

3.5 Crystalline materials Before the interaction of X-rays with crystalline materials can be understood, it is important to understand certain aspects regarding the crystalline materials. An understanding of crystal structure not only helps classify the vast spectrum of crystalline materials into a finite number of fundamental structures, but also helps visualize the outcome of their interaction with X-rays. Solid materials are broadly classified as crystalline and amorphous. The crystalline solids are characterized by a periodic arrangement of atoms. The structure of crystalline solids can either be in the form of a single crystal (namely, a diamond crystal or a calcite crystal) or as an assemblage of multiple crystals with distinct boundaries (namely, grains in metals). This section deals with the concepts of crystal geometry, which are essential for dealing with the subject of XRD by crystals.

3.5.1 Space lattice and unit cell The study of crystal structure had started decades before the advent of X-rays or their application in materials science in the form of diffraction analysis (refer Table 3
1). The structure of crystals is based on some periodic arrangement of atoms according to some particular framework, known as space lattice. The space lattice comprises of a three-dimensional arrangement of points, in which the surroundings of every point are identical. For the convenience of drawing on two-dimensional sheet of paper, consider the planar array of points shown in Fig. 3
4, which is formed by repeated translation of lattice points along two translation (basis) vectors a and b, making an interaxial angle α, while the third vector c points outward from the plane of paper. The parameters a, b and α together govern the geometry of the lattice. Since by definition of lattice, this array is considered to extend infinitely along both the directions, we can

Chapter 3 • X-ray diffraction

Table 3–1

93

Timeline of developments in X-ray techniques.

Year(s)

Description

Nobel award

References

1784 1839 1848 1895 1906
08 1912 1912
13 1913 1913 1912
21 1918
22 1929 1929 1931 1953 1960 1962 1964 1978
81 1973
77 1979 1982 1984 1984 1986 1989 1989 1991 2000 2008 2009 2010 2013 2014 2017

Crystal structure Concept of miller indices Concept of space lattice Discovery of X-rays Characteristic Roentgen radiation Scattering of electromagnetic radiation Diffraction of X-rays in crystals Wave nature of X-rays Diffraction of X-rays in gases Reciprocal lattice Determination of structure of colloidal particles Application of two-dimensional Fourier projections Structure of complex ionic crystals Kiessig fringes in thin films Molecular structure of nucleic acids Structure of hemoglobin Structure of boranes Structure of biochemical substances Crystallographic electron microscopy Computer
assisted tomography (CT-scan) Direct method for determination of crystal structures Ordering in liquid crystals and polymers Three-dimensional structure of photosynthetic reaction center Discovery of quasicrystals Multiwire proportional counter GI-SAXS for thin films Formation of high-density plasmas by ultrafast laser pulses Pulsed emission of X-rays Structure of ribosomes Commissioning of linac coherent light source injector Biomolecular simulation program X-ray laser X-ray observation of a helium atom Synchrotron
based SAXS of proteins Extended X-ray absorption fine structure

N.A. N.A. N.A. 1901 Phy 1917 Phy — 1915 Phy 1929 Phy 1936 Chem — — — 1954 Chem — 1962 Med 1962 Chem 1976 Chem 1964 Chem 1982 Chem 1979 Med 1985 Chem 1991 Phy 1988 Chem 2011 Chem 1992 Phy — — — 2009 Chem — 2013 Chem — — — —

[29] [30] [31] [1] [32
34] [35] [36
41] [42] [43] [44
46] [47,48] [49] [50] [51] [52] [53] [54] [55,56] [57,58] [2
6] [59,60] [61,62] [63] [64] [65
67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77]

GI-SAXS, Grazing-incidence small-angle X-ray scattering.

work-out generalized expressions to calculate the distances to various lattice points surrounding any given lattice point (refer inset in Fig. 3
4, e.g.). The space lattice can be expressed in terms of a unit cell—the smallest building block, which when repeated indefinitely, will generate the framework of the corresponding space lattice. The unit cell for a given space lattice can be selected in various convenient ways as shown by the shaded parallelogram toward bottom of Fig. 3
4. Translation of the first unit cell by vectors 6 a/2 and 6 b/2 would center it on a lattice point, similar to the choice of

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Handbook of Modern Coating Technologies

a

b

p

c

2b sin a

b a

p

a Origin

a+2b cos a

FIGURE 3–4 A lattice with lattice translation (basis) vectors a, b having interaxial angle, α lying in the plane of paper and vector c pointing outwards from the plane of paper.

FIGURE 3–5 A three-dimensional space-lattice.

second unit cell shown in the figure. It should be noted that in either of the cases, the effective number of lattice points per unit cell obviously remains one. Such unit cells, which contain only one lattice point, are termed as primitive cell. Extending the discussion to three dimensions, we arrive at a three-dimensional space lattice, an example of which is shown in Fig. 3
5. It is defined by three basis vectors a, b, and c (refer Fig. 3
6) which are designated in the right-handed sense for uniqueness, that is, if the index finger of right hand points in the direction of a, the middle finger and thumb would point in the directions of vectors b and c respectively. The standard notation regarding angles between these vectors designates the angle between b and c as α, between c and a as β and that between a and b as γ. Sometimes, it becomes more convenient to designate the three basis vectors a, b, and c as a1, a2, and a3, respectively.

3.5.2 The Bravais lattices and crystal structure Changing the relative lengths of lattice basis vectors ai and interaxial angles α, β, and γ (refer Fig. 3
6) leads to formation of differently shaped unit cells and hence, different types of lattice systems. In 1848 French crystallographer Bravais discovered that only fourteen types of lattice systems are possible [31]. In his honor, the term Bravais lattice is often used

Chapter 3 • X-ray diffraction

95

c c 

  a

b 

b

FIGURE 3–6 Designation of lattice basis vectors and interaxial angles.

in place of space lattice. The fourteen Bravais lattices are based on seven types of unit cells, corresponding to seven types of crystal systems, into which all possible crystalline materials can be classified. Each crystal system is characterized by its compliance to a particular combination of macroscopic symmetry transformations of rotation, reflection, inversion and rotoinversion. An n-fold rotational symmetry about an axis calls for self-coincidence for every 360 degrees/n degrees of rotation. It is not possible to have a fivefold or higher than sixfold rotational symmetry, as it will lead to gaps when such unit cells are made to fill space. A detailed discussion on lattice systems and associated symmetries is beyond the scope of this chapter and the interested reader can refer [78] for details. Rotational symmetry of a given lattice about different axes gives rise to different sets of equivalent planes. Known as planes of a form or family of planes, these are represented collectively by enclosing the Miller indices (refer Section 3.5.3 for details) in curl brackets {hkl}. The planes of a form are generally characterized by different Miller indices [30], but same d-spacing. For example, all six faces of a cubic lattice are related by symmetry and have the same d-spacing. Likewise, they can be collectively represented as {100} planes. For a tetragonal unit cell, the four side faces belong to one family {100}, while the top and bottom faces form another family {001}. The interplanar spacing, dhkl for parallel planes belonging to the same set (hkl), depends on the indices (hkl) as well as lattice parameters, namely, a, b, c, α, β, and γ. It should be noted that for cubic lattice, the direction [hkl] is normal to the set of planes (hkl) but may not be obviously so for other types of lattice systems. The procedure for designating lattice directions is explained in Section 3.5.3. A crystal is formed through association of a basis with each lattice point. The bases for different crystals range from a single atom to groups of hundreds of atoms. The atomic arrangement is governed by combinations of lattice type and symmetry elements, to form 230 unique space groups. The number of nearest neighbors in the bulk of a crystal lattice is known as bulk coordination number. As an example, the coordination number is six for simple cubic lattice; but for complex crystals, the coordination number is subject to the way it is calculated. For simplest examples of monoatomic crystals such as Cu, where each atom occupies a face centered cubic (FCC) lattice point, the lattice parameter and packing fraction can be straightaway calculated from coordination number and atomic radius, since the atoms are supposed to be touching each other (refer Figs. 3
10
3
13). Diatomic ionic solids such as NaCl have two atoms associated with each FCC lattice point. It should be

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noted that for ionic solids, the atomic radii are affected by degree of ionization—with the negative ions registering an increase in size and vice versa. Furthermore owing to periodicity and symmetry of lattice, there is no way to tell as to which Na1 ion is bonded to which Cl2 atom and so, the term “molecule” becomes moot in the context of crystal structure. The unit cells of proteins may contain thousands of atoms each.

