COMMENTARY IINSIGHT Is science prepared for atomic- resolution electron microscopy? Knut W.Urban The efforts of microscopists have given aberration-corrected transmission electron microscopy the power to reveal atomic structures with unprecedented precision.It is now up to materials scientists to use this power for extracting physical properties from microscopic atomic arrangements. odern aberration-corrected advanced computer-based techniques from this point it is enough to realize that none transmission electron microscopy data obtained with microscopes equipped of the electrons entering the sample is (TEM)provides genuine atomic with highly coherent field-emission electron actually absorbed there.So although it resolution,and there is no doubt that sources.Even afterwards,although exit is extremely tempting to think of atomic this opens up a new dimension for plane-wavefunction (EPWF)reconstruction structures as being shadow-cast in an materials research'.However,although the developed into a powerful tool in high- electron microscope,this view is incorrect microscopy community may be aware of resolution TEMS,only rarely was it applied and misleading. the giant steps forward that the field has to the study of materials containing atoms As the electron waves propagate made in the past decade,these steps may of low nuclear charge,such as oxygen through the sample,they interact with be difficult for a wider scientific audience or nitrogen7.Direct atomic-resolution the interatomic potential.Owing to the to appreciate.For decades this audience imaging of these elements had to await the high energies of the electrons(typically has seen gratings of bright and dark dots invention of aberration-corrected TEM. 200 to 300 kev)this interaction has to be reported in the literature and has generally described by the Dirac equation,which assumed that they were atomic-resolution The power of this technique is for the conditions applying to TEM adopts images of crystals,almost as though a Schrodinger form with relativistically they had been taken with a very high- that it is possible to determine corrected electron wavelength and magnification light-optical microscope.The local physical properties mass.Solving this equation for a given reality is that TEM has less in common with interatomic potential gives the EPWF- light imaging than it may seem.There are directly from measurements the wavefunction at the exit plane-of several differences in the way in which data of shifts of the individual the specimen.At a time when second- are acquired and interpreted that should be order partial differential equations can be taken into consideration when electron and atom positions. solved in next to no time on a computer, light optical images are compared,or when this sounds simple.But the basic task atomic resolution is discussed. With this new technique,the phenomenon in atomic-resolution TEM is not that of of oxygen-vacancy ordering in YBa Cu,O, calculating how scattering from atoms A brief history of TEM was proven in 2003(ref.9),and oxygen affects the electron wavefunction,rather Examining a handful of crucial concentration measurements on the atomic the opposite:inferring the atomic structure developments in electron microscopy over scale were carried out for the first time in from the experimentally measured electron the past two decades soon shows that atomic an investigation of lattice defects in BaTiO, wavefunction.This is a much more laborious resolution is only a recent achievement. in 2004 (ref.10).More recently it was and demanding task. During 1987,the world's leading electron demonstrated that atomic positions can be The electron wavefunction at the plane microscopy groups tried to contribute to an measured by aberration-corrected TEM where the electrons leave the specimen understanding of the recently discovered at a precision of a few picometres".The contains,in quantum-mechanically encoded phenomenon of high-temperature power of this technique is that it is possible form,all the information on the specimen superconductivity by attempting to image to determine local physical properties that can be obtained.This EPWF is in fact oxygen in YBa,Cu,O,.But although directly from measurements of shifts of the actual object-in optical terms-of structural studies by TEM helped the individual atom positions,fulfilling the microscope.Unfortunately,however, substantially in the development of this the old dream of materials science:a direct the microscope does not provide this field,insufficient optical resolution meant link between atomic-level information and wavefunction in any direct form,certainly that they were unable to contribute to the macroscopic properties. not in the form of an image.As the human solution of one of the key problems-how brain cannot intuitively understand the occupation of specific atomic sites with The correct view on TEM images quantum-mechanical wavefunctions,the oxygen influences electronic properties23. The conventional concept of image,which so-called 'images'recorded in the image Oxygen was not accessible by any imaging applies,for example,to light microscopy,is plane of the instrument are at first nothing technique until 1992,when it was shown that of a spatial display of local variations more than wave interference patterns. that it is visible at atomic resolution in the in the absorption of light.This cannot be These have to be reversed toto extract the electron wavefunction at the exit plane applied to the quantum mechanical world EPWF.As will be explained later,such a task of the specimen when reconstructed by of atoms and electrons.To understand cannot be solved with a single acquisition. 260 NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
