Unsupervised machine learning applied to scanning precession electron diffraction data

A systematic method to identify the space group from PED and CBED patterns part I - theory

A scanning precession electron diffraction system has been integrated with a direct electron detector to allow the collection of improved quality diffraction patterns. This has been used on a two-phase α–β titanium alloy (Timetal® 575) for phase and orientation mapping using an existing pattern-matching algorithm and has been compared to the commonly used detector system, which consisted of a high-speed video-camera imaging the small phosphor focusing screen. Noise is appreciably lower with the direct electron detector, and this is especially noticeable further from the diffraction pattern center where the real electron scattering is reduced and both diffraction spots and inelastic scattering between spots are weaker. The results for orientation mapping are a significant improvement in phase and orientation indexing reliability, especially of fine nanoscale laths of α-Ti, where the weak diffracted signal is rather lost in the noise for the optically coupled camera. This was done at a dose of ~19 e−/Å2, and there is clearly a prospect for reducing the current further while still producing indexable patterns. This opens the way for precession diffraction phase and orientation mapping of radiation-sensitive crystalline materials.

Electron diffraction, and its use to study the nanoscale crystallography of materials, has had something of a renaissance in recent years. The ease with which electron diffraction patterns can now be acquired with modern instrumentation, coupled with developments in electron optical techniques, faster detectors and sensitive cameras have all contributed to microscopists looking again at what novel information electron diffraction can provide. In this presentation, we will focus on scanning electron diffraction (SED), whereby electron diffraction patterns are acquired at each real space pixel, so that following a raster scan across a region of interest, a rich 4D data set is obtained that contains a wealth of information about the phases present, their orientation, defective regions and strain. Automation of pattern acquisition and sensitive recording devices also enable very fast data collection and open new avenues for recording unique crystallographic data from highly beam‐sensitive materials [1]. SED can also be applied whilst precessing the beam [2] and this combination, known, in general, as scanning precession electron diffraction (SPED), which may lead to more accurate measurements of local crystallography through access to higher order reflections and greater sensitivity to in‐plane rotations, strain, etc. Figure 1 shows an example of SED analysis, with and without precession, considering the effects of strain brought about by the addition of Sb in a GaAs nanowire, whose wire axis is parallel to the axis in the zinc blende structure ([0001] in wurtzite). Fig 1 (a) shows a series of ‘virtual dark field’ (VDF) images created by plotting the intensities of particular reflections, from an unprecessed pattern series, as a function of real space position. The contrast seen in the VDF resembles the contrast seen in conventional DF images showing changes in intensity brought about through planar bending in the doped region. In Fig 1(b) the strain components are plotted, derived from measuring the distortions of precessed diffraction patterns relative to a reference (undistorted) region well away from the Sb region. The magnitude and direction of the strain is as expected from finite element modelling. In reality, any 2D crystallographic map such as those shown in Figure 1, is really a projection of a 3D structure. As such, in order to be sensitive to changes in strain and orientation in 3 orthogonal directions, it becomes necessary to tilt the sample and ultimately to record a full tilt series of crystallographic information so that, using tomographic methods, a complete 3D reconstruction of the local crystallography is made possible [3]. Recently, we have combined SPED and tomography to reconstruct both real space morphology and orientation maps in three dimensions, to interrogate the local crystallography of sub‐volumes of material and to determine, for example in the case of a Ni‐base superalloy, a novel 3D orientation relationship between a matrix phase and an embedded carbide particle, see Figure 2. To extend this to map strain, as illustrated in Fig 1 (b), into 3D is considerably more challenging as such ‘tensor tomography’ demands a new approach to recover, in general, six strain components at every voxel. We will discuss progress in this regard and show how a model‐fitting approach may be the best route forward [4].

Two-dimensional X-ray diffraction refers to X-ray diffraction applications with two-dimensional detector and corresponding data reduction and analysis. The two-dimensional diffraction pattern contains far more information than a one-dimensional profile collected with the conventional diffractometer. In order to take advantage of two-dimensional diffraction, new theories and approaches are necessary to configure the two-dimensional X-ray diffraction system and to analyze the two-dimensional diffraction data. This paper is an introduction to some fundamentals about two-dimensional X-ray diffraction, such as geometry convention, diffraction data interpretation, and advantages of two-dimensional X-ray diffraction in various applications, including phase identification, stress, and texture measurement.