3.5.3 Designation of points, lines, and planes Direction vectors are generally required for expressing relative orientation of certain lattice points with respect to one another. Choosing an arbitrary lattice point as origin, the coordinates of any other lattice point can be arrived at by a position vector r expressed in terms of integral multiples u, v, and w respectively of the basis vectors a, b, and c, as follows: r 5 ua 1 vb 1 wc

(3.3)

As an example, taking origin at the tail of vector p shown in Fig. 3
4, the components u, v, and w of p along a, b, and c are found to be 1, 2, and 0, respectively. Corresponding Miller indices (named after the English crystallographer W.H. Miller) for the crystal direction p are then written as [120] in square brackets. In case the indices happen to contain double digit figures, it is advisable to separate them with commas to avoid confusion, namely [1,12,3]. Describing the direction indices with reference to the framework provided by basis vectors is quite simple as it eliminates the need to account for lengths of basis vectors as well as their interaxial angles. The parameters of length or interaxial angles are required only when one is interested in finding actual length of the direction vectors or distances between certain lattice points of interest (refer inset in Fig. 3
4). The Miller indices are expressed as smallest integers, while negative component of a direction is denoted by an overbar. So, the indices for a direction such as 2, 23, and 1 would be expressed as ½231, while indices for a direction 4, 26, and 2 should be written as 2½231. All possible combinations of the direction indices, including both positive and negative values, represent various directions, which are related by symmetry. These are termed as directions of a form or a family of directions and are represented using pointed brackets , . around Miller indices. For example, the directions [231], [213], ½231, [312], [321], [123], etc. can be collectively represented in the form of a family, as ,231.. Similarly the families ,100., ,110., and ,111. represent respectively the 6 edges, 12 face diagonals, and 4 body diagonals of a cubic unit cell. It should be noted that crystal directions of a family are not necessarily parallel and as the reader would be able to observe in the discussion concerning crystal planes, the same rule remains valid for planes as well. For locations other than the lattice points in primitive unit cells (or lattice points in nonprimitive unit cells or for that matter any other location within the unit cell), the vector r is expressed by adding fractions n, p, and q, respectively, to u, v, and w, as r 5 (u 1 n)a 1 (v 1 p) b 1 (w 1 q)c. Rearranging the terms, we get r 5 (ua 1 vb 1 wc) 1 (na 1 pb 1 qc), that is, a vector from origin up to a lattice point of the unit cell containing the location of interest, plus another vector from that lattice point to the location of interest within the unit cell.

Chapter 3 • X-ray diffraction

97

A plane can be uniquely defined in terms of its intercepts along three noncoplanar direction vectors. The lattice basis vectors form a convenient frame of reference for this purpose. However, if a plane is parallel to any of the vector(s), its corresponding intercept will work out to be infinity. To avoid this situation, Miller introduced the concept of taking reciprocals of the intercepts, thereby converting infinity to zero. Thus the Miller indices of a plane are its fractional intercepts with corresponding crystallographic directions. To make a distinction between notations used for directions and planes, the Miller indices for planes are written in parentheses as (hkl). A plane having indices (hkl) would intersect the three axes a, b, and c at distances of a/h, b/k, and c/l, respectively, from the origin. The procedure for writing Miller indices is explained in Table 3
2 with reference to the (112) plane shown in Figs. 3
7 and 3
8. Some examples for writing Miller indices of planes are shown in Fig. 3
9 for a simple cubic lattice (a 5 b 5 c, α 5 β 5 γ 5 90 degrees). In general, the Miller indices for a set of plane are expressed in terms of the plane that is closest to the origin. However, as shown for (022) and (410) planes in Fig. 3
9, the Miller indices may be attributed to an y plane within the set, or even the whole set taken together. Also note how the origin has to be shifted mentally to find intercepts on the negative side. The interplanar spacing dhkl between adjacent planes having Miller indices (hkl) is defined as the distance between first such plane from a parallel plane passing through the origin. Interplanar spacing can be visualized in the examples shown in Fig. 3
9 in the form of a perpendicular dropped from origin (or shifted origin wherever applicable) to the nearest plane. It is apparent that the planes with large indices have small spacing between them and Table 3–2

Procedure for determination of Miller indices.

1. Write the intercepts of the plane in terms of multiples of the basis vectors a, b, and c 2. Take reciprocals of the intercepts 3. Maintaining their ratios, convert them into smallest integers (multiplying by 4 in the present case) and enclose in parentheses

FIGURE 3–7 A (112) lattice plane making intercepts of 4, 4, and 2 along axes a, b, and c.

4 4 2 1 4

1 4

(112)

1 2

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c

b a

FIGURE 3–8 Intercepts of (112) plane in the unit cell.

c

b a

(b)

c

c

(c)

(f)

c

b

b a

a

(d) c

b

b

(e)

a

a

a

b

b

b

(a)

a

c

c

c

a

(g)

(h)

FIGURE 3–9 Examples of some Miller indices: (a): ð010Þ, (b): (020), (c): (111), (d): ð012Þ, (e): ð110Þ, (f): (142), (g): (022) and (h): ð410Þ

pass through fewer lattice points. On the other hand, planes with low indices have large spacing and pass through large number of lattice points. As an aid to visualization, Figs. 3
10 and 3
11 show sections along (110) and (111) planes respectively for a monoatomic simple cubic crystal, while sections through same planes for a monoatomic FCC crystal are shown in Figs. 3
12 and 3
13. Owing to periodicity of lattice, corresponding to every plane (hkl), there exists a whole set of equidistant parallel planes. It must be obvious by now that planes having Miller indices in

Chapter 3 • X-ray diffraction

99

c

b a FIGURE 3–10 Monoatomic simple cubic crystal sectioned along (110) plane.

c b a

FIGURE 3–11 Monoatomic simple cubic crystal sectioned along (111) plane.

multiples of each other should also be parallel. For example, the (010) planes are parallel to (020) planes and consecutive planes from the (010) set coincide with alternate planes from the (020) set. Planes, whose indices are negative of each other, namely, ð110Þ and ð110Þ, are also parallel but lie on opposite sides of the origin. Regardless of their indices, the set of planes that are parallel to a line, are called planes of a zone and exhibit this relationship in Laue diffraction method discussed in Section 3.8.1.

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c

b

a

FIGURE 3–12 Monoatomic FCC crystal sectioned along (110) plane. FCC, Face centered cubic.

c

a

b

FIGURE 3–13 Monoatomic FCC crystal sectioned along (111) plane showing close-packing along this plane. FCC, Face centered cubic.

