modeling nanoscale imaging in electron microscopy thomas vogt, wolfgang dahmen, peter binev, editors.

Stahlberg Abstract In this chapter, the basic principles of atomic resolution scanning transmission electron microscopy STEM will be described.. 2 Z-Contrast Imaging in STEM The main pri

Nanostructure Science and Technology

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Modeling Nanoscale Imaging

in Electron Microscopy

123

Thomas Vogt

NanoCenter and Department

of Chemistry and Biochemistry

University of South Carolina

and Interdisciplinary Mathematics Institute

University of South Carolina

1523 Greene Street

Columbia, SC 29208

USA

Wolfgang DahmenInstitut f¨ur Geometrieund Praktische MathematikDepartment of MathematicsRWTH Aachen

52056 AachenGermany

ISSN 1571-5744

ISBN 978-1-4614-2190-0 e-ISBN 978-1-4614-2191-7

DOI 10.1007/978-1-4614-2191-7

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Imaging with electrons, in particular using scanning transmission electronmicroscopy (STEM), will become increasingly important in the near future, es-pecially in the materials and life sciences Understanding cellular interactionnetworks will enable transformative research such as “visual proteomics,” wherespatial arrangements of the proteome or particular subsets of proteins will bemapped out In the area of heterogeneous catalysis, which in many cases relies

on nanoparticles deposited onto supports recently, achieved advances in imagingand characterization of catalysts and precatalysts are transforming the field andallowing more and more rational design of multifunctional catalysts Advances

in nanoscale manufacturing will require picometer resolution and control as well

as the elimination of routine visual inspection by humans to become viable andimplemented in “real” manufacturing environments There are (at least) two majorobstructions to fully exploit the information provided by electron microscopy

On the one hand, a major bottleneck in all these applications is currentlythe “human-in-the-loop” resulting in slow and labor-intensive selection and accu-mulation of images A “smart” microscope in which instrument control, imageprescreening, image recognition, and machine learning techniques are integratedwould transform the use of electron imaging in materials science, biology, and otherfields of research by combining fast and reliable imaging with automated high-throughput analysis such as combinatorial chemical synthesis in catalysis or themultiple “omics” in biology

On the other hand, even if environmental perturbations could be completelyavoided a principal dilemma remains that results from the fact that the acquiredimages offer only an “ambiguous reflection” of reality due to inherently noisydata and this is the primary issue addressed in this volume The noise structure

is highly complex and far from fully being understood In particular, it depends

in a complex way on the electron dose deployed per unit area Low noiselevels require a high dose that, in turn, may cause damage In most cases, high-energy electrons damage biological and organic matter and thus require specialtechniques for imaging when using electron microscopes with beams in the 100–300

kV range Experiments are frequently performed at “nonbiological” temperatures

v

vi Preface

(i.e., cryo-electron microscopy) to reduce damage But even when investigatinginorganic material at the atomic resolution level, relatively low dose image acquisi-tion is often required to avoid damaging the sample This again impacts significantlythe signal-to-noise ratio of the resulting images The required low doses necessitatenew paradigms for imaging, more sophisticated data “denoising” and image analysis

as well as simulation techniques In combination with ongoing experimental work toreduce the environmental impact during nano-imaging experiments (e.g., vibrations,temperature, acoustic, and electromagnetic interference), we have begun to developand apply nonlinear probabilistic techniques They are enhanced by learning theory

to significantly reduce noise by systematically exploiting repetitive similarities ofpatterns within each frame as well as across a series of frames combined with newregistration techniques Equating “low electron dose” with “few measurements”

is an intriguing idea that is going to radically alter image analysis—and evenacquisition—using techniques derived from “Compressed Sensing,” an emergingnew paradigm in signal processing A key component here is to use randomness toextract the essential information from signals with “sparse information content” byreducing the number of measurements in ranges where the signal is sparse Workingfirst with inorganic materials allows us to validate our methods by selecting on thebasis of high-resolution images an object to be imaged at lower resolution Building

on the insight gained through these we can then proceed to image silicate or organicmaterials which cannot be exposed to high energy electrons for extended periods oftime Examples of such an approach are given in Chap 4

Part of our work has greatly benefitted from three workshops organized at theUniversity of South Carolina by the Interdisciplinary Mathematics Institute andthe NanoCenter entitled “Imaging in Electron Microscopy” in 2009 and 2010 and

“New Frontiers in Imaging and Sensing” in 2011 At these workshops world-classpractitioners of electron microscopy, engineers, and mathematicians began to discusand initiate innovative strategies for image analysis in electron microscopy.The goal of our work is to develop and apply novel methods from signal andimage processing, harmonic analysis, approximation theory, numerical analysis, andlearning theory Simulation is an important and necessary component of electronimage analysis in order to assess errors of extracted structural parameters andbetter understand the specimen–electron interactions It thereby helps improve theimage as well as calibrate and assess the electron optics and their deviations due

to environmental effects such as acoustic noise, temperature drifts, radio-frequencyinterferences, and stray AC and DC magnetic fields The intuition-based approachbased on Z2-contrast can be misleading if for instance in certain less compactstructures electron channeling effects are not correctly taken into account

Over the last 3 years, we have established a global research collaborationanchored around electron microscopists at USC (Thomas Vogt, Douglas Blom) andother people such as Angus Kirkland (Oxford), Nigel Browning (UC Davis andLLNL) with mathematicians at USC’s Interdisciplinary Mathematics Institute (PeterBinev, Robert Sharpley), Ronald DeVore (Texas A&M) and Wolfgang Dahmen(RWTH Aachen) These collaborations are critical in exploring novel denoising,

Preface vii

nonlocal algorithms as well as new methods to exploit Compressed Sensing fornanoscale chemical imaging This book is to be seen as a progress report on theseefforts

We thought it was helpful to have Professor Michael Dickson (Philosophy,University of South Carolina) address issues of realism and perception of nano-images and how we might think of them in a “Kantian” way

Chapters 2 and 3 are from well-established practitioners in the field of scanningtransmission electron microscopy, led by Professors Nigel Browning and AngusKirkland from the University of California Davis and Oxford University, respec-tively Both chapters exemplify what it means to “image at the edge” and push themethod to its current limitations Limitations that might be pushed back a bit furtherusing different image analysis techniques

Chapters 4 and 5 rely heavily on two facilities at USC: many experimentaldata were taken on a JEOL JEM-2100F (200 kV) microscope with field emissiongun, spherical aberration corrector, STEM mode, High Angle Annular Dark Fielddetector (HAADF), EELS, EDX, and tomography mode This instrument providesroutinely sub-Angstrom image resolution and elemental resolution at the atomiclevel and is operated by Dr Douglas Blom Second, we have a state-of-the-art floating-point parallel computing cluster based on general purpose graphicsprocessing units (GPGPUs) achieved through parallel architecture of the GPGPU,which is a mini-supercomputer packed in a graphics card used for floating pointoperations Our major electron imaging simulation code is written in the CUDAprogramming language which uses a single-precision FFT routine in the CUFFTlibrary We have been able to simulate inorganic structures of unprecedentedcomplexity using this hardware These simulations were performed by Sonali Mitra

a Ph.D student working under the supervision of Drs Vogt and Blom in theDepartment of Chemistry and Biochemistry at the University of South Carolina.The work by Amit Singer and Yoel Shkolnisky (Chap 6) is a tour-de-force inexplaining the mathematical theory cryo-transmission electron microscopy is based

on What appears to many practitioners of electron microscopy as “black art” isdeeply rooted in fundamental mathematics This chapter illustrates the deep-rootedconnections between imaging and applied mathematics, illustrating what EugeneWigner coined in 1960 as the “unreasonable effectiveness of mathematics in the nat-

ural sciences” (Communications on Pure and Applied Mathematics 13 (1): 1–14).

