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[Koji Kimoto](https://orcid.org/0000-0002-3927-0492), [Ovidiu Cretu](https://orcid.org/0000-0002-1822-8172), [Koji Harano](https://orcid.org/0000-0001-6800-8023), [Fumihiko Uesugi](https://orcid.org/0000-0003-3346-4218), [Jun Kikkawa](https://orcid.org/0000-0003-0659-1844), [Kohei Aso](https://orcid.org/0000-0001-6935-7655), [Yoshifumi Oshima](https://orcid.org/0000-0003-1898-0142), [Takashi Matsumoto](https://orcid.org/0009-0007-7418-6724), [Yoshiki Sakuma](https://orcid.org/0000-0001-6804-7217)

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[Unveiling Twist Domains in Monolayer MoS<sub>2</sub> through 4D‐STEM and Unsupervised Machine Learning](https://mdr.nims.go.jp/datasets/0a00adee-2414-4314-86ee-f56c7f3a8847)

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Unveiling Twist Domains in Monolayer MoS2 through 4D‐STEM and Unsupervised Machine LearningRESEARCH ARTICLEwww.small-methods.comUnveiling Twist Domains in Monolayer MoS2 through4D-STEM and Unsupervised Machine LearningKoji Kimoto,* Ovidiu Cretu, Koji Harano, Fumihiko Uesugi, Jun Kikkawa, Kohei Aso,Yoshifumi Oshima, Takashi Matsumoto, and Yoshiki SakumaDichalcogenides, such as molybdenum disulfide (MoS2), are being studiedextensively due to their 2D feature and various material properties. Althoughcrystal structures are critical for applications, conventional atomic structureanalyses have a limited field of view. In this study, the crystal domainsof monolayer MoS2 synthesized by metal–organic chemical vapor deposition(MOCVD) are analyzed using 4D scanning transmission electron microscopy(STEM) and unsupervised machine learning. Twist domains (±11°) areidentified through the nonnegative matrix factorization (NMF) and hierarchicalclustering of numerous (>22k) diffraction patterns from a wide field of view.Preprocessing for detecting noncentrosymmetry effectively visualizes thepolarities of distinct MoS2 domains by highlighting the violation of Friedel’s lawin diffraction physics. Analyses reveal that the specimen deposited on Al2O3(0001) at 850 °C consists of domains measuring ≈100 nm in size and featuringmany mirror-twin boundaries. The findings provide valuable insights intooptimizing the MOCVD process and elucidating crystal growth mechanisms.1. IntroductionVarious applications of dichalcogenide compounds have beeninvestigated,[1–3] and excellent semiconductor properties areK. Kimoto, O. Cretu, K. Harano, F. Uesugi, J. Kikkawa, Y. SakumaCenter for Basic Research on MaterialsNational Institute for Materials Science (NIMS)Tsukuba 305-0047, JapanE-mail: kimoto.koji@nims.go.jpK.HaranoResearchCenter for AutonomousSystemsMaterialogyInstitute of IntegratedResearchInstitute of ScienceTokyoYokohama226-8501, JapanK. Aso, Y.OshimaSchool ofMaterials ScienceJapanAdvanced Institute of Science andTechnology (JAIST)Nomi 923-1292, JapanT.MatsumotoTokyoElectronTechnology Solutions Ltd.Nirasaki 407-8511, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/smtd.202501065© 2025 The Author(s). Small Methods published by Wiley-VCH GmbH.This is an open access article under the terms of the Creative CommonsAttribution License, which permits use, distribution and reproduction inany medium, provided the original work is properly cited.DOI: 10.1002/smtd.202501065expected, for example, in monolayerMoS2 transistors.[4] Dichalcogenideshave a layered structure, and theiratomic structures are directly relatedto device performance. In particular,electron mobility and optical proper-ties are sensitive to crystal defects anddomain structures. Therefore, compre-hensive dichalcogenide characterizationrequires crystal structural analysis atthe atomic and submicrometer scales.From the viewpoint of industrial ap-plications, current research effortsare focused on approaches to preparesingle-crystalline films on wafers usingvarious techniques, including metal–organic chemical vapor deposition(MOCVD), instead of the Scotch-tapemethod.[5,6] Uniformity and scalabilityare important considerations in the de-velopment of deposition technologies forsemiconductor devices, and evaluations of multiscale crystallinequalities such as defects, polarity, and grain boundaries over awide field of view are essential.Although high-resolution scanning transmission electron mi-croscopy (STEM) enables the direct observation of the atomic ar-rangement of MoS2, the observable field of view of this techniqueis limited to a few hundred nanometers.