3.5.4 Reciprocal lattice We have seen how the orientation and location of various lattice planes can be described using Miller indices. However, since the lattice is theoretically assumed to have infinite dimensions along all directions and since actual crystals too are much larger in comparison to atomic dimensions, the absolute location of a plane is not of much interest from the

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101

perspective of crystallography. Simply stated, we are generally interested more in orientation and periodicity (i.e., spacing) of a set of planes rather than location of an individual crystal plane. As is apparent from discussion so far, there exists an indefinite number of orientations (hkl) in a crystal and corresponding to each orientation, there exists a whole set of parallel planes. It seems very convenient if we could somehow develop a system for collectively representing the planes belonging to each set. This objective was achieved through the concept of reciprocal lattice, as introduced by J. Willard Gibbs and subsequently developed by P.P. Ewald. As we shall see later, since the spacing between lattice planes dhkl is inversely proportional to the spacing between corresponding diffraction patterns, the reciprocal of a real (direct) lattice is naturally associated to its diffraction pattern. Rather than specifying three points for describing the orientation of a plane, one can specify three components of a vector, which is normal to the plane. Essentially this vector would be normal to the entire set of parallel planes described by the family of Miller indices. For convenience, we shall adopt the notation of a1, a2, and a3 in place of a, b, and c for lattice basis vectors. Fig. 3
14 shows a unit cell OADBCEFG described by three noncoplanar vectors a1, a2, and a3 where a1 5 a3 5 a2/2. Line OR is normal the OADB while R is coplanar with CEFG. It should be noted that the reciprocal vector b3 points in the direction of OR, while its tip does not necessarily coincide with point R. Proceeding further, OQ is normal to OCEA while Q is coplanar with BGFD. Finally OP is normal to OBGC and P is coplanar with ADFE. In other

R b3

C a3

E

b1

a1

a2

b2

D R C,G

Q

F

P

A

D R

E,F

C

F

G

E b3

a3 P b1

O,B

Q

E b1

B

P

a3

B b2

F

O

G a2

O,R

G

a1 A

a3 C

b2

a1 A,D Q

b3 P

A a1 O

a2 b2

D

B Q

FIGURE 3–14 Orthographic and (inset) isometric views showing relationship between direct (ai) and reciprocal (bi) lattice vectors.

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words, OP, OQ, and OR are heights of the unit cell normal to the three planes, or simply put, the d-spacings between opposite faces of the unit cell. Again, the points Q and P do not necessarily coincide with the tips of corresponding reciprocal vectors b2 and b1. Mathematically the area of OADB is given by vector (cross) product as a1 3 a2 and the area vector would point along OR (or along 2 OR for a2 3 a1 ). Furthermore the volume of the parallelepiped in the form of unit cell is given by, V 5 a1Ua2 3 a3 . The reciprocal space vectors bi are formed by dividing the area (a vector quantity) of corresponding normal plane by volume (a scalar quantity) of the unit cell as under: a2 3 a3 a1Ua2 3 a3 a3 3 a1 b2 5 a2Ua3 3 a1 a1 3 a2 b3 5 a3Ua1 3 a2 b1 5

(3.4)

The length of reciprocal vectors is expressed in nm21 or Å21. To develop physical understanding of the concept, we consider the volume of unit cell as the product of its base area and height, that is: V 5 AreaðOCEAÞ 3 ðHeight of cellÞ 5 ða3 3 a1 ÞOQ ða3 3 a1 Þ 1 5 ‘b2 5 V OQ

(3.5)

Similarly; b1 5 1=OP and b3 5 1=OR

Thus the magnitude of reciprocal basis vectors equals the inverse of the d-spacing of the planes to which they are normal. So, the tip of vector b1 in Fig. 3
14 represents the entire set of planes corresponding to ADFE face—that is (100) planes, while their spacing d100 equals reciprocal of the length of b1. Similarly the vectors b2 and b3 signify orientation and d-spacing of the sets of (010) and (001) planes respectively. In this manner, the transformation from direct space to reciprocal space maps the set of direct space planes (hkl) to a single point having coordinates h, k, l in reciprocal space. Note that the indices in reciprocal space are specified without parentheses. Extending the discussion further, it can be proved that a vector Hhkl 5 hb1 1 kb2 1 lb3 drawn from the origin to a point hkl in reciprocal space is normal to the plane having Miller indices (hkl) in direct space, while its length is reciprocal of the spacing dhkl between these planes in real space. As an aid to visualize this concept, an example of a two-dimensional direct space lattice along with the corresponding reciprocal space lattice is shown in Fig. 3
15. It is to reiterate that the reciprocal vectors bi are aligned normal to respective pairs of vectors appearing in cross-product in the numerator of Eq. (3.4). As can be observed, the vectors in reciprocal

100

4 a1

(110) (010)

020

100

120

1/d(100) (Å–1)

3

2 (120)

d(100) = 4sin () Å

(Å)

b3

a2 

(410)

1

2

1/d(010) (Å–1) 010

000

(Å)

1

000

d(010) = 2sin () Å

a3

103

010

Chapter 3 • X-ray diffraction

300

b2

110

400

(100)

b1 410

FIGURE 3–15 A direct space lattice (left) and corresponding reciprocal lattice (right).

lattice are normal to their corresponding planes in direct space. Furthermore the planes with higher indices appear closer to the origin in direct space, while they are farther away from origin in reciprocal space. These properties of the reciprocal lattice make it an indispensable tool in crystallographic diffraction studies. The volume of the reciprocal lattice (V ) works out to be reciprocal of the volume (V) of direct space lattice (refer Eq. 3.6). V  5 b3Ub1 3 b2 2 3 a1 3 a2 4 a2 3 a3 a3 3 a1 5 5 U 3 a3Ua1 3 a2 a1Ua2 3 a3 a2U a3 3 a1 ða1 3 a2 ÞU ½ða2 3 a3 Þ 3 ða3 3 a1 Þ ða3Ua1 3 a2 Þ3      ða1 3 a2 ÞU ða2 3 a3 ÞUa1 a3 2 ða2 3 a3 ÞU a3 a1 5 V3 5

5

ða1 3 a2 ÞU ½V a3 2 0 V3

5

ða1 3 a2 ÞUa3 1 5 2 V V

(3.6)

The direct lattice is reciprocal of its own reciprocal lattice, that is, a1 5 ðb2 3 b3 Þ=V , etc., thereby revealing Pontryagin duality of their respective vector spaces. It also follows from Fig. 3
14 that for simple cubic lattice, since α 5 β 5 γ 5 90 degrees, bi would be drawn parallel to ai and have a magnitude of 1/a (since a1 5 a2 5 a3). Thus the reciprocal of a simple cubic lattice is again a simple cubic with a lattice parameter of 1/a. Apparently a simple cubic lattice of unit dimensions would be its own reciprocal.

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3.6 Interaction of X-rays with crystalline materials As a meticulous experimentor with a sound theoretical base, Röentgen performed a number of experiments to ascertain the properties of X-rays immediately following his initial observations of these penetrating but invisible rays. However, owing to their different kind of interaction with matter—for they could not be reflected or refracted using optical mirrors or lenses, nothing could be concluded about their exact character. At the same time, it was thought that X-rays could be another form of electromagnetic radiation, whose wavelength lies in the range of 0.1
0.2 nm and that they could interact with the periodic structure of crystals to produce the effect of diffraction—similar to the phenomenon of diffraction of visible light by diffraction grating, which was well known at that time. It was Peter Paul Ewald’s doctoral work on scattering of electromagnetic radiation [35] that inspired German physicist Max von Laue to perform experiments involving diffraction of X-rays by crystals. Laue thought that if X-rays were electromagnetic in character and if crystals were made-up of periodic arrays of atoms with spacing comparable to the wavelength of X-rays, interaction of X-rays with crystals should give rise to the formation of diffraction patterns. He was soon able to successfully record the first diffraction pattern on a photographic plate. Till the dawn of 20th century, the knowledge about crystal structure was gathered through macroscopic measurements of angles between various facets of single crystals, while their elemental make-up was determined through chemical techniques. Their interaction with X-rays to produce diffraction patterns opened a whole new domain of possibilities in the study of materials. Laue’s experiments were analyzed by English Physicist, Sir William Henry Bragg and his son William Lawrence Bragg. At a rather young age of 22 years, W.L. Bragg was able to explain the phenomenon of diffraction of X-rays by crystals, following which he proceeded to determine the structures of NaCl, KCl, KBr, and KI.