We believe that the combination of state-of-the-art imaging using corrected electron microscopy with applied and computational mathematics willenable a “new age” of imaging in both the hard and soft sciences This will leveragethe huge infrastructure investments that have been made globally over the past 10years in national laboratories, universities, and selected companies

aberration-Tom Vogt would like to thank the Korean Ministry of Science, Education, andTechnology for a Global Research Laboratory grant and the National AcademiesKeck Future Initiative for support We all would like to acknowledge the supportfrom the Nanocenter, the Interdisciplinary Mathematics Institute, and the College

of Arts and Sciences at the University of South Carolina for the realization of theabove-mentioned workshops that helped shape our ideas presented in this volume

Kantianism at the Nano-scale . 1Michael Dickson

The Application of Scanning Transmission Electron

Microscopy (STEM) to the Study of Nanoscale Systems 11N.D Browning, J.P Buban, M Chi, B Gipson, M Herrera,

D.J Masiel, S Mehraeen, D.G Morgan, N.L Okamoto,

Q.M Ramasse, B.W Reed, and H Stahlberg

High Resolution Exit Wave Restoration 41Sarah J Haigh and Angus I Kirkland

Compressed Sensing and Electron Microscopy 73Peter Binev, Wolfgang Dahmen, Ronald DeVore, Philipp Lamby,

Daniel Savu, and Robert Sharpley

High-Quality Image Formation by Nonlocal Means Applied

to High-Angle Annular Dark-Field Scanning Transmission

Electron Microscopy (HAADF–STEM) 127

Peter Binev, Francisco Blanco-Silva, Douglas Blom,

Wolfgang Dahmen, Philipp Lamby, Robert Sharpley,

and Thomas Vogt

Center of Mass Operators for Cryo-EM—Theory and Implementation 147

Amit Singer and Yoel Shkolnisky

Index 179

ix

Kantianism at the Nano-scale 1

Michael Dickson

1 Introduction

The smallest object that the human eye can detect has dimensions of around

50 microns So there is a sense in which a sphere that is, say, 10 microns indiameter, is invisible to us Some philosophers have argued that the invisibility, to

us, of a 10 microns sphere has epistemological significance that, in particular, ourknowledge about and our understanding of such things may be qualitatively differentfrom our knowledge and understanding of directly observable objects Along withmany other philosophers, I find this view untenable It seems clear that althoughthey are not directly observable to us, 10 microns spheres are nonetheless the same

sort of thing as their larger cousins (the 50 microns spheres) Indeed, there are creatures whose visual apparatus works more or less as ours does that can directly

see 10 microns spheres

However, at first blush, nano-objects raise issues of a different order of tude, literally Being much smaller than a single wavelength of visible light, theyare not visible to anybody, not even in principle For example, creatures (such asourselves) whose visual apparatus works via edge detection in the visible spectrumcould never see a nano-object The nanoworld thus provides an epistemic challenge

magni-to those (such as myself) who would argue that we do in fact have decent epistemicaccess to the unobservable world How exactly do we have this access, and what do

1Thanks to audiences at the University of South Carolina NanoCenter and the University ofCalifornia at Irvine Department of Logic and Philosophy of Science for helpful comments and questions.

M Dickson (  )

Department of Philosophy and USC NanoCenter, University of South Carolina,

Columbia, SC 29208, USA

e-mail: dickson@sc.edu

T Vogt et al (eds.), Modeling Nanoscale Imaging in Electron Microscopy,

Nanostructure Science and Technology, DOI 10.1007/978-1-4614-2191-7 1,

© Springer Science+Business Media, LLC 2012

1

2 M Dickson

our representations of the nanoworld really mean? Clearly they cannot mean “what

we would see, were we small enough” or some such thing So what do they mean?

The central suggestion of this paper is that a more or less Kantian understanding

of what we are doing when we create scientific representations (and more cally, for present purposes, images)—whether they be of 10 microns spheres or ofcarbon nanotubes—resolves this epistemological puzzle It shows how, and in whatsense, we can have genuine knowledge of objects that we either do not, or cannoteven in principle, observe directly

specifi-After a brief discussion (Sect.2) of the nature of nano-images, I will quicklyreview (Sect.3) some aspects of the philosophical debate about our epistemic access

to the “unobservable” In Sect.4, I present in broad outline of a more or less Kantian(really, neo-Kantian) account of science, one that I argue resolves the philosophicaldebates while respecting the science In Sect.5, I conclude by applying this view tonano-images

2 Nano-Images: Seeing the Invisible?

Many images of nanoscale objects and their properties seem to present nano-objects

as “what one would see if one were small enough” Artists’ renditions are especiallynoteworthy here, as they frequently show shadows “caused by” three-dimensionalstructure, changes in reflectance “caused by” changes in contour, and so on Thescales on which these structures are depicted to occur are often in the vicinity of asingle Angstrom

Images created for scientific consumption and study often have similar features.Many STM and AFM images contain what appear to be shadows and othervisual elements that are reminiscent of the middle-sized three-dimensional world(for example, again apparent changes in reflectance)

How do these elements get into the image? The production of images from theraw data produced by STM or AFM, or hosts of other, microscopes is very complex,involving much processing of the data, feedback from data (at various stages ofprocessing) to the configuration of the instrument and even to the preparation of thesample, and so on Often much of the work of transforming data into a visual image

is done by more or less off the shelf software (in the form of a graphics library) thatwas specifically developed for image production (for example, in animated movies).Some bemoan, or at least highlight as epistemically (and even ethically) prob-lematic, the fact that Hollywood or video game industry software is used for thesescientific purposes, and that various methods are used to “clean up” or “simplify”images in ways that may be, so the complaint goes, misleading Pitt ([9], 157),for example, warns that “the images these instruments produce do not allow us tosee atoms in the same way that we see trees.” Indeed, elsewhere ([10]) he questionswhether these machines are “producing an honest replication of the object/surface inquestion” Pitt is especially concerned about the fact that these machines (along withthe software) produce images that are, as we observed above, quite similar in theirfeatures to images of everyday middle-sized dry goods, and thus liable to produce

Kantianism at the Nano-scale 3

serious misunderstanding The epistemological and ethical consequences are, heargues, quite serious

However, purveyors of the imaging products are not at all shy about theprovenance of their software, and its capacity for creating familiar-looking images.Consider, for example, this statement from PNI regarding their AFMs:

“We have taken advantage of some of the latest software and video graphicscapabilities developed for video games to make NanoRuleC fast, intuitive, and easy

to use It gives the AFM user the ability to rapidly visualize data in new ways andgain new insights via controlled 3-dimensional imagery [8].”

For the researcher who must produce and use images from an AFM, ease of useand rapid visualization are no doubt virtues On the one hand, there is no doubt thatnano-images may be misleading in various ways They may convey—especially tothe untrained consumer—a sense of order and controllability that is far beyond whatthe systems “really” have

Reflective scientists do seem to acknowledge both sides Goodsell, for example,

is enthusiastic about the power of imaging technology and embraces the fact that

nano-images can make nano-objects seem familiar: “Imagery is playing an tant role as nanotechnology matures by making the invisible world of the nanoscalecomprehensible and familiar” ([3], 44) On the other hand, he is concerned that

impor-“Pictures carry with them an insidious danger; images are so compelling that theymay compete with the scientific facts” ([3], 47)

Broadly speaking, we find here two opposing attitudes to these images On theone hand, one might say that the human visual system is constructed in such away (or, as Pitt would have it, “trained” or developed in such a way) that it willinterpret these images in the same way that it interprets analogous images of themiddle-sized objects of everyday experience, i.e., wrongly, and thus the images areinherently misleading The more that “Hollywood” has to do with these images, theworse off they are Instead, one should use modes of presentation that do not misleadthe visual system in this way For example, one might use line scans or other modes

of representation that do not suggest a simple 3-dimensional representation to ourvisual system as if the image were a photograph of the nano-object One might think

of this attitude as more or less “realist” in the sense that it insists that in order to be

true, in order not to mislead the viewer about the true nature of the properties that are

being represented, we ought to choose modes of representation that push the vieweraway from misinterpretation and in particular in this case, from visualization (Thispoint applies as well to viewers who are savvy enough to know how correctly tointerpret the image, for their visual systems will be just as misled as the rest of ours

They interpret correctly despite the pseudo-representational elements of the image.)

On the other hand, one might argue that the (scientific) purpose of theseimages is to provide (or to suggest) a theoretical representation that is sufficient

to make predictions about future observations, and to suggest modes of control andmanipulation of nano-objects But success on these scores does not imply that thetheoretical representation suggested to us by the image accurately depicts the object

“as it is” We know (and, as scientists, care) only that the representation is sufficient

to support these other purposes In this case, there is no problem with the images

4 M Dickson

They clearly suggest (among other things) certain spatial, structural, properties of

the objects that are being studied, and as it turns out, presuming the objects to behave

as if they have those properties does lead (sometimes) to successful predictions

and manipulations Whether they actually have the properties is not something thatscience can verify for science can, according to this attitude, do no better than tomake accurate predictions about observation One might think of this attitude asmore or less antirealist, inasmuch as it sets aside as irrelevant to science the issue oftruth and focuses on predictive and manipulative success

3 The Epistemic Significance of Observability

This debate is not new It is perhaps most familiar to contemporary philosophers

of science in the form of the debate over van Fraassen’s [11] claim that directobservability marks the line between scientific claims that we may legitimately

believe (or be said to know), and those that we should merely accept for the

purposes of doing science (e.g., prediction and manipulation) So, on this view,

I can legitimately believe (and possibly even know) that my dog is brown, but notthat a hydrogen atom has one electron (Of course, one can and ought to accept the

latter claim for the purposes of doing science; it is, in that sense, well justified.)

