Defect detection in atomic-resolution images via unsupervised learning with translational invariance

Crystallographic defects can now be routinely imaged at atomic resolution with aberration-corrected scanning transmission electron microscopy (STEM) at high speed, with the potential for vast volumes of data to be acquired in relatively short times or through autonomous experiments that can continue over very long periods. Automatic detection and classification of defects in the STEM images are needed in order to handle the data in an efficient way. However, like many other tasks related to object detection and identification in artificial intelligence, it is challenging to detect and identify defects from STEM images. Furthermore, it is difficult to deal with crystal structures that have many atoms and low symmetries. Previous methods used for defect detection and classification were based on supervised learning, which requires human-labeled data. In this work, we develop an approach for defect detection with unsupervised machine learning based on a one-class support vector machine (OCSVM). We introduce two schemes of image segmentation and data preprocessing, both of which involve taking the Patterson function of each segment as inputs. We demonstrate that this method can be applied to various defects, such as point and line defects in 2D materials and twin boundaries in 3D nanocrystals.

Detection of translational noncrystallographic symmetry in Patterson functions

Detection of translational noncrystallographic symmetry (TNCS) can be critical for success in crystallographic phasing, particularly when molecular-replacement models are poor or anomalous phasing information is weak. If the correct TNCS is detected then expected intensity factors for each reflection can be refined, so that the maximum-likelihood functions underlying molecular replacement and single-wavelength anomalous dispersion use appropriate structure-factor normalization and variance terms. Here, an analysis of a curated database of protein structures from the Protein Data Bank to investigate how TNCS manifests in the Patterson function is described. These studies informed an algorithm for the detection of TNCS, which includes a method for detecting the number of vectors involved in any commensurate modulation (the TNCS order). The algorithm generates a ranked list of possible TNCS associations in the asymmetric unit for exploration during structure solution.

Direct recovery of interfacial topography from coherent X-ray reflectivity: model calculations for a 1D interface

The use of coherent X-ray reflectivity to recover interfacial topography is described using model calculations for a 1D interface. The results reveal that the illuminated topography can be recovered directly from the measured reflected intensities. This is achieved through an analysis of the Patterson function, the Fourier transform of the scattering intensity (as a function of lateral momentum transfer, Q //, at fixed vertical momentum transfer, Q z ). Specifically, a second-order Patterson function is defined that reveals the discrete set of separations and contrast factors (i.e. the product of changes in the effective scattering factor) associated with discontinuities in the effective interfacial topography. It is shown that the topography is significantly overdetermined by the measurements, and an algorithm is described that recovers the actual topography through a deterministic sorting of this information.

Quantitative phase analysis of amorphous components in mixtures by using the direct-derivation method

The direct-derivation (DD) method is a new technique for quantitative phase analysis (QPA) [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. A simple equation, called the intensity–composition (IC) formula, is used to derive weight fractions of individual components (w k ; k = 1–K) in a mixture. Two kinds of parameters are required as input data of the formula. One is the parameter S k , which is the sum of observed powder diffraction intensities for each component, measured in a wide 2θ range and corrected for the Lorentz–polarization factor. The other is the parameter a k −1, defined by a k −1 = M k −1∑nik 2, where M k is the chemical formula weight and n ik is the number of electrons belonging to the ith atom in the chemical formula unit. The parameter a k −1 was originally derived by using the relationship between the peak height and the integrated value of the peak at the origin of the Patterson function, implicitly assuming the presence of periodic structures like crystals. In this study, the formula has been derived theoretically from a general assemblage of atoms resembling amorphous material, and the same expression as the original formula has been obtained. The physical meaning of a k −1, which represents `the total scattering power per chemical formula weight', has been reconfirmed in the present formulation. The IC formula has been tested experimentally by using two-, three- and four-component mixtures containing SiO2 or GeO2 glass powder. In the whole-powder-pattern fitting (WPPF) procedure, incorporated into the DD method, a background-subtracted halo pattern is directly fitted as one of the components in the mixture, together with profile models for crystalline components. In the WPPF, an interaction was observed between the parameters of the background function (BGF) and the parameter for scaling the halo pattern, and this resulted in systematic deviations of w k from weighed values. The deviations were ≤0.7% in the case of binary mixtures when the BGF was fixed at the correct background height, supporting the hypothesis that the DD method is applicable to the QPA of amorphous components.

