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Hirotaka Uryu, Tsunetomo Yamada, Koichi Kitahara, [Alok Singh](https://orcid.org/0000-0001-5515-8305), [Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), [Kaoru Kimura](https://orcid.org/0000-0001-5050-4256), Kanta Hiroki, Naoki Miyao, Asuka Ishikawa, Ryuji Tamura, Satoshi Ohhashi, Chang Liu, Ryo Yoshida

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[Deep Learning Enables Rapid Identification of a New Quasicrystal from Multiphase Powder Diffraction Patterns](https://mdr.nims.go.jp/datasets/889a61be-efe7-4d7e-aa39-f5dd7e70f80a)

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Deep Learning Enables Rapid Identification of a New Quasicrystal from Multiphase Powder Diffraction PatternsRESEARCH ARTICLEwww.advancedscience.comDeep Learning Enables Rapid Identification of a NewQuasicrystal from Multiphase Powder Diffraction PatternsHirotaka Uryu, Tsunetomo Yamada,* Koichi Kitahara, Alok Singh, Yutaka Iwasaki,Kaoru Kimura, Kanta Hiroki, Naoya Miyao, Asuka Ishikawa, Ryuji Tamura,Satoshi Ohhashi, Chang Liu, and Ryo YoshidaSince the discovery of the quasicrystal, approximately 100 stable quasicrystalsare identified. To date, the existence of quasicrystals is verified usingtransmission electron microscopy; however, this technique requiressignificantly more elaboration than rapid and automatic powder X-raydiffraction. Therefore, to facilitate the search for novel quasicrystals,developing a rapid technique for phase-identification from powder diffractionpatterns is desirable. This paper reports the identification of a new Al–Si–Ruquasicrystal using deep learning technologies from multiphase powderpatterns, from which it is difficult to discriminate the presence ofquasicrystalline phases even for well-trained human experts. Deep neuralnetworks trained with artificially generated multiphase powder patternsdetermine the presence of quasicrystals with an accuracy >92% from actualpowder patterns. Specifically, 440 powder patterns are screened using thetrained classifier, from which the Al–Si–Ru quasicrystal is identified. Thisstudy demonstrates an excellent potential of deep learning to identify anunknown phase of a targeted structure from powder patterns even whenexisting in a multiphase sample.H. Uryu, T. Yamada, K. HirokiDepartment of Applied PhysicsTokyo University of Science6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, JapanE-mail: tsunetomo.yamada@rs.tus.ac.jpK. KitaharaDepartment of Materials Science and EngineeringNational Defense Academy1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, JapanK. Kitahara, Y. Iwasaki, K. KimuraDepartment of Advanced Materials ScienceThe University of Tokyo5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, JapanE-mail: IWASAKI.Yutaka@nims.go.jp; bkimura@phys.mm.t.u-tokyo.ac.jpThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202304546© 2023 The Authors. Advanced Science 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/advs.2023045461. IntroductionPowder X-ray diffraction (PXRD) is a widelyused mature technology for the identifi-cation of crystalline materials. However,the analysis of PXRD patterns is challeng-ing when a sample exists in the formof a multiphase mixture. In such cases,phase-identification involves several rule-based protocols that rely upon the ex-perience and intuition of highly trainedexperts. Recent advances in deep learn-ing technologies have led to remarkableperformances in the analysis of PXRDpatterns, including phase-identification[1–5]and symmetry-classification.[6–8] For exam-ple, Lee et al. applied a convolutional neu-ral network (CNN) to determine the volumefractions of already-known phases that existin multiphase inorganic compounds fromthe PXRD patterns.