260 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials commentary | insight Is science prepared for atomicresolution electron microscopy? Knut W. Urban the efforts of microscopists have given aberration-corrected transmission electron microscopy the power to reveal atomic structures with unprecedented precision. It is now up to materials scientists to use this power for extracting physical properties from microscopic atomic arrangements. Modern aberration-corrected transmission electron microscopy (TEM) provides genuine atomic resolution, and there is no doubt that this opens up a new dimension for materials research1 . However, although the microscopy community may be aware of the giant steps forward that the field has made in the past decade, these steps may be difficult for a wider scientific audience to appreciate. For decades this audience has seen gratings of bright and dark dots reported in the literature and has generally assumed that they were atomic-resolution images of crystals, almost as though they had been taken with a very highmagnification light-optical microscope. The reality is that TEM has less in common with light imaging than it may seem. There are several differences in the way in which data are acquired and interpreted that should be taken into consideration when electron and light optical images are compared, or when atomic resolution is discussed. a brief history of tem Examining a handful of crucial developments in electron microscopy over the past two decades soon shows that atomic resolution is only a recent achievement. During 1987, the world’s leading electron microscopy groups tried to contribute to an understanding of the recently discovered phenomenon of high-temperature superconductivity by attempting to image oxygen in YBa2Cu3O7. But although structural studies by TEM helped substantially in the development of this field, insufficient optical resolution meant that they were unable to contribute to the solution of one of the key problems — how the occupation of specific atomic sites with oxygen influences electronic properties2,3. Oxygen was not accessible by any imaging technique until 1992, when it was shown that it is visible at atomic resolution in the electron wavefunction at the exit plane of the specimen when reconstructed by advanced computer-based techniques from data obtained with microscopes equipped with highly coherent field-emission electron sources4 . Even afterwards, although exit plane-wavefunction (EPWF) reconstruction developed into a powerful tool in highresolution TEM5 , only rarely was it applied to the study of materials containing atoms of low nuclear charge, such as oxygen or nitrogen6,7. Direct atomic-resolution imaging of these elements had to await the invention of aberration-corrected TEM8 . With this new technique, the phenomenon of oxygen-vacancy ordering in YBa2Cu3O7 was proven in 2003 (ref. 9), and oxygen concentration measurements on the atomic scale were carried out for the first time in an investigation of lattice defects in BaTiO3 in 2004 (ref. 10). More recently it was demonstrated that atomic positions can be measured by aberration-corrected TEM at a precision of a few picometres11. The power of this technique is that it is possible to determine local physical properties directly from measurements of shifts of the individual atom positions12, fulfilling the old dream of materials science: a direct link between atomic-level information and macroscopic properties. the correct view on tem images The conventional concept of image, which applies, for example, to light microscopy, is that of a spatial display of local variations in the absorption of light. This cannot be applied to the quantum mechanical world of atoms and electrons. To understand this point it is enough to realize that none of the electrons entering the sample is actually absorbed there. So although it is extremely tempting to think of atomic structures as being shadow-cast in an electron microscope, this view is incorrect and misleading. As the electron waves propagate through the sample, they interact with the interatomic potential. Owing to the high energies of the electrons (typically 200 to 300 keV) this interaction has to be described by the Dirac equation, which for the conditions applying to TEM adopts a Schrödinger form with relativistically corrected electron wavelength and mass. Solving this equation for a given interatomic potential gives the EPWF — the wavefunction at the exit plane — of the specimen. At a time when secondorder partial differential equations can be solved in next to no time on a computer, this sounds simple. But the basic task in atomic-resolution TEM is not that of calculating how scattering from atoms affects the electron