[7] Dark-field TEM canvisualize twist domains, although the spatial and angular resolu-tion is limited by the size of the objective aperture (i.e., diffractionlimit).4D STEM[8–11] is a technique used to acquire numerous elec-tron diffractions from nanometer areas under the focus of anincident electron beam; real and reciprocal space informationcan be constructed from the 4D data as maps and diffractions,respectively (Figure 1a). Recent developments in STEM instru-mentation have enabled the acquisition of a large number ofdiffractions at high speeds; thus, 4D-STEM has been applied toa wide range of materials.[10] While primitive 4D-STEM couldconstruct virtual dark-field TEM images, it could not distinguishsmall-angle rotation domains of the actual specimens, similar toconventional TEM techniques. Consequently, twist domains andtheir polarity have not yet been elucidated from a relatively widefield of view.In this study, multidomain MoS2 specimens deposited byMOCVD were analyzed using 4D-STEM. The numerous (e.g.,>22k) diffractions obtained were investigated using diffractionsimulations and unsupervised machine learning. UnsupervisedSmall Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (1 of 8)http://www.small-methods.commailto:kimoto.koji@nims.go.jphttps://doi.org/10.1002/smtd.202501065http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fsmtd.202501065&domain=pdf&date_stamp=2025-08-06www.advancedsciencenews.com www.small-methods.comFigure 1. Schematic of 4D-STEM and nonnegative matrix factorization. a) Experimental configuration of 4D-STEM. b) Schematic representation of thefactorization process for domain analysis. c) Preprocessing for noncentrosymmetry owing to the violation of Friedel’s law in the dynamical diffractions.d) Combination of preprocessing and NMF for polarity analysis.machine learning effectively extracts material information fromactual experimental data without prior knowledge. In previousstudies, we first applied dimensionality reduction by nonneg-ative matrix factorization (NMF)[12] and hierarchical clusteringfor 4D-STEM.[13] Unlike principal component analysis (PCA),which is another conventional dimensionality-reduction tech-nique, NMF yields interpretable electron diffractions withoutthe negative peaks produced by PCA. First, we used NMF tofactorize the experimental diffractions into a smaller number(e.g., seven) of interpretable diffractions and their correspondingmaps (Figure 1b). Based on dynamical diffraction simulationsand high-resolution STEM experiments, we confirmed the direc-tional correspondence between the polarity of monolayer MoS2and its diffraction (Figure 1c). Twist domains consisting ofmirrortwins were visualized for a wide field of view by NMF with pre-processing to enhance their noncentrosymmetry (Figure 1c,d).2. Results and Discussion2.1. Electron Diffraction SimulationUnlike X-ray diffraction, Friedel’s law[14] is often violated in elec-tron diffraction, even inmonolayerMoS2, and the noncentrosym-metry of the electron diffractions can be used to determine thepolarity of the crystals.[11] We confirmed these concepts usingboth kinematical and dynamical simulations. Figure 2a,b showthe crystal structure of monolayer MoS2, representing the lowerhalf of the known 2H-MoS2 structure, used in the simulations.CrystalMaker and SingleCrystal (CrystalMaker Software Ltd.)[15]were used to calculate the structure factor (i.e., kinematical sim-ulation), and a multislice software (xHREM, HREM Research,Inc.)[16,17] was also used for the dynamical simulation, as shownin Figure 2c. In the dynamical diffraction, an intense direct spotat the center and scattered Bragg spots appear as discs owingto the convergent incident probe. Because of the small conver-gence angle 𝛼 of 3 mrad and the diffraction limit, the size d ofthe incident probe (d = 1.22𝜆/𝛼, 1.7 nm) is larger than that of theunit cell of the specimen, where the wavelength 𝜆 of an electronequals to 4.2 pm. In general, complicated intensity modulations(i.e., zero-order Laue zone patterns) exist in each diffraction disc;however, in the present monolayer case, the intensity within thediscs becomes constant.