[2] The key to this work-flow was the generation of realistic artificialA. SinghElectron Microscopy Unit, Research Network and Facility ServicesDivisionNational Institute for Materials Science1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanY. Iwasaki, K. KimuraThermal Energy Materials Group, Research Center for MaterialsNanoarchitectonicsNational Institute for Materials Science1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanN. Miyao, R. TamuraDepartment of Materials Science and TechnologyTokyo University of Science6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, JapanA. IshikawaResearch Institute of Science and TechnologyTokyo University of Science6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, JapanS. OhhashiInstitute of Multidisciplinary Research for Advanced MaterialsTohoku University2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, JapanC. Liu, R. YoshidaThe Institute of Statistical MathematicsResearch Organization of Information and Systems10-3 Midori-cho, Tachikawa, Tokyo 190-8562, JapanE-mail: liu.chang@ism.ac.jpAdv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (1 of 9)http://www.advancedscience.commailto:tsunetomo.yamada@rs.tus.ac.jpmailto:IWASAKI.Yutaka@nims.go.jpmailto:bkimura@phys.mm.t.u-tokyo.ac.jphttps://doi.org/10.1002/advs.202304546http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/mailto:liu.chang@ism.ac.jphttp://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202304546&domain=pdf&date_stamp=2023-11-14www.advancedsciencenews.com www.advancedscience.commultiphase diffraction patterns for the training dataset. Schuet-zke et al. provided a well-established framework for generatingartificial diffraction patterns, demonstrating that the variationin unit-cell parameters is crucial to increase the discriminativepower in phase-identification.[9] However, to the best of ourknowledge, the identification of an unknown phase from mul-tiphase samples has not been successfully performed before.In this study, we aim to establish a machine learning (ML)workflow for phase-identification of an unknown phase of atargeted structure type, that is icosahedral quasicrystal (i-QC),using multiphase diffraction patterns.Quasicrystals (QCs) are long-range ordered solids that ex-hibit self-similarity in their single-grain diffraction patterns;however, their scaling ratio is incompatible with translationalsymmetry.[10] Since the discovery of an Al–Mn i-QC,[11] QCshave been identified in a wide variety of materials, includ-ing alloys,[11–13] liquid crystals,[14] nanoparticle assemblies,[15]mesoporous silica,[16] colloidal crystals,[17] polymers,[18] metaloxides,[19,20] minerals,[21,22] and a metal organic framework.[23]The observation of novel physical properties, such as quantumcriticality in Au–Al–Yb i-QC,[24] superconductivity in Al–Mg–Zni-QC,[25] and very recent long-range magnetic order (ferro- andferrimagnetism) in Au–Ga–(Gd,Tb)[26] and Au–Ga–Dy[27] i-QCs,has always been accomplished by the discovery of new QCs. How-ever, the search for unknown QCs has relied on time-consuming,manual trial-and-error work based on human intuition; there-fore, accelerating the discovery of new QCs is of enormous im-portance in advancing the study of quasiperiodic materials. Inthis context, Liu et al. recently developed an ML algorithm thatcan predict QC-forming chemical compositions with ultra-highaccuracy.[28,29] Since it is desirable to conduct numerous syntheticexperiments based on high-throughput screening across exten-sive libraries of candidate materials using such an ML model,the development of rapid QC phase-identification technologiesis necessary to characterize a large number of samples that aremass-produced in laboratory experiments. Currently, the only ex-isting method that can be applied to the phase-identification ofi-QCs from multiphase PXRD patterns is the scheme proposedby Lu et al.[30] However, their method is applicable only in caseswhere an i-QC phase is dominant in the sample.We devised a versatile deep learning methodology that can de-tect the presence of an i-QC phase, both known and unknown,from intricate multiphase PXRD pattern, even when the i-QCphase is not dominant in the multiphase mixture. A binary classi-fier was constructed using CNNs that determine whether an i-QCphase is present/absent in a sample with its PXRD pattern. Theclassifier was trained on the synthetic multiphase diffraction pat-terns, and its identification performance was evaluated based onboth synthetic patterns and our in-house database of actual pat-terns. The trained classifier was then applied to screen 440 mea-sured diffraction patterns of unknown materials in five alloy sys-tems. This screening indicated the presence of an unknown i-QCphase in multiphase Al–Si–Ru alloys, which was subsequentlyR. YoshidaDepartment of Statistical ScienceThe Graduate University for Advanced Studies10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japanconfirmed