Meetings & Events

fall 1997 logo1997 MRS Fall Meeting & Exhibit

December 1 - 5, 1997 | Boston
Meeting Chairs:
 Harry A. Atwater, Peter F. Green, Dean W. Face, A. Lindsay Greer 
 

Symposium HH—Materials Applications of Electron Holography and Related Techniques

-MRS-

Chairs

Lawrence Allard, Oak Ridge National Laboratory
Altaf Carim, Pennsylvania State Univ
Charles Fadley, Lawrence Berkeley National Laboratory
Yoshimasa Ono, Advanced Research Lab
Edgar Voelkl, Oak Ridge National Laboratory

Symposium Support 

  • Gatan, Inc.
  • Hitachi, Ltd.
  • JEOL USA, Inc.
  • Oak Ridge National Laboratory
  • Philips Electron Optics

1997 Fall Exhibitor

* Invited paper

SESSION HH1: ELECTRON HOLOGRAPHY TECHNIQUES 
Chairs: Lawrence F. Allard and Yoshimasa A. Ono 
Wednesday Morning, December 3, 1997 
Berkeley (S)

8:30 AM *HH1.1 
ELECTRON HOLOGRAPHY AT ATOMIC DIMENSIONS - PRESENT STATE. Hannes Lichte and Michael Lehmann, Institute for Applied Physics, Dresden University of Technology, D-01062 Dresden, GERMANY.

For a complete recovery of the object structure one needs the complex electron wave leaving the object. There are two central problems: One is the fact that the phases of the object exit wave are falsified by the aberrations of the optics under propagation through the microscope, what gives rise to restrictions of point resolution. The second is that there are no tools available in electron optics to retrieve the phases directly by conventional microscopy methods. This means that even with a microscope equipped e.g. with the Rose-Haider corrector for improved point resolution, phase retrieval is not possible in general. Therefore, wave optical (holographic) techniques are under development, e.g. focal series restoration and off-axis holography: The electron wave is recorded and transferred to a computer for numerical wave optic processing. This allows to correct the aberrations hence to reconstruct the complex object exit wave and to analyze it completely both in real space and in Fourier space. After developing off-axis holography beyond the resolution limit of conventional microscopy [1] and powerful software for wave optic reconstruction [2], we presently investigate the possible sources of artefacts [3], the limitations presented by the noise problems and the inaccurate knowledge of the microscope parameters, as well as the interpretation of the obtained amplitude and phase images in terms of the underlying object structure. Having shown the potential of off-axis holography by means of well-known specimen like perfect Si and Au crystals, we presently try to enter real-world problems of materials science like defect structures and grain boundaries. The financial support obtained from Volkswagen-Stiftung, Koerber-Stiftung and Deutsche Forschungsgemeinschaft is gratefully acknowledged.

9:00 AM *HH1.2 
HOLOGRAPHIC RECONSTRUCTION METHODS FOR QUANTITATIVE ATOMIC STRUCTURE DETERMINATION. Dirk Van Dyck, Marc Op de Beeck, University of Antwerp (RUCA), BELGIUM.

If one wants to obtain quantitative structural information from high resoluti on microscopic images, one always ends up with fitting the parameters of a structural model such as atom coordinates with the experimental data. In a usual high resolution electron micrograph, this information is highly entang led in the image due to the dynamical interaction of the electron in the object and due to the blurring effect of the electron microscope. For instance, in an electron microscope with 0.2 nm point resolution and 0.1 nm information limit, the 0.1 nm information can be delocalised in the image over several nm. In principle one could think of a quantitative structural refinement in the space of all model parameters using a fitting criterium such as maximum likelihood or least squares. However, due to the coupling of all model para meters in the image the dimension of the space is so high that even with advanced optimisation techniques (genetic algorithms, steepest descent, etc.) it cannot be carried out unless the structure is very simple. Holographic reconstruction methods aim at disentangling (i.e. deblurring) this information prior to the final structural model fitting. In this way the dimensionality of the parameter space can be reduced drastically and a quantitative fitting procedure becomes manageable. If the object is a perfect crystal one can use electron diffraction data (e.g. using MSLS) for further refinement. In this lecture the possibilities and limitations will be discussed.

9:30 AM *HH1.3 
INTERFERENCE OF THREE ELECTRON WAVES AND ITS APPLICATION TO DIRECT VISUALIZATION OF ELECTROMAGNETIC FIELDS. Tsukasa Hirayama, Japan Fine Ceramics Center, Nagoya, JAPAN.

A method is presented for the interference of three electron waves and its application to direct visualization of pure phase objects with low spatial frequency such as electromagnetic microfields Using a transmission electron microscope, Hitachi HF-2000, equipped with a field-emission electron gun and two electron biprisms, an object wave and two reference waves at either side of the object wave are superposed to produce a new type of interference pattern. In this pattern, equal-phase lines of the object wave are directly displayed as intensity modulation of periodic interference fringes. An electric field around a latex particle, induced by electron-beam irradiation, has been observed. The electric charge of the particle is estimated, from observed phase shift, to be about 400 electrons. A change of the electric field around charged alumina particles at high temperatures has been observed dynamically. Magnetic flux lines emerging from a barium ferrite particle are also visualized.

10:30 AM *HH1.4 
OBSERVATION OF MAGNETIC FINE STRUCTURES BY ELECTRON DIFFERENTIAL MICROSCOPY. Takayoshi Tanji, Shizuo Manabe, Kazuo Yamamoto, CIRSE, Nagoya Univ, Chikusa, Nagoya, JAPAN; Tsukasa Hirayama, JFCC, Nagoya, JAPAN.

A new method for electron differential interferometry is proposed. Remaining the advantages of conventional off-axis electron holography, we have realized differential interferometry. An electron trapezoidal prism, which shears only an object wave while the reference wave remains its position by changing the prism potential, makes it possible to reconstruct an interfering micrograph from one double exposed hologram. Differentiated phase distribution appears in the reconstructed intensity as a cosine function. Electrostatic potential around a charged latex particle is observed with this technique. The amplitude contrasts however affects sometimes the observation, moreover the contrast with the cosine function is less sensitive than a linear function for a small difference of the phase. We can now obtain numerically the wavefunction from each hologram, so we calculate the difference between the two waves' phases by multiplying one of the reconstructed complex wavefunctions with the complex conjugate of the other one. The magnetic structure of a permalloy thin film was observed without a plane reference wave. The difference between two holograms made with a potential difference of 0.25V clearly shows that the reference side of the interference region has been subtracted and presents uniform contrast, while the wave coming from the object side is sheared. The difference between the differentiated phases of both sides of the domain wall is 0.56 on average. Assuming the average flow of the magnetic flax is 45 against both the wall and the differentiated directions and a film thickness of 200 nm, we find this phase difference coincides with the saturation magnetization of the permalloy 1 T. The contrast due to the magnetic ripples is 0.03 which corresponds to a fluctuation of 6.