[18] The dynamical diffraction intensitiesof spots 100 and 010 differ, as indicated by the blue open circlesreflecting relatively intense spots in Figure 2c. This is the viola-tion of Friedel’s law, showing noncentrosymmetry. Details of theFigure 2. Crystal structure of monolayer MoS2 and dynamical diffractionsimulation. a, b) Atomic arrangements along the (a) [001] and (b) [100]directions. c) Dynamical calculation of diffraction along the [001] direction.Small Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (2 of 8) 23669608, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202501065 by National Institute For, Wiley Online Library on [25/08/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.small-methods.comwww.advancedsciencenews.com www.small-methods.comFigure 3. Conventional 4D-STEM results of the MoS2 layer. a) ADF image. b) Integrated diffraction from the entire field of view and enlarged diffraction.The open circles indicate detection areas selected for virtual dark-field imaging. c) Examples of diffractions at four points. d, e) Virtual dark-field imagesof spots (d) 100 and (e) 110.kinematical and dynamical intensities are shown in the Table S1(Supporting Information).Note the directional correspondence between the polarity ofmonolayer MoS2 (Figure 2a) and the three intense innermostspots (−100, 1–10, 010) (Figure 2c). This relationship in exper-imental data is often rotated owing to various practical reasons,such as variations in the microscope post-specimen lens, scan-ning unit, and camera mechanical/software settings, and the re-sults described in the few reports on rotational correspondencehave been inconsistent. To confirm the actual rotational corre-spondence in our experiment, we observed an atomic-resolutionADF image and a diffraction pattern of the same area, and con-firmed the directional correspondence. In the present experi-mental configuration, the correspondence of the diffractions ac-quired using the energy filter (Figure 1c) was found to be ro-tated by 180° compared with the simulated results (Figure 2a,c).Hence, we analyzed the polarities at each position based on theconfirmed correspondence; the details and experimental resultsof this directional correspondence are described in the Support-ing Information (Figure S1, Supporting Information).2.2. Conventional 4D-STEM AnalysisFigure 3 shows the conventional 4D-STEM analyses of the MoS2specimen. The ADF image (Figure 3a) shows an amorphous car-bon film of Quantifoil (upper left corner) and the MoS2 film,which has several cracks. The ADF image shows nearly uniformintensity, suggesting a monolayer of MoS2, although crystallinedomains are not visualized. The diffraction pattern integratedfrom the entire field of view is shown in Figure 3b. Each diffrac-tion spot is split into three directions, although the polarity couldnot be identified due to the integration. Figure 3c shows exam-ples of diffractions observed at four points (p1, p2, p3, p4). Thediffraction at p1 reveals the amorphous rings of the carbon filmand crystalline spots. Because MoS2 is in monolayer form, itsdiffraction intensity is comparable with that of the carbon film.The diffractions at positions p2, p3, and p4 show single-crystallinespots, with each direction rotating slightly. The rotation angle is±11°, and the rotated innermost spots are overlapped, as shownin Figure 3b.Virtual dark-field imaging, a conventional 4D-STEM tech-nique, was conducted, and the images were constructed by select-ing part of the diffractions from the acquired 4D data. Figure 3d,eshow the virtual dark-field images of spots 100 and 110, whichare indicated by the open circles in the magnified diffraction inFigure 3b. In the dark-field image of spot 100 (Figure 3d), all do-mains are bright because of overlapping, rendering the clarifi-cation of each domain complicated. By contrast, the domains inspot 110 are separated and could be clearly identified (Figure 3e).The second-innermost spots, such as spot 110, cannot be usedfor polarity determination, as shown in Table S1 (SupportingSmall Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (3 of 8) 23669608, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202501065 by National Institute For, Wiley Online Library on [25/08/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.small-methods.comwww.advancedsciencenews.com www.small-methods.comFigure 4. NMF and hierarchical clustering of the 4D-STEM results. a) Seven pairs of factorized diffractions andmaps and the dendrogram of hierarchicalclustering. b) Integration of the diffractions and maps using the clustering. c) Experimental diffractions at p5 and p6, which are minority componentsneglected in the integrated diffraction and NMF.Information). In addition, the intensity of spot 110 changes sen-sitively owing to the specimen tilt (e.g., the dark areas near thecrack in Figure 3e). The effect of specimen tilt (i.e., bending) wasconfirmed by multislice simulations, as discussed in the FigureS2 (Supporting Information). Although the intensities of the sixinnermost spots did not change, those of the second-innermostspots changed significantly, even with a small tilt of <10°. Notethat the problems of intensity variation owing to the specimentilt and diffraction spot overlap are not unique to 4D-STEM; theyare also encountered in general TEM techniques, including dark-field TEM.2.3. Dimensionality Reduction by NMF and HierarchicalClusteringBased on the integrated diffraction shown in Figure 3b, we firstattempted to factorize the experimental many (>22k) diffractionsinto seven components consisting of one amorphous and threepairs of crystalline mirror domains in this field of view. The de-tails of NMF for 4D-STEM are provided in the Experimental Sec-tion. Figure 4a shows the seven pairs of diffractions and the cor-responding maps obtained using NMF. The first component w1appears to be amorphous. The remaining six crystalline com-ponents (w2 – w7) show centrosymmetric diffractions, indicat-ing intensity changes in the second-innermost spots owing tospecimen tilting. Thus, NMF alone cannot effectively discrimi-nate polarity from the actual experimental results. Figure 4a alsoshows a dendrogram obtained by hierarchical clustering basedon the similarity of the seven diffractions. The horizontal axisrepresents the similarity (pseudo-distance) between diffractions,which is calculated as the correlation coefficient. According tothe dendrogram, the seven components can be categorized intofour groups as follows: (i) amorphous w1; (ii) crystalline w2, w3,and w4; (ii) crystalline w5 and w6; and (iv) crystalline w7; how-ever, the major component is the crystalline domains (ii). Eachintegrated diffraction and map is shown in Figure 4b. Thus, hi-erarchical clustering is effective in regrouping the componentsand correcting the effect of specimen tilting on the experimentalresults.Small Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (4 of 8) 23669608, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202501065 by National Institute For, Wiley Online Library on [25/08/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.small-methods.comwww.advancedsciencenews.com www.small-methods.comHowever, these analyses fail to separate mirror domains withdifferent polarities because the intensity variation owing to spec-imen tilting is larger than the difference (≈12%) expected fromthe violation of Friedel’s law. This issue can be solved by appro-priate preprocessing, as described in Section 2.4.A few bright domains, as indicated by p5 and p6, can be ob-served in map (i), which is identical to the amorphous map h1.Figure 4c shows the diffractions of regions p5 and p6; in these re-gions, other domains with different orientations can be observedas minority components. These domains could not be detectedby integrated diffraction (Figure 3b) owing to their weak inten-sity. Although these domains could not be resolved by NMF witha seven-component assumption, their minor components can beobserved using both maps and diffractions, as demonstrated inthis study.2.4. Polarity Mapping Using Preprocessed Diffractions and4D-STEMWe apply appropriate preprocessing to mitigate the effects ofspecimen tilting and analyze the domains, including their po-larities. Some preprocessing techniques, such as cepstrum, havealready been reported to deduce diffraction symmetry[19] therebyavoiding the effect of specimen tilting. However, because the cep-strum includes amodulus procedure after the Fourier transform,the cepstrum always becomes centrosymmetric, prohibiting thedetection ofmaterial