wavefunction, rather the opposite: inferring the atomic structure from the experimentally measured electron wavefunction. This is a much more laborious and demanding task. The electron wavefunction at the plane where the electrons leave the specimen contains, in quantum-mechanically encoded form, all the information on the specimen that can be obtained. This EPWF is in fact the actual object — in optical terms — of the microscope. Unfortunately, however, the microscope does not provide this wavefunction in any direct form, certainly not in the form of an image. As the human brain cannot intuitively understand quantum-mechanical wavefunctions, the so-called ‘images’ recorded in the image plane of the instrument are at first nothing more than wave interference patterns. These have to be reversed to to extract the EPWF. As will be explained later, such a task cannot be solved with a single acquisition. the power of this technique is that it is possible to determine local physical properties directly from measurements of shifts of the individual atom positions. nmat_2407_APR09.indd 260 11/3/09 11:17:46 © 2009 Macmillan Publishers Limited. All rights reserved
INSIGHT COMMENTARY Typically 20 images are required,and these into amplitude information)needs to be Image series have to be taken to form are recorded by varying,for example,the applied in TEM as well.In light microscopy the starting point of wavefunction objective lens focus in discrete steps over this is achieved by using Zernike's 90 reconstruction and subsequent atomic- a certain range.Because varying the focus phase plate which advances the phase structure computation.Unfortunately,in induces phase shifts into the electron wave of the scattered beams into an antiphase quantum mechanical dimensions,there is field,this technique has similarities to relation to the incident beam.This makes also no way to know a priori the exact focus interferometry.On the basis of this image the scattering regions appear dark on a of the lens,nor can the focus be judged series,the EPWF can be calculated using bright background.Unfortunately there is reliably by visual inspection.Recording the fairly involved computer codes of the no analogue of Zernike phase shifters in a series of images at varying lens defocus wavefunction reconstruction technique45. TEM.But,inconvenient though it may be provides us with a solution to this problem. The second step is to extract the the necessary phase shift can be introduced Following an iterative procedure,the specimen structure from the EPWE In by making use of the aberration-induced correct focus is obtained and the EPWF is spite of some progress344,no technique is phase-shifting properties of the microscope's computed.With the EPWF and the eventual yet known that allows direct calculation of objective lens's.6.To obtain contrast,the sample structure available,it is no problem the interatomic potential to plug into the lens's spherical aberration parameter has to to select from a series of images the one equations,and thus calculate the structure be tuned for a certain positive or negative whose intensity distribution best fits the back from the EPWF.The only solution residual value (a few per cent of the original measured atomic structure.This is generally is to do a forward calculation.That is,a aberration).Because a deviation from the image that electron microscopists model structure based on a first guess is exact focus also contributes to the desired include in their publications,as it permits constructed and iteratively improved to phase shift,this is combined with a certain in most cases the intuitive interpretation for obtain a best fit between the calculated and amount of defocusing.Colloquially,we which the reader is prepared.But without experimental EPWE In addition to the can say that the price for seeing anything thorough investigation of their background, formidable task of properly adjusting the at all is to accept that the images have to be as just described,such single images are of positions of a large number of atoms with unsharpened to a certain extent. limited value. sub-atomic precision in the model,the procedure is hampered by the fact that in Not just a single image Atomic resolution in TEM atomic dimensions there is no direct access As mentioned previously,atomic-resolution So,why are the images that appeared in to such important imaging parameters as TEM is,despite common understanding, the literature for so long not necessarily sample thickness and the precise direction generally not based on a single acquisition. atomically resolved?Resolving a structure of the incident electrons.The only way is to treat these parameters as variables that must also be determined by means of the fitting procedure.The final result is a computer model with atomic species and coordinates,rather than an image in the conventional sense Aberrations not wanted but needed Once again in contrast to light microscopy, where total elimination of aberrations is routinely achieved with high-precision optics,imaging in the fully aberration- 00 0 0、 0 corrected mode,although technically 0 0 0 0 feasible,is never used in transmission 0 0 electron microscopy.This is because 0 d 10 0 optical resolution is not