Precession electron diffraction using a digital sampling method

Structural health monitoring has been increasingly used due to the advances in sensing technology and data analysis, facilitating the shift from time-based to condition-based maintenance. This work is part of the efforts which have applied structural health monitoring to the Sydney Harbour Bridge – one of Australia’s iconic structures. It combines dimensionality reduction and pattern recognition techniques to accurately and efficiently distinguish faulty components from well-functioning ones. Specifically, random projection is used for dimensionality reduction on the vibration feature data. Then, healthy and damaged patterns of bridge components are learned in the lower dimensional projected space using supervised and unsupervised machine learning methods, namely, support vector machine and one-class support vector machine. The experimental results using data from a laboratory-based building structure and the Sydney Harbour Bridge showed high feasibility of applying machine learning techniques to dimensionality reduction and damage detection in structural health monitoring. Random projection combined with support vector machine significantly reduces the computational time while maintaining the detection accuracy. The proposed method also outperformed popular dimensionality reduction techniques. The computational time of the method using random projection can be more than 200 times faster than that without using dimensionality reduction while still achieving similar detection accuracy.

Among lithium battery cathode materials, Li1.2Ni0.13Mn0.54Co0.13O2 (LR-NMC) has a high theoretical capacity, but suffers from voltage and capacity fade during cycling. This is partially ascribed to transition metal cation migration, which involves the local transformation of the honeycomb layered structure to spinel-like nano-domains. Determination of the honeycomb layered/spinel phase ratio from powder X-ray diffraction data is hindered by the nanoscale of the functional material and the domains, diverse types of twinning, stacking faults, and the possible presence of the rock salt phase. Determining the phase ratio from transmission electron microscopy imaging can only be done for thin regions near the surfaces of the crystals, and the intense beam that is needed for imaging induces the same transformation to spinel as cycling does. In this article, it is demonstrated that the low electron dose sufficient for electron diffraction allows the collection of data without inducing a phase transformation. Using calculated electron diffraction patterns, we demonstrate that it is possible to determine the volume ratio of the different phases in the particles using a pair-wise comparison of the intensities of the reflections. Using this method, the volume ratio of spinel structure to honeycomb layered structure is determined for a submicron sized crystal from experimental three-dimensional electron diffraction (3D ED) and precession electron diffraction (PED) data. Both twinning and the possible presence of the rock salt phase are taken into account. After 150 charge–discharge cycles, 4% of the volume in LR-NMC particles was transformed irreversibly from the honeycomb layered structure to the spinel structure. The proposed method would be applicable to other multi-phase materials as well.

An efficient approach to characterize pseudo-merohedral twins by precession electron diffraction: Application to the LaGaO 3 perovskite

Scanning precession electron diffraction is an emerging promising technique for mapping phases and crystal orientations with short acquisition times (10–20 ms/pixel) in a transmission electron microscope similarly to the Electron Backscattered Diffraction (EBSD) or Transmission Kikuchi Diffraction (TKD) techniques in a scanning electron microscope. In this study, we apply this technique to the characterization of deformation microstructures in an aggregate of bridgmanite and ferropericlase deformed at 27 GPa and 2,130 K. Such a sample is challenging for microstructural characterization for two reasons: (i) the bridgmanite is very unstable under electron irradiation, (ii) under high stress conditions, the dislocation density is so large that standard characterization by diffraction contrast are limited, or impossible. Here we show that detailed analysis of intracrystalline misorientations sheds some light on the deformation mechanisms of both phases. In bridgmanite, deformation is accommodated by localized, amorphous, shear deformation lamellae whereas ferropericlase undergoes large strains leading to grain elongation in response to intense dislocation activity with no evidence for recrystallization. Plastic strain in ferropericlase can be semiquantitatively assessed by following kernel average misorientation distributions.