polarity. Hence, we applied different prepro-cessing strategies to detect deviations from the central symmetry.Figure 5a shows the integrated diffraction and a virtual dark-field image of spot 100. The diffractions at positions p7 and p8 areshown in Figure 5b, with the three innermost spots showing thestrongest intensity indicated by white open circles. The bright-ness of each image corresponds to the number of electrons, asindicated by the brightness bar. The polarity in real space, whichwas rotated by 180° compared with that in Figure 2b, as men-tioned earlier, is shown as insets.The noncentrosymmetry of each diffraction was calculated asa positive value by subtracting the diffractions rotated by 180°using the following equation:Noncentrosymmetry = max(I2D(u, v) − I2D(−u,−v), 0) (1)where I2D(u,v) is the experimental diffraction in the reciprocal co-ordinates (u,v). Part of the beam stopper and its symmetrical areawere masked before the preprocessing. The processed diffrac-tions at p7 and p8 are shown in the lower part of Figure 5b. Thispreprocessing step transformed all (>22k) diffractions of the ex-perimental 4D data. Noncentrosymmetric preprocessing is sus-ceptible to diffraction off-centering (i.e., the origins of u and v)because of the steep intensity changes at the edges of the diffrac-tion discs. In this study, the center of the diffraction was deter-mined with subpixel accuracy from the cross-correlation of theintegrated diffraction.As shown in Figure 5b, the preprocessed diffractions appear tobe noisy. The intensity for the innermost spots obtained in the ex-periment was ≈100 electrons per pixel. Because quantum noisefollows a Poisson distribution, the expected quantum noise-to-signal ratio (√n/n) of n electrons is slightly smaller than the dif-ference between that of spots 100 and 010 (≈12%), as listed onTable S1 (Supporting Information). In other words, the experi-mental setup was optimized to obtain the required signals withinthe shortest possible time with the minimum electron dosepossible.Figure 5c shows the results of dimensionality reduction usingNMF, assuming seven components. One amorphous componentand six crystalline components with different polarities were suc-cessfully factorized. Although amorphous diffraction (w1) mustbe eliminated because of its centrosymmetry, the intensity resid-uals owing to Poisson noise exhibit halo rings. Crystalline diffrac-tion (w2–w7) was used to determine the crystal orientation and po-larity, as indicated by thewhite circles and each inset, respectively.The factorized diffractions (w2–w7) have a higher signal-to-noiseratio than the individual preprocessed diffractions, and their po-larities can be easily determined. Figure 5d visualizes these re-sults by showing a pseudocolor image of the three orientations,with the polarity reversed for each orientation. The mirror do-mains are often adjacent to each other, and the grain boundariesare very complex. Localized polarity inversion has been reportedwhen using atomic-resolution STEM; however, it has not beenpreviously visualized for wide-area measurements. In particular,this study allows for statistical observations of unique cases suchas complicated multidomain specimens. These results are ex-pected to provide useful information for the future developmentof single-domain growth through MOCVD optimization.3. ConclusionIn this study, we analyzed the twist domains of monolayer MoS2using dynamical electron diffraction, 4D-STEM, and unsuper-vised machine learning techniques, and discussed the advan-tages of these combinations. Compared to conventional dark-field TEM imaging, the 4D-STEM study not only exhibits supe-rior spatial/angular resolution but also demonstrates robustnessagainst specimen tilting and dose efficiency. A detailed compari-son of the twomethods is provided in the supporting informationsection.While virtual dark-field imaging by conventional 4D-STEM al-lows for the versatile selection of spots, it cannot resolve over-lapped diffraction spots. In this study, we demonstrated thatNMFenables the factorization of these overlapped spots into their cor-rect positions. Moreover, preprocessing for noncentrosymme-try is highly effective in separating the effects of polarity andspecimen tilt.Notably, conventional 4D-STEM is insufficient for visualizingthe mirror-twin boundary of monolayer MoS2. Advanced ma-terial characterization with effective physics-informed machinelearning techniques can be established by integrating knowledgefrom electron microscopy, diffraction crystallography, and ma-terials science. This method can be applied to other dichalco-genides and single- or few-layer 2D materials.4. Experimental SectionSpecimen Preparation: AMoS2 monolayer was deposited on an Al2O3(0001) substrate at a temperature of 850 °C by MOCVD. The sourcegases utilized for MOCVD were MoO2Cl2 and H2S, with N2 as the carriergas. Details of the deposition process have been reported elsewhere.