sufficient:contrast 0 0 0 0 is also needed.For simplicity,in the 0 following explanation I will refer only to 0 9 0 the most important lens aberration,the 0 0 0 spherical aberration.The reason why the microscope has to be operated with a Figure 1 Computer-simulated images for a SrTiO,crystal oriented along a crystallographic [110] certain value of residual aberration is that direction.a-c,Images corresponding to different widths of aperture in the back focal plane(f)of the atomic-resolution electron microscopy microscope's objective lens selecting the beams that contribute to image formation.In the sequence a is mainly based on phase contrast.This to c,the sample contains a microhole consisting of an empty atom column.With the smallest aperture means that information on the specimen (the full circle in f),only the transmitted and four diffracted beams are used to form the image.This structure is encoded in the EPWF in terms situation corresponds to classical uncorrected electron microscopy where wider apertures cannot be of a locally varying phase shift.This can tolerated because of the effect of lens aberrations.Superficially,a appears to show an atomic lattice,but intuitively be understood by considering this bears little resemblance to the real lattice imaged in c with the widest aperture setting (dashed line the atoms as regions of elevated refractive in f).Atomic resolution is only provided in c.Note the artefacts in b taken with the intermediate aperture index leading locally to an advancement size (dash-dotted line in f).Two 'atomic maxima'appear on both sides of the hole.In a the hole appears, of the phase of the electron waves.To unrealistically,to be a more intense maximum.Images d and e,corresponding to the smallest and the visualize the phase differences,a technique largest aperture size,respectively,show simulations for a 30%reduction in occupancy of the atomic analogous to Zernike phase contrast in position marked with an arrow in e.To reveal this reduction in occupancy,the large aperture used in an light microscopy(that is,converting phase aberration-corrected instrument is essential. NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 261 2009 Macmillan Publishers Limited.All rights reserved
nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 261 insight | commentary Typically 20 images are required, and these are recorded by varying, for example, the objective lens focus in discrete steps over a certain range. Because varying the focus induces phase shifts into the electron wave field, this technique has similarities to interferometry. On the basis of this image series, the EPWF can be calculated using the fairly involved computer codes of the wavefunction reconstruction technique4,5. The second step is to extract the specimen structure from the EPWF. In spite of some progress13,14, no technique is yet known that allows direct calculation of the interatomic potential to plug into the equations, and thus calculate the structure back from the EPWF. The only solution is to do a forward calculation. That is, a model structure based on a first guess is constructed and iteratively improved to obtain a best fit between the calculated and experimental EPWF. In addition to the formidable task of properly adjusting the positions of a large number of atoms with sub-atomic precision in the model, the procedure is hampered by the fact that in atomic dimensions there is no direct access to such important imaging parameters as sample thickness and the precise direction of the incident electrons. The only way is to treat these parameters as variables that must also be determined by means of the fitting procedure. The final result is a computer model with atomic species and coordinates, rather than an image in the conventional sense aberrations not wanted but needed Once again in contrast to light microscopy, where total elimination of aberrations is routinely achieved with high-precision optics, imaging in the fully aberrationcorrected mode, although technically feasible, is never used in transmission electron microscopy. This is because optical resolution is not sufficient: contrast is also needed. For simplicity, in the following explanation I will refer only to the most important lens aberration, the spherical aberration. The reason why the microscope has to be operated with a certain value of residual aberration is that atomic-resolution electron microscopy is mainly based on phase contrast. This means that information on the specimen structure is encoded in the EPWF in terms of a locally varying phase shift. This can intuitively be understood by considering the atoms as regions of elevated refractive index leading locally to an advancement of the phase of the electron waves. To visualize the phase differences, a technique analogous to Zernike phase contrast in light microscopy (that is, converting phase into amplitude information) needs to be applied in TEM as well. In light microscopy this is achieved by using Zernike’s 90° phase plate which advances the phase of the scattered beams into an antiphase relation to the incident beam. This makes the scattering regions appear dark on a bright background. Unfortunately there is no analogue of Zernike phase shifters in TEM. But, inconvenient