3.6.1 Diffraction of X-rays by crystals Diffraction of X-rays is essentially a phenomenon involving their scattering in all directions by individual atoms. When a beam of X-rays falls on a crystal, it causes oscillations of electrons, which in-turn emit X-rays of same frequency as the incident beam. This emission occurs in all directions and is termed as scattering of the incident beam. The radiation thus scattered from individual atoms undergoes systematic constructive or destructive interference in certain select directions owing to regular arrangement of atoms within the crystal, thereby leading to the formation of a diffraction pattern. The conditions for constructive or destructive interference occur due to introduction of path-difference between the wavelets diffracted by different sets of atoms within the crystal. The phenomenon can be easily understood by considering Bragg’s law. Fig. 3
16 shows schematic of a crystal being exposed to X-rays. It should be noted that the interaction of X-rays with matter is rather weak and so, only a small fraction of the incident beam will be scattered by the atoms. First, we consider the topmost plane of the crystal, where the incident X-rays make an angle θi with the plane. Note that in XRD parlance, the

Chapter 3 • X-ray diffraction

2′′

Normal to Planes

Fi

1 2

Fe 1′′

2’ 1′

3

3’ M

4

105

I Fi

N

e

i A

4’

C

B i e

II

III

Q

P E

Fe

D S

R F

d

2

FIGURE 3–16 Scattering of X-rays by atoms and formation of diffraction pattern.

angles are defined from the surface tangent—unlike surface normal, which is the norm in optics. As said earlier, each atom will scatter the incident beam in all possible directions. Accordingly the rays 1 and 2 will be scattered in all directions by atoms C and B, respectively. Two such directions, namely, 10 ; 20 and 100 ; 200 are shown in the figure. The difference in the paths traversed by rays 1 2 C 2 10 and 2 2 B 2 20 is given by: Path Difference 5 CM 2 BN 5 BCcosθi 2 BCcosθe

(3.7)

The rays 10 and 20 would undergo constructive interference if they are in phase, which would happen if the path-difference is zero. This condition would be satisfied for θe 5 θi and will result in formation of strong emergent beam. The resultant intensity of emergent beam would diminish as θe deviates from θi. Thus elastic scattering from regularly spaced atoms lying on a planar crystal surface leads to a kind of “reflection” where the angles made by incident and emergent beams with the crystal surface are equal. Accordingly the symbol θ will be used henceforth in place of θi or θe . Since X-rays interact rather weakly with the atoms, a major portion of the incident beam passes-on to the layers beneath the surface. Accordingly the resulting diffraction pattern incorporates cumulative effects of not only the surface layer, but up to a certain depth below the surface. Considering interference between rays 10 and 30 reflected from the two topmost planes (planes I and II), path-difference works out to be PD 1 DQ or 2dsinθ. According to Bragg’s condition, constructive interference will take place whenever path-difference is an integral multiple of wavelength, λ. Mathematically: nλ 5 2dsinθ or λ 5 2dsinθ for n 5 1; i:e: ; for first order reflection from planes I and II

(3.8)

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Similarly Bragg’s condition for constructive interference between rays 10 and 40 reflected by planes I and III respectively, works out to be: nλ 5 RF 1 FS 5 4dsinθ or λ 5 2dsinθ for n 5 2; i:e: for second-order reflection from planes I and III

(3.9)

Thus second-order reflection from planes I and III coincides with the first-order reflection from planes I and II. In general, higher order reflections from successive parallel planes will coincide with the first-order reflections from the first two planes of the family. For the same reason, the second-order diffraction for (100) planes will superimpose over the first-order diffraction from (200) planes and so on. Accordingly n is always taken to be unity and the Bragg’s condition is therefore written as: λ 5 2dsinθ

(3.10)

To make the discussion more complete, it needs to be considered that second or higher order constructive interference between the rays reflected from planes I and II can occur if path-difference equals nλ, where n $ 2. However, the typical wavelength of X-rays used for diffraction analysis lies in the range of 0.1
0.2 nm, which is comparable to the interatomic distance. Hence, higher order diffraction peaks may not occur at all while using X-rays, since that may require sinθ in Eq. (3.8) to be greater than 1, which is not possible. However, if the wavelength were small—as is the case with electron diffraction, it would be possible to “fitin” one or more wavelengths within the path-difference. Hence, higher order peaks are quite uncommon in XRD, while they are a norm in electron diffraction.

3.6.2 Ewald sphere The preceding discussion implies that wavelength of incident X-rays puts a limit on the minimum spacing of planes for which diffraction (to be precise, constructive interference) can occur. Since planes with small interplanar spacing have large Miller indices, it means that strong (first order) diffraction peaks can be recorded only up to certain limit of Miller indices. This condition can be easily worked-out through Ewald sphere construction. Fig. 3
17 shows perspective projection of a reciprocal lattice corresponding to a simple cubic lattice in direct space. As noted earlier, the reciprocal of simple cubic lattice is again a simple cubic and so, makes it easier to understand the concept. We take S0 as a unit vector in the direction of incident beam and Si as unit vectors along various diffracted beams. Then vector S0/λ lies parallel to the incident radiation, while its magnitude is reciprocal of the wavelength. Placing the tip of this vector at a lattice point (henceforth termed as origin) in reciprocal space, Ewald sphere of radius 1/λ is constructed at the tail of S0/λ. Lattice points lying on the Ewald sphere in reciprocal space (namely, 122 and 122 in Fig. 3
18A and B) correspond to the sets of planes, which would result in diffraction under the given conditions of wavelength and direction of incident X-rays, while the vectors S1/λ and S2/λ drawn to these lattice points depict the directions of corresponding diffracted beams.

Chapter 3 • X-ray diffraction

S0 

Ewald sphere

b3

107

b2

b1 Origin

Limiting sphere

FIGURE 3–17 Construction of Ewald sphere and limiting sphere.

(A) 002 122 122 S2/λ

101 001 101

S1/λ

b3

S0 λ

b2 b1

Ewald sphere

Origin

(B) 122

101 Origin

S2/λ S0/λ

S1/λ 122

b2 b1 101

Ewald sphere FIGURE 3–18 (A) Side and (B) top views of Ewald sphere and reciprocal lattice points.

If the crystal is slowly rotated about the origin, the vector S0/λ will change its direction relative to the lattice, while its tip remains hinged at the origin. During the course of rotation, the surface of Ewald sphere will successively intersect different lattice points. Likewise, if the crystal is rotated about all three axes in space, lattice points corresponding to all such sets of

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planes, for which diffraction is possible, will intersect the Ewald sphere at some instance of time or the other. The set of all such lattice points in reciprocal space that can intersect the Ewald sphere can be identified by constructing a limiting sphere centered at the tip of S0/λ (refer Fig. 3
17). The radius of this limiting sphere equals diameter of the Ewald sphere. Only the hkl points lying inside or on the surface of the limiting sphere can produce diffraction when the crystal is suitably oriented. Since radius of Ewald sphere (S0/λ) will increase on decreasing the wavelength of incident X-rays, it follows that the Ewald sphere corresponding to a shorter wavelength can intersect with a larger number of reciprocal space lattice points, while that corresponding to a longer wavelength will contain fewer lattice points. In other words, shorter wavelengths can produce diffraction patterns corresponding to planes having higher Miller indices (i.e., smaller d-spacing), while longer wavelengths would be able to form diffraction patterns only for planes of lower indices.

3.6.3 Extinction of X-rays Extinction refers to an increase in absorption by a single crystal under conditions suitable for Bragg reflection. The absorption occurs not just for the transmitted beam, but also affects the reflected beam. It was in 1914 that Bragg [79], while passing an X-ray beam through a thin flake of diamond and subsequently through a crystal of rock salt (so oriented, as to reflect the incident beam), both the reflected beams being detected by an ionization chamber, observed a drastic reduction in the intensity of transmitted beam (as reflected by the rock salt crystal) whenever the condition for reflection was met for the thin diamond flake. The factors responsible for this phenomenon are explained below. As said earlier in the section concerning absorption of X-rays, the transmitted beam gets reduced in intensity both due to Bragg reflection as well as absorption through various thermal and nonthermal processes. For perfect crystals, the moment crystal gets so oriented, as to satisfy the condition for Bragg reflection, the absorption increases by around 100 times. At such high levels of absorption, the transmitted beam does not penetrate far into the crystal and so, the lower layers do not interact with the incident X-rays. The effect is known as primary extinction and it not only affects the transmitted beam, but also the reflected beam. Primary extinction occurs because the rays undergo a phase shift of π/2 on reflection by an array of atoms. Likewise, a doubly reflected ray will have a phase shift of π. So, even though the doubly reflected ray would be parallel to the transmitted beam, but would destructively interfere with it. Similarly a triple-reflected ray will reduce the intensity of reflected beam. Obviously the number of rays decreases with each reflection and so would be their annihilation effect. The transmitted beam therefore loses energy not just by reflection of a part thereof, but also by destructive interference with the out of phase, doubly reflected beam. Same phenomenon of destructive interference serves to adversely affect the reflective power of the crystal. Furthermore since the primary beam does not reach lower layers of the crystal, the reflections too are the result of contributions from the outermost skin layers of the crystal up to a depth of around 1 μm.