11:00 AM HH1.5 
TIME-RESOLVED ELECTRON MICROSCOPY FOR PHASE CONTRAST IMAGING. Nobuyuki Osakabe, Hiroto Kasai, Ken Harada, Mark I. Lutwyche, Akira Tonomura, Advanced Research Lab, Hitachi Ltd, Hatoyama, Saitama, JAPAN; Tetsuji Kodama, Nagoya Univ, Dept of Information Electronics, Nagoya, JAPAN.

A new time-resolved electron microscopy4 for phase contrast imaging has been developed and applied to the study of the vortex-line dynamics in a type-II superconductor3 and to the measurement of the elastic properties of nanoscaled materials2. Exploiting a newly developed electron counting technique1, time-dependent electron microscope image beam current, position-selected by an probing aperture in the image plane, is measured as sequentially sampled electron counts or a temporal and spatial correlation function. The electron intensity correlation measurement enables one to characterize fast events, which cannot be accessed by the conventional observation due to the shot noise. A 30-MHz digital correlator with 128 delay channels has been constructed for the purpose. A 5-GHz digital correlator with 5 delay channels has also been constructed, showing the possibility of accessing sub-nanosecond events.

11:15 AM *HH1.6 
LOW MAGNIFICATION ELECTRON HOLOGRAPHY. Bernhard Frost, Univ of Tennessee, Sci and Engg Res Fac, Knoxville, TN; Edgar Voelkl, ORNL, Oak Ridge, TN.

Low magnification holography is usually achieved by switching off the objective lens and imaging the sample by the first intermediate lens. When engaging such an arrangement the holographic field of view can be significantly increased by increasing the voltage on the biprism and a weak excitation of the objective lens, which then acts as additional condenser lens. Using the objective lens like a condenser lens can have a strong qualitative and quantitative influence on the image phase of some samples. This is seen, e.g., in holograms of the electric field of pn-junctions, the electric field of latex spheres, and the magnetic field of a MFM probe. An explanation will be discussed to describe this phenomenon quantitatively and attempts will be presented to minimize the problem.

11:45 AM HH1.7 
THE EVALUATION OF HOLOGRAPHIC INFORMATION. Edgar Voelkl, Larry Allard, Oak Ridge National Laboratory, High Temperature Materials Laboratory, Oak Ridge, TN.

Digital data acquisition and image processing is an inevitable part of recent electron holography. Images are in almost all cases recorded and processed digitally while photographic film is hardly used anymore. Digital processing of electron holograms still is a time consuming task (reconstruction time on a Mac with a 604 processor at 225MHz is around 5 seconds for a 1024 by 1024 pixel image) and does not compare with the digital recording/analog reconstruction procedure described by [1]. However, we probably can quite savely assume that within the next few years new computer generations will enable live display of e.g., phase images, based on fully digital reconstruction. The fully digital approach is essential, as it allows for a higher flexibility in the reconstruction process e.g., to include the correction of distortions. One question has received little attention so far, both in the light optics and electron optics area of holography. How can the overwhelming information contained in a complex image be displayed such that it is easily comprehended? To display the complex image information in two images, i.e., the amplitude and the phase image, is the conventional wisdom, but certainly not ideal. For example, phase images can be converted into surface plots which can present the phase information in a much more comprehensive manner. Several approaches will be addressed and their computational requirements for live display will be discussed.

SESSION HH2: APPLICATIONS I (ELECTRIC AND MAGNETIC FIELDS) 
Chairs: Altaf H. Carim and Matthew R. Libera 
Wednesday Afternoon, December 3, 1997 
Berkeley (S)

1:30 PM *HH2.1 
REAL-TIME OBSERVATION OF THE DYNAMICS OF VORTICES BY ELECTRON WAVE MICROSCOPY. Akira Tonomura, Advanced Research Lab., Hitachi, Ltd., Hatoyama, Saitama, JAPAN.

Magnetic vortices in Type II superconductors are shaped like extremely thin filaments. However, they hold the key in practical applications of superconductors: When a current is applied to a superconductor, vortices begin to move due to the Lorentz force thus breaking down the superconducting state unless defects pin down vortices. In order to directly observe the microscopic pinning mechanism, we developed new kinds of microscopy utilizing the wave nature of electrons: The magnetic lines of force of individual vortices were observed as contour fringes in an electron-holographic interference micrograph[l] with a 300 kV field-emission transmission electron microscope. Vortices were also dynamically observed in a Lorentz micrograph by defocusing the electron image[2]. Both vortices and defects in a superconducting thin film were observed in real time with this method, though the defect image was blurred. The experimental results obtained by Lorentz microscopy are introduced here showing the vortex behaviors in both metal and oxide superconductor. To cite an example, the effect of sparse pinning centers in a Nb thin film was observed when a magnetic field changed: When vortices were sparse, vortices hopped individually and detoured around the vortex pinned at a defect. While when vortices were dense, they tended to form a single-crystalline lattice but formed domains of lattices due to the trapped vortices at defects. Therefore, vortices did not flow as a whole keeping the lattice form but flowed intermittently forming ``vortex rivers'' along the domain boundaries [3].

2:00 PM *HH2.2 
INTERPRETATION OF INTERFERENCE- AND LORENTZ-IMAGES OF VORTICES IN SUPERCONDUCTORS. Giulio Pozzi, Bologna Univ, Dept of Physics, Bologna, ITALY.