though it may be, the necessary phase shift can be introduced by making use of the aberration-induced phase-shifting properties of the microscope’s objective lens15,16. To obtain contrast, the lens’s spherical aberration parameter has to be tuned for a certain positive or negative residual value (a few per cent of the original aberration). Because a deviation from exact focus also contributes to the desired phase shift, this is combined with a certain amount of defocusing. Colloquially, we can say that the price for seeing anything at all is to accept that the images have to be unsharpened to a certain extent. not just a single image As mentioned previously, atomic-resolution TEM is, despite common understanding, generally not based on a single acquisition. Image series have to be taken to form the starting point of wavefunction reconstruction and subsequent atomicstructure computation. Unfortunately, in quantum mechanical dimensions, there is also no way to know a priori the exact focus of the lens, nor can the focus be judged reliably by visual inspection. Recording a series of images at varying lens defocus provides us with a solution to this problem. Following an iterative procedure, the correct focus is obtained and the EPWF is computed. With the EPWF and the eventual sample structure available, it is no problem to select from a series of images the one whose intensity distribution best fits the measured atomic structure. This is generally the image that electron microscopists include in their publications, as it permits in most cases the intuitive interpretation for which the reader is prepared. But without thorough investigation of their background, as just described, such single images are of limited value. atomic resolution in tem So, why are the images that appeared in the literature for so long not necessarily atomically resolved? Resolving a structure a d e f b c Figure 1 | Computer-simulated images for a SrTiO3 crystal oriented along a crystallographic [110] direction. a–c, Images corresponding to different widths of aperture in the back focal plane (f) of the microscope’s objective lens selecting the beams that contribute to image formation. In the sequence a to c, the sample contains a microhole consisting of an empty atom column. With the smallest aperture (the full circle in f), only the transmitted and four diffracted beams are used to form the image. This situation corresponds to classical uncorrected electron microscopy where wider apertures cannot be tolerated because of the effect of lens aberrations. Superficially, a appears to show an atomic lattice, but this bears little resemblance to the real lattice imaged in c with the widest aperture setting (dashed line in f). Atomic resolution is only provided in c. Note the artefacts in b taken with the intermediate aperture size (dash-dotted line in f). Two ‘atomic maxima’ appear on both sides of the hole. In a the hole appears, unrealistically, to be a more intense maximum. Images d and e, corresponding to the smallest and the largest aperture size, respectively, show simulations for a 30% reduction in occupancy of the atomic position marked with an arrow in e. To reveal this reduction in occupancy, the large aperture used in an aberration-corrected instrument is essential. nmat_2407_APR09.indd 261 11/3/09 11:17:47 © 2009 Macmillan Publishers Limited. All rights reserved
COMMENTARY INSIGHT precision is that it cannot be allowed by 0.0 a microscope with a 70-pm Rayleigh or 0.02 年年◆季专果果票 0 point resolution2.However,resolution -0.02 华◆*中中蒙单 and precision are two separate physical -0.04 60 terms.Although resolution is defined by the minimum separation of two optically 80■■ 40 ■■ broadened intensity peaks at which these ■ OA can just be separated in the image,the -40 distance between two well-isolated peaks, -80 ■■■■■■■ fitted for example by two-dimensional 0 10 Gaussians,can be measured at a precision Distance (in units of c) more than an order of magnitude higher. It would be a real pity to turn down the Figure 2 Polarization domain wall in ferroelectric PZT.a,Atomic structure.Arrows give the direction extraordinary opportunities offered by of the spontaneous polarization,which can be directly inferred from the local atom displacements.The aberration-corrected electron microscopy shifts of the oxygen atoms (blue circles)out of the Ti/Zr-atom rows (red circles)can be seen directly,as because of an unfortunately common can the change in separation between Ti/Zr and Pb(yellow circles).b,Atomic-resolution measurements misunderstanding. of the shifts of oxygen(),and titanium/zirconium (atoms as a function of distance from the wall centre (units of c-lattice parameter)in a longitudinal-inversion domain wall;c,The value of the local A question to conclude polarization Ps that can be calculated from these data.Adapted from ref.12.2008 NPG. Is the scientific community ready to receive the extraordinary new results achievable through aberration-corrected with atomic resolution means that the and c),which in early work could not be transmission electron microscopy?Readers information must be entirely local on the used for the image formation because of the may find their own individual answer to atomic level.Any change in