in transmission electron microscopy (TEM) observa-tions.2. Results and Discussion2.1. Building and Training the Binary ClassifierThe icosahedral lattice constant a of the i-QCs found so far rangesfrom approximately 0.45 (Al65Cu20Fe15 i-QC[31]) to 0.58 nm (Cd-Mg-Yb i-QC[32]). Thus, the classifier was composed of 80 differentCNNs, where the i-th CNN determined the presence/absence ofi-QCs with an icosahedral lattice constant given by ai = 0.4000+ 0.0025i nm (i = 0, 1, …, 79). This facilitates the investigationof any arbitrary alloy for the presence of an i-QC phase. Themodel architecture and hyperparameters, which were commonto these CNNs, were designed to optimise the classification accu-racy in hold-out validation through Bayesian optimisation[33] (seeFigure 1). To train each CNN, a dataset of artificial multiphasePXRD patterns was prepared. Each pattern was synthesized bymixing two patterns denoted as “single-QC” for single-phase i-QCs and “non-QC” for other phases (see Figure 2). In accordancewith a previous study showing that the variation of unit-cell pa-rameters in a training set has a significant impact on the per-formance of the phase-identification task,[9] the “single-QC” pat-terns were generated using an icosahedral lattice constant var-ied randomly between ai and ai + 0.0025 nm. A total of 30,000“single-QC” patterns were generated using a simple i-QC modelas shown in Figure 3. Two different sets of “non-QC” were alsogenerated using a rule-based procedure, each containing 30 000patterns (“non-QC-1” and “non-QC-2”). To create the multiphasei-QC diffraction patterns using these sets (hereafter referred toas “multi-QC”), each “single-QC” was mixed with a randomly se-lected pattern of “non-QC-1” with a mixing weight sampled be-tween 0.0 and 5.0. The “non-QC-2” set was used as the negativeinstance set, denoted by “non-QC”, with respect to the positiveinstances in “multi-QC”.Each CNN was trained using the “multi-QC” and “non-QC-2”datasets. Its prediction performance was then evaluated using anunseen dataset of 6,000 additionally generated artificial patterns.The prediction accuracy reached 98.9% (Table S1, SupportingInformation). Furthermore, the prediction performance wasevaluated using an unseen dataset of 424 manually annotatedexperimental patterns. The accuracy reached 92.2% (Table S1,Supporting Information). Here, a classification probability,denoted by p, of the classifier was defined to be the highest valueamong all probabilities given by the CNNs. The performancewas also examined based on two additional metrics, namelyrecall and precision. Recall is a measure of the number of i-QCinstances accurately predicted by the classifier, while precisionis the measure of the number of instances predicted to be i-QCthat are actually true. The recall and precision reached 0.989 and0.990 for the artificial dataset and 0.959 and 0.700 for the experi-mental dataset, respectively. Although the precision, with respectto the experimental dataset, was slightly lower than that of theartificial dataset, the recall was maintained at a significantlyhigh level. Importantly, during high-throughput screening, it isnecessary to avoid overlooking the presence of QCs; therefore,it is crucial to achieve a high level of recall even if the precisionis slightly lower. These results indicate that our classifier provedAdv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (2 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 1. A CNN architecture for phase-identification from the PXRD patterns. The model is composed of an input layer, three pairs of convolution andmax-pooling layers, a flatten layer, two fully connected layers, a softmax layer, and an output layer. The number of neurons in each layer are given alongwith the hyperparameters, the number of filters, the filter size, the stride, the pool-size, the dropout rate, and the number of neurons in each layer.to be useful in practice. Moreover, experimental PXRD patternsof known i-QCs were successfully identified by the trainedclassifier (Table S2, Supporting Information). It is interesting tonote that the classifier could identify the i-QCs of three differentfamilies, i.e., Bergman-, Mackay- ,and Tsai-types, althougha simple structure model was used in the generation of the“single-QC” patterns. Broadly speaking, the powder diffractionpatterns