In this work, the precipitation and the morphology of secondary phases after severe plastic deformation (SPD) processing followed by an isothermal treatment was investigated. High-pressure torsion (HPT) was the SPD process carried out on superduplex 2507 (UNS S32750) stainless steel material under P = 6 GPa at room temperature. At this high strain levels (ε up to 170) samples have shown grain size decrease and strained microstructure with high dislocation density and nanostructure features. After a short isothermal treatment at 830 °C, the sigma phase and chromium nitrides were revealed as the main secondary phases identified by scanning and transmission electron microscopy and element analysis by energy dispersive spectroscopy. Scanning precession electron diffraction and automated crystal orientation mapping have been carried out in order to confirm the precipitation of the secondary phases. In fact, the results provide evidence that the precipitation of chromium nitrides seems to be the preferred nucleation site for sigma phase at higher deformation strain, in addition to the intergranular precipitation of sigma. Both the sigma phases nucleated integranularly and besides chromium nitrides are randomly orientated.

The key microstructural feature providing strength to age-hardenable Al alloys is nanoscale precipitates. Alloy development requires a reliable statistical assessment of these precipitates, in order to link the microstructure with material properties. Here, it is demonstrated that scanning precession electron diffraction combined with computational analysis enable the semi-automated extraction of precipitate statistics in an Al-Mg-Si-Cu alloy. Among the main findings is the precipitate number density, which agrees well with a conventional method based on manual counting and measurements. By virtue of its data analysis objectivity, our methodology is therefore seen as an advantageous alternative to existing routines, offering reproducibility and efficiency in alloy statistics. Additional results include improved qualitative information on phase distributions. The developed procedure is generic and applicable to any material containing nanoscale precipitates.

Aluminium alloy design supported by scanning precession electron diffraction

Information derived from precession electron diffraction (PED) patterns can be used to advantage in combination with high-resolution X-ray powder diffraction data to solve crystal structures that resist solution from X-ray data alone. PED data have been exploited in two different ways for this purpose: (1) to identify weak reflections and (2) to estimate the phases of the reflections in the projection. The former is used to improve the partitioning of the reflection intensities within an overlap group and the latter to provide some starting phases for structure determination. The information was incorporated into a powder charge-flipping algorithm for structure solution. The approaches were first developed using data for the moderately complex zeolite ZSM-5, and then tested on TNU-9, one of the two most complex zeolites known. In both cases, including PED data from just a few projections facilitated structure solution significantly.

Two-dimensional x-ray diffraction (XRD 2 ) refers to x-ray diffraction applications with two-dimensional (2D) detector and corresponding data reduction and analysis. The two-dimensional diffraction pattern contains far more information than a one-dimensional profile collected with the conventional diffractometer. In order to take the advantages of the 2D detector, new approaches are necessary to configure the two-dimensional x-ray diffraction system and to analyze the 2D diffraction data. The present paper is an introduction to some fundamentals about stress and texture analysis with two-dimensional x-ray diffraction using the Bruker GADDS system as an example.

Polycrystalline materials properties and behaviour are ultimately determined by their crystallinity, phase composition and microstructure (i.e., crystal size, preferential orientation). Two-dimensional (2D) diffraction patterns collected with an area detector (i.e., CDD), available in modern X-ray diffractometers, contain detailed information about all these important material characteristics. Furthermore, recent advances in detector technologies permits the collection of high resolution diffraction patterns in which the microstructure of the material can be directly imaged. If the size of beam relative to the crystal size in the sample is adequately choosen, the diffraction pattern produced will have spotty rings in which the spots are the diffracted images of individual grains. The resolution of the image is mainly dependent on the characteristics of the X-ray beam (i.e., diameter, angular divergence), which can be modulated by X-ray optics, sample to detector distance, the pixel size of the detector and the sharpness of the point spread function. From these patterns, the crystal size distribution of different crystalline phases present in the sample can be independently determined using specialized software capable of extracting and combining the information contained in these patterns. This technique is applicable to materials with crystal sizes ranging from submicron to mm sizes and is complementary to techniques based on peak profile analyses (i.e., Scherrer method) which are applicable only to nanocrystalline materials. Finally, given the high sensitivity of current detectors, crystal size evolution can be followed in real-time to study important transformation processes such as crystallization, annealing, etc. The use of 2D X-ray diffraction as applied to microstructure characterization will be illustrated through several examples.