A recent discussion of van Fraassen’s view will be helpful here One worry(from the beginning) about van Fraassen’s view is that the distinction itself is vague,and that the obvious ways of making it precise are inherently circular Muller [4,5]

is correct to notice that one of the most powerful objections to van Fraassen’s viewcame from Musgrave [7], who, translated into the current context, argued thus:Premise 1: It is correct to accept the wave theory of light, including whatever it

tells us about the observable

Premise 2: The wave theory of light implies that certain nano-objects are strictly

unobservable

Premise 3: This implication of the wave theory of light is, clearly, an implication

about unobservables

Premise 4: The constructive empiricist accepts, but does not believe, theoretical

claims about what is unobservable

Conclusion: The constructive empiricist does not believe that it is not the case that

nano-objects are unobservable

This conclusion is a problem, because van Fraassen wants to rely on science totell him which things are unobservable (and this strategy is quite reasonable, lestone appear to be engaging in armchair science), but the argument suggests that hecannot do so Hence he cannot draw the distinction that he wants

Muller proposes a solution, which involves taking “observable” to be more or lessco-extensive with “directly perceptible by the senses unaided” I find this solutionbizarre, because it makes epistemic considerations depend in a very odd way onpersonal idiosyncrasies—for example, the sort of justification thatI have of certain

claims may be different from the sort of justification that those of you who are not

Kantianism at the Nano-scale 5

as blind as me have Yours is directly visual and can support legitimate beliefs Mine

is indirect and theoretical, involving an appeal to the laws of optics as they apply

to eyeglasses, and as such cannot support belief but only acceptance This viewwill have a hard time making good sense of scientific knowledge The epistemicquality of scientific knowledge-claims does not depend on who is uttering them(for example, whether that person happens to wear eyeglasses), but on the overallstate of the scientific enterprise geared toward the verification of the claim inquestion.2

Although I have not established the point here,3 I believe that van Fraassen’sposition does naturally lead to this dilemma—either the distinction between theobservable and the unobservable must be established without appeal to science, or

it must be co-extensive with the distinction between what is directly perceptibleand what is not directly perceptible, and therefore different for different individuals.Neither option is very attractive

But lacking a viable distinction between which scientific representations tounderstand realistically and which to understand instrumentally, it seems then that

we are left with either the “fully realist” position that all scientific representations

should aspire to be “true representations”, or the “fully antirealist” position that

all scientific representations are nothing more than instruments for prediction,

manipulation, and other scientific or technological activities

4 A Neo-Kantian Understanding of Science

There is a third way [1] The view that I would like us to consider combines aspects

of both of these two attitudes The basic idea is that the first attitude is correctinsofar as it acknowledges that we are “wired” to see the image in a certain way—the visual stimulus provided by the image prompts us to apply certain concepts

to the image (For example, where there are appropriate changes in reflectance,

we see three-dimensional spatial contour.) The first attitude is incorrect to see anepistemological problem here, for according to the (Kantian) attitude that I willoutline below, science is not about the properties of things independently of howthey are conceptualized by us

2 There are other reasons to think that the perceptible/imperceptible distinction is not epistemically

relevant Consider graphene What are we to make of the fact that we can see (albeit through an

optical microscope, but the point clearly extends to other cases where unaided perception applies) flakes of graphene whose thickness, by all reasonable accounts, is less than we can discern Can we seriously entertain agnosticism (acceptance but not belief) regarding the existence or properties of

objects (e.g., atoms or small molecules) that could apparently be (and indeed can be) of the overall

dimensions of the thickness of graphene? And what of the flakes them selves? Is their width and breadth real, but their thickness not?

3 In particular, the discussion has advanced beyond the paper by Muller See Muller and van Fraassen [ 6 ] and the references therein.

6 M Dickson

In other words, the second attitude is correct insofar as it acknowledges

that scientific claims ultimately must “refer themselves” to human observations

(And these are epistemically relevant for us Indeed, on what else could we base our

knowledge?) Indeed, the Kantian attitude goes a step further and says that science

is about the properties of physical objects as conceptualized by us This process of

conceptualization (of the stimuli that we get via observation) is what brings theory

to bear on the physical world However, the second attitude is incorrect insofar as itsinstrumentalism implies that we ought not to draw inferences about the properties ofunobservable objects from these images We can and should draw such inferences—the fact that these inferences concern unobservable objects “as conceptualized byus” makes their conclusions no less objective

In short: images of nano-objects portray the properties as conceivable by us of

very small things These are the empirically meaningful properties They representthe manner in which attributions of various theoretical properties to nano-objectsbecome observationally grounded in some possible perceptions

Something like this general view of science has a pedigree going back to Kant.4

Prior to Kant, Hume had argued against many contemporary accounts of empiricalknowledge on the grounds that we can never have any good reasons to think thatthe representations of the world that we have “in our heads” are in fact faithfulrepresentations of the things in the world, for whenever we seek to compareour represents with “the world” we necessarily first represent the world in someway or another to ourselves, and thus we end up comparing representation withrepresentation, not representation with “the world unrepresented” Hume was led toskepticism Kant, on the other hand, took scientific knowledge as given, and sought

to understand how scientific knowledge is possible at all, in light of Hume’s critique.His solution to Hume’s problem was what he called a new “Copernican revo-lution” Just as Copernicus made it clear that we are not observing the objectivemotions of heavenly bodies directly, but their motions relative to ourselves, so Kant

turned Hume on his head and argued that science is not about those “things in

themselves” in the world, to which we can never have direct mental access True, ouraccess to those things is always mediated by our perceptual and conceptual faculties

(which is what gives rise to Hume’s problem), but science is about those things as perceived and conceived by us It is nonetheless entirely objective, because there are

objective facts about how we perceive and conceive

For example, on Kant’s view we necessarily represent external objects as existing

in space and we do so, necessarily, in accordance with the laws of Euclideangeometry Those laws therefore become objective facts about space (a plausibleview when Newtonian physics was taken to be true) Similarly, Kant argued that weconceive of things in such a way that places them in various relations, for example,causal relations

4 Interpretation of Kant is both complex and controversial I generally follow the views of Friedman [ 2 ], though I am here leaving out almost all of the details.

Kantianism at the Nano-scale 7

At least some aspects of Kant’s view are called seriously into question by modernphysics For example, the theory of relativity strongly suggests that the laws of

Euclidean geometry are not facts about space In response to relativity (amongst

other mathematical and scientific developments), some philosophers developed

a “neo-Kantian” view according to which what structures our perceptions andconceptions of the objects of scientific inquiry flows not from unavoidable factsabout human perceptive and cognitive faculties, but from the categories and modes

of conception that are best suited to provide a framework within which the scientifictheory is conceivable and expressible For example, Euclidean geometry (amongother things) provides a suitable framework within which one can conceive andexpress Newtonian mechanics

The notion of “best suited” can be spelled out in various ways, but simplicity

often plays a role For example, it is possible to express general relativity in a fully Euclidean geometry, but the laws become unwieldy They are far simpler (although

the precise definition of simplicity is at best an unresolved matter) when expressed

in a non-Euclidean geometry On this neo-Kantian view, then this non-Euclideangeometrical structure provides the framework within which is it possible to conceiveand express Einstein’s theory, and thus its laws govern the structure within which

we make scientific spatial observations

Note that just as, for Kant, the facts of Euclidean geometry are a priori, i.e.,prior to experience in the sense of being the (for him, necessary) form of spatialrepresentation, so also, on this neo-Kantian view, the non-Euclidean geometryemployed in general relativity is a priori, i.e., prior to experience in the sense ofbeing the (now contingent insofar as general relativity could be replaced by anothertheory) form of spatial representation

Again, there is no pejorative or epistemically worrying sense in which this

neo-Kantian view is “subjective” or “antirealist” We do not simply choose a form of representation We discover which form of representation best suits the development

of a successful theory that accommodates our perceptions represented in this way.Neither, however, is this view that of the traditional realist who presumes thatthe representations that we find in successful scientific theories are in some sense

“isomorphic” to the things in themselves (or approximately so), unperceived and

unconceived by us Science is not about those things on this view It is about things

as perceived and conceived by us.

