Maximum diameter of the rod-shaped specimen for transmission electron microtomography without the "missing wedge"

In our recent study, the complete rotation of a rod-shaped specimen during transmission electron microscopy (TEM) has been successfully carried out, yielding a truly quantitative three-dimensional (3D) structure of a ZrO(2)/polymer nano-composite. This result allows the further development of transmission electron microtomography (TEMT) for materials science. The diameter of the rod-shaped specimen was about 150 nm, which may not be statistically large enough to evaluate structural parameters, e.g., volume fraction of Zr nano-particles. Thus, it is preferable to image rods with larger diameters in 3D. In this study, several rod-shaped specimens whose diameters ranged from 150 to 530 nm were subjected to the "distortion-free TEMT". The maximum diameters, l, observable under 200 and 300 kV-TEMTs were, respectively, 460-470 and 600-670 nm (corresponding the maximum relative diameters, l/lambda (lambda: mean free path), were ca. 2.2 and 2.7-3.0).     

Three-dimensional reconstructions from incomplete data: interpretability of density maps at "atomic" resolution

Three dimensional data collection in electron microscopy is normally limited to a range of tilt angles that is less than +/- 90 degrees. Thus, even under the best conditions, experimental values of the structure factors will be missing within a solid cone in reciprocal space. Previous work has already shown that the missing cone of data can produce serious artifacts in three-dimensional density maps at modest resolution, for example approximately 15A. We now report, however, that a missing cone as large as +/- 30 degrees appears to have no serious effect on the three-dimensional density map of a protein at 3.6 A resolution, and we attribute this result to the fact that the electron density features are quite well separated from one another at that resolution. The map calculated with a +/- 30 degree missing cone is, furthermore, no more sensitive to noise (error) than is the full (isotropic) Fourier map. This result does not seem to be unreasonable in view of the fact that less than 14% of the data (i.e., signal) is lost due to the missing cone. Our numerical simulations therefore indicate that there should be no difficulty in interpreting high-resolution Fourier maps that can be produced with data that fall within realistic estimates of achievable resolution, tilt angles, and experimental error.     

Observation of three-dimensional elemental distributions of a Si device using a 360 degrees -tilt FIB and the cold field-emission STEM system

A technique for preparation of a pillar-shaped specimen and its multidirectional observation using a combination of a scanning transmission electron microscope (STEM) and a focused ion beam (FIB) instrument has been developed. The system employs an FIB/STEM compatible holder with a specially designed tilt mechanism, which allows the specimen to be tilted through 360 degrees [T. Yaguchi, M. Konno, T. Kamino, T. Hashimoto, T. Ohnishi, K. Umemura, K. Asayama, Microsc. Microanal. 9 (Suppl. 2) (2003) 118; T. Yaguchi, M. Konno, T. Kamino, T. Hashimoto, T. Ohnishi, M. Watanabe, Microsc. Microanal. 10 (Suppl. 2) (2004) 1030]. This technique was applied to obtain the three-dimensional (3D) elemental distributions around a contact plug of a Si device used in a 90-nm technology. A specimen containing only one contact plug was prepared in the shape of a pillar with a diameter of 200nm and a length of 5mum. Elemental maps were obtained from the pillar specimen using a 200-kV cold-field emission gun (FEG) STEM model HD-2300C equipped with the EDAX genesis X-ray energy-dispersive spectrometry (XEDS) system through a spectrum imaging technique. In this study, elemental distributions of minor elements with weak signals were enhanced by applying principal component analysis (PCA), which is a superior technique to extract weak signals from a large dataset. The distributions of elements, especially the metallization component Ti and minor dopant As in this particular device, were successfully extracted by PCA. Finally, the 3D elemental distributions around the contact plug could be visualized by reconstruction from the tilt series of maps.     

Axial tomographic confocal fluorescence microscopy

By physical rotation of the sample, axial tomography enables the acquisition of otherwise inaccessible spatial information from an object. In combination with confocal microscopy, the method can fundamentally improve the effective three‐dimensional (3D) resolution. In this report we present a novel method for high resolution reconstruction of confocal axial tomographic data. The method automatically determines the relative angles of rotation, aligns the data from different rotational views and reconstructs a single high resolution 3D dataset. The reconstruction makes use of a known point spread function and is based on an unconstrained maximum likelihood deconvolution performed simultaneously from multiple (in our case three) angular views. It was applied to simulated as well as to experimental confocal datasets. The gain in resolution was quantified and the effect of choice of overrelaxation factors on the speed of convergence was investigated. A clearly improved 3D resolution was obtained by axial tomography together with reconstruction as compared with reconstruction of confocal data from only a single angular view.     