of these i-QCs is similar to each other; therefore, theclassification performance of the present model is not sufficientto distinguish different types of the i-QCs. The classificationAdv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (3 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 2. Flowchart outlining preparation of the artificial PXRD patterns for model training. Based on the structural model of the i-QC in Figure 3d–f,single-phase diffraction patterns of the i-QC (”single-QC”) with variation in the icosahedral lattice constant, the constituent elements, and the peakwidths were generated. Each ”single-QC” pattern was then added to one of the patterns generated randomly (”non-QC-1”) with a mixing weight 𝜔selected randomly in the range of 0.0–5.0 (”multi-QC”). The ”non-QC-2” set was generated in the same manner as ”others-1”, with the exception thatthe number of “strong” peaks was selected randomly from a range of 5–35. All patterns were generated in a 2𝜃-range between 20 and 80° with a Δ(2𝜃)interval equal to 0.01°. The peak positions and heights in each pattern were convoluted using the Lorentzian profile function.of different types of i-QCs is one of our research topics inthe feature.For comparison, we constructed deep neural network modelswith a single CNN as shown in Figure 1 to determine the pres-ence/absence of i-QCs with an icosahedral lattice constant rang-ing from 0.4 to 0.6 nm. The prediction performance of these mod-els was found to be much lower than that of the above binaryclassifier using multi-CNN, shown by the following.First, the single CNN was trained with a dataset of 30 000patterns of “single-QC” and 30 000 patterns of “non-QC”, andthe prediction performance of the model evaluated using an un-seen dataset of 10 000 additionally generated artificial patterns,that is 5,000 “single-QC” and 5,000 “non-QC” patterns. The pre-diction performance was most likely perfect, with accuracy, re-call, and precision equal to 99.67, 99.96, and 99.38%, respec-tively (see Table S3a, Supporting Information). The performancedecreased however when evaluated using an unseen dataset ofartificial patterns of multiphase mixture, that is 5,000 “multi-QC” and 5,000 “non-QC” patterns (see Table S3b, Supporting In-formation), where the accuracy and recall decreased to 57.92%and 16.36%, respectively. Although the precision remained high(96.92%), the recall was too low for practical use.Second, the model was trained with a dataset of artificial mul-tiphase patterns, i.e., 30 000 “multi-QC” and 30 000 “non-QC”patterns. The accuracy, recall and precision respectively reached79.30, 75.54, and 81.68% against an unseen dataset of 10 000additionally generated multiphase patterns (see Table S3c, Sup-porting Information). Although the prediction performance im-proved over the above single CNN model, it was beyond the bi-nary classifier using multi-CNN.Adv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (4 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 3. The simple 6D structure model of an i-QC based on the Cd5.7Yb model.[34] The three independent occupation domains (ODs) in the Cd5.7Ybmodel are located at a) the vertex, b)the edge-center, and c) the body-center positions of the 6D lattice. These ODs were simplified as follows: d) a spherewith a radius r1 at the vertex, e) a spheroid with an equatorial radius of r2 and a distance of r3 from the center to the pole at the edge-center, and f) asphere with a radius r4. The sphere in (f) is decomposed into two parts, that is, a central spherical shell with a radius of r5 and the remainder. g) Thefivefold section of the 6D structure model. The bars indicate the five-fold section of the ODs, while 5f‖ and 5f⊥ indicate the fivefold axes in E‖ and E⊥,respectively. The PXRD patterns for the h) Cd5.7Yb and i) Zn88Sc12 i-QCs are compared to those computed based on the ODs in (d–f). The six indicesare given using an indexing scheme for i-QCs.