Comparison of EBSD patterns simulated by two multislice methods

The extraction of crystallography information from electron backscatter diffraction (EBSD) patterns can be facilitated by diffraction simulations based on the dynamical electron diffraction theory. In this work, the EBSD patterns are successfully simulated by two multislice methods, that is, the real space (RS) method and the revised real space (RRS) method. The calculation results by the two multislice methods are compared and analyzed in detail with respect to different accelerating voltages, Debye–Waller factors and aperture radii. It is found that the RRS method provides a larger view field of the EBSD patterns than that by the RS method under the same calculation conditions. Moreover, the Kikuchi bands of the EBSD patterns obtained by the RRS method have a better match with the experimental patterns than those by the RS method. Especially, the lattice parameters obtained by the RRS method are more accurate than those by the RS method. These results demonstrate that the RRS method is more accurate for simulating the EBSD patterns than the RS method within the accepted computation time.     

Method for determination of the displacement field in patterned nanostructures by TEM/CBED analysis of split high-order Laue zone line profiles

A method to extract accurate information on the displacement field distribution from split high‐order Laue zones lines in a convergent‐beam electron diffraction pattern of nanostructures has been developed. Starting from two‐dimensional many beam dynamical simulation of HOLZ patterns, we assembled a recursive procedure to reconstruct the displacement field in the investigated regions of the sample, based on the best fit of a parametrized model. This recursive procedure minimizes the differences between simulated and experimental patterns, taken in strained regions, by comparing the corresponding rocking curves of a number of high‐order Laue zone reflections. Due to its sensitivity to small displacement variations along the electron beam direction, this method is able to discriminate between different models, and can be also used to map a strain field component in the specimen. We tested this method in a series of experimental convergent‐beam electron diffraction patterns, taken in a shallow trench isolation structure. The method presented here is of general validity and, in principle, it can be applied to any sample where not negligible strain gradients along the beam direction are present.     

Fortran source listing for simulating three-dimensional convergent beam patterns with absorption by the Bloch wave method

The FORTRAN source code is given for a computer program that calculates the two-dimensional intensity distribution in convergent-beam transmission electron microdiffraction (CBED) patterns from perfect crystals. The program uses the eigenvalue or Bloch-ware method. It allows three-dimensional dynamical diffraction, and so includes all higher-order Laue zone effects without approximation. No symmetry reduction is included. The program accepts noncentrosymmetric or centrosymmetric crystal structures and allows absorption corrections to be included. It uses the “EISPACK” subroutines for the diagonalisation of a general complex matrix. Up to 100 CBED disks may be included. The code is also available via “Bitnet”.     

The application of convergent beam electron diffraction (CBED) analysis on transformation‐induced plasticity (TRIP) steels

Convergent beam electron diffraction (CBED) in transmission electron microscopy (TEM) was applied to determine local carbon concentrations in low‐carbon transformation‐induced plasticity (TRIP) steels. High‐order Laue‐zone (HOLZ) lines were experimentally obtained for comparison with simulation results. A new procedure for calculating carbon content is thus proposed. Retained austenite (RA) is classified into three types by morphology; the relationship between the carbon content and the corresponding RA morphology is discussed based on CBED results. Furthermore, results of X‐Ray diffractometry measurements are also used for comparison.     

A dynamical Bragg equation for high-order Laue zone reflections

A dynamically corrected Bragg equation for high-order Laue zone (HOLZ) reflections is derived directly from the Bloch wave formalism instead of the geometric argument used to deduce the kinematical Bragg condition. It differs from the kinematical Bragg equation by replacing the plane wave vector in the kinematical equation with the Bloch wave vectors. This dynamical equation reduces to the kinematical equation when the crystal potential is zero. It also demonstrates the occurrence of dynamical shifts for the HOLZ reflections but their absence for the zero-order Laue zone (ZOLZ) reflections in the symmetrical Laue case.     

A simplified method of electron microscope voltage measurement

A simple, rapid procedure for the determination of the accelerating voltage of a transmission electron microscope is described, which involves the measurement of the ratio of two easily found distances in the Kikuchi pattern near the [111] zone of a silicon crystal. Using enlarged prints the accuracy of voltage determination is around 0.2%, and in good conditions, direct viewing of the flourescent screen gives an accuracy of better than 1%. Data are given for 5% variation from nominal voltages of 100, 120, and 200 kV.     