the position detrimental influence of lens aberrations this question.The everyday life of electron or occupancy of an atomic site in the Over the past three decades,taking microscopists active in this field shows that sample must show up in the image as an so-called 'high-resolution'images has there is still some way to go in alerting the individual signal localized only at the become a common technique in materials scientific community to the opportunities corresponding atomic position.In this science.Some of this work was capable of offered by measuring quantum mechanical stringent sense,apart from a few favourable atomic-scale resolution.In particular this wavefunctions in atomic dimensions. cases,only the images obtainable in applies to studies in which the EPWF was So great is the potential of these new modern aberration-corrected instruments calculated from an image series,even in techniques that it will be well worth match these standards.The concept is non-corrected instruments,when in EPWF engaging in such a process. illustrated in Fig.1. reconstruction the optical aberrations were corrected to a certain extent by software. Knut W.Urban is at the Institute of Solid State It would be a real pity to Nevertheless,the bulk of this earlier work Research and the Ernst Ruska Centre for Microscopy was concerned not with individual atoms and Spectroscopy with Electrons,Research Centre turn down the extraordinary but rather with collective properties such Juilich,D-52425 Jilich,Germany opportunities offered by as crystal structures,lattice parameters and e-mail:k.urban@fz-juelich.de crystal symmetry. abberation-corrected electron In contrast,today's aberration-corrected References microscopy because of an instruments yield images of such quality 1.Urban,K.W.Science 321,506-510(2008). that we can virtually put our finger on 2.Gibson.LM.Nare329,763-764(19871. unfortunately common individual atomic positions.Figure 2a, 3.Huxford,N.P..Eaglesham.D.I.Humphreys,C.I.Natture 329.812-81319871. misunderstanding. for example,shows a ferroelectric domain Coene.W.Janssen.G.Op de Beeck.M.Van Dyck.D. boundary in the microelectronic storage Phrys.Rev.Let69,3743-3746(1992). material PbZro2TisO,(PZT)(ref.12).Not 5.Coene.W.M.Thust,A.Op de Beeck.M.Van Dyck,D. As a matter of fact,the first images Ultramicroscopy 64,109-135 (1996). only are the different atomic positions well 6.Jia,C.-L Thust,A.Phys.Rev.Lett. showing contrast resembling that of atomic resolved,but we can even measure the 82,5052-5055(19991. structures were published more than individual lateral atomic shifts (Fig.2b),of 7.Kisielowski,C.etal Ulramicroscopy 89,243-263(2001) 50 years ago.These images were obtained the order of 40 pm,of the oxygen,zirconium 8.Haider.M.tal.atre392,768-769(1998). and titanium atoms out of their symmetry 9.Jia,C.L.Lentzen,M.Urban,K.Science by placing an aperture in the back focal 299.870-87320031 plane of the objective lens so that only a positions,inducing electronic lattice 10.Ja.CL.&Urban.K.Science303,2001-2004(2000. few low-angle reflections were selected polarization(Fig.2c). 11.Houben,L.Thust,A.Urban,K.Ultramicroscopy to form the image.This is equivalent to An investigation using Gaussian 106,200-214(2006). 12.l.C-L et al Nature Moter.7.57-61 (2008) constructing an image taking into account regression analyses"revealed that such 13.Lentzen,M.Urban,K.Acta Cryst.A 56,235-247 (2000) the basic Fourier components only(Fig.la). position measurements can be carried out 14.Tang.C.Y.Chen.I H.Zandbergen.H.W.Li.F.H. Although such an image shows a periodic at a precision of better than +5 pm (at a 95% Utramicroscopy106,539-546(2006). structure consisting of black and white areas confidence level).Such a precision is far 15.Scherzer,O.I Appl.Phys.20,20-29(1949) 16.Lentzen,M.Microsc.Microunal 12,191-205(2006). or dots,which superficially resembles an superior to that of any other microscopic 17.Menter,L W.Proc.R.Soc.Lond.A 236,119-135 (1956) atomic lattice,it is entirely inadequate with technique,including the scanning 1&.Smith.D.1Rcp.ogP%x60,1513-1580(1997. respect to atomic resolution in the sense transmission electron microscope or even 19.Williams,D.B.Carter,C.B.Transmission Elec (Plenum,1996). just defined.Atomic 'individuality'requires the scanning tunnelling microscope.The 20.Spence,C.H.High Resolution Electron Microscopy,3dedn high-order Fourier components(Fig.1b standard objection to such extremely high (Oxford Univ.Press,2007). 262 NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 2009 Macmillan Publishers Limited.All rights reserved
