On-axis versus off-axis Transmission Kikuchi Diffraction technique: application to the characterisation of severe plastic deformation-induced ultrafine-grained microstructures

Diffraction-Based Multiscale Residual Strain Measurements

Modern analytical tools, from microfocus X-ray diffraction (XRD) to electron microscopy-based microtexture measurements, offer exciting possibilities of diffraction-based multiscale residual strain measurements. The different techniques differ in scale and resolution, but may also yield significantly different strain values. This study, for example, clearly established that high-resolution electron backscattered diffraction (HR-EBSD) and high-resolution transmission Kikuchi diffraction (HR-TKD) [sensitive to changes in interplanar angle (Δθθ)], provide quantitatively higher residual strains than micro-Laue XRD and transmission electron microscope (TEM) based precession electron diffraction (PED) [sensitive to changes in interplanar spacing (Δdd)]. Even after correcting key known factors affecting the accuracy of HR-EBSD strain measurements, a scaling factor of ∼1.57 (between HR-EBSD and micro-Laue) emerged. We have then conducted "virtual" experiments by systematically deforming an ideal lattice by either changing an interplanar angle (α) or a lattice parameter (a). The patterns were kinematically and dynamically simulated, and corresponding strains were measured by HR-EBSD. These strains showed consistently higher values for lattice(s) distorted by α, than those altered by a. The differences in strain measurements were further emphasized by mapping identical location with HR-TKD and TEM-PED. These measurements exhibited different spatial resolution, but when scaled (with ∼1.57) provided similar lattice distortions numerically.

Transmission Kikuchi diffraction: The impact of the signal-to-noise ratio

Signal optimization for transmission Kikuchi diffraction (TKD) measurements in the scanning electron microscope is investigated by a comparison of different sample holder designs. An optimized design is presented, which uses a metal shield to efficiently trap the electron beam after transmission through the sample. For comparison, a second holder configuration allows a significant number of the transmitted electrons to scatter back from the surface of the sample holder onto the diffraction camera screen. It is shown that the secondary interaction with the sample holder leads to a significant increase in the background level, as well as to additional noise in the final Kikuchi diffraction signal. The clean TKD signal of the optimized holder design with reduced background scattering makes it possible to use small signal changes in the range of 2% of the camera full dynamic range. As is shown by an analysis of the power spectrum, the signal-to-noise ratio in the processed Kikuchi diffraction patterns is improved by an order of magnitude. As a result, the optimized design allows an increase in pattern signal to noise ratio which may lead to increase in measurement speed and indexing reliability.

Kikuchi pattern simulations of backscattered and transmitted electrons

We discuss a refined simulation approach which treats Kikuchi diffraction patterns in electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction (TKD). The model considers the result of two combined mechanisms: (a) the dynamical diffraction of electrons emitted coherently from point sources in a crystal and (b) diffraction effects on incoherent diffuse intensity distributions. Using suitable parameter settings, the refined simulation model allows to reproduce various thickness- and energy-dependent features which are observed in experimental Kikuchi diffraction patterns. Excess-deficiency features are treated by the effect of gradients in the incoherent background intensity. Based on the analytical two-beam approximation to dynamical electron diffraction, a phenomenological model of excess-deficiency features is derived, which can be used for pattern matching applications. The model allows to approximate the effect of the incident beam geometry as a correction signal for template patterns which can be reprojected from pre-calculated reference data. As an application, we find that the accuracy of fitted projection centre coordinates in EBSD and TKD can be affected by changes in the order of 10 - 3 - 10 - 2 if excess-deficiency features are not considered in the theoretical model underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer from biases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.

Crystallographic Orientation Analysis of Nanocrystalline Tungsten Thin Film Using TEM Precession Electron Diffraction and SEM Transmission Kikuchi Diffraction

Two advanced, automated crystal orientation mapping techniques suited for nanocrystalline materials—precession electron diffraction (PED) in transmission electron microscopy (TEM) and on-axis transmission Kikuchi diffraction (TKD) in scanning electron microscopy (SEM)—are evaluated by comparing the orientation maps obtained from the identical location on a 30 nm-thick nanocrystalline tungsten (W) thin film. A side-by-side comparison of the orientation maps directly showed that the large-scale orientation features are almost identical. However, there are differences in the fine details, which arise from the fundamentally different nature of the spot pattern and Kikuchi line pattern in terms of the excitation volume and the angular resolution. While TEM-PED is more reliable to characterize grains oriented along low-index zone axes, the high angular resolution of SEM-TKD allows the detection of small misorientation between grains and thus yields better quantification and statistical analysis of grain orientation. Given that both TEM-PED and SEM-TKD orientation mapping techniques are complementary tools for nanocrystalline materials, one can be favorably selected depending on the requirements of the analysis, as they have competitive performance in terms of angular resolution and texture quantification.

Spatial Resolutions of On-Axis and Off-Axis Transmission Kikuchi Diffraction Methods

Spatial resolution is one of the key factors in orientation microscopy, as it determines the accuracy of grain size investigation and phase identification. We determined the spatial resolutions of on-axis and off-axis transmission Kikuchi diffraction (TKD) methods by calculating correlation coefficients using only the effective parts of on-axis and off-axis transmission Kikuchi patterns. During the calculation, we used average filtering to evaluate the spatial resolution more accurately. The spatial resolutions of both on-axis and off-axis TKD methods were determined in the same scanning electron microscope at different accelerating voltages and specimen thicknesses. The spatial resolution of the on-axis TKD was higher than that of the off-axis TKD at the same parameters. Furthermore, with an increase in accelerating voltage or a decrease in specimen thickness, the spatial resolutions of the two configurations could be significantly improved, from tens of nanometers to below 10 nm. At a voltage of 30 kV and sample thickness of 74 nm, both on-axis and off-axis TKD methods exhibited the highest resolutions of 6.2 and 9.7 nm, respectively.

On the depth resolution of transmission Kikuchi diffraction (TKD) analysis

In this paper, we have analyzed the depth resolution that can be achieved by on-axis transmission Kikuchi diffraction (TKD) using a Zr-Nb alloy. The results indicate that the signals contributing to detectable Kikuchi bands originate from a depth of approximately the mean free path of thermal diffuse scattering (λ_TDS) from the bottom surface of a thin foil sample. This existing surface sensitivity can thus lead to the observation of different grain structures when opposite sides of a nano-crystalline foil are facing the incident electron beam. These results also provide a guideline for the ideal sample thickness for TKD analysis of ≤ 6λ_TDS, or 21 times the elastic scattering mean free path (λ_MFP) for samples of high crystal symmetry. For samples of lower symmetry, a smaller thickness ≤ 3λ_TDS, or ≤ 10λ_MFP is suggested.

Depth Resolution Dependence on Sample Thickness and Incident Energy in On-Axis Transmission Kikuchi Diffraction in Scanning Electron Microscope (SEM)

Transmission Kikuchi diffraction is an emerging technique aimed at producing orientation maps of the structure of materials with a nanometric lateral resolution. This study investigates experimentally the depth resolution of the on-axis configuration, via a twinned silicon bi-crystal sample specifically designed and fabricated. The measured depth resolution varies from 30 to 65 nm in the range 10-30 keV, with a close to linear dependence with incident energy and no dependence with the total sample thickness. The depth resolution is explained in terms of two mechanisms acting concomitantly: generation of Kikuchi diffraction all along the thickness of the sample, associated with continuous absorption on the way out. A model based on the electron mean free path is used to account for the dependence with incident energy of the depth resolution. In addition, based on the results in silicon, the use of the mean absorption coefficient is proposed to predict the depth resolution for any atomic number and incident energy.