Calibration method of tilt and azimuth angles for alignment of TEM tomographic tilt series

This paper describes the calibration method of the tilt and azimuth angles of specimen using a digital protractor and a laser autocollimator for alignment of electron tomography. It also suggests an easy method to check whether the specimen is tilted by 180.0°, and whether the azimuth angle is 0.0°; the method involves the use of two images of a rod-shaped specimen collected before and after a 180.0° tilt. The method is based on the assumption that these images are symmetric about the tilt axis when the azimuth angle is 0.0°. In addition, we used an experiment to demonstrate the effect of the incorrect angles on reconstructed images and simulated the image quality against distance away from tilt axis.     

High-angle triple-axis specimen holder for three-dimensional diffraction contrast imaging in transmission electron microscopy

Electron tomography requires a wide angular range of specimen-tilt for a reliable three-dimensional (3D) reconstruction. Although specimen holders are commercially available for tomography, they have several limitations, including tilting capability in only one or two axes at most, e.g. tilt-rotate. For amorphous specimens, the image contrast depends on mass and thickness only and the single-tilt holder is adequate for most tomographic image acquisitions. On the other hand, for crystalline materials where image contrast is strongly dependent on diffraction conditions, current commercially available tomography holders are inadequate, because they lack tilt capability in all three orthogonal axes needed to maintain a constant diffraction condition over the whole tilt range. We have developed a high-angle triple-axis (HATA) tomography specimen holder capable of high-angle tilting for the primary horizontal axis with tilting capability in the other (orthogonal) horizontal and vertical axes. This allows the user to trim the specimen tilt to obtain the desired diffraction condition over the whole tilt range of the tomography series. To demonstrate its capabilities, we have used this triple-axis tomography holder with a dual-axis tilt series (the specimen was rotated by 90° ex-situ between series) to obtain tomographic reconstructions of dislocation arrangements in plastically deformed austenitic steel foils.     

Lattice parameters from direct-space images at two tilts

Lattices in three dimensions are oft studied from the "reciprocal space" perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes. Such data can come from electron-phase (or less easily Z contrast images) taken at two tilts, provided that one image shows two non-parallel lattice periodicities, and the other shows a periodicity not coplanar with the first two. We outline here protocols for measuring the 3D parameters of cubic lattice types in this way. For randomly oriented nano-crystals with cell side greater than twice the continuous transfer limit, orthogonal +/-15 degrees and +/-10 degrees tilt ranges might allow one to measure 3D parameters of all such lattice types in a specimen from only two well-chosen images. The strategy is illustrated by measuring the lattice parameters of a 10nm WC(1-x) crystal in a plasma-enhanced chemical-vapor deposited thin film.     

High-precision tilt stage for the high-voltage electron microscope

The high-voltage electron microscope is used to study thick samples (0.25 to several micrometers) to obtain three-dimensional information at ultrastructural resolution. Three-dimensional image reconstructions are often employed to extract, process and display this information. The sets of images used to form reconstructions must be recorded for precisely known specimen-beam orientations, especially if tomographic methods are employed. The design and operation of a precision (+/- 0.06 degrees) single-tilt stage to support this type of imaging is reported. All motions including two translations, height adjustment and tilting are accomplished via a single objective lens entry port. The specimen rod is supported on two rubber gaskets for vibration isolation, and motorized precision micrometers with encoder readouts for position monitoring drive the motions. The stage is stable to 0.6 nm for at least 16 s and is capable of tilt angles of +/- 70 degrees.     

Accurate marker-free alignment with simultaneous geometry determination and reconstruction of tilt series in electron tomography

An image alignment method for electron tomography is presented which is based on cross-correlation techniques and which includes a simultaneous refinement of the tilt geometry. A coarsely aligned tilt series is iteratively refined with a procedure consisting of two steps for each cycle: area matching and subsequent geometry correction. The first step, area matching, brings into register equivalent specimen regions in all images of the tilt series. It determines four parameters of a linear two-dimensional transformation, not just translation and rotation as is done during the preceding coarse alignment with conventional methods. The refinement procedure also differs from earlier methods in that the alignment references are now computed from already aligned images by reprojection of a backprojected volume. The second step, geometry correction, refines the initially inaccurate estimates of the geometrical parameters, including the direction of the tilt axis, a tilt angle offset, and the inclination of the specimen with respect to the support film or specimen holder. The correction values serve as an indicator for the progress of the refinement. For each new iteration, the correction values are used to compute an updated set of geometry parameters by a least squares fit. Model calculations show that it is essential to refine the geometrical parameters as well as the accurate alignment of the images to obtain a faithful map of the original structure.     