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109

3.6.4 Determination of crystal structure and lattice parameter It follows from the discussion in previous subsections that for a known crystal structure, one can easily determine the directions corresponding to constructive interference of radiation, when the crystal is irradiated by a collimated beam of monochromatic X-rays. However, the converse of this problem is not as straightforward—especially for complex crystals (namely, proteins), since placement of diffraction dots on a photographic film alone does not provide complete information about the crystal structure. For crystals, whose basis comprises of two or more atoms, in addition to knowing the diffraction directions, it becomes important to quantify the beam intensities as well, namely, using a diffractometer. For complex crystals, structure determination might require rigorous analysis of diffraction data, along with the results of chemical tests and macroscopic observations. On the other hand, the structure of simple crystals with high symmetry can be determined relatively easily. It also helps develop an understanding of the basic procedure, which is essential for analyzing diffraction data pertaining to structures with higher degree of complexity. The structure of a cubic crystal with monoatomic basis can be assessed by substituting the expression for lattice spacing in the Bragg’s equation as under: λ2 5 4d 2 sin2 θ a2 sin2 θ 54 2 h 1 k2 1 l2



2  2 2 2
1
_ 5 h 1 k 1 l for cubic system.sin2 θ 5 λ h2 1 k 2 1 l 2
d2 2 2 a 4a


(3.11)

The above expression holds for all Bravais lattices belonging to the cubic system, namely, SC, BCC, and FCC. It is possible to write down all possible combinations of  2 h 1 k2 1 l 2 and arrange them in ascending order, which would also be the ascending 2 order the same ratios  2 for angle, θ. Since λ and a are constants, values of sin θ will follow 2 2 as h 1 k 1 l . Occurrence of reflection for all combinations of h2 1 k 2 1 l 2 is feasible only for the simple cubic lattice, while reflections in certain directions get canceled for BCC and FCC lattices, thereby facilitating distinction between the three lattices of the cubic system. For example, in a monoatomic BCC lattice, the corner atoms lie on the (100) planes, while the body-centered atoms lie on the (200) planes. The count of atoms per unit area on a (200) plane is same as that for a (100) plane. Accordingly if the firstorder reflection from two adjacent (100) planes is having a path-difference of λ, its pathdifference from (200) planes will be λ/2, thereby leading to complete cancellation of intensity through primary extinction. Following similar reasoning, it is possible to frame extinction rules for all possible diffraction directions pertaining to a given lattice system. The rules pertaining to cubic system are given in Table 3
3 to serve as an aid to understanding the concept. The lattice structure can be determined by finding ratios of sin2 θ corresponding to the recorded θ values of diffraction peaks and comparing them with the ratios mentioned in Table 3
3. An example is provided in Section 3.10.1.1.

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Table 3–3

Extinction rules for cubic crystal system.

Miller indices

Lattice structure BCC

SC hkl



h2 1 k2 1 l2

100 1 110 2 111 3 200 4 210 5 211 6 220 8 221 9 310 10 311 11 222 12 321 14  Ratios of h2 1 k2 1 l 2



FCC

All of  2 values h 1 k2 1 l 2

Even values of ðh 1 k 1 l Þ

All odd or all even values of h, k, and l

1 2 3 4 5 6 8 9 10 11 12 14 1:2:3:4:5:6:8. . .

1, Not allowed 2, Allowed 3, Not allowed 2, Allowed 3, Not allowed 4, Allowed 4, Allowed 5, Not allowed 4, Allowed 5, Not allowed 6, Allowed 6, Allowed 2:4:6:8:10:12. . . or 1:2:3:4:5:6:7. . .

Not allowed Not allowed Allowed Allowed Not allowed Not allowed Allowed Not allowed Not allowed Allowed Allowed Not allowed 3:4:8:11:12. . .

FCC, Face centered cubic.

3.6.5 Estimation of crystallite size For d-spacings corresponding to a path-difference, which is only slightly different from an integral multiple of wavelength, the photons “reflected” by successive planes lying beneath the top layer will be progressively out of phase against the ones reflected by the topmost few planes. In such a scenario, the planes corresponding to 180 degrees phase shift would be lying at considerable depth below the outermost plane. However, sufficiently deep planes may become nonexistent for crystallites of small sizes. As a result, complete cancellation of the scattered beam will not take place corresponding to directions for which the pathdifference varies only slightly from an integral multiple of wavelength. This will result in a relatively fuzzy diffraction pattern, which, from the perspective of diffractometers, is termed as line broadening. An estimate of the crystallite size (thickness, t) is given by the historical equation developed by Scherrer in his paper concerning determination of major and the inner structure of colloidal particles by means of X-rays [47], which solves to give: t5

0:9λ BcosθB

(3.12)

Here, λ depicts the wavelength (in any suitable units of length) of monochromatic X-rays used in the diffraction experiment, B refers to full width at half maximum (FWHM) of the given diffraction peak (in radians) occurring at the location 2θB. It is apparent that B would work out to be broader for smaller values of t, that is, for smaller-sized crystallites and vice versa.

Chapter 3 • X-ray diffraction

111

3.7 Specimen preparation There is a whole spectrum of combinations of specimens and analyses types that can be done through XRD. Specimens may be in the form of single crystals, polycrystalline materials, powder conglomerates, thin films, biomolecules, and so on. Commensurate with the title of this handbook, the present section provides an outline of specimen preparation procedures for polycrystalline metallic materials in uncoated or coated condition. Further detail or procedures pertaining to other types of specimens can be found in relevant literature [27,80]. XRD is inherently a nondestructive technique and does not require much in terms of specimen preparation. A primary requirement for XRD is that the specimen surface should be flat with good finish—unless there is specific interest in carrying out analysis under the given surface conditions—namely, for specimens coated with some thin film. Besides, specimen preparation also depends on the location of interest, that is, whether the surface or bulk of the specimen is to be characterized. The latter would require sectioning and essentially render the technique as destructive. Sometimes, sectioning could also be required for extracting specimen from components of large dimensions that cannot be accommodated on the stage of standard laboratory equipment. It might be advisable to consider use of portable diffraction equipment under such situations; though there would obviously be some compromise in terms of precision and capability. It is clear from the above discussion that some surface-finishing, flattening, or sectioning is often required while preparing specimens for XRD analysis. Most of these operations can be readily done using saws, surface grinders, slitting wheels or angle grinders, and so on (refer Fig. 3
19). Soft materials, such as aluminum should only be sectioned using some hard saw or microtome, so as to avoid abrasive particles from getting embedded into the specimen. While performing above operations, care needs to be exercised at all times not to

Specimen

FIGURE 3–19 Specimen extraction for X-ray diffraction analysis.