[35]2.2. Screening 440 Experimental Powder XRD Patterns andCharacterization of Candidate MaterialsSubsequently, the trained classifier, which is composed of multi-CNNs, was employed to screen 440 entries of unlabeled PXRDpatterns. These laboratory data were accumulated for the pur-pose of material exploration in six alloy systems, including Al–Si–Ru,[36] Al–Fe–Ir, Al–Mn–Ir, Al–Cu–Pt, Al–Pt–Co, and Al–Cu–Ir;therefore, most samples were likely to be multiphase mixtures.The presence or absence of i-QC was determined by the magni-tude of p being greater or <0.950. Furthermore, each pattern wasclassified into one of the following four classes according to thep: A (p > 0.999), B (0.990 < p ⩽ 0.999), C (0.950 < p ⩽ 0.990), andD (p ⩽ 0.950).The number of master alloys and diffraction patterns are givenin Table 1, together with the number of patterns classified as theprediction class 𝜙 = {A, B, C, D}. The last column in the table istotal score estimated from the diffraction pattern of each alloysystem. The score is defined as score = 1/N∑ϕSϕnϕ, where N,nϕ, Sϕ are the number of diffraction patterns for each alloy sys-tem, number of patterns classified as ϕ, and partial score givento each pattern classified as ϕ, respectively. We set SA, SB, SC,and SD equal to 3, 2, 1, and 0, respectively. Among the six al-loy systems, the highest score was obtained in the Al–Si–Ru al-loy system, where the screening result yielded 4, 16, and 53 pat-terns classified as A, B, and C, respectively. The alloy composi-tion of the Al–Si–Ru samples is shown in a ternary diagram inFigure S1 (Supporting Information) with the predicted class ofits corresponding diffraction pattern. It was found that the com-positions of the samples exhibiting a diffraction pattern classifiedas B or C were distributed around those classified as A. Four ofthese candidate patterns were then selected (denoted by I to IV inTable 1. Details of the 440 PXRD patterns of unknown materials. Numberof master alloys is shown in the 2nd column for each alloy system shown inthe 1st column. The number of PXRD patterns is given in the 3rd columnand number of patterns classified to as A, B, C, or D is given in the 4–7th columns. The last column is the total score estimated for the PXRDpatterns of each alloy system.Alloy system N. of master alloy N. of data A B C D ScoreAl–Si–Ru 79 237 4 16 53 164 0.401Al–Fe–Ir 52 130 2 13 15 100 0.362Al–Mn–Ir 12 42 0 0 2 40 0.048Al–Cu–Pt 8 21 0 0 0 21 0.000Al–Pt–Co 8 8 0 0 1 7 0.125Al–Cu–Ir 2 2 0 0 0 2 0.000total 161 440 6 29 71 334Adv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (5 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 4. a) Measured PXRD patterns of four different Al–Si–Ru alloys. The red-coloured pattern on the bottom is a measured diffraction pattern fora single-phase of the Al–Cu–Fe i-QC. The classification probabilities of including an i-QC phase are indicated in the figure. The SAED patterns of theAl–Si–Ru samples related to powder b,c) patterns-I and d,e) IV are shown. These patterns were taken along (b,d) the fivefold and (c,e) the twofold axes,depicting the formation of the i-QC. e) The peaks A, B, C, and D on the twofold pattern are indexed as 200000, 111111, 311111, and 422222, respectively,according to a previous report.[35] f) 𝜏-scaling property of the diffraction pattern.Figure 4a); pattern-I was classified as class A, patterns-II and IIIas B, and pattern-IV as C. The presence of i-QCs in these alloys(hereafter denoted as ASR(I) to ASR(IV)) was then examined indetail through scanning electron microscopy (SEM).For pattern-I, the majority of peaks were assigned to a prim-itive i-QC with a equal to 0.4353 nm. However, some intensepeaks were not assigned to an i-QC. The SEM observationsrevealed that three different phases were present in ASR(I),and their compositions were determined to be Al43Si32Ru25,Al26Si34Ru20, and Al38Si42Ru20 using energy dispersive X-ray(EDX) spectroscopy. Moreover, through electron back-scattereddiffraction (EBSD), we confirmed that the first phase exhibitedKikuchi patterns with icosahedral symmetry, while the others didnot, indicating the presence of the i-QC phase in the multiphasemixture (see Figure S2, Supporting Information).As shown in Figure 4a, the diffraction patterns-II, III, and IVexhibit a large number of peaks that are absent in pattern-I. Us-ing SEM-EDX, it was observed that ASR(II) is a single-phasewith a composition of Al73Si1Ru26. In addition, ASR(III) wasfound to be composed of two different phases with compositionsof Al69Si5Ru26 and Al61Si3Ru36. From their Kikuchi patterns, itwas confirmed that these phases are not i-QC. For pattern-IV,ASR(IV) was found to be composed of three different phases withcompositions of Al44Si31Ru25, Al55Si17Ru28, and