Use of reciprocal lattice layer spacing in electron backscatter diffraction pattern analysis

In the scanning electron microscope using electron backscattered diffraction, it is possible to measure the spacing of the layers in the reciprocal lattice. These values are of great use in confirming the identification of phases. The technique derives the layer spacing from the higher-order Laue zone rings which appear in patterns from many materials. The method adapts results from convergent-beam electron diffraction in the transmission electron microscope. For many materials the measured layer spacing compares well with the calculated layer spacing. A noted exception is for higher atomic number materials. In these cases an extrapolation procedure is described that requires layer spacing measurements at a range of accelerating voltages. This procedure is shown to improve the accuracy of the technique significantly. The application of layer spacing measurements in EBSD is shown to be of use for the analysis of two polytypes of SiC.     

Many-beam dynamical simulation of electron backscatter diffraction patterns

We present an approach for the simulation of complete electron backscatter diffraction (EBSD) patterns where the relative intensity distributions in the patterns are accurately reproduced. The Bloch wave theory is applied to describe the electron diffraction process. For the simulation of experimental patterns with a large field of view, a large number of reflecting planes has to be taken into account. This is made possible by the Bethe perturbation of weak reflections. Very good agreement is obtained for simulated and experimental patterns of gallium nitride GaN{0001} at 20kV electron energy. Experimental features like zone-axis fine structure and higher-order Laue zone rings are accurately reproduced. We discuss the influence of the diffraction of the incident beam in our experiment.     

Using the Hough transform for HOLZ line identification in convergent beam electron diffraction

The Hough transform as a means for automatic line detection is applied for higher order Laue zone (HOLZ) line identification in convergent beam electron diffraction. The HOLZ line positions are commonly used to measure the strain state in the investigated material. Besides the automation, a very important aspect is the accuracy of the detected line positions. The limits are determined by the amount of noise in the pattern relative to the contrast of the HOLZ lines and the line width. Our investigations show that sub-pixel resolution can be achieved routinely. We have also developed a new strain analysis procedure in which the dynamical shift of each individual line can be taken into account using a model based on several Ewald spheres with different radii. In comparison to the effective high voltage method, finer details of the dispersion surface can be considered, which increases the accuracy of the strain analysis. A measurement of the thermal expansion of aluminium is presented as a model experiment. The lattice constants were determined with an accuracy of about 10⁻⁴.     

Dynamical simulations of zone axis electron channelling patterns of cubic silicon carbide

We have observed and simulated energy-dependent intensity distributions in electron channelling patterns (ECP) of cubic silicon carbide (3C SiC) which were recorded close to the (111) zone axis. The kinetic energies used were in the range from 4 to 8 keV, covering the low-energy region of the ECP technique. We explain the observed patterns by dynamical many beam simulations using a bloch wave approach for the diffraction of the incoming beam and the forward-backward-approximation for the backscattering of the electrons. The dynamical simulations reproduce the experimental patterns very well. It is found that higher-order Laue zone reflections are responsible for the strong energy sensitivity of the intensity distributions.     

Retro‐fitting an older (S)TEM with two Cs aberration correctors for 80 kV and 60 kV operation

For the characterization of light materials using transmission electron microscopy, a low electron acceleration voltage of 80 kV or even 60 kV is attractive due to reduced beam damage to the specimen. The concomitant reduction in resolving power of the microscope can be restored when using spherical aberration (C_s) correctors, which for the most part are only available in the latest and most expensive microscopes. Here, we show that upgrading of existing TEMs is an attractive and cost‐effective alternative. We report on the low‐voltage performance on graphitic material of a JEOL JEM‐2010F built in the early 1990s and retro‐fitted with a conventional imaging C_s corrector and a probe C_s corrector. The performance data show C_s retro‐fitted instruments can compete very favourably against more modern state‐of‐the‐art instruments in both conventional imaging (TEM) and scanning (STEM) modes.     

