Detection and quantitative assessment of image aberrations from single HRTEM lattice images

For utilizing the full capabilities of quantitative high-resolution transmission electron microscopy in materials characterization, a precise knowledge of the various aberrations blurring the object information is essential. Here, we describe an extended approach to the detection and quantitative assessment of image aberrations from lattice images of crystal samples. The approach is based on a theoretical analysis of five-beam lattice images in the presence of all relevant optical aberrations and for partial beam coherence. Compact analytical expressions for linear and nonlinear image Fourier coefficients as explicit functions of the aberration parameters are derived. In particular, a fundamental relationship between the occurrence of erroneous image symmetries and the simultaneous presence of optical misalignments and partial beam coherence is established. An image analysis procedure is proposed which allows for the detection of even- and odd-order residual aberrations and for the quantitative determination of defocus, two-fold astigmatism and axial coma if the three-fold astigmatism is known. For coma-free images, the three-fold astigmatism can also be determined quantitatively. Moreover, the procedure allows for a reliable detection of crystal misalignment for images of wedge-shaped crystal samples.     

A new way of measuring microscope aberrations

Two-fold astigmatism, three-fold astigmatism and misalignment (coma) can be found from the orientations only of the diffractograms of a set of images with injected beam tilts--typically eight images with tilts of equal magnitude and azimuths 45 degrees apart. The spherical aberration must be determined independently, and the defocus is not measured; however, the measurement required is very much simpler than the measurement of image displacements or induced defocus/astigmatism values, and no calibration of the microscope magnification is needed.     

基于波面面形的滤波计算

为提高光学干涉测量的精度,研究了用来消除干涉条纹图噪声的滤波算法。讨论了不同波面和不同干涉仪噪声下不同滤波方法的滤波效果。考虑干涉仪噪声对条纹图的影响与检测中的不同波面情况,基于泽尼克多项式原理用matlab仿真法建立了离焦、像散、彗差、球差4种不同的干涉条纹图,计算了滤波后不同波面面形的PV值和GRMS值差别的大小。结果表明:同种噪声与滤波器情况下,在离焦、像散、彗差、球差4种面型中,滤波后球差波面的PV差值最大,高达0.11λ,与在乘性噪声下其它波面的最高PV值0.08λ相比,滤波效果较差;滤波后像散波面的PV差值最小,除乘性噪声中值滤波情况外,PV差值均在0.05λ以下,最低达0.01λ,滤波效果较好。此外,彗差波面滤波情况要略优于离焦波面。滤波器中,低通滤波稳定性高,PV差值局限于0.01λ~0.04λ,滤波效果相对好;而空域滤波后波面的PV差值最高达0.09λ,但噪声针对性更好。     

Structure of the (110) antiphase boundary in gallium phosphide

The morphology of antiphase boundaries in GaP films grown by molecular beam epitaxy on Si (001) has been studied by transmission electron microscopy. The inversion of the crystal polarity between antiphase domains was confirmed by convergent‐beam electron diffraction. The APBs were often found to facet parallel to {110} planes. Strong‐beam α‐fringe contrast observed along the (110) facets indicates that adjacent antiphase domains are related by an additional rigid‐body lattice translation. Diffraction‐contrast analysis shows that this R corresponds to a shear parallel to the [001] direction and a small expansion. The magnitude of the translation was inferred, quantitatively, through a comparison between energy‐filtered zero‐loss images of the α‐fringe contrast with numerical calculations. The components of the rigid‐body lattice translation were determined to be 0.023 ± 0.0033 nm in the [001] direction and 0.005 ± 0.002 nm in the 0 direction. Based upon a geometric model of the {110} antiphase boundary, the lengths of the Ga and P antisite bonds were calculated to be 254 ± 2 pm and 227 ± 4 pm, respectively.     

High resolution imaging of defects in sigma phase in a stainless steel

The high resolution axial lattice imaging technique has been applied to the study of the faults which commonly occur in the sigma phase which can be formed from ferrite in a duplex high chromium stainless steel on ageing at 973 K. It was noted that axial lattice fringe images at (001)_σ show no detailed correspondences with thickness and it was further demonstrated that lattice fringe displacements in axial images at strain free boundaries can be used to give an accurate measure of the magnitude of the associated lattice displacements. The displacement vectors associated with the common (100)_σ faults in the material were classified.     

Higher-order aberration corrector for an image-forming system in a transmission electron microscope

We developed a new electron optical system with three dodecapoles to compensate for spherical aberration and six-fold astigmatism, which generally remains in a two-hexapole type corrector. In this study, we applied the corrector for image-forming system in transmission electron microscope. Compensation for higher-order aberration was demonstrated through a diffractogram tableau using a triple three-fold astigmatism field system, which was then compared with a double hexapole field system. Using this electron optical system, six-fold astigmatism was measured to be less than 0.1 mm at an acceleration voltage of 60 kV, showing that the system successfully compensated for six-fold astigmatism.     