The successful observation of superconducting vortices (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz microscopy and electron holography has required two basic ingredients: on one hand the technological development of the instrumentation, stimulated also by the introduction in electron microscopy of interferometry and holography methods, and on the other hand a better comprehension of the contrast mechanisms when non-conventional set-ups are investigated, e.g., when the thin specimen is not perpendicular but tilted with respect to the electron beam. The initial theoretical approach has been to model the fluxon as a bundle of straight flux tubes perpendicular to the specimen surface, where the electron optical phase shift for a single flux tube has an analytical form. The magnetic flux distribution can be described by the Clem or London model, this latter corresponding to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth , completely characterizes the superconducting fluxon. However, the discrepancy between experimental results and theoretical simulations when the bulk value for the London penetration depth is taken calls for an improvement of the model. In this work a further model is presented and discussed, which takes into account the finite specimen thickness and its influence on the broadening and bending of the field lines near the surface. It turns out that such broadening is able to account for the observed discrepancy, and this fact points out the relevance of the assumed model in the intrepretation of the experimental data.

2:30 PM HH2.3 
OBSERVATION OF MATCHING EFFECT IN SUPERCONDUCTORS WITH REGULAR ARRAYS OF DEFECTS BY LORENTZ MICROSCOPY. Ken Harada, Osamu Kamimura, Hiroto Kasai, Tsuyoshi Kasai, Akira Tonomura, Advanced Research Laboratory, Hitachi, Ltd., Saitama, JAPAN; Victor V. Moshchalkov, Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Univ., Leuven, BELGIUM.

In order to realize practical superconducting magnets, it is necessary to increase the critical current density Jc of superconductors by introducing defects as pinning centers into superconductors. For this purpose a large number of works have been carried out to obtain stronger pinning centers, whose effect, however, can only be estimated when the whole behavior of vortices are taken into account. In fact, Jc has peak values at specific applied magnetic fields. In the present work, the microscopic mechanism of the ``matching effect'' was studied by directly observing interactions between vortices and regular arrays of defect by Lorentz microscopy using a 3OO-kV field emission electron microscope. Square ways of artificial defects were produced in singles-cystalline Nb films by irradiating a focused ion beam. By changing the amplitude of Fe applied magnetic fields H. it was possible to form regular lattices at the matching field, its multiples and its fractions. At the matching field, all of the defects (pinning centers) were occupied by vortices. At the multiple fields, vortices were squeezed into the regular lattices and began to occupy the interstitial positions. At the fractional fields, vortices formed configurations in which some of the defects worst regularly skipped. The dynamic observation furthennore revealed that it was difficult for vortices to move when they formed a regular structure at the matching field, whereas excess vortices hopped easily between interstitial positions. Those results explains the microscopic mechanism of the matching effect: A Lorentz force larger than the elementary pinning force is necessary to move the vortices forming a regular and consequently rigid lattice, while only a small force is necessary to move excess vortices. As a result, Jc peaks appear at specific magnetic fields in the Jc vs. H figures.

3:15 PM *HH2.4 
ELECTRON HOLOGRAPHY OF NANOSTRUCTURED MATERIALS AND INTERFACES. Vinayak P. Dravid, Department of Materials Science & Engineering, Northwestern University, Evanston, IL.

The phase sensitivity in transmission electron holography can be effectively exploited to obtain useful information about many aspects of materials microstructure, especially in dimensionally and spatially constrained systems which are spatial inhomogeneous and no other technique can come close to solving the problem.Transmission electron holography of single-layer buckytubes shows the exceptional sensitivity of the technique to changes in mean inner potential (MIP) of just two carbon atoms stacked on top of each other. We have utilized this sensitivity of holography to several problems in electrically active interfaces in electroceramics. These charged interfacial phenomena present ideal problems for the application of electron holography which is sensitive to phase change owing to interactions of electron wave with the electrostatic fields at interfaces. As a part of a broad program, we are investigating the interrelationship among interface variables (structure, chemistry and electronic structure) and interface induced properties (varistor behavior, FE fatigue and switching) in model electroceramics such as SrTiO3 and PZT thin films. Clear presence of charged GBs and associated space-charge across was imaged by holography in doped SrTiO3, while the presence of space-charge was detected at FE-eletrode interfaces. The presentation will highlight the above results and emphasize the powerful approach of synergistic combination of diverse high spatial resolution electron beam technique to problems of interfaces and defects in solids.

3:45 PM *HH2.5 
OFF-AXIS ELECTRON HOLOGRAPHY OF SINGLE FERROMAGNETIC NANOWIRES. C. Beeli, P.A. Stadelmann, Center of Interdepartmental Electron Microscopy, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland; B. Doudin, J.-Ph. Ansermet, Institute of Experimental Physics, Ecole Polytechnique Federale de Lausanne,Lausanne, Switzerland.

Off-axis TEM electron holography has been applied to the study of the remanent magnetization state of single ferromagnetic nanowires of radius ranging from 20 to 150 nm and of a few microns in length. Since the objective lens of the electron microscope is switched off, the spatial resolution of the reconstructed phase images is presently limited to 70 nm. The measurement of the phase shift induced by Co and Ni nanowires has been performed with a precision better than 3 percent. The magnetization reversal of an individual nanowire has been followed by observing a series of remanent states, obtained ex-situ by applying different external magnetic field sweeps parallel to the nanowire axis. Multilayered nanowires, formed by a periodic arrangement of Co segments separated by Cu segments, showed several magnetic configurations, from the parallel to antiparallel alignment of the magnetic segments. The interpretation of the experimental results is confirmed by the simulation of phase images.

4:15 PM HH2.6 
DIRECT OBSERVATION OF POTENTIAL DISTRIBUTION ACROSS FERROELECTRIC CAPACITOR USING OFF-AXIS ELECTRON HOLOGRAPHY. Koichiro Honda and Naomichi Abe, Micro Process Development Dept. Device Technology Development Div. Fujitsu Ltd, Kawasaki, JAPAN.