Al53Si23Ru24. Itwas confirmed that the first phase exhibited icosahedral Kikuchipatterns, whereas the others did not, indicating that the i-QCphase was present in the multiphase mixture (see Figure S3, Sup-porting Information).To further examine the presence of i-QC phase, TEM observa-tions were performed for ASR(I) and ASR(IV). Figure 4b–e showsthe selected-area electron diffraction (SAED) patterns of these al-loys with incidence along the fivefold and twofold rotational sym-metry axes, indicating the presence of the i-QC phase in thesesamples. To the best of our knowledge, there are no previous re-ports on the presence of i-QC in Al–Si–Ru alloy systems. Impor-tantly, these SAED patterns allowed characterization of the i-QCphase in more detail. More specifically, the twofold diffractionpattern was found to exhibit 𝜏-scaling (see Figure 4f), where 𝜏 isthe golden mean equal to (1 +√5)∕2; this observation indicatesthat these i-QC phases form a face-centered type superstructurewith a doubled lattice parameter, a′ = 2a = 0.8706 nm.The alloy composition of Al–Si–Ru i-QC reported herein dif-fers from those of known i-QCs. To date, stable face-centeredi-QCs have been observed in Al transition metal systems, suchas Al65Cu20Fe15 (a′ = 0.890 nm),[31] Al65Cu20Ru15 (0.906 nm),Al65Cu20Os15 (0.902 nm),[37] Al70Pd20Mn10 (0.914 nm),[38,39]Al70Pd20Tc10 (0.921 nm),[40] and Al70Pd20Re10 (0.922 nm).[38,41]Therefore, an Al concentration of approximately 43 at.% in theAl–Si–Ru i-QC is significantly lower than the corresponding val-ues for the previously synthesized i-QCs. Furthermore, the Al–Si–Ru i-QC contained approximately 30 at.% of Si; no Al-basedi-QC containing such a large amount of Si has been previouslyreported, with the exception of the Si61Cu30Ca7Fe2 i-QC, whichwas observed in a sample created in the first atomic bomb test.[42]Moreover, the lattice constant a′ of the Al–Si–Ru i-QC is thesmallest among those of the above-mentioned Al-based i-QCs,with a difference of at least 0.02 nm.Although pattern-I is similar to the PXRD pattern of the Al–Cu–Fe i-QC (Figure 4a), several differences were observed. First,the second intense peak at 2𝜃 = 45.72° in pattern-I was ab-sent in the Al–Cu–Fe i-QC, and this peak originated from thesecondary phases in ASR(I). Second, the peak positions wereshifted in pattern-I owing to the large difference in the latticeconstants (approximately 0.2 nm). Third, the 311111 peak ob-served at 2𝜃 = 26.06° in the diffraction pattern of the Al–Cu–Fe i-QC was not observed in pattern-I. Since this peak corre-sponds to a strong superstructure reflection that has been ob-served in diffraction patterns for known Al-based face-centeredAdv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (6 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comi-QCs, the presence of this peak forms the basis for judgingwhether the i-QC phase is present/absent in the search for newAl-based i-QCs containing transition metals. In rule-based identi-fication, the aforedescribed differences would lead to human ex-perts misjudging the absence of the i-QC phase in ASR(I). Asregards pattern-IV, the visual recognition of the presence of theAl–Si–Ru i-QC is considerably difficult, even for highly skilledresearchers.3. ConclusionThe classifier, which is composed of multi-CNNs and trainedfrom artificial multiphase PXRD patterns, achieved a high dis-criminative power in the phase-identification of i-QCs. There-fore, it significantly accelerates the phase-identification task formultiphase samples, which is one of the bottlenecks in the QCexploration process. The applicability of the current method isnot limited to i-QC analysis, but the same ML approach couldbe used in phase-identification of new decagonal and dodecago-nal QCs, using their prototype models.[43,44] Further, the presentML approach is expected to be applicable to various types of crys-talline materials and facilitates the materials discovery process.4. Experimental SectionConvolutional Neural Network: The CNNs for the different lattice con-stants were designed with a common model architecture, as shown inFigure 1.