Optical fiber index profiling by video analysis of interference fringes

An electronic technique to make fringe displacement measurements on the output field of an interference microscope to 1/1000 of a fringe, not including systematic errors, is described. The method, based upon line-selected video signal analysis, is applied to the evaluation of the refractive index profile of a graded index optical fiber. The index difference at a given point between the core and cladding is determined to better than 1 part in 10(5), implying a precision in the profile parameter alpha of +/-0.005, an order of magnitude better than existing techniques.     

Aspects regarding measurement of thickness of intergranular glassy films

Materials such as Si₃N₄, SiC and SrTiO₃ can have grain boundaries characterized by the presence of a thin intergranular amorphous film of nearly constant thickness, in some cases (e.g. Si₃N₄) almost independent of the orientation of the bounding grains, but dependent on the composition of the ceramic. Microscopy techniques such as high‐resolution lattice fringe imaging, Fresnel fringe imaging and diffuse dark field imaging have been applied to the study of intergranular glassy films. The theme of the current investigation is the use of Fresnel fringes and Fourier filtering for the measurement of the thickness of intergranular glassy films. Fresnel fringes hidden in high‐resolution micrographs can be used to objectively demarcate the glass–crystal interface and to measure the thickness of intergranular glassy films. Image line profiles obtained from Fourier filtering the high‐resolution micrographs can yield better estimates of the thickness. Using image simulation, various kinds of deviation from an ideal square‐well potential profile and their effects on the Fresnel image contrast are considered. A method is also put forth to objectively retrieve Fresnel fringe spacing data by Fourier filtering Fresnel contrast images. Difficulties arising from the use of the standard Fresnel fringe extrapolation technique are outlined and an alternative method for the measurement of the thickness of intergranular glassy films, based on zero‐defocus (in‐focus) Fresnel contrast images is suggested. The experimental work is from two ceramic systems: Lu‐Mg‐doped Si₃N₄ and SrTiO₃ (stoichiometric and nonstoichiometric). Further, a comparison is made between the standard high‐resolution lattice fringe technique, the standard Fresnel fringe extrapolation technique and the methods of analyses introduced in the current work, to illustrate their utility and merits. Taking experimental difficulties into account, this work is intended to be a practical tool kit for the study of intergranular glassy films.     

Dual laser interferometer for plasma density measurements on large tokamaks

A two-wavelength plasma density interferometer utilizing a CO(2) laser and an HeNe laser is described. The interferometer is being designed for use on Doublet III, a large noncircular cross-section tokamak. The use of the two wavelengths allows the distinction between fringe shifts due to plasma density and fringe shifts due to mirror vibrations. Plasma density fringe shifts of 1/10 of a fringe shift can be measured in the presence of mirror vibrations which cause several fringe shifts. A simple digital phase comparing electronic system is used.     

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.     

Effect of temperature and strain-rate on the stress-optic law of celluloid

To reassess rigorously the possibility of using celluloid as model material for studying photoplasticity, the relations between stress and strain, and stress and fringe order in celluloid under uniaxial tension are examined carefully for various strain-rates at varying ambient temperatures by means of isochronous and continual measurement. The fringe order at the yield stress does not depend on strain-rate, which shows the possibility of easily finding the evolution of the elastic-plastic boundary in plane stress problems.     

Quasi-quadrature interferometer for plasma density radial profile measurements

A cw Mach Zehnder multichannel interferometer has been developed to measure time-dependent fractional fringe shifts with an accuracy of one-fortieth fringe. The design is quasi-quadrature in that known phase shifts, introduced in the reference beam, are time multiplexed with the normal reference beam. This technique requires only one detector per interferometer channel as compared to two detectors for most quadrature designs. The quadrature information makes the sense of density changes unambiguous, it automatically calibrates the instrument during the plasma event, and it makes fringe shift measurements virtually independent of fringe contrast fluctuations caused by plasma refractive and/or absorptive effects. The interferometer optical design is novel in that the electro-optic crystal used to introduce the 90 degrees phase shifts is located in the common 2-mm-diam HeNe entrance beam to the interferometer, by exploiting polarization techniques, rather than in the expanded 1-2-cm reference beam itself. This arrangement greatly reduces the size, cost, and high-voltage requirements for the phase modulating crystal.     

Measurement of translation component at ordered interfaces by weak-beam α-fringe electron microscopy

Lattice translations at a stacking fault and a twin boundary were measured from fringe shifts at a set of common weak-beam diffraction conditions (weak-beam α-fringe imaging) in stainless steel SUS316. It is suggested that the present technique is applicable in determining the translation component between neighbouring crystals with coincidence related boundaries.     

Imaging and thickness measurement of amorphous intergranular films using TEM

Fresnel fringe analysis is shown to be unreliable for grain boundaries in yttrium-doped alumina: the determined thicknesses do not agree well with those measured from high resolution transmission electron microscopy (HRTEM), the asymmetry between under- and overfocus is very large, and Fresnel fringes are sometimes shown at boundaries which contain no amorphous film. An alternative approach to the analysis of HRTEM images of grain boundary films is demonstrated: Fourier filtering is used to remove the lattice fringes from the image thereby significantly enhancing the visibility of the intergranular films. The apparent film thickness shows a discrepancy between measurements from the original HRTEM image and the filtered image. It was shown that fringe delocalisation and diffuseness of the amorphous/crystalline interfaces will lead to a significant underestimate of the thickness in unprocessed HRTEM images. In contrast to this, the average thickness can be much more accurately measured from the Fourier-filtered image, provided the boundary is oriented accurately edge-on.     

The effect of vacancies on the annular dark field image contrast of grain boundaries: a SrTiO(3) case study

The analysis of grain boundary structure in high resolution electron microscopy is often hindered by contrast variation within the grain boundary region which is not explained by simple models of the grain boundary structure. Recent work suggests that structural disorder along the beam direction and the presence of vacancies contribute significantly to this effect. One might expect a significant reduction in contrast in a Z-contrast image of a grain boundary would imply that vacancies present must result from the absence of heavier elements. Using a [001](210) Σ5 grain boundary in SrTiO₃ as a test case and first principles structure relaxation to calculate stable defect structures, we show that the reduction in the intensity from fully occupied Sr columns due to the structural distortion resulting from a nearby O vacancy can be as great as that due to introducing a Sr vacancy in the column itself. The effect on energy dispersive X-ray spectroscopy signals is also considered, but found to be smaller than that on Z-contrast images.     

Analysis of rotation in the lubrication of a porous slider bearing: Small rotation

A mathematical model is developed to investigate the behaviour of a plane-inclined porous slider bearing under the effect of a uniform small rotation. The Beavers-Joseph slip condition was used for the slip velocity at the porous boundary. The expressions for dimensionless pressure distribution, load-carrying capacity and coefficient of friction are obtained. It is concluded that the load-carrying capacity and coefficient of friction depend on the direction and magnitude of rotation. For a negative rotation the load-carrying capacity increases and the coefficient of friction decreases. The load-carrying capacity also decreases with increase in the slip velocity parameter.     

The contribution of phonon scattering to high-resolution images measured by off-axis electron holography

The contribution of electrons that have been phonon scattered to the lattice fringe amplitude and the background intensity of a high-resolution electron microscope (HREM) image is addressed experimentally through the analysis of a defocus series of energy-filtered off-axis electron holograms. It is shown that at a typical specimen thickness used for HREM imaging approximately 15% of the electrons that contribute to an energy-filtered image have been phonon scattered. At this specimen thickness, the phonon-scattered electrons contribute a lattice image of opposite contrast to the elastic lattice image. The overall lattice fringe contrast is then reduced to 70% of the value that it would have in the absence of phonon scattering. At higher specimen thickness, the behaviour is defocus-dependent, with the phonon image having lattice fringe contrast of either the same or the opposite sense to the elastic image as the defocus is varied.     

Measurement of lens aberrations by means of image displacements in beam-tilt series

Electron microscope image aberrations are determined by means of the beam tilt/image displacement method with respect to the precision required to obtain a resolution of 1 A. The method simultaneously yields all image aberrations to the fourth order and it is independent of the material used for the procedure. The experimental procedure using amorphous carbon is described and errors in measuring beam-tilt angles, magnifications and image displacements can be kept sufficiently small to achieve the required accuracy. The method is applied to determine aberration constants of a CM300 FEG/UT microscope with correction of the three-fold astigmatism. The coefficient of spherical aberration and the modulus of the three-fold astigmatism were measured to 0.60 (+/- 0.02) mm and 150 (+/- 50) nm, respectively. The beam tilt/image displacement procedure is also computer simulated using an amorphous model structure yielding the same values for the lens aberrations which are used for imaging. However, a coefficient of spherical aberration of 0.67 mm is obtained by applying the focus variation/diffractogram analysis on the same model.     

Five-parameter grain boundary analysis of a grain boundary–engineered austenitic stainless steel

Two different grain boundary engineering processing routes for type 304 austenitic stainless steel have been compared. The processing routes involve the application of a small level of strain (5%) through either cold rolling or uni-axial tensile straining followed by high-temperature annealing. Electron backscatter diffraction and orientation mapping have been used to measure the proportions of Σ3ⁿ boundary types (in coincidence site lattice notation) and degree of random boundary break-up, in order to gain a measure of the success of the two types of grain boundary engineering treatments. The distribution of grain boundary plane crystallography has also been measured and analyzed in detail using the five-parameter stereological method. There were significant differences between the grain boundary population profiles depending on the type of deformation applied.     

纳米多晶铜单点金刚石切削亚表层损伤机理

基于Poisson-Voronoi和Monte Carlo方法构建了多晶铜分子动力学模型,研究了纳米切削中多晶铜材料去除、切削力变化及晶界与位错间的相互转化机制。研究结果表明：晶界的阻碍作用使得切屑流向发生了改变,并在已加工表面形成凹槽和毛刺;切削过程中晶界前方材料变形能的逐渐积聚及晶界的最终断裂,造成了切削力发生由最大峰值到最小谷值的大幅波动;晶界附近的材料去除经历了材料变形积聚、位错穿越晶界、晶界转变为位错及晶界最终断裂等过程。通过详细分析多晶铜纳米切削中位错与晶界间的演化过程,揭示了晶界与位错间的相互转化机制,丰富了多晶铜亚表层损伤机理的内涵。