Three-dimensional distributions of elements in biological samples by energy-filtered electron tomography

By combining electron tomography with energy-filtered electron microscopy, we have shown the feasibility of determining the three-dimensional distributions of phosphorus in biological specimens. Thin sections of the nematode, Caenorhabditis elegans were prepared by high-pressure freezing, freeze-substitution and plastic embedding. Images were recorded at energy losses above and below the phosphorus L2,3 edge using a post-column imaging filter operating at a beam energy of 120 keV. The unstained specimens exhibited minimal contrast in bright-field images. After it was determined that the specimen was sufficiently thin to allow two-window ratio imaging of phosphorus, pairs of pre-edge and post-edge images were acquired in series over a tilt range of +/-55 degrees at 5 degrees increments for two orthogonal tilt axes. The projected phosphorus distributions were aligned using the pre-edge images that contained inelastic contrast from colloidal gold particles deposited on the specimen surface. A reconstruction and surface rendering of the phosphorus distribution clearly revealed features 15-20 nm in diameter, which were identified as ribosomes distributed along the stacked membranes of endoplasmic reticulum and in the cytoplasm. The sensitivity of the technique was estimated at < 35 phosphorus atoms per voxel based on the known total ribosomal phosphorus content of approximately 7000 atoms. Although a high electron dose of approximately 10(7)e/nm2 was required to record two-axis tilt series, specimens were sufficiently stable to allow image alignment and tomographic reconstruction.     

A 360° single-axis tilt stage for the high-voltage electron microscope

A new type of specimen stage that permits more than 180° of tilting about the axis of a side-entry rod has been developed for a high-voltage electron microscope (HVEM). Roughly cylindrical specimens, with radial dimensions of less than a few micrometres, that can be mounted on the tip of a microneedle or micropipette are applicable. For glass micropipettes, the energy of the 1-MeV beam of the HVEM is sufficient to image specimens through both walls. The stage employs a spindle mechanism that holds these needles or micropipettes coaxial with the tilt axis, allowing the specimen to be rotated without restriction. This arrangement, along with the cylindrical form of the specimen, is an important development for single-axis tomography, because it permits a complete 180° set of projections to be recorded. The angular accuracy of the stage was demonstrated to be within ±0.20°, with a cumulative error of less than 1.0° over a 180° span. The new stage was tested using puffball spores mounted on a micropipette. A 180° tilt series was recorded and processed to yield a tomographic three-dimensional reconstruction which was displayed both as a cross-sectional view perpendicular to the tilt axis, and as a shaded surface viewed from different directions. The same computations were repeated using subsets of the tilt series to assess the effect of various amounts of missing information. Visual inspection of a selected cross-section from these reconstructions indicated that limiting the angular range to 160° produced results nearly as good as the full data set. Limiting the range to 140°, however, produced a noticeable geometric distortion, which became increasingly severe with ranges of 120° and 100°.     

Nondestructive three-dimensional characterization of grain boundaries by X-ray crystal microscopy

The results from an emerging method of nondestructive grain boundary characterization, with unprecedented sensitivity to neighbor-grain misorientation and grain boundary morphology are reported. The method utilizes differential aperture X-ray microscopy to determine the local crystallographic orientation of submicron volumes within polycrystalline materials. Initial measurements are described for a recrystallized Ni sample where the grain boundary type was identified at 85 grain boundaries within the framework of an ideal coincident site lattice (CSL) model. The remarkable resolution of this method is demonstrated by the <0.03 degrees deviations of misorientation measured for Sigma3 (twin) boundaries. Because of its high angular and spatial resolution, this new approach to grain boundary characterization can provide quantitative tests of grain boundary models with new insights for grain boundary engineering efforts.     

Effects of tilt on high-resolution ADF-STEM imaging

A study of the effects of small-angle specimen tilt on high-resolution annular dark field images was carried out for scanning transmission electron microscopes with uncorrected and aberration-corrected probes using multislice simulations. The results indicate that even in the cases of specimen tilts of the order of 1 degree a factor of 2 reduction in the contrast of the high-resolution image should be expected. The effect holds for different orientations of the crystal. Calculations also indicate that as the tilted specimen gets thicker the contrast reduction increases. Images simulated with a low-angle annular dark field detector show that tilt effects are more pronounced in this case and suggest that these low-angle detectors can be used to correct specimen tilt during scanning transmission electron microscopes operation.     