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let the specimen heat-up or hold it too tight in the machine’s mount—especially for specimens meant for residual stress measurements. Any sectioning or abrasive machining operation will leave a plastically deformed layer, which can be up to a few micrometers in thickness—often extending beyond the zone up to which X-rays can penetrate into the material. Hence, it is important to limit the thickness of plastically deformed layer in the first place and its subsequent removal through some less abusive processes, such as manual polishing and eventually, through electrochemical polishing or chemical etching (namely, using Nital etch for ferrous materials). The amount of material removed through chemical etching can be determined by measuring thickness of specimens before and after etching. In general, chemical dissolution of 2
10 μm layer from the surface should be sufficient to remove plastically deformed layer. To prevent extensive roughening of surface during the course of electropolishing or etching, it might help to prepare the specimen through a cyclic process of etching to remove 1 or 2 μm of material, followed by light polishing on a fine-grit emery paper, making sure to end the cycle with etching. Coated specimens should not be subjected to any of the above specimen preparation steps. For specimens coated with crystalline films up to several tens of nanometers thick, or amorphous coatings having thickness up to of a few micrometers, X-rays can easily penetrate through the coating to produce diffraction from the underlying substrate, while signal from the film would be much weaker, unless grazing-incidence method is used. However, in case the coated specimen does not possess a flat surface, one can either opt for X-ray characterization using a smaller cross-section X-ray beam, or make corrections in the diffraction data (possible for regular, namely, cylindrical specimens) or plan to fabricate a flat specimen using the same material, processing and coating deposition, by which the actual component had been prepared. While mounting the specimen thus prepared onto the XRD equipment, its flat surface must be made coplanar with the plane on which the machine is calibrated to make measurements. This task can be simplified by using a specimen-holder (refer Fig. 3
20), which allows mounting by pressing the specimens against clay-dough, so that their flat surface becomes coplanar with the top face of the specimen-holder.

3.8 X-ray diffraction methods Broadly speaking, the XRD measurements can be made either on transmitted or backscattered radiation, or both. The diffraction procedure to be followed in a given case depends on specimen, type of analysis, and equipment available. Fundamental diffraction procedures are briefly explained in following subsections.

3.8.1 Laue method As said earlier, Max von Laue was the first to perform diffraction experiments using X-rays. He irradiated a single crystal using white X-rays, so that individual sets of hkl planes diffracted a particular wavelength that satisfied the Bragg condition for the given interplanar d-

Chapter 3 • X-ray diffraction

113

Specimens

Aluminium holder FIGURE 3–20 Mounting of specimens for XRD. XRD, X-ray diffraction.

spacing and orientation. As explained in previous sections, the set of planes, which are parallel to a line, are called planes of a zone. The diffracted beams originating from the planes of a particular zone emerge in the form a cone. The axis of the cone thus formed coincides with the zone axis, while its semiapex angle equals the angle between zone axis and beam direction (refer Fig. 3
21). Accordingly the spots on photographic plate can be seen to lie along conic sections—namely, on elliptical curves for transmitted radiation and parabolic curves for back-scattered radiation.

3.8.2 Rotating crystal method This method involves rotation of a single crystal placed in the path of a collimated beam of monochromatic X-rays. As shown in Fig. 3
22, a photographic film is so placed, as to form a cylinder around the crystal’s rotation axis. The beams diffracted by individual sets of hkl planes each form cones, which are coaxial with the crystal’s axis of rotation. The intersection of these cones with the coaxially placed cylindrical film occurs along circular trajectories, which open-up as lines on straightening the film.

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Zone axis Photographic plates Transmission cone Laue points Crystal Laue points

Incident beam

Backscatter cone

Zone axis

FIGURE 3–21 Laue method.

Crystal

Incident beam Photographic film FIGURE 3–22 Rotating crystal method.

3.8.3 Hull/Debye
Scherrer powder method Powder method is one of the most widely used procedures in materials science, as most metals and alloys have polycrystalline grain structure, which is more or less similar to an assemblage of randomly oriented powder particles. Owing to very large number of crystallites and their random orientation, when a powder specimen is placed in the path of a collimated beam of monochromatic X-rays, all such sets of hkl planes, which can produce diffraction by satisfying the Bragg’s condition, will do so, with each set forming its own cone of diffracted

Chapter 3 • X-ray diffraction

Back-scatter cone

Photographic film Transmission cones

Incident beam

Polycrystallin specimen

115

2

FIGURE 3–23 Hull/Debye
Scherrer powder method.

beams, all cones being coaxial with the axis of incident beam and having semiapex angle 2θ corresponding to the Bragg condition (refer Fig. 3
23). A flat photographic plate placed normal to the incident beam on either side of the specimen would intersect these cones to form Debye
Scherrer rings. Another approach is to place the photographic film wrapped in cylindrical fashion around the specimen, with the film axis being orthogonal to that of the incident beam (refer Fig. 3
23). If the number of crystallites is large, their cumulative effect is similar to that of rotation of a single crystal and the resulting arcs on the film are formed as continuous curves. However, their appearance becomes grainy for lesser number of crystallites in the specimen, which might necessitate switching from 1D detectors to 2D detectors on modern diffraction equipment [81]. Any bias with respect to orientation of crystallites is termed as crystallographic texture and manifests as relative strength of the diffracted beams corresponding to directions of preferred orientation [82]. Over the course of years, the photographic film has got replaced with solid state detectors, which have not only helped improve the angular accuracy by several orders of magnitude, but also made it possible to quantify the relative peak intensities. Development of two-dimensional detectors has brought together the merits of photographic plates and solid state detectors [83]. At present, the commercially available diffraction equipment offers angular resolution (goniometer step-size) of 0.0001 degree or even better. All these capabilities are of prime importance in addressing characterization requirements of present-day materials scientists.

3.9 Powder diffractometer geometry As said earlier, a materials scientist is often dealing with characterization of polycrystalline materials, which facilitates the application of powder method. Furthermore the transmitted patterns are generally too weak, especially in case of metallic specimens thicker than a few tens of micrometers. Accordingly most of the diffraction studies in materials science are based on back-scattered radiation. As a consequence of enhancement in complexity and precision of X-ray equipment over time, the techniques have progressed from the most basic scan for bulk material to more sophisticated analysis techniques capable of characterizing thin films. Before attempting to learn different diffraction techniques, it is important to understand a few terms regarding geometry of the diffraction equipment.

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Various rotational and translational degrees of freedom in modern diffractometers facilitate irradiation of sample from the desired direction and detection of beams diffracted in different directions. Fig. 3
24 identifies different axes of a diffractometer using Eulerian cradle. As an aid to visualization, Fig. 3
25 shows some axes overlayed on a picture of Panalytical X’Pert Pro MRD. The main axes in the XRD equipment are meant for coaxial rotation of sample and detector in the plane of incident and scattered beams. Detector rotation is controlled by the 2θ axis, while sample rotation in the plane of diffraction is controlled by the ω-axis. 2θ signifies angle between incident and diffracted beams (refer Figs. 3
16 and 3
25), while ω refers to the angle between specimen surface and the incident beam of X-rays. In the most basic equipment, which can only perform 2θ/θ scan, ω is same as θ (i.e., always half of 2θ). The resulting scan shows diffraction peaks from the lattice planes oriented parallel to the specimen surface. Practically as the beam is not fully collimated, all those lattice planes, whose orientations with respect to the specimen surface lie within the divergence angle of the incident beam, will contribute toward diffraction peaks. For equipment permitting independent control of ω and 2θ axes, it becomes possible to record diffraction peaks for those lattice planes, which are inclined at a given angle to the specimen’s surface. The angle between normal to specimen’s planar surface (vector Z) and normal to lattice planes producing the diffracted beam (vector N) is denoted by ψ (psi). Apparently the incident beam, diffracted beam and normal N all lie in one plane and the angle between incident and diffracted beams is bisected by the normal N, while the normal to specimen surface, Z would be oriented differently. Furthermore it should be obvious that for equipment permitting only 2θ/θ scan, vectors N and Z would be collinear and hence, the tilt angle ψ would always be zero in such a geometry. The ability of diffraction equipment to record diffraction pattern for different ψ angles allows estimation of residual stress. Y X Z Rotational and translational DoF provided on specimen stage -axis

Incident beam

-axis

,2 axes

Plane of diffraction

2 -axis (for detector)

Detector

FIGURE 3–24 Configuration of an X-ray diffractometer.

Chapter 3 • X-ray diffraction

117

Sample stage Specimens mounted in aluminium holder X-ray source Detector

 2

–

Z

N

2,–axes

–axis



2

FIGURE 3–25 Diffraction geometry of Panalytical X’Pert Pro MRD.

More advanced diffractometers permit additional rotational and translational degrees of freedom through Eulerian cradle (refer Fig. 3
25), Kappa goniometer or Universal Motion Concept (namely, Bruker AXS). The χ (chi) axis controls rotation in a plane normal to the plane of diffraction (which contains ω and 2θ angles). The in-plane rotation of sample about its surface normal (i.e., azimuth angle about vector Z in Figs. 3
24 and 3
25) is controlled by φ axis. Translation along X and Y (TX and TY) permits bringing the specimen’s area of interest into the path of X-ray beam, while translation along Z (TZ) allows precise location of specimen surface at the intersection of incident beam and ω axis. Rotation about X and Y (i.e., RX and RY) on the specimen stage helps control precession by aligning specimen’s normal (Z) with rotation axis φ. To summarize, the degrees of freedom ω, χ, φ, TX, TY, TZ, RX, and RY are meant for locating and orienting the specimen in the path of the incident beam, while 2θ controls the angular position of detector. To facilitate measurements that are noncoplanar with the plane of diffraction (i.e., measurement in-plane with specimen surface) two additional degrees of freedom are provided to the detector. One is translation (T2θ) in the radial direction along 2θ, while the other is rotation (2θχ) about the in-plane rotation axis (namely, Rigaku

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SuperLab diffractometer). The in-plane rotation axis lies in the diffraction plane and is perpendicular to the 2θ direction.

3.10 Powder diffraction measurements The kind of information that can be extracted from an X-ray measurement depends on the diffraction geometry. Traditionally only out-of-plane measurements were possible (refer Fig. 3
26), but recent advances in instrumentation have made it possible to carry out in-plane measurements as well. As mentioned in the beginning of this chapter, thin films have been at the forefront of advancements in materials science. Determination of physical, chemical and mechanical properties of thin films is both important and challenging—primarily because in comparison to the substrate, films generally contain a miniscule amount of material and second because these parameters often follow anisotropic distribution along thickness of the film. Despite imposition of constraints when dealing with thin films, X-ray techniques offer inherent advantages, such as nondestructive nature of the procedure, flexibility in selection of sampling area and depth, possibility of performing analysis under conditions similar to those in the operating environment, etc. It is worth mentioning here that while some recent X-ray techniques have been developed especially from the perspective of thin film analysis, a major chunk of the diffraction techniques were essentially meant for characterization of bulk material and subsequently adapted for thin films. Accordingly for many procedures, a clear-cut demarcation between techniques meant for bulk or thin film analysis may not exist. Various diffraction and reflection techniques are discussed in following subsections, along with notes regarding their suitability for thin films.

Symmetric reflction

Incident beam Specimen surface normal Lattice plane normal Diffracted beam

=0 = 2

=



 t





2

Asymmetric reflection

Specular reflection

~c In-plane reflection

2

Specimen FIGURE 3–26 Schematic of in-plane and out-of-plane diffraction measurements.

Chapter 3 • X-ray diffraction

119

(a)

(b)

FIGURE 3–27 Angular limits for 2θ/θ scan: (A) lower limit as detector will receive glare from incident beam and (B) upper limit due to physical interference between X-ray tube and detector assemblies.

3.10.1 Symmetric reflection measurement The most commonly used out-of-plane measurement is the symmetric reflection, also known as Bragg
Brentano scan. It involves turning the detector by 2θ corresponding to rotation of the specimen surface by θ (or ω). Some machines achieve the same relative motion by keeping the specimen stationary, while the X-ray tube and detector are turned by equal angles in opposite directions. In either case, the lower value of scan angle (2θ) is limited by the glare from strong incident beam, while the upper limit is imposed by physical interference between the X-ray source and detector (refer Fig. 3
27A and B).

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In 2θ/θ scan, the detector records reflections from those lattice planes, that are oriented parallel to the specimen’s surface. In other words, the diffraction vector (the vector N, which bisects the angle between incident and scattered beams) is always normal to the specimen surface. In case of a polycrystalline specimen, as θ is increased, planes with lesser d-spacing (higher Miller indices) will successively contribute toward diffraction pattern. The procedure is generally used for determining lattice structure of polycrystalline materials from recorded diffraction peaks.

3.10.1.1 Structure determination Fig. 3
28 shows a 2θ/θ scan using Cu Kα radiation (λ 5 1.54 Å) for a steel specimen, wherein fluorescence has been removed by using a secondary monochromator [84]. The lattice planes corresponding to the observed peaks have been identified by using extinction rules, as summarized in Table 3
4. It is noteworthy here that since iron is already known to have BCC lattice structure at room temperature, the sin2θ ratios corresponding to just three peaks have been multiplied with 2 to yield the ratios corresponding to BCC structure given in Table 3
3. The lattice parameter (a) corresponding to the cubic system (BCC in the present case) can be calculated from any one of the three peaks by rewriting Eq. (3.11) as under:

Intensity (a.u.)

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ2 a5 ðh2 1 k2 1 l 2 Þ 4 sin2 θ

500 450 400 350 300 250 200 150 100 50 0

(3.13)

(110)

(200) 30

50

(211) 90

70

110

130

2 FIGURE 3–28 2θ/θ scan of SAE 8620 steel specimen [84].

Table 3–4

Determination of lattice structure.

i

2θi

sin θi

sin2 θi

1 2 3

44.55 64.65 82.35

0.3791 0.5347 0.6584

0.1437 0.2859 0.4334



Ratios

sin2 θi sin2 θ1

1 1.99 3.02

 Normalized ratios 2 3.98
4 6.03
6

Lattice planes (110) (200) (211)

Chapter 3 • X-ray diffraction

121

The lattice parameter works out to be 2.87 Å in the present case, which corresponds to the lattice constant of iron reported in the literature [85]. It is important to mention here that there is not much importance associated with the standard lattice parameter of pure iron, or for that matter, of individual grades of steels, since it exhibits considerable variation, depending on composition and processing.

3.10.1.2 Application to coated specimens Owing to relatively high angle of incidence in this procedure, the X-ray beam penetrates several tens of micrometers into the specimen. As a result, the thin films would produce a weak diffraction pattern, which would be accompanied by a strong diffraction from the underlying substrate. So, the 2θ/θ scan is not quite suitable for characterizing thin films. Rather, the method can be successfully used for determining lattice structure of the underlying substrate, which has been coated with a thin crystalline film (with film thickness on the order of a few nanometers) or with amorphous coatings as thick as a few micrometers.

3.10.2 Asymmetric reflection measurement Unlike symmetric reflection, which always records reflections from planes parallel to the specimen surface, the asymmetric method records reflections from planes which are tilted with respect to the specimen surface. The procedure has traditionally been used as a nondestructive technique for estimation of residual stress. A variant of the procedure, termed as small-angle X-ray scattering (SAXS), using very small angle of incidence is suitable for characterization of thin films. Both these procedures are discussed below.

3.10.2.1 Estimation of residual stress XRD is a widely used nondestructive technique for residual stress estimation [86
91]. The procedure involves determination of strain by measuring d-spacings of some suitable set of lattice planes, which are oriented differently in relation to the specimen’s macroscopic directions. The information thus obtained is then used for estimating the corresponding stresses. Diffraction peaks provide information about both micro- and macrostrains. Microstrains (namely, those resulting from quenching) manifest as random variation in d-spacings (corresponding to any given set of hkl planes) within individual grains, thereby resulting in broadening of corresponding diffraction peaks. On the other hand, the alteration in d-spacing of a given set of planes under the influence of macrostrain is more systematic and manifests as a shift in corresponding diffraction peak. The peak-shift depends on the orientation of these planes in relation to the direction of macrostrain. The effect of peak-shifting is more pronounced for diffraction from planes with higher Miller indices, though their peaks are not as intense owing to lower atomic density. Accordingly diffractometers capable of achieving 2θ values in excess of 150 degrees are desirable for residual stress estimation. Residual stress estimation can be done by tilting the specimen either about ω-axis (ψ-tilt) or about χ-axis (refer Fig. 3
32). The χ-tilt measurements are generally done with pointfocus configuration using poly or monocapillary optical module for minimizing defocusing

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effects. These measurements also require a more complex design of diffractometer, namely, that shown in Fig. 3
25, using an open Eulerian cradle. The ψ-tilt measurements on the other hand are carried out using line-focus configuration and can be done on any diffractometer that permits independent motion of specimen (ω) and detector (2θ) axes. Only this latter method is therefore described in this section. The systematic variation of d-spacing with orientation is conveniently described as dϕψ in terms of the azimuth (φ) and tilt (ψ) angles (refer Fig. 3
29A and B). This dependence causes a shift in the diffraction peak for different values of φ and ψ, thereby leading to the formation of noncircular Debye
Scherrer rings in the powder (polycrystalline) pattern [92].