How does this view apply to nano-images? Recall the two views mentionedabove The “fully realist” position was that scientific images (and indeed allrepresentations) must strive to be “just like” (i.e., in some sense, isomorphic or

at any rate homomorphic, to) their target In the current context of nano-images,this view faces two challenges First, current practices employed in the depiction ofnano-objects do not seem to conform to it Neither artistic renditions nor scientific

8 M Dickson

images of nano-images pretend to be “accurate depictions”—they contain manyelements (reflectance, color, etc.) that nobody thinks are properties of the objectsthat they depict Second, even if we abstract from those properties, supposing them

to be inessential to the representational content of the images, we are stuck with the

fact that we have no way to verify that the objects really have the properties depicted

by the image (e.g., such and such spatial structure) apart from employing the verytechnology and assumptions used to create the images in the first place Unlike, say,the image of a distant mountain produced by binoculars, we cannot “go there and

check” Instead, in essence we presume that the objects in question have certain

types of property (e.g., spatial structure) and then design instruments to measureand manipulate that structure

On the fully antirealist view, these presumptions are pure “as if” they turn out

to be useful for the purposes of making predictions and producing technologicalmarvels, but they have nothing to do with “truth” or “the world”

On the neo-Kantian view, the antirealist’s mistake here lies in presuming thatscience (properly understood, epistemologically speaking5) was ever about anythingother than the world as perceived and conceived by us Nano-images are perfectly

“objective” and “accurate” and “true” from this point of view We structure ourrepresentations of nano-objects as we do because it is the best way (so far as weknow right now) to theorize about them The antirealist points out that sciencecannot verify that our representations faithfully depict the “thing in itself” The neo-Kantian suggests that the very idea that such a feat could be accomplished—even formiddle-sized dry goods!—is incoherent We do not, and never could, have “directaccess” to “things in themselves”—we always perceive and conceive them in oneway or another, and what is verified (if anything) about a scientific theory is that itconforms (or not) to things as perceived and conceived in this way

On this neo-Kantian view, both the practices surrounding the generation of images, and the procedures that we use to verify those images make perfect sense

nano-In the first place, we should depict nano-objects as having color, casting shadows,

etc Why? Because we conceive of them as having spatial structure, and as far as we(human observers) are concerned, objects with spatial structure are like that In otherwords, if we wish to convey to another (or to ourselves) an image of an object withspatial structure, we ought to include such properties as color and shading in theimage Indeed, if we fail to include such properties, we are likely to fail to convey

the intended spatial structure, and thus fail to represent the object as perceived and conceived by us Note that it does not follow that we cannot (or should not) add

as a proviso that it is impossible “actually to see” the objects in this way One canunderstand perfectly well that nano-objects are smaller than a wavelength of light,

5 The point here is not that practitioners have always understood their practice in this way, but that understanding the practice in this way gives it epistemic credibility (i.e., we can legitimately say that the practice produces knowledge) without doing serious violence to (for example, misrepresenting) the practice itself.

Kantianism at the Nano-scale 9

and yet admit that including features such as color and shadow enables portrayingthem as having spatial structure

In the second place, there is nothing wrong with the procedures of verificationused to verify that the images we get from our instruments “accurately” representthe objects The antirealist’s contention against the realist is that our instruments

and procedures assume that nano-objects have the sorts of properties that we are

attributing to them This contention is correct, but on the neo-Kantian view missesthe point of “verification” in the first place The point is not to verify that the objects

“really have” the properties in question, but to verify that the theories6 that we arebuilding, based on the (often tacit and granted) assumption that the objects havesuch properties are panning out so far

Of course, nothing guarantees that these procedures of verification will work out

In the most extreme case, it could turn out that what is at fault is the very manner

in which we conceive of nano-objects In this case, we will be forced to rethink thevery foundations of our scientific activity (as we have been in the case of quantumtheory, where the usual modes of conception have broken down) Indeed, one of theexciting aspects of research in this area is precisely that such a result is possible

References

1 Dickson M (2004) The view from nowhere: quantum reference frames and quantum tainty Stud Hist Philos Mod Phys 35:195–220

uncer-2 Friedman M (2010) Synthetic history reconsidered In: Domski M, Dickson M (eds) Discourse

on a new method: essays at the intersection of history and philosophy of science Open Court Press, Chicago, pp 571–813

3 Goodsell D (2006) Seeing the nanoscale NanoToday 1:44–49

4 Muller FA (2004) Can constructive empiricism adopt the concept of observability? Philos Sci 71:637–654

5 Muller FA (2005) The deep black sea: observability and modality afloat Br J Philos Sci 56:61–99

6 Muller FA, van Fraassen BC (2008) How to talk about unobservables Analysis 68:197–205

7 Musgrave A (1985) Constructive empiricism and realism In: Churchland P, Hooker CA (eds) Images of science University of Chicago Press, Chicago, pp 196–208

8 Pacific Nanotechnology, Inc (2003) Press Release: “New Image Display and Analysis ware for Atomic Force Microscopy” 17 March Available online at http://www.thefreelibrary com

Soft-9 Pitt J (2004) The epistemology of the very small In: Baird D, Nordmann A, Schummer J (eds) Discovering the Nanoscale IOS Press, Amsterdam, pp 157–163

10 Pitt J (2005) When is an image not an image? Techn´e: Research in Philosophy and Technology 8:23–33

11 Van Fraassen BC (1981) The scientific image Clarendon Press, Oxford

6 I have nothing grand in mind by using the term ‘theory’ here It is being used here to refer

to models, hypothesis, simple assertions (such as ‘each molecule of X is surrounded by several

molecules of Y ’) and so on.

The Application of Scanning Transmission

Electron Microscopy (STEM) to the Study

of Nanoscale Systems

N.D Browning, J.P Buban, M Chi, B Gipson, M Herrera, D.J Masiel,

S Mehraeen, D.G Morgan, N.L Okamoto, Q.M Ramasse, B.W Reed, and H Stahlberg

Abstract In this chapter, the basic principles of atomic resolution scanning

transmission electron microscopy (STEM) will be described Particular attentionwill be paid to the benefits of the incoherent Z-contrast imaging technique forstructural determination and the benefits of aberration correction for improvedspatial resolution and sensitivity in the acquired images In addition, the effectthat the increased beam current in aberration corrected systems has on electronbeam-induced structural modifications of inorganic systems will be discussed

N.D Browning (  )

Department of Chemical Engineering and Materials Science, University of California-Davis, One Shields Ave, Davis, CA 95618, USA

Department of Molecular and Cellular Biology, University of California-Davis,

One Shields Ave, Davis, CA 95618, USA

Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, WA 99352, USA

e-mail: Nigel.Browning@pnnl.gov

J.P Buban • S Mehraeen

Department of Molecular and Cellular Biology, University of California-Davis,

One Shields Ave, Davis, CA 95618, USA

e-mail: jpbuban@math.ucdavis.edu ; smehraeen@ucdavis.edu

T Vogt et al (eds.), Modeling Nanoscale Imaging in Electron Microscopy,

Nanostructure Science and Technology, DOI 10.1007/978-1-4614-2191-7 2,

© Springer Science+Business Media, LLC 2012

11

12 N.D Browning et al.

Procedures for controlling the electron dose will be described along with imageprocessing methods that enable quantified information to be extracted from STEMimages Several examples of the use of aberration-corrected STEM for the study

of nanoscale systems will be presented; a quantification of vacancies in clathratesystems, a quantification of N doping in GaAs, a quantification of the sizedistribution in nanoparticle catalysts, and an observation of variability in dislocationcore composition along a low-angle grain boundary in SrTiO3 The potential forfuture standardized methods to reproducibly quantify structures determined bySTEM and/or high-resolution TEM will also be discussed

in the beam current and subsequently the signal-to-noise levels (contrast) in theacquired images This means that small differences in structure and compositioncan be more readily observed and, for example, in the STEM mode of operation,complete 2-D atomic resolution elemental maps can be generated using electronenergy loss spectroscopy (EELS) [6,7] Furthermore, the EEL spectra that areobtained using a monochromated microscope also show vast improvements overthe spectra that could be obtained a few years ago—allowing bonding state changes

to be observed from core-loss spectra with high precision [8] and the low-loss region

Condensed Matter and Materials Division, Physical and Life Sciences Directorate,

Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94550, USA

e-mail: reed12@llnl.gov

Q.M Ramasse

SuperSTEM Laboratory, J Block, STFC Daresbury, Daresbury WA4 4AD, UK

e-mail: qmramasse@superstem.org

The Application of Scanning Transmission Electron Microscopy (STEM) 13

of the spectrum to be used to map fluctuations in optical properties [9 11] Taken alltogether, these newly developed capabilities for (S)TEM provide a comprehensiveset of tools to measure, quantify, and understand the atomic scale properties ofnanoscale materials, interfaces, and defects

However, although the tools now exist to obtain very high-quality images fromnanoscale materials, defects, and interfaces, as yet there has been very little work toquantify the information contained in them—other than to identify a structure andreport composition variations in obvious cases across a hetero-interface Images ofindividual interfaces, grain boundaries, or dislocations are typically presented asbeing “representative” of the whole structure with little proof that this is actuallythe case In addition, the history of the sample is usually poorly defined in terms

of its synthesis, preparation for the TEM, and beam irradiation history (whichcan easily have a significant effect on the structure, particularly when aberration-corrected microscopes are used) This is in stark contrast to the work that has beenperformed using TEMs for structural biology, where quantifying the informationpresent in low-dose images has been the major emphasis of research for over 20years [12–24] Image processing and analysis methods for the study of organicsystems can now routinely cope with variations across an image caused by samplemovement and noise and can quantify the contribution of each—leading to a well-defined measurement of resolution and the accurate incorporation of these essentialexperimental factors into the structure determination procedure In the case of theanalysis of point defects in nanoscale systems, dislocations, grain boundaries, andinterfaces by aberration-corrected (S)TEM, the lack or periodicity in the structure,large composition variations, and a sensitivity of the structure to beam modificationactually make the experimental considerations very similar to those employed fororganic systems We can therefore use the image processing/analysis tools that havealready been defined for structural biology to provide an unprecedented atomic scalecharacterization of nanoscale materials, defects, and interfaces—potentially evendefining the effect of single atom composition variations on the structure and thesubsequent properties