Techniques of convergent beam electron diffraction

The techniques required to record standard convergent beam electron diffraction patterns in an analytical electron microscope are discussed in detail, with emphasis on the design of electron optics in commercial instruments. Practical comments are included on specimen preparation, the influence of crystal defects, tilting to major zone axes, and alignment of the instrument. The influence of parameters under experimental control such as probe size, accelerating voltage, temperature, specimen tickness, and convergence angle is discussed in detail. Some comments are included on the alignment and limitations of large angle patterns formed by a defocused probe.     

Effects of focused ion beam milling on electron backscatter diffraction patterns in strontium titanate and stabilized zirconia

This study investigates the effect of focused ion beam (FIB) current and accelerating voltage on electron backscatter diffraction pattern quality of yttria-stabilized zirconia (YSZ) and Nb-doped strontium titanate (STN) to optimize data quality and acquisition time for 3D-EBSD experiments by FIB serial sectioning. Band contrast and band slope were used to describe the pattern quality. The FIB probe currents investigated ranged from 100 to 5000 pA and the accelerating voltage was either 30 or 5 kV. The results show that 30 kV FIB milling induced a significant reduction of the pattern quality of STN samples compared to a mechanically polished surface but yielded a high pattern quality on YSZ. The difference between STN and YSZ pattern quality is thought to be caused by difference in the degree of ion damage as their backscatter coefficients and ion penetration depths are virtually identical. Reducing the FIB probe current from 5000 to 100 pA improved the pattern quality by 20% for STN but only showed a marginal improvement for YSZ. On STN, a conductive coating can help to improve the pattern quality and 5 kV polishing can lead to a 100% improvement of the pattern quality relatively to 30 kV FIB milling. For 3D-EBSD experiments of a material such as STN, it is recommended to combine a high kV FIB milling and low kV polishing for each slice in order to optimize the data quality and acquisition time.     

An experimental method for calibration of the plasmon mean free path

Transmission electron microscopy specimens in the form of elongated, conical needles were made using a dual‐beam focused ion beam system, allowing the specimen thickness to be geometrically determined for a range of thickness values. From the same samples electron energy loss maps were acquired and the plasmon mean free path (λ) for inelastic scattering was determined experimentally from the measured values of specimen thickness. To test the method λ was determined for Ni (174 ± 17 nm), α‐Al₂O₃ (143 ± 14 nm), Si (199 ± 20 nm) and amorphous SiO₂ (238 ± 12 nm), and compared both to experimental values of λ taken from the literature and to calculated values. The calculated values of λ significantly underestimate the true sample thickness for high accelerating voltages (300 kV) and large collection angles. A linear dependence of λ on thickness was confirmed for t/λ < 0.5–0.6, but this method also provides an approach for calibrating λ at sample thicknesses for which multiple scattering occurs, thus expanding the thickness range over which electron energy loss spectroscopy can be used to determine the absolute sample thickness (t/λ > 0.6). The experimental method proposed in this contribution offers a means to calibrate λ for any type of material or phase that can be milled using a focused ion beam system.     

Standards for quantification of elements in the otolithic membrane by electron probe X-ray microanalysis: Calibration curves and electron beam sensitivity

An absolute quantitative standardization technique has been developed to measure Ca and K weight fractions (WF) in the otolithic membrane of the saccule and utricle by scanning electron microscopy and electron probe X-ray analysis using the peak-to-background (P/B) ratio method. Microcrystalline salt standards were used to calibrate Ca and K Kα P/B or Y = (P/B) · Z²/A (Z = atomic number; A = atomic weight) against WF at 10, 15, 20 and 25 kV accelerating voltage. The effect of voltage on the calibration, plotting the coefficient of correlation (r) as a function of voltage, was not dependent on the voltage in the range 10–25 kV for Ca standards. K standards were also independent when P/B was corrected for Z²/A. Background counts in the otoconia (B_o) were obtained at 5, 25, 50, 100, 200 and 500 s and used to test the electron beam sensitivity of saccular and utricular otoconia. B_o was not dependent on the spectra acquisition time, with the exception of B_o under Kα K peak in the saccule at 10 kV. Ca and K WF were determined at 10, 15, 20 and 25 kV in the saccule and utricle, showing similar values regardless of the voltage used. This method of calibration offers several advantages, such as stability, homogeneity, known composition of the standards, high reproducibility at different voltages even without Z²/A correction and the similarity between the otoconia and crystal standards. We recommend the application of this method for other elements and biomineral systems.     

A linear accelerator for simulating micrometeorites

The theory, the estimated parameters, and the design features of the linear accelerator capable of accelerating charged dust particles 0.1–10 μm in diameter to velocities of 12 km/s are presented. The electrodynamical circuit of the accelerator is composed of 27 acceleration gaps, each of which is held at a potential of 20 kV. Particles are injected into the linear electrodynamical accelerator after preliminary acceleration in the linear electrostatic accelerator with an effective voltage of 145 kV. The total effective accelerating voltage is 670 kV. The total length of the accelerating sections is 3.62 m. The essential difference of this accelerator from the existing machines is that the drift tubes of the dynamical circuit are identical and that synchronism of particle motion with the voltage applied to the drift tubes is achieved by forming the accelerating voltage as a function of the particle velocity and specific charge. The measured performance data of the accelerator are presented.     

The cutting of ultrathin sections with the thickness less than 20 nm from biological specimens embedded in resin blocks

Low voltage electron microscopes working in transmission mode, like LVEM5 (Delong Instruments, Czech Republic) working at accelerating voltage 5 kV or scanning electron microscope working in transmission mode with accelerating voltage below 1 kV, require ultrathin sections with the thickness below 20 nm. Decreasing of the primary electron energy leads to enhancement of image contrast, which is especially useful in the case of biological samples composed of elements with low atomic numbers. As a result treatments with heavy metals, like post‐fixation with osmium tetroxide or ultrathin section staining, can by omitted. The disadvantage is reduced penetration ability of incident electrons influencing the usable thickness of the specimen resulting in the need of ultrathin sections of under 20 nm thickness. In this study we want to answer basic questions concerning the cutting of extremely ultrathin sections: Is it possible routinely and reproducibly to cut extremely thin sections of biological specimens embedded in commonly used resins with contemporary ultramicrotome techniques and under what conditions? Microsc. Res. Tech. 79:512–517, 2016. © 2016 Wiley Periodicals, Inc.     

Convergent-beam and small-area-parallel-beam electron diffraction of icosahedral quasicrystals of a melt-quenched Al-Mn alloy

Intensity distribution in convergent-beam electron diffraction (CBED) patterns obtained from icosahedral quasicrystas of a melt-quenched Al-Mn alloy reveal that the quasicrystals do not have fivefold, threefold and twofold rotation axes and have no inversion center, although ordinary diffraction patterns obtained thus far showed these rotation symmetries. CBED patterns taken from specimen areas of about 3 nm in diameter show a deviation in geometry in spot positions from the fivefold rotation symmetry. Ring patterns due to higher-order Laue zone reflections are not observed in CBED patterns. Kikuchi bands are composed of two sub-bands in the five equivalent directions, and each band has a different intensity profile. Parallel-beam (3 × 10^-5 rad) electron diffraction patterns obtained from specimen areas less than 100 nm in diameter also show a deviation from the fivefold symmetry in spot positions and make clear that each Bragg reflection consists of many fine spots which show no fivefold symmetry. It is proven experimentally that all the observed reflections occur already in the approximation of kinematical diffraction, although their intensities may be modified by dynamical diffraction effect.     

Microstructural characterization of laser surface melted AISI M2 tool steel

We describe the microstructure of Nd:YAG continuous wave laser surface melted high‐speed steel, namely AISI M2, treated with different laser scanning speeds and beam diameters on its surface. Microstructural characterization of the remelted surface layer was performed using light optical and scanning electron microscopy and X‐ray diffraction. The combination of the three techniques provided new insights into the substantial changes induced by laser surface melting of the steel surface layer. The advantage of the method is that it avoids the difficult and tedious work of preparing samples of this hard material for transmission electron microscopy, which is the technique normally used to study these fine microstructures. A melted zone with a dendritic structure and a partially melted zone with a heterogeneous cellular structure were observed. M₂C carbides with different morphologies were identified in the resolidified surface layer after laser melting.