[6]Although the authors had already optimized the growth conditions forSmall Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (5 of 8) 23669608, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202501065 by National Institute For, Wiley Online Library on [25/08/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.small-methods.comwww.advancedsciencenews.com www.small-methods.comFigure 5. Polarity analysis of MoS2. a) Integrated diffraction and virtual dark-field images of spot 100. b) Experimental diffractions at positions p7 andp8, and the corresponding pre-processed diffraction for detecting noncentrosymmetry. The white circles indicate the positions of the six innermost spotswith strong diffraction. c) NMF results based on the preprocessed data. d) Images colored by the polarity of each of the three orientations based on theNMF results.synthesizing micrometer-sized single-crystalline MoS2, multidomainspecimens were analyzed for material characterization in the presentstudy. Subsequently, the MoS2 layer was peeled off from the Al2O3 sub-strate using polymethyl methacrylate[20] and transferred to a holey carbonfilm for STEMobservations (Quantifoil, Quantifoil Micro Tools GmbH). Toprevent contamination during STEM observations, the transferred speci-men was cleaned by UV irradiation in an O2 atmosphere[21] for 25 min.Although the specimen underwent partial etching and cracking owing toUV irradiation, there was no atomic defect as observed by an atomic-resolution STEM image (Figure S1a, Supporting Information)4D-STEM Measurements: The 4D-STEM measurements were con-ducted using an aberration-corrected scanning transmission electronmicroscope (Titan Cubed, Thermo Fisher Scientific) at an accelera-tion voltage of 80 kV. The convergence semi-angles for 4D-STEM andSmall Methods 2025, e01065 © 2025 The Author(s). Small Methods published by Wiley-VCH GmbHe01065 (6 of 8) 23669608, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smtd.202501065 by National Institute For, Wiley Online Library on [25/08/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.small-methods.comwww.advancedsciencenews.com www.small-methods.comatomic-resolution STEM were 3 and 25 mrad, respectively. The descanfunction of the microscope, which was carefully adjusted by a ThermoFisher Scientific engineer, stabilized the positions of the diffraction spotsduring scanning. A custom-made ϕ 20 micrometer aperture (DaiwaTechno Systems) was utilized for 4D-STEM, the circularity of whichwas im-portant for the preprocessing of noncentrosymmetry. Diffraction patternswere acquired using an energy-filtered camera (Continuum HR, GatanInc.)[22] with an energy width of 20 eV. The conversion efficiency (58 countsper electron) of the energy-filtered camera was experimentally calibrated,and the detected counts were converted into numbers of electrons. Toavoid afterglow artifacts (see Figure S1b, Supporting Information) owingto spots with intense transmission (i.e., 1000 times higher than that of thediffracted spots of monolayer MoS2), a beam stopper was inserted to ac-quire the diffractions. ADF images were obtained using a Gatan HAADFdetector (Model 806, Gatan Inc.). The 4D measurement conditions wereset to 150 × 150 points in real space and 256 × 256 pixels in reciprocalspace. The exposure time for each diffraction was set to 50 ms for Figure 3and 100 ms for Figure 5. The 4D-STEM data were clipped (228 × 228) tocenter the diffraction patterns after acquisition.Overview of NMF for 4D-STEM: The combination of machine learn-ing and STEM has attracted considerable attention.