2 Z-Contrast Imaging in STEM

The main principle behind the scanning transmission electron microscope is to usethe electron lenses to form a small focused beam (probe) of electrons on the surface

of the specimen [25] (Fig.1a) As this electron probe is scanned across the surface ofthe specimen, the electrons that are scattered by the specimen are collected in aseries of detectors that cover different angular ranges—the signal in each detectortherefore contains a different part of the physics of the interaction of the beam withthe specimen [26] A 2-D image is created by displaying the output from one of thesedetectors as a function of the beam position as it is scanned across the specimen.Most STEM images use a high-angle annular dark field (HAADF) detector, in whichthe scattering that is collected is proportional to the Rutherford scattering cross-section that has a second power Z2 dependence on the atomic number Z of the

Fig 1 (a) The geometry of the probe, detector and sample produce an overlapping CBED pattern

at the detector plane (b) The Z-contrast image (and electron energy loss spectrum) can, to a first

approximation, be treated as a convolution between the probe intensity profile and the scattering cross section for the signal of interest (i.e inelastic or elastic) The two probes shown illustrate the effect of aberration correction on the final image

scattering center—giving rise to the name Z-contrast imaging From the earliestimages of individual heavy atoms on a light support [25], the technique evolved to

be able to image crystals with atomic spatial resolution [27] In the remainder of thissection, the principles behind the spatial resolution and the compositional sensitivity

of the method will be described and the effect of aberration correction discussed

As described above, a Z-contrast image [27–32] is formed by collecting thehigh-angle scattering on an annular detector and synchronously displaying itsintegrated output on a TV screen or computer monitor while the electron probe

is scanned across the specimen Detecting the scattered intensity at high anglesand integrating it over a large angular range effectively averages coherent effectsbetween atomic columns in the specimen, allowing each atom to be considered toscatter independently with a cross-section approaching a Z2dependence on atomicnumber (Fig.1b) This cross-section forms an object function that is strongly peaked

at the atom sites The detected intensity is, to a first approximation, a convolution

of this object function with the probe intensity profile The small width of the

object function ( 0:1 ˚A) means that the spatial resolution is limited only by the

probe size of the microscope For a crystalline material in a zone–axis orientation,where the atomic spacing is greater than the probe size ( 0:1 nm for the JEOL

2100Cscorrected STEM at UC-Davis,  0:1 nm for the Nion-corrected VG STEM

at Lawrence Berkeley National Laboratory (LBNL), and 0.05–0.1 nm for the Cs

The Application of Scanning Transmission Electron Microscopy (STEM) 15

corrected FEI Titans at Lawrence Livermore National Laboratory (LLNL), LBNL,and Oak Ridge National Laboratory (ORNL)—these microscopes were used toobtain the results presented later in this chapter), the atomic columns can beilluminated individually Therefore, as the probe is scanned over the specimen, anatomic resolution compositional map is generated in which the intensity depends

on the average atomic number of the atoms in the column An important feature ofthis method is that changes in focus and thickness do not cause contrast reversals

in the image, so that atomic sites can be identified unambiguously during theexperiment As the images can be interpreted directly in real time while working

on the microscope, they can be used to position the probe to obtain electron energyloss spectra from defined locations in the structure [33–39], thus permitting a fullspectroscopic analysis to be correlated with the image on the atomic scale

Since the initial development of the Z-contrast imaging technique, there havebeen many studies that have confirmed the general concept of incoherent imagingdescribed above—in particular, identifying the location of atomic columns in theimage is straightforward However, interpretation of the intensities within the atomiccolumns seen in the images is a little more complicated than the simple incoherentmodel suggests [38–42] If you want to interpret the absolute intensities in theindividual columns in terms of the presence of vacancies and impurities, then firstprinciples simulations of the atomic structures must be accompanied by imagesimulations—there are currently several available packages to perform these simula-tions [43,44] As the aim of this chapter is to discuss the applications of quantitativeimaging in STEM, we will not discuss the details of the simulations further here,other than to mention in the subsequent sections when simulations were used

In conventional high-resolution TEM imaging and in atomic resolution Z-contrastimaging, the resolution of the final image is limited by the aberrations in theprincipal imaging lens For STEM, this means the aberrations in the final probe-forming lens—which determines the spatial extent of the electron beam on thesurface of the specimen As with other high-resolution methods, defocus can beused to balance out the effects of aberrations up to some optimum value, usuallycalled the Scherzer defocus, with a resolution given by

of Cs correction is shown schematically in Fig.2 Practically the effect of Cs

correction means that a larger area of the lens is free from spherical aberration,allowing larger apertures to be used and a higher resolution to be obtained [46]

An important corollary to the increase in spatial resolution is that the larger aperturesize means that the smaller probe that is formed can have up to an order of magnitudemore beam current than a conventional STEM probe [6] Now that sphericalaberration has essentially been removed as the limitation in the probe size, higherorder aberrations are the limiting factors As was the case with the Scherzer defocus,the aberration corrector can now be adjusted to compensate for those higher orderaberrations by tuningCsitself to an optimal value Although due to the complexity

of the multipole electron optics of correctors many more parameters actually controlthe probe size, (1) can be modified to yield the probe full-width-at-half-maximum

of a simplified system limited only by 5th order aberration C5[47]:

For a state-of-the-art aberration-corrected STEM, the probe size can now approach0.05 nm [5] and designs are currently being implemented that should push resolutioneven further to  0:03 nm [48] Aberration-corrected STEMs are now becomingthe standard for high-resolution imaging, with many applications to solve materialsscience problems being present in the literature [49–53]

Another advantage of the aberration corrector for STEM is the increasedusefulness of other imaging signals not traditionally exploited in scanning mode.Instead of the annular-shaped detector used for Z-contrast imaging, a detector placeddirectly on this axis will form a bright field image, which can be shown by simpleoptical reciprocity considerations to be equivalent to a conventional high-resolutionTEM phase contrast image Thanks to the larger aberration-free area of the electronwavefront, the collection angle for this bright field detector can be increased in acorrected instrument and high-quality images can be obtained [26] As a supplement

to the Z-contrast images described above, simultaneous phase-contrast images can

The Application of Scanning Transmission Electron Microscopy (STEM) 17

provide information on the location of light elements in the structure that are notimaged clearly by the Z-contrast technique On the other hand, one issue that isbrought up by the use of large apertures is the reduction in depth of focus, whereas

in the analogous case of photography, for instance, where a very small depth offocus is highly sought after to produce pleasant out-of focus backgrounds with largeaperture portrait lenses, it means in an aberration-corrected STEM that the couplingbetween the probe on the surface of the sample and the atomic columns is morecomplex While this decrease in depth of focus can have a negative effect on high-resolution imaging, it has been proposed as a method to perform optical sectioning

of samples to deliver 3-D imaging [54–57] Although in the straight STEM approach(as opposed to the confocal approach), the 3-D images suffer from distortion due tothe missing wedge of information (the same way that tilt tomography does [58,59]),

it can have applications in the study of nanostructures [60]

As stated in the previous section, the increase in spatial resolution provided byaberration correctors is accompanied by an increase in the beam current Whilethere are materials that are still able to withstand the >105e= ˚A2dose that a typicalaberration-corrected STEM image now contains, beam modification of the sample

is now a significant issue for materials science This is especially true when we start

to consider what we would like to do with the aberration-corrected STEM One

of the big impacts that the increase in resolution and sensitivity can give us is theability to look at interfaces and defects in more detail and to examine the distribution

of point defects (vacancies and impurities) around these structures However, pointdefects are mobile and by definition, the defect and interface structures are going

to be less stable than the bulk material To overcome some of the effects of beamdamage, recent work in aberration-corrected STEM has moved to lower voltages.While this will significantly reduce the effects of knock-on damage, it does not tellthe whole story of beam damage Experience from the structural biology field showsthat for organic systems, it is the electron dose that is the important thing, rather thanthe accelerating voltage This implies that knock-on damage is not going to be thelimitation for every materials system

In the case of aberration-corrected TEM, high-resolution images of organicsystems can be obtained by using the standard low-dose approach to imaging [61].Applying a similar approach to STEM is not as straightforward, as the typicalmechanism to reduce beam current is to change the parameters of the electron gun.However, this changes the electron optics in the column and leads to a misalignment

of the corrector—which is then hard to realign under low-dose conditions as the autotuning software typically requires high signal-to-noise images or diffractograms toconverge accurately Despite all of the problems, it is possible to control the dose

in the aberration-corrected STEM to permit atomic scale images to be obtained of

beam current at normal operating conditions was measured at 50 pA using theammeter behind the small phosphorus viewing screen For conventional high-doseSTEM operation, the JEM-2100F is typically operated with a gun extraction voltage(A1) of 2.8 to 3.2 kV, and an electrostatic gun lens voltage (A2) between 6.8 and7.3 kV To record images with a reduced beam current, A1 and A2 were reduced

to 0.9 kV and 6.2 kV, respectively Images were obtained using an annular field (ADF) detector with an inner cutoff angle of  30 mrad, corresponding to

dark-low-angle annular dark-field (LAADF) imaging—here incoherence is sacrificed formore electrons reaching the detector The Gatan Digiscan 688 system was used asthe scan driver, which was controlled by the Gatan Digital Micrograph softwarepackage Figure3a shows an image of SrTiO3[001] taken under the typical high-dose imaging conditions described above Here, the imaging conditions are a beamcurrent of  50 pA, a pixel dwell time of 20 s per pixel, and a pixel size of0:05 ˚A2 These imaging conditions correspond to a radiation dose of approximately