Off-axis electron holography was used to observe the potential distribution across ferroelectric PZT capacitor and the surrounding electric field made by the spontaneous polarization of the polycrystalline PZT (poly-PZT) thin film. In the electron holograph, the visualizing of the phase changes of an electron wave affected by a local scalar and/or a vector potential make it possible to directly image the distribution of an electro or magnetic field at high resolution. Therefore, electron holography may be a valuable tool in the study of ferroelectric materials. This method was used to the study of bulk ferroelectric material. In this method, the electron phase changes resulting from the polarization change, across the domain wall provide a direct measurement of both domain wall thickness and the spontaneous polarization. We succeeded in applying it to observations on ferroelectric capacitor. On the phase image of the cross section of poly-PZT capacitor the electron phase charge which was due to the polarization of poly-PZT film was clearly observed in the vacuum region, vicinity of the capacitor. In other words, the dielectric film of the capacitor polarizes spontaneously, then it indicating that the film is ferroelectric. From the interferogram of the same area we could see a grain boundary of poly-PZT film. The interferogram reveals significant changes of electric field across the grains of poly-PZT film. In one grain, there is also changes of the field, which reflects domains in the grain. We showed that the off-axis electron holography was one of the most powerful method to characterize the ferroelectric thin film.

4:30 PM HH2.7 
CHARACTERIZATION OF POTENTIAL BARRIERS AT ZnO INTERFACES IN A VARISTOR MATERIAL USING ELECTRON HOLOGRAPHY. E. Olsson, Department of Physics, Chalmers University of Technology, Goteborg, SWEDEN; P.A. Midgley*, J. Barnard, J.W. Steeds, H.H. Wills Physics Laboratory, University of Bristol, Bristol, UNITED KINGDOM. *Now at Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, UNITED KINGDOM.

ZnO varistor materials exhibit extremely non-linear current voltage characteristics with low conduction at low voltages whereafter it increases dramatically as the breakdown voltage is reached. The materials are polycrystalline, mainly consisting of ZnO grains but there are also several secondary phases. The ZnO interfaces provide the barriers to electrical conduction and thus give rise to the desirable non-linear behaviour. It has been shown experimentally that the detailed barrier behaviour of a ZnO interface is determined by its microstructure. However, the full characterization of the electrical behaviour of individual interfaces in complex polycrystalline ZnO varistor materials has not yet been carried out due to the difficult geometry and small dimensions of the junctions. The present work is concerned with electron holography of ZnO grain boundaries in a varistor material. The grain boundaries were oriented parallel to the incoming electron beam and with both grains in a weakly diffracting condition. The change in phase of the electron wave as a function of distance from a ZnO grain boundary was extracted from the obtained holograms. During the evaluation it was considered that the change in phase is proportional to the specimen thickness and crystal potential, Vo. The change in Vo in the vicinity of the boundaries was studied by choosing electron phase profiles where the thickness of the specimen was constant as determined using electron energy loss spectroscopy. The obtained results verified the presence of potential barriers at the ZnO interfaces and also provided information of the charge carrier depletion width at the interfaces.

4:45 PM HH2.8 
IS THE MEAN INNER POTENTIAL OF SILICON AFFECTED BY DOPING? Marija Gajdardziska-Josifovska, Dept. of Physics, Univ. of Wisconsin Milwaukee, Milwaukee, WI.

Electron holography allows the measurement of the phase, an information which is normally lost in conventional imaging. The phase of the object wave is affected by all scalar and vector potentials along its path, making electron holography an attractive technique for measuring electrostatic fields and magnetic fields with high spatial resolution. An important example which has been studied by electron holography is the spatially resolved measurement of the contact potential at silicon p-n junctions. The typical assumption made in this case is that the phase change across the interface is due only to the electrostatic field at the interface. However, every holographic phase measurement is also affected by the mean inner potential of the sample. Therefore, one of the basic questions is whether the mean inner potential is the same in the n-doped and p-doped silicon? To answer this question we attempted to use the cleaved wedge technique for holographic measurements of the mean inner potential of heavily n- and p- doped Si. Unfortunately, the difficulty in cleaving p-doped Si has made it impossible to produce the needed well defined crystal wedges. We then studied refraction effects in reflection high energy electron diffraction (RHEED) patterns from n- and p- doped Si(111) surfaces. These RHEED experiments allow us to pursue the original question since, just like the phase, the electron-optical index of refraction is also related to the mean inner potential of the solid. Our preliminary data indicate a marked difference in the amount of refraction, the p-doped Si having a higher mean inner potential than the n-doped Si.

SESSION HH3: APPLICATIONS II (MATERIALS CHARACTERIZATION) 
Chairs: Marija Gajdardziska-Josifovska and Edgar Voelkl 
Thursday Morning, December 4, 1997 
Berkeley (S)

8:30 AM *HH3.1 
PHASE-CONTRAST IMAGING OF POLYMER MICROSTRUCTURE BY TRANSMISSION ELECTRON HOLOGRAPHY. M. Libera, Stevens Institute of Technology, Hoboken, NJ.

Traditional transmission electron microscopy (TEM) techniques for studying polymer microstructure are based on amplitude-contrast imaging where heavy-element stains preferentially decorate the microstructure. These methods have been extremely powerful in establishing such features as the size, shape, and distribution of dispersed minor phases in polymer blends and the morphological properties of microphase-separated block copolymers. Higher resolution work to answer, for example, questions on interphase structure or trace-additive distributions require alternate techniques which are intrinsically sensitive to the polymer structure and do not require heavy-element stains. This paper describes the use of transmission electron holography as a means to image and quantify the microstructure of unstained polymers by phase-contrast rather than amplitude-contrast methods. The phase shift imparted by the electron-optical refractive properties of an amorphous polymer specimen to an incident electron wave is related to the specimen¹s mean inner (coulombic) potential. Work to quantify the magnitude of the inner potential in polystyrene and compare it to values characteristic of other polymers will be discussed as well as issues related to limits imposed by the effects of electron-irradiation on polymer specimens.

9:00 AM *HH3.2 
ELECTRON HOLOGRAPHIC CHARACTERIZATION OF CARBON ONIONS, FILMS AND GOLD PARTICLES. Q. Ru, Japan Science and Technology Corporation, Takayanagi Particle Surface Project, Tokyo, JAPAN.

Carbon onions can be formed by intense electron beam irradiation of graphitic particles in a transmission electron microscope (TEM). Based on TEM observations, it has been found that some of the onions are icosahedral or quasi-icosahedral rather than spherical. In order to confirm the TEM observation results, electron holography was used to measure the thickness distribution of the onions. The measured phase profiles show that the onions are close to facetted polyhedrons rather than spheres, consistent with the TEM observations. Amorphus carbon thin films used for supporting TEM specimens are believed to have a good electric conductivity. Electron holographic observations of the carbon films thinner than about 10 nm, however, showed that the films are dynamically overcharged and discharged during an intense electron beam irradiation. The charging dynamics have been observed in real time, showing that the charging-discharging rate is proportional to the intensity of the incident electron beam. Identical phenomena have been observed for amorphus silicon oxide thin films, which are known as semiconductors. It has also been confirmed that no charging effects were observed when the carbon films had been coated with an aluminum film. Recently we have found that when a micrometer-sized spherical particle of metal (Au, Ag, or Cu) is supported with a thin carbon film and irradiated with an intense pulse-like electron beam, unusually large amount of small clusters and nanocrystals can be ejected out from the particle. The 3-dimensional morphologies and structures of the ejected nanocrystals deposited on the carbon film have been characterized by TEM and electron holography. It is shown that the largest facet of a bar- or plate-like crystal is usually covered with the stable (111) surface.

9:30 AM HH3.3 
HIGH RESOLUTION ELECTRON HOLOGRAPHY OF CdTe AND ZnTe. Guenter Lang*, Michael Lehmann***, David J. Smith**, Martha R. McCartney** and Hannes Lichte***. *Institute for Applied Physics, Tuebingen University, Tuebingen, GERMANY; ** CSSS, Arizona State University, Tempe, AZ; *** Institute for Applied Physics, Dresden University of Technology, Dresden, GERMANY.

Electron holography has developed beyond the point resolution limit of medium voltage electron microscopes [1] offering the full wave optics for analysis of the underlying object structure. In Tuebingen, off-axis electron holograms are recorded using the Philips CM30FEG-Special Tuebingen electron microscope which was recently upgraded with a high resolution UT-lens improving point resolution from 0.2nm to 0.17nm. Thus, the following advantages are expected: First, since holographic resolution scales with the point resolution limit [2], the hitherto achieved resolution of about 0.13nm should approach 0.1nm. Second, the information limit given by both Cs and chromatic aberration Cc should improve beyond about 0.09nm. Third, there should be a gain in SNR of the reconstructed wave. CdTe and ZnTe are very interesting specimens for holography, because they have the zincblende structure. The dumbbell atoms representing different atomic numbers should show up in phase images with different strength allowing their identification. We have used high-resolution electron holography to study dislocations and stacking defects in CdTe and ZnTe, and to characterize the atomic structure at a heteroepitaxial Ge/ZnTe interface.

10:15 AM *HH3.4 
CHARACTERIZATION OF NANOCRYSTAL STRUCTURED SUPERLATTICE MATERIALS. Z.L. Wang, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA.

Nanocrystal superlattice (NCS) is a self-assembling of passivated nanocrystals into monolayers, thin films, and superlattices of size selected clusters encapsulated in a protective compact coating. The passivation layer not only acts as a protection for the size and even shape selected nanocrystals, but serves as the interparticle molecular bonds for forming the superlattice. The nanocrystals behave like molecular matter and their packing has translation and even orientation order [1,2,3]. The properties of this new materials depends not only on the structure of individual particles, but the 3-D packing crystallography of the nanocrystals. In this presentation, a review is given on the current status of structure analysis of this type of materials using advanced transmission electron microscopy (TEM), electron holography and associated techniques. Electron holography is a powerful tool for determining the 3-D shape of nanocrystals. The darkfield TEM imaging is an effective technique for determining the orientation order of the nanocrystal superlattices. Results from our recent studies of Au, Ag and CoO [4] NCS's will be presented to illustrate the techniques for quantitative structure analysis. More importantly, the role played by the particle shape of nanocrystals in 3-D packing will be demonstrated.

10:45 AM HH3.5 
ELECTRON HOLOGRAPHY OF CATALYTIC MATERIALS. Lawrence F. Allard, Edgar Voelkl, Oak Ridge National Laboratory, Oak Ridge, TN; Abhaya K. Datye, Center for MicroEngineered Ceramics, University of New Mexico, Albuquerque, NM.

The active phase in heterogeneous catalysts consists of nanometer-sized metal or oxide particles dispersed within the tortuous pore structure of a high surface area matrix. Such catalysts are extensively used for controlling emissions from automobile exhausts or in industrial processes such as the refining of crude oil to produce gasoline. The morphology of these nano-particles is of great interest to catalytic chemists since it affects the activity and selectivity for a class of reactions known as structure-sensitive reactions. In this paper, we describe some of the challenges in the study of heterogeneous catalysts, and provide examples of how electron holography can help in extracting details of particle structure and morphology on an atomic scale. Image plane off-axis electron holography using a M–llenstedt biprism in a field emission gun electron microscope can produce holograms of nanoparticles from which the amplitude and phase information can be separately reconstructed. When the specimen is sufficiently thin so that phase changes less than 2 are obtained, a profile across the phase image is essentially a map of specimen thickness. This information can then be directly related to particle morphologies. Applications of electron holography to characterization of morphologies of platinum group metals and cobalt molydenum sulfides on a variety of oxide supports will be described.

11:00 AM HH3.6 
ELECTRON HOLOGRAPHY OF INTERFACIAL PHASES AT HETEROINTERFACES AND GRAIN BOUNDARIES. Altaf H. Carim and Anteneh Kebbede, Dept of Materials Science and Engineering, The Pennsylvania State University, University Park, PA.

Off-axis electron holography provides another tool for the detection and characterization of interfacial phases. Such phases often control properties ranging from electronic behavior in semiconductor devices through mechanical strength in structural materials. There are several possible benefits to electron holographic imaging of interfacial phases. In some cases, the phase profile across a boundary or interface may allow detection of an interfacial phase even if the interface is not aligned parallel to the electron beam. Of particular interest for systems with amorphous interfacial materials, extraction of the phase image may permit observation of local chemical nonuniformities, layering, or phase separation. Furthermore, the rate of phase change at interfaces provides another criterion for assessing the sharpness or diffuseness of the boundaries being investigated. Preliminary results will be presented for the model system of thin oxides and/or oxynitrides on silicon surfaces, and for the observation of glassy silicate films at grain boundaries in ceramics.

11:15 AM HH3.7 
STUDIES OF ELECTRON REFRACTION BY HOLOGRAPHIC PHASE IMAGING OF NANOSPHERES. Alex Chou, Y.C. Wang,* and M. Libera, Stevens Institute of Technology, Hoboken, NJ; *Lawrence Berkeley Nat. Lab., Berkeley, CA.

The mean inner potential measures the average electrostatic potential in a volume of matter. In a Fourier representation of the potential characteristic of a crystalline material, the mean inner potential corresponds to the first (constant) term in the expansion and is often calculated as part of a first-principles study of electronic structure. It can be measured experimentally via high-energy electron refraction. This paper describes measurements of mean inner potential based on holographic phase images. Spherical specimens are used so the effects of electron refraction can be separated from specimen thickness effects. Results are presented for amorphous polystyrene (8.4V) and amorphous Si (11.9V) and compared to procrystal values. Crystalline specimens are subject to increased dynamical scattering effects as well as to deviations from perfect sphericity. Nevertheless, this work finds values for crystalline Si of 12.1V in good agreement with LAPW calculations by Spence et al. (1997) and 22V for crystalline Au in good agreement with previous experiments by Keller (1961).

11:30 AM HH3.8 
APPLICATIONS OF ELECTRON HOLOGRAPHY FOR THE CHARACTERIZATION OF SMALL PARTICLES. Alexander Orchowski, Exxon Research and Engineering Co, Annandale, NJ.

Electron holography is a method of Transmission Electron Microscopy (TEM) enabling the measurement of the complete complex electron wave as transferred by the microscope into the detector plane. In comparison with conventional TEM additional information can be obtained about microstructural properties of the sample under investigation. In the case of nanoscale particles knowledge about particle shape and morphology can be derived by measurement of the local phase shift of the electron wave due to the particle. The phase shift is proportional to the mean inner potential of the sample times the thickness in direction of observation. Examples presented include colloidal Au-particles in the size range of 10-20 nm principally having a spherical shape. High resolution imaging shows the crystalline nature of the particles and diffraction effects in the image intensity give a clue for the presence of surface facetting. Closer examination of the image wave derived from holograms confirm this assumption: Line scans across the phase image of such particles reveal sharp edges in the otherwise smooth slope of the phase, corresponding to edges between surface facettes. At the example of a specific system of Palladium metal particles the presence of internal voids in many particles is shown from phase distributions. Preliminary results of electron holography with oxidized Pd particles of the same system do not show the existance of these voids. High Angle Annular Dark Field (HAADF) Scanning Transmission Electron Microscopy (STEM) makes use of the Z-contrast (signal approximately proportional Z2 ) to detect higher atomic number clusters on low atomic number support materials. The image intensity being linearly proportional to the number of probed atoms enables the measurement of the approximate number of atoms in metal clusters. This technique is routinely applied for dispersion measurements of supported catalysts. A comparison of the practical detection limits and quantization capabilities of electron holography and STEM regarding small particles is presented.

11:45 AM HH3.9 
A COMBINED HRTEM/DIRECT METHODS SOLUTION OF OXYGEN POSITIONS IN A (Ga,In)2SnO5 CERAMIC. Wharton Sinkler, Laurence D. Marks, Doreen D. Edwards, Thomas O. Mason, Northwestern Univ., Dept. of Materials Science and Engineering, Evanston, IL; Kenneth R. Poeppelmeier, Northwestern University, Dept. of Chemistry, Evanston, IL.

So-called direct methods for solving crystal structures are among the few techniques which, in addition to electron microscopic techniques, can provide real space information towards solving crystal structures. In the present work, direct methods are combined with high resolution transmission electron microscopy (HRTEM) in the solution of a previously unreported (Ga,In)2SnO5 ceramic oxide which was synthesized in connection with research into transparent conducting oxides[1]. Phases of several strong beams of small spatial frequency (<4.5 nm-1) were determined from an HRTEM image taken near Scherzer defocus. These were combined with experimental diffraction intensities from small-probe transmission electron diffraction. The use of experimental phases counteracts the uncertainty in the direct methods approach which is introduced by the use of dynamical diffraction data. Direct methods solutions are shown which image the oxygen atoms in the structure to a resolution of 9.0 nm-1. The emphasis of light atom positions by this technique is explained based on electron channeling theory and using calculated dynamical exit waves.

SESSION HH4: RELATED TECHNIQUES - 
X-RAY AND PHOTOELECTRON HOLOGRAPHY
Chairs: Charles S. Fadley and Gerhard Materlik 
Thursday Afternoon, December 4, 1997 
Berkeley (S)

1:30 PM *HH4.1 
STRUCTURE DETERMINATION WITH INTERFERENCE FIELDS: FROM X-RAY STANDING WAVES TO X-RAY HOLOGRAPHY. G. Materlik, Hamburger Synchrotronstrahlungslabor HASYLAB am Deutschen Elektronen-Synchrotron DESY, Hamburg, GERMANY.

Direct methods have been outstandingly successful to determine the atom order and electron density maps from kinematical (single-scattering) X-ray diffraction patterns [1]. Nevertheless, the challenge to determine directly the phase of scattered waves has been discussed extensively in the literature. One approach was the use of X-ray interference fields [2]. Such interference fields provided a powerful tool for establishing the X-ray standing wave method (XSW) to determine surface absorbate structures and bulk dopant positions. A different approach to measure structures on the atomic scale has recently been realized in the direct way [3] and in the reciprocal approach [4]. In the first scheme a direct fluorescence wave is rescattered by the neighboring atoms and forms a far-field interference pattern which is recorded by a detector outside the crystal. The resulting interference pattern of a plane wave coming in and being elastically scattered within the crystal can alternatively be measured by using internal atoms which emit fluorescence photons when the crystal is rotated relative to the incident wave. These atoms thus serve as detectors for the local electrical field intensity. Both interference patterns which are connected by the optical reciprocity theorem can be reconstructed by Fourier transform analysis techniques to yield directly the local atomic arrangement with 0.1 nm spatial resolution. The method will be discussed as well as their connection to XSW and Kossel lines [5] and will be illustrated by recent experimental results from inorganic crystals [6]. Possible applications in material science will also be presented as well as new detector schemes.

2:00 PM *HH4.2 
IDEAS AND ANALYSIS OF SOME SCHEMES FOR X-RAY HOLOGRAPHY. Malcolm R. Howells, Stephen Lindaas, Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley CA; Chris J. Jacobsen, Physics Dept, SUNY Stony Brook, NY; John Spence, Dept of Physics and Astronomy, Arizona State University, Tempe, AZ.