Characterization of individual stacking faults in a wurtzite GaAs nanowire by nanobeam X-ray diffraction

Coherent X-ray diffraction was used to measure the type, quantity and the relative distances between stacking faults along the growth direction of two individual wurtzite GaAs nanowires grown by metalorganic vapour epitaxy. The presented approach is based on the general property of the Patterson function, which is the autocorrelation of the electron density as well as the Fourier transformation of the diffracted intensity distribution of an object. Partial Patterson functions were extracted from the diffracted intensity measured along the [000\bar{1}] direction in the vicinity of the wurtzite 00\bar{1}\bar{5} Bragg peak. The maxima of the Patterson function encode both the distances between the fault planes and the type of the fault planes with the sensitivity of a single atomic bilayer. The positions of the fault planes are deduced from the positions and shapes of the maxima of the Patterson function and they are in excellent agreement with the positions found with transmission electron microscopy of the same nanowire.

Quadruple space-group ambiguity owing to rotational and translational noncrystallographic symmetry in human liver fructose-1,6-bisphosphatase

Fructose-1,6-bisphosphatase (FBPase) is a key regulator of gluconeogenesis and a potential drug target for type 2 diabetes. FBPase is a homotetramer of 222 symmetry with a major and a minor dimer interface. The dimers connectedviathe minor interface can rotate with respect to each other, leading to the inactive T-state and active R-state conformations of FBPase. Here, the first crystal structure of human liver FBPase in the R-state conformation is presented, determined at a resolution of 2.2 Å in a tetragonal setting that exhibits an unusual arrangement of noncrystallographic symmetry (NCS) elements. Self-Patterson function analysis and various intensity statistics revealed the presence of pseudo-translation and the absence of twinning. The space group isP41212, but structure determination was also possible in space groupsP43212,P4122 andP4322. All solutions have the same arrangement of threeC2-symmetric dimers spaced by 1/3 along an NCS axis parallel to thecaxis located at (1/4, 1/4,z), which is therefore invisible in a self-rotation function analysis. The solutions in the four space groups are related to one another and emulate a body-centred lattice. If all NCS elements were crystallographic, the space group would beI4122 with acaxis three times shorter and a single FBPase subunit in the asymmetric unit.I4122 is a minimal, non-isomorphic supergroup of the four primitive tetragonal space groups, explaining the space-group ambiguity for this crystal.

Application of synchrotron through-the-substrate microdiffraction to crystals in polished thin sections

The synchrotron through-the-substrate X-ray microdiffraction technique (tts-μXRD) is extended to the structural study of microvolumes of crystals embedded in polished thin sections of compact materials [Rius, Labrador, Crespi, Frontera, Vallcorba & Melgarejo (2011).J.Synchrotron Rad.18, 891–898]. The resulting tts-μXRD procedure includes some basic steps: (i) collection of a limited number of consecutive two-dimensional patterns (frames) for each randomly oriented crystal microvolume; (ii) refinement of the metric from the one-dimensional diffraction pattern which results from circularly averaging the sum of collected frames; (iii) determination of the reciprocal lattice orientation of each randomly oriented crystal microvolume which allows assigning thehklindices to the spots and, consequently, merging the intensities of the different frames into a single-crystal data set (frame merging); and (iv) merging of the individual crystal data sets (multicrystal merging) to produce an extended data set suitable for structure refinement/solution. Its viability for crystal structure solution by Patterson function direct methods (δ recycling) and for accurate single-crystal least-squares refinements is demonstrated with some representative examples from petrology in which different glass substrate thicknesses have been employed. The section of the crystal microvolume must be at least of the same order of magnitude as the focus of the beam (15 × 15 µm in the provided examples). Thanks to its versatility and experimental simplicity, this methodology should be useful for disciplines as disparate as petrology, materials science and cultural heritage.