1:0  108e= ˚A2 As expected, the calculated power spectrum shows clearly visiblediffraction spots at 1.3 ˚A resolution However, the electron dose is approximately 10million times too high for most biological specimens

The most straightforward way to reduce the electron dose during image quisition in STEM is to reduce the pixel dwell time (i.e., increasing the STEMscanning speed) The Gatan Digiscan system allows the dwell time to be reduced

ac-to a minimum of 0:5 s per pixel In the STEM, magnification corresponds to

changing the pixel size We chose a magnification to give a pixel size of1:0 ˚A2.Figure3b shows an image of SrTiO3taken with a dwell time of0:5 s per pixel with

a typical probe current of approximately 50 pA The specimen is exposed to a totalradiation dose estimated to be150 e= ˚A2 A close inspection of the image, however,reveals a streaking artifact parallel to the scan direction The power spectrum andFourier-filtered image are shown inset Fourier filtering was done by masking theFourier transform spots, using a mask size of15 nm1and edge blurring of 5 pixels(1:0 nm1) Noticeable streaking is observed in the raw image, which influencesthe anisotropic background noise This observed streaking artifact is caused by

a slow reaction time of the photomultiplier/read-out electronics, which leads to

an anisotropic smearing out of individual signal peaks An additional artifact thatcontributes to the anisotropic background is a random horizontal offset of scan lines.This streaking effect can be significantly reduced by increasing the dwell time,i.e., scanning slower Using the JEOL JEM-2100F/Cs, the streaking effect wasnoticeably reduced when images were recorded with a dwell time of2:0 s per

pixel However, the fourfold increase in the dwell time would increase the electrondose from  450 e= ˚A2to  1;800 e= ˚A2 Since beam sensitive specimens often

The Application of Scanning Transmission Electron Microscopy (STEM) 19

Fig 3 Images of SrTiO3 [001] (a) acquired with aC s-corrected JEOL 2010F with a radiation dose of  5  10 8 e= ˚A2(inset fourier transform shows reflections corresponding to a resolution

of 1.3 ˚A) (b) Taken with a dwell time of0:5 s per pixel, a pixel size of 0:3 ˚A2and a typical gun current of approximately 50 pA, yielding an estimated radiation dose of  450 e  = ˚A2(inset fourier transform/inverse transform show higher order reflections at 2.0 ˚A) (c) Taken with a dwell

time of 2:0s per pixel and pixel area of 0:1 ˚A2, using a gun current of 4 pA, which gives a dose of  220 e  = ˚A2 The streaking effect is reduced in both the image and the inset fourier

transform/inverse transform) (d) Obtained with 2% of the standard gun current with a pixel dwell

time of 1:0 s and pixel size of 0:4 ˚A2 The dose is estimated to be 25 e= ˚A2(reflections at 2.7 ˚ A with corresponding lattice fringes are seen in the fourier transform/inverse transform)

require imaging with much lower electron doses, additional dose reduction isrequired We achieve this by decreasing the probe current Figure3c shows an image

of SrTiO3, that was recorded with a dwell time of2:0 s per pixel and a pixel size of0:1 ˚A2, while using a probe current of only  4% of the current used for the image

in Fig.3a The scan artifacts are noticeably less in both the image and the powerspectrum and the apparent resolution is increased with only a small increase in thetotal electron dose, estimated to be220 e= ˚A2 Note that the orientation of the lattice

20 N.D Browning et al.

is at a significant angle to the scan direction in order to minimize potential artifacts

in the Fourier transform due to periodicities induced by the scan lines In the powerspectrum, one can see spots at 1.3 ˚A, which is close to the expected resolution limit

of 1.0 ˚A for the Cs-corrected JEOL 2100F/Cs

Next, we reduced the electron dose to  15 e= ˚A2 by lowering the probecurrent further to only  2% of the probe current at full emission (corresponding

to a current  1 pA) and by decreasing the scan speed to 1:0 s per pixel, and

increasing the pixel size to 0:4 ˚A2 An example image is shown in Fig.3d TheSNR of the resulting real-space image is so low that the naked eye does not discernany structural information in this image Nevertheless, near atomic resolutionfeatures can still be documented in the power spectrum and Fourier-filtered image.Spots at 3.95 ˚A and 2.7 ˚A can be clearly seen in the calculated power spectrum

of the nonprocessed image Increasing the scan speed to 2:0 s per pixel (and

consequently doubling the dose to 30 e= ˚A2/, the power spectrum of the recorded

image showed clearly visible diffraction spots at 2.0 ˚A resolution Lowering theprobe current below 2% resulted in images that had no discernible features in thepower spectrum

The images shown in Fig.3 demonstrate that it is still possible to get highresolution from aberration-corrected images even under low-dose conditions Whilelow dose is not necessary for all samples—the examples cited above demonstratethat for the right problem, aberration-corrected STEM gives beautiful images—itdoes mean that we can use it for problems that have so far been ignored because

of the beam damage issue Furthermore, the control of the dose described here

is not the optimum approach A far better approach would be to use a set of fastdeflector plates to move the beam on/off the specimen to control the dose—therebyavoiding any change in the electron optics Such a deflector system is already underdevelopment for the dynamic transmission electron microscope (DTEM) and itsapplication to STEM should be straightforward [64]

3 Application to Nanoscale Systems

The STEM methods described above can be applied to any materials system Theinformation that can be obtained depends only on the signal to noise in the imagesthat are obtained—essentially controlled by the ability of the sample to absorbelectron dose without modifying the structure In this section, a series of exampleswill be presented that show how the STEM methods can be applied to extractquantitative information from materials systems In the first example from thestudy of clathrates, 2-D crystallography methods are used to understand and correctdistortions in STEM images and then determine an average structure In the secondexample, averaging methods are described that enables the effects of point defects

on the structure to be observed These effects are used to determine the formation

of small clusters of impurities distributed in the bulk The third example presents

The Application of Scanning Transmission Electron Microscopy (STEM) 21

an analysis of grain boundaries In this case the symmetry of the structure is broken

by the presence of grain boundary dislocations, limiting the use of crystallographicaveraging methods However, it is still possible to use multiple images of the grainboundary to infer details of statistical deviations in structure and composition in thedislocation core The fourth and final example, describes a mathematical method

to quantify the size of nanostructures to an accuracy of  10 pm The use of these

methods either individually or in combination can provide unprecedented insightsinto the structural properties of nanoscale materials

As discussed above, zone axis Z-contrast images reveal the atomic structure ofthe sample with a resolution that is defined by the probe size of the microscope

In the aberration corrected microscopes that are now standard, this resolutioncan be on the subangstrom level and is typically accompanied by an increase

in signal to noise—resulting in higher contrast images However, in some casesthe increase in beam current (that gives rise to the increase in signal to noise)results in beam damage to the sample For each material being studied, there istherefore an optimum electron dose that does not modify the structure For systemswhere this is a low number, the aberration-corrected images do not “look better”than conventional STEM images (and may even be worse) meaning that many ofthe benefits of the aberration corrector are lost As there are many expectationsamong microscopists for aberration-corrected images, sometimes experimentalistspush the beam current further than the damage limit to obtain the best lookingimages While many of the published images may be truly “representative” of thestructure, it is impossible to say for sure without an attempt to quantify the resolutionunder different beam conditions Fortunately, in most experimental cases this isrelatively straightforward to do, as the full images contain many subimages of thecrystal unit cell and/or interface structure The repetitive nature of these imagesallows standard image processing techniques that have been developed for electroncrystallography of biological macromolecules (i.e., developed to extract the highestresolution information from the noisiest images) to be applied These methods can

be used to enhance the signal-to-noise present in the original images, to removedistortions in the images that arise from either the instrumentation or the specimenitself, and to quantify properties of the material in ways that are difficult withoutsuch data processing, i.e., the improved data from aberration-corrected microscopescan be recovered even from poorer quality low-dose conditions Here this concept

is demonstrated through the analysis of Si46clathrate samples [65,66]

The test images of the K8Si46clathrate have been obtained from a 100 kV corrected VG HB501 with nominal 0.1 nm probe size (Fig.4a) Figure4b showsthe Fourier transform obtained after the image in (a) had been floated into a largerarea that was filled with a constant gray level based on the average density value

Nion-of the original image The red and blue arrows marked in this panel indicate the

22 N.D Browning et al.

Fig 4 (a) Z-Contrast image of K8Si46, (b) Fourier transform of the image and (c) the definition

of the reciprocal lattice points used to construct the lattice The scale bar in (a) represents 1.0 nm and the white arrow in (b) marks a reflection at0:164 nm1resolution

Fig 5 (a) Unit cell locations, (b) distortion field, (c) reciprocal lattice from Fig.4

reciprocal space lattice vectors that describe the unit cell Figure4c is identical to(b), with the reciprocal space lattice points being marked using green circles Thered and blue circles nearest the origin of the Fourier transform respectively mark thepositions of the (10) and (01) reflections that were used to build this lattice and thatdefine the unit cell Note that this lattice marks both the clearly visible diffractionspots and also extends the regions of the Fourier transform that appear featureless

in this representation The total number of possible lattice points in this Fouriertransform is >2;600 while the number that fall within the default resolution limits

of the microscope is only  1;000

Having defined the image and Fourier transform of the image, standard ing techniques can then be applied In Fig.5, the unit cell locations and vectordistortion field found during unbending and IQ plot of structure factors is shown.Figure5a shows the location of unit cells found in the image created after floatingFig.4a into a larger array for image processing The size of the point marking eachunit cell is related to the quality (IQ, or strength of the signal in the cross-correlationmap) of the unit cell, with the largest points indicating the best locations The bestunit cell locations are limited to the region of the image that contains the imageshown in Fig.4a Figure5b shows the distortion field mapping the deviation between

process-The Application of Scanning Transmission Electron Microscopy (STEM) 23

Fig 6 (a) Z-Contrast image of the K8Si46 clathrate, (b) reconstructed image using parameters

from Figs 1 and 2, (c) reconstructed image after shifting phases, (d) reconstructed image after

imposing the correctp4mm symmetry and (e) reconstruction with incorrect phase offset

found locations and expected locations for individual unit cells For clarity, thevectors have been magnified by a factor of 10 as within the region of the crystalthe vectors are very small and point in similar directions The vectors associatedwith noise (the unit cell locations marked by very small points in Fig.5a) are muchlarger and random compared to their neighbors Figure5c shows the full reciprocalspace lattice shown only partially in Fig.4c and maps structure factor IQ (a measure

of local S/N) to location on the lattice Larger boxes mark higher local S/N andreflections with the highest S/N (lowest IQ) cluster near the origin of the FFT.The analysis described above essentially allows us to identify and “correct” some

of the artifacts in the image and to quantify the details in the image In Fig.6a, whichagain shows a [001] zone axis view of the structure, the outline of the central unitcell is marked using red lines A second repeating motif is marked with black lines.Both the red and black lines delineate motifs that use identical unit cell vectors butdiffer with regard to the central atom of the unit cell (phase origins in Fourier space).Figure6b shows a2  2 array of unit cells generated by crystallographic methods

using the structure factors extracted from the image in Fig.6a after two cycles ofunbending (following the method in Figs.4and5) Figure6c shows the same2  2

array of unit cells after phase shifting the unit cell origin so that the expectedp4mm

symmetry is best obeyed Figure6d shows a2  2 array of unit cells generated by

crystallographic methods after enforcingp4mm symmetry This involves forcing all

the phases to be either 0 or180ıand averaging symmetry-related reflections ure6e shows the incorrect result of enforcingp4mm symmetry without phase shift-

Fig-ing the structure factor data to the correct phase origin—i.e., we can clearly identifyand impose the correct symmetry on the image The summation of all these steps

is that the effects of low signal to noise on images can be accounted for and highquality images can be obtained where the contributions to contrast can be quantified

24 N.D Browning et al.

These methods have been successfully used to quantify site occupancy inclathrates through direct comparison to Z-contrast image simulations [65]—thisinvolves simulating the image and comparing the results to the processed images.Through such methods, high-resolution images can be obtained under a variety ofconditions so that the effect of the beam on the sample can be easily identified.Furthermore, the structure that is determined under the varying conditions can

be statistically defined—the number of images needed to obtain a given structureconverged to a particular resolution under a given set of beam conditions With data

in this form, any statistical variability in the structure/composition can focus onunderstanding the synthesis rather than the experimental measurement

Another area where aberration correctors can make a large impact is the analysis of adistribution of diffuse point defects across an extended sample To demonstrate this,

a systematic study of nitrogen-doped GaAs samples was undertaken [67] Figure7shows a series of Z-contrast images from four groups of three GaAsN quantumwells grown between GaAs barriers by molecular beam epitaxy (MBE), each groupwith different N compositions (0.1%, 0.4%, 1%, and 2.5%) The N compositionwas controlled by monitoring the optical intensity of the atomic N plasma emissionduring growth As with the results on the clathrates, the high-resolution HAADF–STEM study was performed using a Nion aberration-corrected VGHB501-dedicatedSTEM operated at 100 kV with a nominal probe size of 0.1 nm

The initial HAADF–STEM analysis of the GaAsN QWs at low magnification led

to an interesting result As can be observed in the inset in Fig.7a, the GaAsN0:025quantum wells appear brighter than the GaAs barriers when imaged in HAADF–STEM despite the reduced average atomic number As pointed by early studies byPerovic et al [68] and Treacy et al [69] and more recently by Grillo et al [70],the local distortion of the lattice plays a major role in HAADF–STEM imaging ofnonperfect crystals Thus, the origin of the observed contrast may rely on the localdistortion of the lattice due to the introduction of N, as pointed by Wu et al [71]

As we can see from Fig.7a, the evolution of contrast with the N content does notfollow a linear behavior; the slope of the curve for low N concentration is relativelylarge and for the higher N content the curve levels off The origin of this change

in contrast with %N is not immediately clear for what is supposed to be a randomsubstitutional alloy (note that the contrast behavior is similar for a wide range ofdetector angles, suggesting that it is an intrinsic function of the material rather than

a unique experimental condition that causes this contrast)

To investigate the origin of the observed evolution of contrast with %N, higherresolution images were obtained (Fig.7b) For each high resolution image, the

The Application of Scanning Transmission Electron Microscopy (STEM) 25

Fig 7 (a) Z-Contrast image intensity increases as a function of N concentration, (b) high resolution Z-contrast image for the 2.5% doping case, (c) image contrast on the columns, (d) image contrast between the columns, (e) average dumbbell spacing

contrast from the valley between the atomic columns and from the atomic columns

is plotted vs %N in Fig.7c and d, respectively The intensity valley/peak hasbeen measured individually for each dumbbell in each image for up to 6 imagesper concentration; the error bars correspond to the standard error over all thesemeasurements (this measurement makes use of the fact that there are hundreds

of dumbbells in each high resolution image) As can be clearly seen, the contrastfrom the valleys between columns shows a strong increase and then flattens off forhigher N concentration, similar to the behavior obtained from the low magnificationimages, whereas the increase in contrast from the atomic columns is negligible.This reveals that the increased intensity found in GaAsN originates specifically fromthe valleys between the atomic columns rather than from the columns themselves.Additionally, the average dumbbell spacing was measured from the images, finding

a nonlinear reduction with increasing N content (Fig.7e) This behavior is likelycaused by the incorporation of N introducing an additional strain component in thelattice

26 N.D Browning et al.

Fig 8 (a) Plot of the contrast vs N content from the simulated images of the different complexes,

where open symbols correspond to the valley between the columns and solid symbols to the atomic

columns; a schematic picture of each complex is included where the dark atoms represent N,

the dark grey Ga and the light grey As; (b) averaged dumbbell spacing ratio measured from the

simulated images

In order to interpret the experimental results [67], a series of possible defectstructures was simulated by density functional theory and then image calculationswere performed using a multislice code [72] Figure8 shows a summary of theresults for the possible defect configurations in GaAsN As can be seen fromFig.8, the 2N substitutional complex is the only one for which the simulationsagree with the experimental results These results clearly point to the absence ofinterstitials in the alloy and to the onset of N clustering Substitutional N pairingwith up to four neighbor positions in GaAs1xNx alloys withx < 0:025 has been

reported previously, in good agreement with these experimental observations [73].The important aspect of these results is that by using the small variations that occuracross the image (again, there are hundreds of GaAs dumbbells per image) highlyquantitative analyses of images can deduce the effect of diffuse point defects onthe overall structure This type of defect analysis can of course be coupled with theimage processing techniques demonstrated for the clathrates in the previous section.The key aspect of such an analysis is that the processing techniques can removeimage to image variability caused by the experimental parameters, and allow us

to define a structure with confidence limits and compare directly many differentmeasurements

The Application of Scanning Transmission Electron Microscopy (STEM) 27

magnetore-is a necessary component for understanding the mechanics of grain boundarydoping—a powerful method to alter or control the influence of the grain boundary

on the bulk properties The importance of the grain boundary plane in controllingthe properties of perovskites (and in particular SrTiO3/ has led to many studies by

TEM and STEM over the last 20 years [79–85]

The basis for understanding the structure of [001] tilt grain boundaries in SrTiO3

is the structural unit model proposed by Sutton [86] and expanded further bySTEM studies in the mid-1990s [87–90] The basic principle of the structuralunit model is that the atoms in a dislocation core will arrange themselves into arepeating “structural unit.” Any grain boundary that forms will then be composed

of a sequence of these structural units with a distribution that correlates directlywith the expected dislocation core spacing from Frank’s rule [91] along the grainboundary plane (Fig.9) The structural unit model provides an identical description

of the grain boundary plane as is obtained from dislocation core models thatuse the burgers vector of the dislocation to define the spacing and energy of theboundary The difference is that the structural unit model focuses on the atomicstructure of the cores rather than the strain fields associated with them As such, thestructural unit model allows the presence of a sublattice to be incorporated into anymodel that interprets properties and there is a seamless transition from low-anglegrain boundaries to high-angle grain boundaries The initial analysis of structuralunits obtained from nonaberration-corrected microscopes allowed models for grainboundaries that incorporated partially occupied columns [87–90], and later oxygenvacancies [92–94] and the presence of dopant atoms on sites determined by the localstrain at the grain boundary rather than the bulk defect chemistry [50] However,while the structural units that were observed at [001] tilt grain boundaries alwaysappeared to have the same structure, there was a large variability in the bond lengthsand the apparent composition of the cores Unfortunately, given the resolution andlack of stability of the nonaberration-corrected instruments it was difficult to seeall of the atoms in the cores and impossible to quantify the contrast variations

28 N.D Browning et al.

Fig 9 (a) Schematic of an asymmetric [001] tilt grain boundary In SrTiO3showing the structural

units as dislocation cores and (b) the structural units necessary to make up all [001] tilt grain

boundaries from 0–90ıon both sub-lattices

(i.e., composition changes) on the required atomic scale Nevertheless, the modelstructures allowed the effects of grain boundary chemistry to be predicted

The success of the structural unit model in describing grain boundaries in SrTiO3led to a6ı low-angle [001] tilt grain boundary being used as one of the first testspecimens for the FEI 80–300 kV double corrected and monochromated Titan atLLNL [95] Here the main aim of the test was not resolution (the important spacingfor images is  0:27 nm and probe size in the Titan is  0:1 nm), but rather to

see the level of contrast and sensitivity that could be achieved with an corrected instrument With the advances in specimen preparation technology, theincreased signal to noise in the images and the improved stability of the microscope,many images were obtained from the grain boundary plane that highlighted the corestructure From a single day’s analysis, images containing 167 dislocation coreswere obtained These cores showed a high degree of variability from the simplestructural unit model described above (which may be due only to the ability to seethe structure more clearly with the aberration-corrected microscope or may also bedue to the method of grain boundary synthesis)

aberration-The Application of Scanning Transmission Electron Microscopy (STEM) 29

Fig 10 Z-Contrast images of (a) the elongated core, (b) the composite core and (c) the

transformed core (spacing between the brightest spots in the image is the Sr sub-lattice  0:4 nm).

(d) Probability density map of the sum of 167 cores showing the potential for variability in the core

region

The three types of dislocation cores shown in Fig.10(which occur in addition

to the standard structural unit cores) are referred to as elongated, composite,and transformed The elongated core appears in both a Sr- and Ti-rich varietyand is marked by the splitting of the column closest to the usual reconstructedcolumns seen in the structural units—elongating the core The composite corehas the termination of (100) planes in different places on the two sublatticesmaking it a composite structural unit of both sublattices This core structure isreminiscent of partial dislocations but there is no stacking fault separating them.The transformed core is the most surprising, containing closely packed Ti columns(confirmed by EELS) closer to a TiO2 arrangement than a SrTiO3 arrangement of

The variability in the core structures observed here has potential implications formany aspects of the properties of grain boundaries Typically for electroceramics,the electronic and ionic properties of grain boundaries are controlled by thecomposition of the grain boundary core The results here show that variability exists

in the pristine structure even before you try and dope the grain boundary to modifythe properties Future work in this area will move toward quantifying the numbers

of each type of core that are present, and defining their locations along the grainboundary plane—by a detailed statistical analysis of thousands of cores it may bepossible to tailor a processing step that addresses the worst/best core for a givenmaterials property

Catalysis is the key to controlling chemical change It is the enabling technology ofchemical manufacture, energy conversion, and much of green chemistry via pollu-tion avoidance and pollution abatement More than 60% of the industrial productsand 90% of the processes involving chemical change are based on catalysis, andinnovations are increasingly reliant on catalysis [96–98] Many important catalystsare metals, and the most useful of them are dispersed on high-area supports Assupported metal particles are made smaller and smaller into the nanoscale regime,their properties deviate more and more from those of the bulk, and they offer newopportunities attributed to both size and support effects To understand the properties

of nanoscale catalysts the most important factor that must be characterized by STEM

is therefore the size of the nanoclusters Quantifying the size of nanoclusters seemslike a trivial proposition for a microscope with0:05 nm resolution, particularly

when the typical heterogeneous catalyst system consists of heavy metal nanoclusters

on a light support (very good for Z-contrast imaging) However, the issue with thenanoclusters is that they tend to move across the surface of the support under theinfluence of the beam The more intense the beam gets through the use of aberrationcorrectors, the more likely it is that the metal clusters will move [99] Hence, aswith the previous examples, we would like to have the resolution of the aberrationcorrector but with significantly lower beam current—leading to poorer signal tonoise in the images and increased error bars in particle size measurements

To generate an accurate measurement, meas, of nanocluster sizes, a generalmathematical formalism involving a convolution-blurring/curve-fitting algorithmhas been developed [100,101] For this method, we assume that we have a Z-contrast

The Application of Scanning Transmission Electron Microscopy (STEM) 31

STEM image with identifiable bright spots representing isolated small atomicclusters on a relatively slowly varying background (support), and that the clustersare drawn from a statistical distribution of perhaps a few different sizes and shapes.What we need to be able to generate is a precise measurement of the size of eachkind of cluster, as well as an ability to distinguish various clusters on the basis oftheir size in order to produce population statistics of the various species present To

do this, we curve fit each particle image with a Gaussian peak plus a polynomialbackground to extract an estimate of its root-mean-square radiusrRMS (as well asits total “mass,” which can also be used to help classify particles into species).This initial estimate may be subject to bias arising from the background signal,from random noise peaks, from the fact that the particle itself is not a Gaussiandistribution of mass density, and from various point spread functions that blurthe image In order to try to average out the effects of some of these biases, wedeliberately blur the image—digitally—using a Gaussian kernel with widthgb.Small values ofgbmay be more prone to random noise spikes and limited quality

of the curve fit, whereas larger values may be more influenced by effects from thebackground and, eventually, from the fact that the measured size will be dominated

by the blur A curve fit of the extractedr2

RMSversus2

gbresults in an estimate of whatwould have been measured in a noise-free measurement with zero artificial blurring.This measurement is further corrected for systematic effects arising from the knownpoint spread function including contributions from the probe size, vibrations, andfocus errors [101] Focus errors in particular are minimized by taking a through-focus series and analyzing, for each particle, its image at the focus value for which

it appeared smallest

We used the method described above to analyze images of MgO-supporteddecaosmium carbido carbonyl clusters, [Os10C.CO/242, formed by the reaction

of triosmium carbonyl precursors, Os3.CO/12, in the presence of CO Osmium

in various forms is a catalyst for various conversions of hydrocarbons, includingalkene hydrogenation [102] MgO-supported osmium carbonyl clusters were chosenbecause; (1) osmium clusters of various nuclearities (such as 3, 5, and 10 atoms)can be synthesized uniformly and selectively on MgO support surfaces [103–105].(2) the structures ofŒOs10C.CO/242and Os3.CO/12are well characterized (in thesolid state by X-ray diffraction crystallography [106,107] and on MgO surfaces byEXAFS spectroscopy and infrared spectroscopy [103–105]); and (3) the heavy Osatoms show high contrast relative to the light MgO support in HAADF imaging Thecore structural models of theŒOs10C.CO/242and Os3.CO/12clusters determinedfrom the crystallographic data are illustrated in Fig.11

The RMS radii of Os3.CO/12 andŒOs10C.CO/242 were calculated from thecrystal structures in Fig.11and the electron elastic scattering cross-section databasedistributed by the National Institute of Standards and Technology (NIST) [109].The resultant theoretical RMS radii of Os3.CO/12 andŒOs10C.CO/242are 0.202and 0.295 nm, respectively Note that the CO ligands (not shown in the figure) aresignificant contributors to the overall RMS radii Figure12a shows a raw HAADF–STEM image of the MgO-supported clusters obtained from an uncorrected JEOL2500SE 200 kV TEM/STEM It is very difficult to measure the cluster size from the