X-ray holography was first proposed in 1952 by Baez, four years after Gabor had proposed holography as an electron technique and demonstrated it with visible light. A number of x-ray-holography geometries were proposed during the 1950's and 60's but holograms of reconstructible quality were not made until the 1970's and submicron images not until the 1980's. These latter required undulator radiation and a high-resolution optical device (lens or detector). At the present time short-wavelength lasers are improving and new types of synchrotron-radiation source are becoming available so that it is desirable to reconsider the possible holographic geometries in light of the new technical conditions. In this presentation we discuss some available geometries and try to analyse them in as unified a way as possible. We review actual results achieved by the various methods (including some of our own) and project the results that may be obtained using new approaches. We include in this discussion the methods of reconstruction that are available and comment on their effectiveness in avoiding or removing the twin-image signal.

2:30 PM HH4.3 
MATERIALS ANALYSIS BY X-RAY FLUORESCENCE HOLOGRAPHY AND MULTI-ENERGY X-RAY HOLOGRAPHY: COMPARISON OF METHODS AND SOME FUTURE DIRECTIONS. Daniel Lattimore, Patrick Len, Charles Fadley, Michel Van Hove, Dept. of Physics, Univ. of California-Davis, Davis, CA. and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA.

Two new holographic methods have recently been demonstrated as element-specific probes of short-range atomic structure: x-ray fluorescence holography (XFH) [1] and multiple-energy x-ray holography (MEXH) [2]. In XFH, the diffraction pattern of fluorescent x-rays is treated as a hologram, and in MEXH (which is in essence a time-reversed version of XFH), the diffraction of the incoming exciting beam is used to generate a hologram. In both methods, it is possible to reconstruct three-dimensional atomic images using Fourier-transform-like algorithms, but MEXH has the advantage of measuring holograms at several energies. Both of these methods hold considerable promise as new element-specific probes of atomic structure that would complement existing x-ray diffraction methodologies [3]. We will compare these two approaches, pointing out advantages and disadvantages of each, and then focus on theoretical simulations designed to answer some important questions regarding the ultimate potential of these methods, including the imaging of dopant-atom environments in semiconductors, the sensitivity to lower-atomic-number atoms, the influence of atomic vibrations, and the effects of variable radiation polarization in MEXH studies.

2:45 PM HH4.4 
HIGH ENERGY X-RAY HOLOGRAPHY. Carsten Raven, Markus Haverkamp, Anatoly Snigirev, Irina Snigireva, European Synchrotron Radiation Facility, Grenoble, FRANCE; Viktor Kohn, Russian Research Center Kurchatov Institute, Moscow, RUSSIA.

The beam properties of third generation synchrotron sources allow coherent imaging techniques with micro- and submicrometer resolution. Going to higher energies offers a number of advantages like the investigation of thicker samples, reduced absorbed dose and larger object-to-detector distance that gives the possibility to install high pressure cells or cryostats. Of these techniques, Gabor (in-line) holography is particularly interesting since it does not require focusing optical elements and gives the possiblity to reconstruct the refractive index distribution in the sample. We developed two different reconstruction algorithms, one based on a modified Gerchberg-Saxon algorithm which works in the energy range 10-20 keV and requires two holograms taken at 0 cm distance and 100 cm resp. The other algorithm is especially designed for the region of Fresnel diffraction and gives very promising results in simultions with X-ray energies up to 80 keV. First experimental results on fibers, i.e. in one-dimensional samples, are shown. The reconstructed holograms have a spatial resolution of a few microns and give the refractive index within 15% of the theoretical value. In Gabor holography the spatial resolution is limited eventually by the detector resolution to about 1 m. Alternatives, like Fourier holography , will be considered with respect to resolution, signal-to-noise ratio and feasibility at the ESRF.

3:30 PM *HH4.5 
TWO CASE STUDIES OF SURFACE STRUCTURE DETERMINATIONS ASSISTED BY PHOTOELECTRON HOLOGRAPHY WITH SYNCHROTRON RADIATION. Brian P. Tonner, S. Banerjee, S. Ravy, X. Chen, D. K. Saldin, Department of Physics, University of Wisconsin-Milwaukee; E. Rotenberg, J. Denlinger, Advanced Light Source, LBNL, Berkeley, CA.

Photoelectron diffraction is a method of surface structure determination that can, when combined with computer simulations, determine the structure of a surface with a precision of a few hundredths of an Angstrom. The time consuming nature of the search for the ideal structure can be substantially shortened by direct inversion of the experimental data to produce an 'image' of the local atomic structure, a method called photoelectron holography. We will present case studies of the use of 'complete data set' photoelectron holography in application to a two-dimensional magnetic surface alloy, Mn on Ni(100), and to a complex surface reconstruction with a large unit cell, high coverage S on Cu(100). In both cases, the holographic results are used in combination with other structural probes, inluding electron diffraction, quantitative photoelectron diffraction, and surface x-ray scattering. Examples of recent results can be seen at http://www-als.lbl.gov/als/science /sci archive/surfalloy.html.

SESSION HH5: IN-ROOM POSTERS 
Thursday Afternoon, December 4, 1997 
4:00 P.M. 
Berkeley (S)

HH5.1 
TOWARD 1 HOLOGRAPHIC INFORMATION WITH TEM. Y.C. Wang, C.J. Hetherington, E.C. Nelson, M.A. O'Keefe, and U. Dahmen, National Center for Electron Microscopy, Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, CA.

A Philips CM300FEG microscope has been installed at the NCEM to provide HRTEM information down to spacings of 1Å. To achieve this resolution, both the number of image points and image magnification must be adequate. A previous study [1] has shown that more than 1024x1024 re-corded image points are required to achieve holographic resolution beyond 1Å. This constraint is mainly set by undersampling of the aberration function for higher spatial frequencies due to the insufficient pixel number of the CCD camera system. To reach a 1Å information limit, magnification must be sufficient to record 0.3Å holographic fringes. In addition, we need to sample at four times this frequency during the reconstruction, so image pixel size must be less n 0.075Å, requiring a magnification of 3.2Mx for a CCD detection system with 24m pixels. However, the maximum magnification of the CM300FEG with a directly-attached CCD is only lMx. To reach sufficient magnification and sampling, we have installed a 2048x2048 CCD coupled to a Gatan Imaging Filter system. In addition, to achieve an image with less than /4 phase change in the 1Å spatial frequency, three-fold astigmatism [2] must be corrected to lie below 0.6 m. This presentation will give preliminary results of our effort to reach the 1Å information limit by electron holography. A Au test specimen with lattice fringes of known spacing was used to calibrate the holographic interference fringes. The focus of the present study is the achievement of 0.3Å holographic fringes with adequate fringe contrast.