262 nature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials commentary | insight with atomic resolution means that the information must be entirely local on the atomic level. Any change in the position or occupancy of an atomic site in the sample must show up in the image as an individual signal localized only at the corresponding atomic position. In this stringent sense, apart from a few favourable cases, only the images obtainable in modern aberration-corrected instruments match these standards. The concept is illustrated in Fig. 1. As a matter of fact, the first images showing contrast resembling that of atomic structures were published more than 50 years ago17. These images were obtained by placing an aperture in the back focal plane of the objective lens so that only a few low-angle reflections were selected to form the image. This is equivalent to constructing an image taking into account the basic Fourier components only (Fig. 1a). Although such an image shows a periodic structure consisting of black and white areas or dots, which superficially resembles an atomic lattice, it is entirely inadequate with respect to atomic resolution in the sense just defined. Atomic ‘individuality’ requires high-order Fourier components (Fig. 1b and c), which in early work could not be used for the image formation because of the detrimental influence of lens aberrations. Over the past three decades, taking so-called ‘high-resolution’ images has become a common technique in materials science18. Some of this work was capable of atomic-scale resolution. In particular this applies to studies in which the EPWF was calculated from an image series, even in non-corrected instruments, when in EPWF reconstruction the optical aberrations were corrected to a certain extent by software. Nevertheless, the bulk of this earlier work was concerned not with individual atoms but rather with collective properties such as crystal structures, lattice parameters and crystal symmetry. In contrast, today’s aberration-corrected instruments yield images of such quality that we can virtually put our finger on individual atomic positions. Figure 2a, for example, shows a ferroelectric domain boundary in the microelectronic storage material PbZr0.2Ti0.8O3 (PZT) (ref. 12). Not only are the different atomic positions well resolved, but we can even measure the individual lateral atomic shifts (Fig. 2b), of the order of 40 pm, of the oxygen, zirconium and titanium atoms out of their symmetry positions, inducing electronic lattice polarization (Fig. 2c). An investigation using Gaussian regression analyses11 revealed that such position measurements can be carried out at a precision of better than ±5 pm (at a 95% confidence level). Such a precision is far superior to that of any other microscopic technique, including the scanning transmission electron microscope or even the scanning tunnelling microscope. The standard objection to such extremely high precision is that it cannot be allowed by a microscope with a 70-pm Rayleigh or point resolution19,20. However, resolution and precision are two separate physical terms. Although resolution is defined by the minimum separation of two optically broadened intensity peaks at which these can just be separated in the image, the distance between two well-isolated peaks, fitted for example by two-dimensional Gaussians, can be measured at a precision more than an order of magnitude higher. It would be a real pity to turn down the extraordinary opportunities offered by aberration-corrected electron microscopy because of an unfortunately common misunderstanding. a question to conclude Is the scientific community ready to receive the extraordinary new results achievable through aberration-corrected transmission electron microscopy? Readers may find their own individual answer to this question. The everyday life of electron microscopists active in this field shows that there is still some way to go in alerting the scientific community to the opportunities offered by measuring quantum mechanical wavefunctions in atomic dimensions. So great is the potential of these new techniques that it will be well worth engaging in such a process. ❐ Knut W. Urban is at the Institute of Solid State Research and the Ernst Ruska Centre for Microscopy and Spectroscopy with Electrons, Research Centre Jülich, D‑52425 Jülich, Germany. e‑mail: k.urban@fz‑juelich.de references 1. Urban, K. W. 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Lentzen, M. Microsc. Microanal. 12, 191–205 (2006). 17. Menter, J. W. Proc. R. Soc. Lond. A 236, 119–135 (1956). 18. Smith, D. J. Rep. Prog. Phys. 60, 1513–1580 (1997). 19. Williams, D. B. & Carter, C. B. Transmission Electron Microscopy (Plenum, 1996). 20. Spence, J. C. H. High Resolution Electron Microscopy, 3rd edn (Oxford Univ. Press, 2007). 1 nm Ps Ps Distance (in units of c) –5 0 1 5 0 P –80 s (µC cm–2) δO δ (nm) δZr/Ti –0.04 –0.02 0.02 0.04 0 –40 40 80 0 a b c Figure 2 | Polarization domain wall in ferroelectric PZT. a, Atomic structure. Arrows give the direction of the spontaneous polarization, which can be directly inferred from the local atom displacements. The shifts of the oxygen atoms (blue circles) out of the Ti/Zr-atom rows (red circles) can be seen directly, as can the change in separation between Ti/Zr and Pb (yellow circles). b, Atomic-resolution measurements of the shifts of oxygen (δO), and titanium/zirconium (δTi/Zr) atoms as a function of distance from the wall centre (units of c-lattice parameter) in a longitudinal-inversion domain wall; c, The value of the local polarization PS that can be calculated from these data. Adapted from ref. 12. © 2008 NPG. It would be a real pity to turn down the extraordinary opportunities offered by abberation-corrected electron microscopy because of an unfortunately common misunderstanding. nmat_2407_APR09.indd 262 11/3/09 11:17:48 © 2009 Macmillan Publishers Limited. All rights reserved