Computer image analysis of two-dimensional crystals of beef heart NADH: ubiquinone oxidoreductase fragments. II. Comparison of frozen hydrated and negatively stained specimens

Two-dimensional crystals of bovine NADH: ubiquinone oxidoreductase fragments were studied by cryo-electron microscopy and computer image analysis at two focus settings. The lattice parameters of the crystals were determined as a = 14.5 +/- 0.2 nm, b = 14.8 +/- 0.3 nm with gamma = 87.8 degrees +/- 0.2 degrees. Translation and rotation alignment resulted in a final resolution of 1.38 (close-to-focus) or 1.9 nm (1.3 microns underfocus). When only translational alignment was employed 1.6 nm resolution resulted (close-to-focus case). The application of a further correction procedure surprisingly lowered the achieved resolution to 2.2 nm. A combination of the projected structures for the two focus settings in Fourier space resulted in a noise-free image displaying enhanced image contrast for reciprocal spacings from 1/5.0 to 1/1.4 nm-1. The structure in amorphous ice comprises four separate quasi-identical motifs, each resembling a distorted triangle. Two symmetry-related (p2) motifs reveal a pore-like feature. In negative stain the structure has p4mm symmetry. The absence of in-plane symmetry elements (i.e. twofold rotation and screw axes) and other differences might be accounted for (at least in part) if the crystal studied was slightly tilted.     

Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage

In this study, a laser linear encoder with three degrees of freedom (3-DOFs) based on diffraction and interference was developed to measure the linear displacement and two angular errors of a linear moving stage. Parts of the linear motion errors induced from the two angular errors can be calculated by this prototype 3-DOF laser encoder. It was an effective method for online error calculation and compensation to improve precision stage performance. This new function was superior to other laser encoders. The verification results showed that the resolution is 20 nm. It detected displacements relative to an external grating scale with accuracy of about +/-150 nm for a measuring range of +/-1 mm, and detected the angular errors with related accuracy of about +/-1 arc sec for a measuring range of +/-100 arc sec.     

Computed tomography of cryogenic biological specimens based on X-ray microscopic images

Soft X-ray microscopy employs the photoelectric absorption contrast between water and protein in the 2.34-4.38 nm wavelength region to visualize protein structures down to 30 nm size without any staining methods. Due to the large depth of focus of the Fresnel zone plates used as X-ray objectives, computed tomography based on the X-ray microscopic images can be used to reconstruct the local linear absorption coefficient inside the three-dimensional specimen volume. High-resolution X-ray images require a high specimen radiation dose, and a series of images taken at different viewing angles is needed for computed tomography. Therefore, cryo microscopy is necessary to preserve the structural integrity of hydrated biological specimens during image acquisition. The cryo transmission X-ray microscope at the electron storage ring BESSY I (Berlin) was used to obtain a tilt series of images of the frozen-hydrated green alga Chlamydomonas reinhardtii. The living specimens were inserted into borosilicate glass capillaries and, in this first experiment, rapidly cooled by plunging into liquid nitrogen. The capillary specimen holders allow image acquisition over the full angular range of 180 degrees. The reconstruction shows for the first time details down to 60 nm size inside a frozen-hydrated biological specimen and conveys a clear impression of the internal structures. This technique is expected to be applicable to a wide range of biological specimens, such as the cell nucleus. It offers the possibility of imaging the three-dimensional structure of hydrated biological specimens close to their natural living state.     

A second-order focusing electrostatic toroidal electron spectrometer with 2pi radian collection

This paper presents a toroidal electron energy spectrometer designed to capture electrons in the full 2pi azimuthal angular direction while at the same time having second-order focusing optics. Simulation results based upon direct ray tracing predict that the relative energy resolution of the spectrometer will be 0.146% and 0.0188% at input angular spreads of +/- 6 degrees and +/- 3 degrees, respectively, comparable to the theoretically best resolution of the cylindrical mirror analyzer (CMA), and an order of magnitude better than existing toroidal spectrometers. Also predicted for the spectrometer is a parallel energy acquisition mode of operation, where the energy bandwidth is expected to be > +/- 10% (20% total) of the pass energy. The spectrometer is designed to allow for retardation of the pass energy without the need to incorporate auxiliary lenses.     

Dynamic characteristics of gas-lubricated externally pressurized porous bearings with journal rotation II

The dynamic tilt stiffness and damping coefficients of an externally pressurized porous gas bearing with journal rotation have been calculated theoretically. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the dynamic pressure distribution is determined by small perturbations of the Reynolds equation. Non-dimensional tilt stiffness and damping coefficients for various design conditions are calculated numerically using a digital computer and presented in the form of figures and tables.     

扭转复合微动的数值模拟

扭转复合微动是扭动和转动模式微动的复合.以实验研究为基础,在有限元软件ABAQus中建立三维球/平面接触弹塑性有限元模型,通过改变球体旋转轴与平面试样法向的倾斜角度α,实现球/平面接触的扭转复合微动.恒定法向载荷作用下,通过对角位移θ分量做量纲-化处理,建立倾斜角α与完全滑移角位移幅值θ0的函数关系,分析倾斜角对接触状态、接触压力、摩擦剪应力及滑移量的影响规律.结果表明:角位移θ0随倾斜角的增大而减小,并符合量纲-扭动转动分量平方和为一的规律;倾斜角α显著影响接触面力学参数的分布,与纯扭动和纯转动相比,损伤呈现明显的非对称性.