HH5.2 
A METHOD OF CONFOCAL SCANNING LASER HOLOGRAPHY FOR MATERIALS CHARACTERIZATION. Rodney A. Herring, Space Science, Canadian Space Agency, St. Hubert, Quebec, Canada.

A method for characterizing the phase of mesoscopic materials by means of Confocal Scanning LASER Holography (CSLH) is described. CSLH is based upon holography methods used for scanning transmission electron microscopy, where each focused-probe point produces a hologram having a carrier spatial frequency which changes due to phase shifts introduced by an object. From the proposed CSLH method, the optics for a possible CSLH microscope are presented for both a transmitted-light beam through the specimen and a reflected-light beam from the specimen's surface. The proposed CSLH microscope requires a small change in the optics of a standard confocal scanning LASER microscope (CSLM) with the addition of two optical biprisms and two additional focusing lenses around the specimen. One optical biprism splits the primary beam in order to establish a reference wave and an object wave, and then it is used again to recombine the waves in the return optics. The other biprism interferes the object wave and reference wave on the specimen's back focal plane. The two additional focusing lenses aid in the separation of the object beam and reference beam so large mesoscopic features of the object can be characterized. Fast retrieval of the specimens amplitude and phase information is achieved by recognizing two features 1) the spatial frequency of the fringes is constant during the scanning of the object so a complete Fourier transform of the interference pattern does not need to be calculated for each probe position, only its coefficients, and 2) recording a two-dimensional hologram is not necessary as a one-dimensional recording perpendicular to the fringes is sufficient for determining the phase and amplitude for each position of the object.

HH5.3 
X-RAY HOLOGRAPHY SIMULATION OF CRYSTAL DEFECTS IN SEMICONDUCTOR STRUCTURE. I.Na and C.R.Wie, Dept. of Electrical and Computer Engineering, State Univ. of New York at Buffalo, Amherst, NY.

X-ray hologram is capable of producing 3D atomic images in a crystal. One interesting application may be in studying crystal defects. In order to probe this possibility, we do computer simulation of crystal lattices with different kinds and/or amounts of defects. For a crystal with a cluster of vacancies, the reconstructed image is clearly different from the corresponding perfect crystal image. The reconstructed image for a crystal with a single isolated vacancy, however, does not show much difference from the reconstructed images of a perfect crystal due to the twin image effect. We presently investigate possible sources of spurious dots on the reconstructed image. We shall study the possibility of applying the x-ray hologram techniques to the studies of isolated point defects, point defect clusters and extended defects such as dislocations. We shall report our findings.

HH5.4 
PHOTOELECTRON HOLOGRAPHY ANALYSIS OF W(110)(11)-O BY USING FULL-SOLID-ANGLE X-RAY PHOTOELECTRON DIFFRACTION DATA WITH CHEMICAL-STATE-RESOLUTION. Hiroshi Daimon, Nara Inst of Science and Technology, Ikoma, Nara, JAPAN; Hiroshi Takagi, Faculty of Engineering Science, Osaka Univ, Toyonaka, Osaka, JAPAN; Ramon Ynzunza, Charles S. Fadley, Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, Dept of Physics, Univ of California-Davis, Davis, CA.

The structure of the W(110)(11)-O surface has been studied by photoelectron holography using full-solid-angle x-ray photoelectron diffraction (XPD) patterns with chemical state resolution. The W 4f binding energy of atoms directly bonded to oxygen is 0.73 eV higher than that of bulk W atoms in the photoelectron spectrum taken with Al K excitation. The full-solid-angle XPD data for this shifted peak, the non-shifted bulk peak, and the O 1s peak show characteristic diffraction patterns, which were used in holographic reconstruction. Each reconstructed image was compared with the structure1 determined by the R-factor structure analysis in the fitting of the theoretically calculated pattern to the observed XPD data.

HH5.5 
FIRST RESULTS FROM A RETARDING FIELD ANGLE-RESOLVED ELECTRON DISPLAY ANALYZER. W. J. Antel Jr., G. R. Harp, Ohio Univ., Athens, OH.

A LEED-like display analyzer is discussed. It uses four retarding field grids and projects the electron distribution onto a hemispherical phosphor screen. This analyzer has no coaxial electron gun, to permit measurements of electron intensity over a large angular range. A fiber-optic faceplate projects the hemispherical image onto a plane, where the light intensity is measured ex-situ with a high dynamic range CCD camera. This analyzer is optimized for the measurement of angle-resolved Auger and photoemission spectroscopy. Finally, we evaluate the effectiveness of this analyzer for the measurement of photoemission diffraction patterns for electron holography.

HH5.6 
OFF-AXIS ELECTRON HOLOGRAPHY OF VOIDS IN SELF-ANNEALED IMPLANTED SILICON.  C. Beeli, Center of Interdepartmental Electron Microscopy, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland; G. Matteucci, Department of Physics, University of Bologna and Istituto Nazionale per la Fisica della Materia, Bologna, Italy.

The characterization of defects produced during self annealing implantation of P ions in silicon is of great interest for the realization of good quality p-n junctions in silicon and to understand the peculiarity of beam-solid interactions occurring during implantation performed under conditions of extremely high current and power density. High-resolution electron holography is employed here to study the three-dimensional configuration of sphere-like cavities obtained by 100 keV P-ion bombardment of a silicon wafer using a beam with a power density of 15 W, respectively 37 W per square centimeter for 4 sec. Phase difference amplification techniques have been used to obtain maps in which the electron phase distribution indicates the thickness contours. From these maps a qualitative topography of the cavity shape as well as measurements of its depth variations are obtained. The measured depths of spherical voids can be correlated with the diameters of the voids as measured by TEM. These two measurements are in good agreement, thus proving that the voids are indeed empty. Electron holography can also be employed to display the various different internal shapes that a void structure can assume when bounded by crystal planes with different orientations.