[23,24] Dimensionalityreduction using NMF was a representative method of unsupervised ma-chine learning. Here, a brief overview of NMF[25–27] and its combinationwith 4D-STEM was provided. The experimental data, matrix X, were ap-proximated by the product of the lower-rank matricesW andH consistingof nonnegative elements:X ≅ WH (2)where W and H denote the basis and its coefficient, respectively. The 4Ddata were transformed into a 2D matrix (i.e., unfolding) for matrix calcu-lation. In this study, the rows and columns of X represent the reciprocaland real-space coordinates of 4D-STEM, respectively. The column vectorsof matrix W and row vectors of matrix H represent the diffractions andcorresponding maps, respectively. The low-rank matrices W and H weredetermined by minimizing a cost functionD based on the Frobenius norm||·||F of the error as follows:D (X ‖WH ) = 12‖X −WH‖2F (3)Equation (3) can be minimized in several ways. Here, the alternatingleast-squares (ALS) algorithm was employed, also called coordinate de-scent. The ALS algorithm was applied using the following equations:W ←[(XHT) (HHT)−1]+(4)H ←[(WTW)−1 (WTX)]+(5)The symbol [·]+ represents a nonnegativity constraint projection,[26]which was defined as [W]+ = max(W, 0). Finally, the converged matricesW and H were transformed into diffraction wk(u,v) and map hk (x,y) (k =1,2,…) pairs (i.e., refolding).In general, the number of components, which was the columns of Wand the rows inH, was unknown; however, it can be estimated to be sevenbased on the present experimental diffraction (Figure 3b) and the MoS2crystal structure (Figure 2a,b). Convergence of the iterations of Equa-tions (4) and (5) can be determined by the tolerance[28] or monitoring themean square errors.[12,13] The possibility of convergence to a local mini-mum was a known feature of NMF, and a sufficiently reliable global min-imum can be found by performing multiple calculations and comparingthe mean square errors. Further details on NMF and its combination with4D-STEM have been reported elsewhere.[12,13]In the present study, DigitalMicrograph software (Gatan Inc.) was usedto acquire and analyze the experimental 4D data.[29] The various pre-processing steps (e.g., noncentrosymmetry calculations) were performedusing in-house DigitalMicrograph scripts. Python on DigitalMicrographwas also utilized for unsupervised machine learning, e.g., Scikit-Learn,[30]NumPy,[31] SciPy,[32] and MatPlotLib.[33] Hierarchical clustering was per-formed by calculating the similarity of diffractions using cross-correlationto obtain a pseudo-distance. These calculations were also carried out us-ing in-house scripts on DigitalMicrograph. Examples of DigitalMicrographscripts have been reported elsewhere.[12,13,34]The computational cost was a drawback of NMF because iterative ma-trix calculations of Equation (4) and (5) were required. The required num-ber of iterations may range from tens to hundreds (e.g., ≈100 in our previ-ous study).[12] Due to the large 4D-STEM dataset, the computational costwas high. The 4D-STEM data in this study were calculated using a desktopcomputer with an AMD Ryzen 9 9950X. Assuming seven components asshown in Figures 3 and 5, 100 iterations for 4D-STEM data (4.6 GB, 150 ×150 × 228 × 228) took ≈1 min.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis study was supported by a Grant-in-Aid for Transformative ResearchAreas (A) “Supra-ceramics” (JSPS Grant Number JP 22H05145) and KAK-ENHI JP 20H02624 awarded to K.K., J.K., and O.C. This study was partlysupported by KAKENHI JP 23H04874 awarded to K.H., JP 24K08253 toO.C., and JP 17H03241 to Y.S. Y.S. was also supported by JST-CREST (GrantNumber: JP MJCR24A3). The authors would like to thank Han Zhang,Naoyuki Kawamoto, Atsushi Togo, and Tomoki Shiga for their invaluablediscussions. Funding: KAKENHI: JP22H05145, JP20H02624, JP23H04874,JP24K08253, JP17H03241; JST-CREST: JPMJCR24A3.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywords4D STEM, dichalcogenide, metal–organic chemical vapor deposition(MOCVD), MoS2, scanning transmission electron microscopy (STEM),unsupervised machine learningReceived: June 2, 2025Revised: July 11, 2025Published online:[1] D. Voiry, A. Mohite, M. Chhowalla, Chem. Soc. Rev. 2015, 44, 2702.[2] M. Chhowalla, D. Jena, H. Zhang, Nat. Rev. Mater. 2016, 1, 16052.[3] Q. H. Wang, K. 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