(a)

Z, Specimen surface azimuth



d 90



d 

N1

d o

a1

1

N2

2

21



Incident beam a2 Debye cone

22

Detector



(b)

 d 90

Detector N1

d 

d 





21

1

2

22

a1 a2

Incident beam N2 Detector



FIGURE 3–29 Estimation of residual stress based on diffraction from differently oriented hkl planes belonging to the same set, while specimen surface is under (A) tensile and (B) compressive stresses.

Chapter 3 • X-ray diffraction

123

The estimation of strain and corresponding stress in the crystal lattice is made through application of classical continuum mechanics, based on the linear elastic distortion models of Reuss or Voigt [93,94]. The Reuss model assumes stress to be homogeneous over differently oriented crystallites, thereby resulting in heterogeneous distribution of strain. The Voigt model on the other hand assumes homogeneous distribution of strain, which results in heterogeneous distribution of stress. For a bar made of an isotropic material and loaded with uniaxial stress σy along the longitudinal (y) direction, the corresponding strains in various directions are given by: εy 5

σy E

εx 5 εz 5 2 νεy

(3.14) (3.15)

Here, E is Young’s modulus and ν is Poisson’s ratio. For a specimen subjected to tensile stress, the spacing (along longitudinal direction) for lattice planes oriented perpendicular to the surface will be increased, while due to Poisson’s ratio, it will get somewhat reduced for the planes parallel to the surface. However, it is not possible to measure εy by XRD, since it requires recording of diffraction by planes, which are oriented perpendicular to the longitudinal direction, that is, ψ 5 6 90 degrees and X-rays can penetrate only to a very limited depth in the metallic specimens. However, it is possible to measure strain over a certain range of tilt, namely, 240 # ψ # 40 degrees. These measurements can then be used for calculating the uniaxial internal strain εy. In principle, it is possible to estimate εy by recording diffraction patterns for just two values of tilt, namely, ψ 5 0 and some other value, say ψ 5 40 degrees. The corresponding measured strains are termed as ε33 and εψ. This procedure is generally used in portable residual stress equipment and makes a fair trade-off between speed and accuracy. Once εy is known, the corresponding stress σy for the free surface can be estimated using the following equation: σij 5

E εij 1 λεkk δij 11ν

(3.16)

where δij is the Kronecker delta and λ 5 ð1 1 ν ÞνE ð1 2 2ν Þ is the Lame’s parameter, which is a function of the rigidity and compressibility of the material. For details of treatment, the reader can refer to Appendix A in Ref. [95]. The preceding discussion treats stress and strain in the crystallite or laboratory frame of reference. As an aid to understanding, the relationships between crystallite or laboratory coordinate system (Li) and specimen coordinate system (Si) are depicted in Fig. 3
30. The diffraction peaks from lattice planes hkl are obtained whenever they are so oriented, as to satisfy Bragg condition in the laboratory coordinate system Li. While the laboratory and specimen coordinate systems are inherently independent of each other, it might be of interest to know the stress along some direction of interest along the specimen surface—namely, direction of rolling or drawing. If the direction of interest makes an angle φ with the direction of principal stress σ11 then estimation of stress (σϕ ) in the direction of interest requires

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Handbook of Modern Coating Technologies

S3 L2



Specimen surface

L1

S1

11

22



S2  L3

FIGURE 3–30 Laboratory and specimen coordinate systems.

 determination of strain ε033 ϕψ in that direction. The prime superscript signifies that the strain in above is in the specimen coordinate system. The following expression is  0 expression obtained for ε33 ϕψ through application of matrix transformations on the strain vector: 

ε033

ϕψ

5

 11ν 11ν σ11 cos2 ϕ 1 σ22 sin2 ϕ 2 σ33 1 σ12 sin2ϕ sin2 ψ 1 σ33 E E  ν 11ν σ13 cosϕ 1 σ23 cosϕ sin2ψ 2 fσ11 1 σ22 1 σ33 g 1 E E

(3.17)

In case of a free surface, the stress in the direction normal to surface is zero (i.e., σ33 5 0). For such a case of biaxial stresses, Eq. (3.17) reduces to: 

ε033

ϕψ

5

 11ν  ν σ11 cos2 ϕ 1 σ22 sin2 ϕ sin2 ψ 2 fσ11 1 σ22 g E E

(3.18)

Eq. (3.18) can be used for deriving the following relationship between lattice spacing dϕψ and stress σϕ : 1 @dϕψ 11ν  5 σϕ d0 @ sin2 ψ E

(3.19)

For detailed treatment, the reader can refer to Appendices B and C in Ref. [95]. The factor (1 1 ν)/E appearing in Eq. (3.19) relates the strain measured along a certain crystallographic direction to the macroscopic stress, known as effective elastic parameter, the value of E/(1 1 ν) can be estimated as per ASTM E 1426 standard [96]. If d0, E and ν in Eq. (3.19) are known, σϕ can be estimated by determining dϕψ corresponding to two different ψ-tilts. However, as mentioned in Section 3.10.1.1, for materials containing alloying elements, there does not exist a standard lattice spacing (d0). So, for practical purposes, d0 is taken to be same as dϕ0 which is the d-spacing corresponding to ψ 5 0. With this understanding, if two measurements corresponding to dϕψ and dϕ0 are  made, then in the above equation, @dϕψ 5 dϕψ 2 d0 while, @ sin2 ψ 5 sin2 ψ as sin2 0 5 0.

Chapter 3 • X-ray diffraction

125

If dϕψ is recorded over a range of ψ-tilts, a more accurate estimate of σϕ can be obtained from the slope of dϕψ versus sin2ψ plot. As shown in Fig. 3
31A, the plot exhibits positive slope in case of tensile stresses and negative slope when the stresses are compressive in nature. Since X-rays penetrate up to certain depth into the specimen (depending on the angle of incidence), the diffraction pattern results from cumulative contribution from both surface as well as subsurface layers. Accordingly the condition of σ33 5 0, assumed while deriving Eq. (3.18) may not hold true in the presence of triaxial stress states. In such situations, lattice spacings corresponding to positive and negative values of ψ would not be identical [97]. As a result, the dϕψ versus sin2ψ plot exhibits ψ-splitting [84], as shown schematically in Fig. 3
31B. In the presence of crystallographic texture, the plot takes the form shown in Fig. 3
31C [88,89]. The anisotropic character associated with texturing also compromises the accuracy with which residual stresses can be estimated, since the underlying models are based on the condition of isotropy of stress and strain [94]. While dealing with residual stress estimation by dϕψ versus sin2ψ method, it is important to know the difference between positive and negative ψ-inclination. Unlike the schematic shown in Fig. 3
29, it is not possible for detector to physically cross-over the incident beam (i.e., the X-ray tube). Rather, the detector’s scan about 2θ axis remains confined within a narrow range around the diffraction peak of interest, while the ψ-tilt is achieved by rotating the specimen about ω-axis (refer Fig. 3
32A and B). As a result, the angle of incidence (ω 5 θ 6 ψ) becomes quite small for negative ψ-tilts (Fig. 3
32B), which can lead to

(a)

(b) 1.1735

1.1735

Conpressive (