[45] Keras[45] was used for implementation. This model consistedof the nine layers that define the mapping from any given diffraction pat-tern to the output probability of the binary classification. Each of the layersconsisted of convolutional and max-pooling layers, followed by a flattenlayer, two fully connected layers, and a softmax layer.Hyperparameter Search: The hyperparameters of the CNN were tunedby running Optuna[46] for 50 trials. The objective function to be optimizedwas the accuracy of the validation data, where 20% of the 60 000 train-ing samples were randomly chosen. The search space is summarized inTable S4 (Supporting Information), and included the number of convolu-tional layers, number of kernels and the kernel size for each convolutionallayer, number of layers and neurones for the fully connected layers, pool-ing size, dropout rate, and choice of optimiser. The black-box function wasoptimized by performing Bayesian optimization using a tree-structuredParzen estimator.[33] The resulting values are given in Figure 1.Performance Measures: The classification performance was examinedbased on the recall and the precision with respect to the discriminationcapability of “i-QC”: recall = TP/(TP + FN) and precision = TP/(TP + FP),where TP, TN, FP, and FN denoted the occurrence numbers of true posi-tive, true negative, false positive, and false negative instances in the pre-diction, respectively. The overall accuracy was defined as follows: accuracy= (TP + TN)/(TP + FN + FP + TN).Calculation of Powder X-ray Diffraction Patterns for Training: Single-phase diffraction patterns of the primitive-type i-QCs were gen-erated (“single-QC” patterns in Figure 2) based on hyperspacecrystallography.[47–49] In the structure generator, the atomic struc-ture of an i-QC was described as a 3D section of a 6D periodic structureconsisting of occupation domains (ODs). Each OD represented a hypo-thetical 3D object in a 3D complementary space called the perpendicularspace (E⊥), which was perpendicular to the 3D real space known as theparallel space (E‖).A simple 6D structure model was constructed based on the modelof Tsai-type Cd5.7Yb i-QC[34] (Figure 3a–c). The Cd5.7Yb model consistedof ODs located at three independent positions of a 6D hyper-cubic lat-tice with a 6D unit-cell parameter (a6D) as follows: Vertex position (V) at(0,0,0,0,0,0) Edge-center position (EC) at (1,0,0,0,0,0)/2, and Body-centerposition (BC) at (1,1,1,1,1,1)/2. In this model, Yb atoms occupied the cen-tral part of the OD at the BC, and Cd atoms occupied the remainder of theOD. The resulting atomic structure possessed an icosahedral lattice con-stant a (= a6D∕√2) of 0.5689 nm. To reduce the computational cost ofobtaining the diffraction patterns, the ODs were approximated as spheres,spheroids, or spherical shells as follows: i) The OD at V was approximatedas a spherical OD with a radius of r1, ii) OD at EC was approximated asa spheroid-shaped OD with an equatorial radius of r2 and a distance ofr3 from the center to the pole, and iii) OD at BC was approximated as aspherical OD with a radius of r4 that was further decomposed into twoobjects, namely a central sphere with a radius of r5 and a spherical shell(see Figure 3d–g). Using this spherical 6D model, the PXRD patterns werecalculated according to a previous literature approach,[50] in which theparameters ri(i = 1, 2, …, 5) were optimized based on the experimentaldiffraction pattern of Cd5.7Yb i-QC.[51,52] Here, it was assumed that thespherical OD at BC was occupied by Yb and the remainder of the OD wasoccupied by Cd. The resulting PXRD pattern well reproduced the experi-mental observations (Figure 3h). Moreover, when replacing the Cd and Ybatoms in the model with Zn and Sc, respectively, it was confirmed that thesimulated PXRD pattern successfully reproduced the experimental diffrac-tion pattern of Zn88Sc12 i-QC[53] (see Figure 3i).In the generation of “single-QC” patterns, the constituent elements ofeach i-QC were randomly selected from the 60 different metal elementsto generate binary, ternary, and quaternary i-QC structures. Each patternwas calculated based on the use of Cu-K𝛼1 radiation with Bragg–Brentanogeometry in a 2𝜃-range between 20and 80°, which is a typical setup for measuring i-QC alloys.The “non-QC-1” pattern set in Figure 2 was generated based on therule that each pattern consisted of “strong” and “weak” peaks, whose in-tensities were selected randomly in the ranges of 0.1–1.0 and 0.0–0.1, re-spectively. In addition, the number of peaks was selected randomly in theranges of 0–30 and 0–100 for the “strong” and “weak” peaks, respectively.The “non-QC-2” patterns in Figure 2 set was generated in the same man-ner, with the exception that the number of the “strong” peaks was selectedrandomly between 5 and 35.To mimic experimental diffraction patterns, the peak positions and in-tensities in the above synthetic patterns were convoluted with a Lorentzianprofile function with a half width at half maximum (hwhm) randomly se-lected between 0.03 and 0.3°. The hwhm of the individual peaks was mul-tiplied by a value selected randomly between 0.95 and 1.0 to increase thevariability in the training set.Labeled Powder X-ray Diffraction Patterns for Performance Testing: The424 labeled PXRD patterns stored by the research group were used toevaluate the prediction performance of the trained classifier. The PXRDpatterns were measured using a 𝜃–2𝜃 diffractometer (either MiniFlex 600or SmartLab (Rigaku)) with Cu K𝛼 radiation. All patterns were analyzedand labeled according to whether an i-QC phase was present/absent inthe sample.Powder X-Ray Diffraction Measurements of Unknown Materials: A totalof 161 alloys were synthesized via the arc melting technique during ex-ploratory research on phase diagrams of six different alloy systems, includ-ing Al–Si–Ru,[36] Al–Fe–Ir, Al–Mn–Ir, Al–Cu–Pt, Al–Pt–Co, and Al–Cu–Ir.The numbers of master ingots were 79, 52, 12, 8, 8, respectively. Diffrac-tion patterns of the as-cast alloys were measured using a 𝜃–2𝜃 diffrac-tometer SmartLab (Rigaku) with Cu K𝛼 radiation. The alloys were thenannealed, and diffraction measurements were performed. The cycle of an-nealing and diffraction measurement was repeated, resulting in the 440unlabeled diffraction patterns.Scanning Electron Microscopy: The microstructure of the alloy was ob-served using SEM (SU6600, Hitachi). The composition of each samplewas analyzed using an EDX detector (Oxford Instruments) combined witha SEM apparatus. Kikuchi patterns were obtained using the EBSD methodand recorded using a 2D detector combined with SEM. The obtainedKikuchi patterns were analyzed using the software EBSD12.[54]Transmission Electron Microscopy: Small pieces of the alloy were lightlycrushed in methanol. Fine alloy particles, many of which were thin and suf-ficiently transparent for carrying out TEM observations, were suspendedon a lacey carbon thin film over a copper grid. For this purpose, a dropAdv. Sci. 2024, 11, 2304546 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2304546 (7 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comof the particles suspended in methanol was placed over the carbon film.The grid containing the sample was mounted on a double-tilt goniome-ter and inserted into the TEM to obtain the electron diffraction patternsby tilting to various zone axes. A JEOL microscope model 2800 equippedwith a field-emission electron gun operated at 200 kV was used to recordthe TEM images.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis work was supported in part by an MEXT KAKENHI Grant-in-Aid forScientific Research on Innovative Areas (Grant Numbers 19H05818 and19H05820). R.T. acknowledges financial support from JST CREST Grant(Grant Number JPMJCR22O3). R.Y. acknowledges financial support froma Grant-in-Aid for Scientific Research (A) (Grant Number 19H01132) fromthe Japan Society for the Promotion of Science (JSPS) and a JST CRESTGrant (Grant Number JPMJCR19I3). Correction added on January 5, 2024,after first online publication: The first name of N.M. was corrected.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe source codes are available from the GitHub website (https://github.com/SuperspaceLab/ml-qc-pxrd). 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Advanced Science published by Wiley-VCH GmbH2304546 (9 of 9) 21983844, 2024, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202304546 by National Institute For, Wiley Online Library on [11/12/2024]. 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.advancedscience.com Deep Learning Enables Rapid Identification of a New Quasicrystal from Multiphase Powder Diffraction Patterns 1. Introduction 2. Results and Discussion 2.1. Building and Training the Binary Classifier 2.2. Screening 440 Experimental Powder XRD Patterns and Characterization of Candidate Materials 3. Conclusion 4. Experimental Section Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords