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[KOYAMA, Yukinori](https://orcid.org/0000-0002-7090-4430), [SEKO, Atsuto](https://orcid.org/0000-0002-2473-3837), [TANAKA, Isao](https://orcid.org/0000-0002-4616-118X), [FUNAHASHI, Shiro](https://orcid.org/0000-0002-9381-3603), [HIROSAKI, Naoto](https://orcid.org/0000-0001-9218-9557)

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[Combination of recommender system and single-particle diagnosis for accelerated discovery of novel nitrides](https://mdr.nims.go.jp/datasets/531d69d9-bd75-4fe6-a22d-ad3899fa8825)

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Combination of recommender system and single-particle diagnosis for accelerated discovery of novel nitridesJ. Chem. Phys. 154, 224117 (2021); https://doi.org/10.1063/5.0049981 154, 224117© 2021 Author(s).Combination of recommender system andsingle-particle diagnosis for accelerateddiscovery of novel nitridesCite as: J. Chem. Phys. 154, 224117 (2021); https://doi.org/10.1063/5.0049981Submitted: 11 March 2021 . Accepted: 20 May 2021 . Published Online: 14 June 2021 Yukinori Koyama,  Atsuto Seko,  Isao Tanaka,  Shiro Funahashi, and Naoto Hirosakihttps://images.scitation.org/redirect.spark?MID=176720&plid=1401534&setID=378408&channelID=0&CID=496958&banID=520310234&PID=0&textadID=0&tc=1&type=tclick&mt=1&hc=ed5dd4029e63a2f75704dfd96619305ac85f9c8d&location=https://doi.org/10.1063/5.0049981https://doi.org/10.1063/5.0049981http://orcid.org/0000-0002-7090-4430https://aip.scitation.org/author/Koyama%2C+Yukinorihttp://orcid.org/0000-0002-2473-3837https://aip.scitation.org/author/Seko%2C+Atsutohttp://orcid.org/0000-0002-4616-118Xhttps://aip.scitation.org/author/Tanaka%2C+Isaohttp://orcid.org/0000-0002-9381-3603https://aip.scitation.org/author/Funahashi%2C+Shirohttps://aip.scitation.org/author/Hirosaki%2C+Naotohttps://doi.org/10.1063/5.0049981https://aip.scitation.org/action/showCitFormats?type=show&doi=10.1063/5.0049981http://crossmark.crossref.org/dialog/?doi=10.1063%2F5.0049981&domain=aip.scitation.org&date_stamp=2021-06-14The Journalof Chemical Physics ARTICLE scitation.org/journal/jcpCombination of recommender systemand single-particle diagnosis for accelerateddiscovery of novel nitridesCite as: J. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981Submitted: 11 March 2021 • Accepted: 20 May 2021 •Published Online: 14 June 2021Yukinori Koyama,1,a) Atsuto Seko,2 Isao Tanaka,2,3 Shiro Funahashi,4 and Naoto Hirosaki4AFFILIATIONS1 Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, Tsukuba,Ibaraki 305-0044, Japan2 Department of Materials Science and Engineering, Kyoto University, Kyoto, Kyoto 606-8501, Japan3Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya, Aichi 456-8587, Japan4Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, JapanNote: This paper is part of the JCP Special Topic on Computational Materials Discovery.a)Author to whom correspondence should be addressed: KOYAMA.Yukinori@nims.go.jpABSTRACTDiscovery of new compounds from wide chemical space is attractive for materials researchers. However, theoretical prediction and validationexperiments have not been systematically integrated. Here, we demonstrate that a new combined approach is powerful in significantly accel-erating the discovery rate of new compounds, which should be useful for exploration of a wide chemical space in general. A recommendersystem for chemically relevant composition is constructed by machine learning of Inorganic Crystal Structure Database using chemical com-positional descriptors. Synthesis and identification experiments are made at the chemical compositions with high recommendation scores bythe single-particle diagnosis method. Two new compounds, La4Si3AlN9 and La26Si41N80O, and two new variants (isomorphic substitutions)of known compounds, La7Si6N15 and La4Si5N10O, are successfully discovered. Finally, density functional theory calculations are conductedfor La4Si3AlN9 to confirm the energetic and dynamical stability and to reveal its atomic arrangement.Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0049981I. INTRODUCTIONDiscovery of new high-performance materials often triggersnew technology, which has been one of the central topics of materialsresearch. Although real materials usually consist of multiple phasesand synergistic effects with point defects, dopants, surface, grainboundary, etc., are often crucial to key properties, we focus on thebulk of single-phase compounds in this study as the first step. Thereare at least three types of “new compounds.” The first type of newcompounds are variants of known compounds in a specific field.Isomorphic substitution of elements is a common strategy for thistype. The second type of new compounds are already-known com-pounds in another field which have not been investigated in thefield of concern. A typical strategy for this type is a high-throughputscreening of compounds in databases, such as Inorganic CrystalStructure Database (ICSD),1 International Centre for DiffractionData Powder Diffraction File (ICDD-PDF),2 SpringerMaterials,3Pearson’s Crystal Data,4 Crystallography Open Data (COD),5 andAtomWork-Adv.6 The third type of new compounds are as-yet-unknown compounds having new crystal structures and/or newchemical compositions. Improvement in performance may beachieved by searching the first type of new compounds, whereasbreakthroughs are expected by the discovery of the second and thirdtypes of new compounds. Especially, the discovery of the third typeof new compounds from wide chemical space is quite attractive formaterials researchers. However, no systematic approach has thus farbeen established.Density functional theory (DFT) calculation is one of themost powerful approaches to predict energetics and physical prop-erties. Some databases of computed information are available,such as the Materials Project,7 AFLOW,8 the Open QuantumMaterials Database (OQMD),9 and the Novel Materials DiscoveryJ. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-1Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcphttps://doi.org/10.1063/5.0049981https://www.scitation.org/action/showCitFormats?type=show&doi=10.1063/5.0049981https://crossmark.crossref.org/dialog/?doi=10.1063/5.0049981&domain=pdf&date_stamp=2021-June-14https://doi.org/10.1063/5.0049981http://orcid.org/0000-0002-7090-4430http://orcid.org/0000-0002-2473-3837http://orcid.org/0000-0002-4616-118Xhttp://orcid.org/0000-0002-9381-3603mailto:KOYAMA.Yukinori@nims.go.jphttps://doi.org/10.1063/5.0049981The Journalof Chemical Physics ARTICLE scitation.org/journal/jcp(NOMAD).10 However, it should be emphasized that the major-ity of these databases consist of known compounds. DFT calcula-tions can be routinely made for new compounds of the first andsecond types. For the third type of new compounds, chemical com-positions and crystal structures should be determined before DFTcalculations, and this requires great challenges because of two rea-sons. First, chemically relevant compositions are unknown a priori.Considering vast chemical space, a huge number of compounds areuninvestigated. However, stable compounds are very sparse in thechemical space. According to Villars and Iwata, the average numberof compounds per chemical system is only 3.2 for ternary and 2 forquaternary systems.11 Searching new compounds is like looking fora needle in a haystack. The second challenge is to search the stablecrystal structures for given chemical compositions. Although a fewmethods have been used for searching stable structures,12–16 it is stilla long time-consuming task.Machine learning approaches have been proposed to predictprobable substitution elements for known compounds,17,18 forma-tion energies of arbitrary compositions,19 and chemically relevantcompositions.20,21 These approaches enable systematic prediction ofnew compounds. Suzuki et al.22 succeeded in experimental synthe-sis of new lithium-ion conducting oxides based on machine learningprediction.21 They adopted the conventional synthesis method andpowder x-ray diffraction (XRD) analysis to identify the new com-pounds and successfully found two new compounds. As the com-position of one of the two new compounds was deviated from theexact value by the machine learning prediction, a systematic series ofsynthesis experiments were needed. In the conventional approach,the synthesized sample needs to be mostly composed of a singlephase to identify the composition and crystal structure of the newcompound.In this paper, we adopt the single-particle diagnosis approach23for efficient identification of new crystal structures. In the single-particle diagnosis approach, starting powders are mixed in composi-tions of machine learning prediction and fired under predeterminedconditions. Then, well grown particles of about 10 μm in size arehand-picked in an optical microscope from the fired samples. Aswell-grown particles are usually single crystals, it is not necessaryfor the whole sample to be a single phase at this stage. The pickedparticles are then characterized one by one using scanning elec-tron microscopy energy dispersive x-ray (SEM-EDX) spectroscopyto evaluate ratios of cations, followed by a single-crystal XRD analy-sis to reveal the crystal structures. The ability to identify phases andcrystal structures of single particles even from mixed-phase sam-ples is a great strength of the single-particle diagnosis approach.Hirosaki et al. successfully discovered new phosphor materials usingthis approach.23 We adopted this approach to the LaN–Si3N4–AlNpseudo-ternary system to search new nitrides.II. METHODSA. Machine learningA machine learning model of a compositional descriptor-basedrecommender system was built to evaluate chemical relevance ofcompositions.21 In this study, target compounds were restricted toionic ones with normal oxidation states. The training dataset con-sisted of compositions registered in ICSD as positive cases andcompositions not registered in ICSD as negative cases. Compoundshaving partial occupancy, unusual oxidation states, and more than15 atoms in the chemical formula for any constituent element wereexcluded from the training dataset. The number of positive caseswas 33 367. The negative cases were hypothetical compositions com-posed of 1.3 × 106 pseudo-binary compounds and 2.6 × 106 pseudo-ternary oxides, nitrides, and sulfides. A set of descriptors composedof means, standard deviations, and covariances of 22 types of ele-mental representations were used to describe the compositions. Arandom forest classifier was used. The size of the ensemble of therandom forest classifier was increased to get convergence of pre-diction on a validation dataset, which consisted of pseudo-binaryand pseudo-ternary oxides registered in ICDD-PDF but not reg-istered in ICSD. Finally, the size of the ensemble was 10 000. Theexpectant probabilities as the positive cases were used as recom-mendation scores of the compositions. Other details can be foundin Ref. 21.B. ExperimentsSamples in the LaN–Si3N4–AlN pseudo-ternary system wereprepared by firing a mixture of appropriate amounts of LaN(Kojundo Chemical Laboratory, 3N), Si3N4 (Ube Industries, SN-E10), and AlN (Tokuyama, Type-E) with an additional trace amountof EuN (MATERION, −60 mesh typically 99.9% pure) at 1900 ○C for2 h in 1.0 MPa nitrogen atmosphere using a gas-pressure sinteringfurnace (Fujidempa High Multi 5000). EuN was added to distinguishparticles of different phases by color,23 and the amount of Eu wasfixed at 0.1 at. % of the compositions by the machine learning pre-diction. Nominal contents of oxygen impurity in starting powderswere <2.0 and 0.8 wt. % for Si3N4 and AlN, respectively.The products were characterized by powder XRD using Smart-Lab (Rigaku) with Cu-Kα1 radiation operated at 45 kV and 200 mA.The diffraction patterns were collected at room temperature in a 2θrange of 5○–95○ with a step width of 0.05○. The obtained XRD pat-terns were analyzed using PDXL software (Rigaku) to match phasesagainst known compounds and to refine lattice constants. TheXRD patterns were first matched against known compounds in theLa–Si–Al–N–O system. Oxygen is a probable impurity in real exper-iments introduced from the starting powders or during the synthe-sis process. If a notable amount of unidentified diffraction peaksremained, the patterns were then matched against all compoundsin the pattern library to find variants (isomorphic substitutions) ofknown compounds.Single-crystal XRD data of single particles were collected on aSMART APEX II Ultra diffractometer (Bruker) with Mo-Kα radia-tion and multilayer mirrors as a monochromator, operated at 50 kVand 50 mA. Applied absorption corrections were done usingthe multi-scan procedure SADABS. The structures were solved bydirect methods implemented in SHELX. Refinement of crystal struc-tures was conducted with anisotropic displacement parameters forall atoms by full-matrix least-squares calculation. The elementalanalysis was carried out using a SEM (Hitachi High-TechnologiesSU1510) equipped with an energy dispersive spectroscope (BrukerXFlash SDD) operated at 10 kV.C. DFT calculationsDFT calculations were conducted to investigate discoveredcompounds in detail using the plane-wave basis projectorJ. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-2Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcpThe Journalof Chemical Physics ARTICLE scitation.org/journal/jcpaugmented wave (PAW) method as implemented in theVienna ab initio simulation package (VASP) 6.1.24,25 ThePerdew–Burke–Ernzerhof (PBE) exchange–correlation func-tional26 was used. The cut-off energy was set at 520 eV. The numberof k-points was determined so that the k-point density in the recip-rocal space was more than 100 Å3. The total energy converged to 0.1meV/atom. Atomic positions and lattice constants were optimizeduntil the total energy converged to 1 meV/atom. The dynamicalstability of crystals was examined by harmonic phonon calcula-tions using phonopy code27 with the total energy convergence of10−10 eV/atom and force convergence of 0.01 eV/Å.III. RESULTS AND DISCUSSIONA. Chemical relevance of compositionsFigure 1 illustrates recommendation scores of compositionsin the LaN–Si3N4–AlN pseudo-ternary system. In this pseudo-ternary system, LaN, Si3N4, AlN, LaSi3N5, La3Si6N11, La5Si3N9, andLa17Si9Al4N33 are registered in ICSD. La17Si9Al4N33 is registeredbut not used to build the machine learning model because of itscomplex composition. The machine learning model suggested var-ious compositions having relatively high recommendation scores,especially for La-rich compositions. However, to our experience,La-rich nitrides are often unstable in the ambient atmosphere, andit is difficult to characterize samples by the single-particle diagno-sis. Therefore, we set our experimental target to compositions inwhich La atoms are fewer than or equal to sum of Si and Al atoms,La/(Si + Al) ≤ 1. Top 15 recommended compositions are summa-rized in Table I. They are seven LaN–Si3N4 pseudo-binary, twoLaN–AlN pseudo-binary, and six LaN–Si3N4–AlN pseudo-ternarycompositions.B. Powder XRD analysisTable I summarizes sample compositions and identified can-didate phases by powder XRD analysis. Most of samples exhibitedFIG. 1. Chemically relevant compositions in the LaN–Si3N4–AlN pseudo-ternarysystem. Closed circles correspond to compositions with non-zero recommendationscores as indicated by colors. Large circles indicate top 15 recommended compo-sitions with notations of their ranks (see also Table I). Small dots are compositionswhose scores are zero. Black triangles are compositions that are registered inICSD and used to build the machine learning model.peaks that could not be identified, apart from the amount. Thoseminor unidentified diffraction peaks are not shown in Table I. Mostof the identified candidate phases are already known compoundsin the LaN–Si3N4–AlN pseudo-ternary system, namely, LaN, Si3N4,AlN, LaSi3N5, and La3Si6N11. In addition to these nitrides, twoknown oxynitrides, LaSiNO2 and La11Si13N27.64O1.04, were identi-fied. Oxygen impurity must be introduced from the starting powdersor during the synthesis process. Seven samples, namely, No. 1, No.4, No. 8, No. 9, No. 11, No. 12, and No. 15, were shown as mixturesof these known compounds. La/(Si + Al) ratios in the products ofTABLE I. Top-15 recommended compositions, corresponding recommendation scores, and identified candidate phases by powder XRD analysis.Rank and sample number Composition Recommendation score Identified candidate phases1 La1 Al1 N2 0.054 LaN, AlN2 La4 Si9 N16 0.042 LaSi3N5, La3BaSi5N9O2, La3Si6N113 La3 Si3 N7 0.032 La11Si13N27.64O1.04, Ce7Si6N154 La5 Si6 N13 0.018 La11Si13N27.64O1.045 La4 Si3 Al1 N9 0.014 No identified phase6 La5 Si3 Al2 N11 0.014 No identified phase7 La2 Si3 Al1 N7 0.012 La3BaSi5N9O2, La3Si6N11, La26−xSrxSi41Ox+1N80−x8 La1 Si6 N9 0.010 LaSi3N5, Si3N49 La2 Si3 N6 0.010 La3Si6N11, La11Si13N27.64O1.04, LaSiNO210 La5 Si9 N17 0.010 La3Si6N11, La3BaSi5N9O211 La7 Si15 N27 0.010 LaSi3N5, La3Si6N11, LaN12 La1 Al2 N3 0.010 AlN, LaN13 La5 Si9 Al1 N18 0.010 La3Si6N11, La3BaSi5N9O214 La7 Si6 Al1 N16 0.010 La11Si13N27.64O1.04, Ce7Si6N1515 La7 Si12 Al1 N24 0.008 La3Si6N11, LaSi3N5J. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-3Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcpThe Journalof Chemical Physics ARTICLE scitation.org/journal/jcpthe seven samples were estimated from the powder XRD analysis,which were found to be comparable to those in the starting pow-ders. The identified candidate phases were confirmed to be existent.Sample No. 15 was found as a mixture of La3Si6N11 and LaSi3N5,whereas the starting powders contained Al. It is well known thatsilicon (oxy)nitrides often form solid solutions, as exemplified inSiAlON, in which Al and O atoms substitute for Si and N atoms,respectively.28,29 It is likely that one or both of the identified phasesform solid solutions. The products of sample No. 7, No. 13, and No.14 may also contain solid solutions with Al and O.By the powder XRD analysis, three other candidate phases wereidentified: La3BaSi5N9O2 in sample No. 2, No. 7, No. 10, and No. 13,Ce7Si6N15 in sample No. 3 and No. 14, and La26−xSrxSi41Ox+1N80−xin sample No. 7. As Ba, Ce, and Sr are unlikely introduced as impu-rities, the products are most probably new variants of the candi-date phases, namely, La4Si5N10O, La7Si6N15, La26Si41N80O, and theirsolid solutions with Al and O.The first candidate, La4Si5N10O, had an orthorhombic struc-ture of space group Pmn21 (No. 31). Lattice constants of La4Si5N10Oin sample No. 10 were refined as a = 9.4772(14) Å, b = 19.116(3) Å,c = 12.0804(16) Å, and V = 2188.5(6) Å3. The lattice constants a andc are slightly (less than 1%) smaller than those of La3BaSi5N9O2,30whereas the lattice constant b is slightly larger. The cell volume isslightly smaller than that of La3BaSi5N9O2.The second candidate, La7Si6N15, had a high recommendationscore of 0.040. As a matter of fact, A7Si6N15 (A = La, Ce, and Pr)have been reported by Schmolke et al.31 La7Si6N15 is not registeredin ICSD, but Ce7Si6N15 and Pr7Si6N15 are registered and used tobuild the machine learning model. This composition was, however,excluded from the experimental target because of the larger La/Siratio than 1.The third candidate, La26Si41N80O, was a valiant ofLa26−xSrxSi41Ox+1N80−x (x = 12.72–12.90) reported by Zhanget al. in 2020.32 The original phase, La26−xSrxSi41Ox+1N80−x, is notyet registered in ICSD, but it has been registered in our in-housepattern library. Therefore, it was identified by the powder XRDanalysis. It should be noted that the Sr/La ratio in Ref. 32 is0.958–0.985 and is quite different from zero in this study. Its struc-ture is hexagonal of space group P6 (No. 174). The lattice constantsof this phase in sample No. 7 were refined as a = 17.3738(18) Å,c = 22.500(3) Å, and V = 5881.6(12) Å3. The lattice constant a ofthis phase is almost the same as that of La13.1Sr12.9Si41O13.9N67.1,whereas the lattice constant c and the cell volume are slightly larger.The solubility of Al and O was not analyzed, but this phase wouldbe a solid solution with Al and O.C. Single-particle diagnosisThe powder XRD analysis identified no known phases in sam-ple No. 5 and No. 6. Therefore, single-particle diagnosis was adoptedto these samples. The diagnosed particle of sample No. 5 was8 × 10 × 10 μm3 in size, as shown in Fig. 2(a). The measured ratioof cations by SEM-EDX analysis was La:Si:Al = 44.3:42.5:13.2 (at. %).The amount of Eu was below the detection limit. The measured Si/Alratio (3.22) is in good agreement with the ratio of the starting pow-ders, whereas the measured La/(Si + Al) ratio (0.797) was somewhatsmaller than the ratio of the starting powders. This may be due tothe large energy difference between the La-L line and the Si- andFIG. 2. (a) The diagnosed particle taken from sample No. 5 supported on a needleand (b) a schematic view of the crystal structure of La4Si3AlN9 from the a-axisdirection. The b-axis is horizontal, and the reciprocal lattice vector of c∗is vertical.Light and dark blue tetrahedra represent (Si/Al)N4 at the Si/Al1 and Si/Al2 sites,respectively. Large green spheres and small light-blue spheres represent La andN atoms, respectively.Al–K lines used in the SEM-EDX analysis. The chemical composi-tion may not have been calibrated correctly. The Si/Al ratio of thisnew phase will be hereafter assumed as the ratio of the starting pow-ders (3). Based on the single-crystal XRD analysis, the particle wasidentified to be La4Si3AlN9 having a new monoclinic structure ofspace group P21/c (No. 14) with a = 6.7353(5) Å, b = 5.5648(4) Å,c = 12.8828(9) Å, β = 105.4423(13)○, V = 465.42(6) Å3, andZ = 2 with R = 2.2%, wR = 4.3%, and S = 1.03. The crystal struc-ture data are summarized in Table II and the supplementary material(S1 and S2). A schematic view of the crystal structure is illustrated inFig. 2(b). Here, Si and Al atoms were assumed to share the samesites with random distribution. This structure accommodates twotypes of La sites, two types of Si/Al sites, and five types of N sites.Both of the two symmetrically inequivalent La sites are coordinatedto seven N atoms. Si/Al sites are coordinated to four N atoms, and(Si/Al)N4 tetrahedra are linked via common corners. The powderXRD pattern of sample No. 5 can be fitted well using this structureonly.The powder XRD pattern of sample No. 6 can be fittedusing the structure of La4Si3AlN9. The refined lattice constants area = 6.7293(5) Å, b = 5.5659(4) Å, c = 12.8598(9) Å, β = 104.731(3)○,and V = 465.82(6) Å3. As the Si/Al ratio of the starting powders isdifferent between sample No. 5 and No. 6, this phase might forma solid solution with Al and O. However, the lattice constants arealmost the same, and minor unidentified diffraction peaks remainedin the powder XRD pattern of sample No. 6. Further study isnecessary to identify the origin of the unidentified peaks and toevaluate the solubility of Al and O in La4Si3AlN9. La4Si3AlN9 wasalso identified in the powder XRD pattern of sample No. 14.J. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-4Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcphttps://www.scitation.org/doi/suppl/10.1063/5.0049981The Journalof Chemical Physics ARTICLE scitation.org/journal/jcpTABLE II. Crystal structure data of La4Si3AlN9. Space group P21/c (No. 14), a = 6.7353(5) Å, b = 5.5648(4) Å, c = 12.8828(9)Å, β = 105.4423(13)○, V = 465.42(6) Å3, and Z = 2.Site Wyckoff x y z U iso (Å2) Occupancy (<1)La1 4 e 0.305 54(3) 0.691 04(3) 0.048 56(2) 0.008 69(4)La2 4 e 0.121 57(3) 0.211 49(3) 0.206 12(2) 0.006 51(4)Si1 4 e 0.165 88(14) 0.326 34(16) 0.447 98(7) 0.004 57(15) 0.75Al1 4 e 0.165 88(14) 0.326 34(16) 0.447 98(7) 0.004 57(15) 0.25Si2 4 e 0.551 24(15) 0.157 65(17) 0.177 46(8) 0.007 25(17) 0.75Al2 4 e 0.551 24(15) 0.157 65(17) 0.177 46(8) 0.007 25(17) 0.25N1 4 e 0.374 6(5) 0.251 2(5) 0.052 1(2) 0.010 1(5)N2 4 e 0.232 3(4) 0.528 6(5) 0.358 2(2) 0.008 8(5)N3 4 e 0.041 3(5) 0.079 0(5) 0.383 5(2) 0.010 5(5)N4 4 e 0.571 7(5) 0.417 6(6) 0.263 5(3) 0.013 3(6)N5 2 a 0 0 0 0.009 2(7)D. DFT calculations on La4Si3AlN9In the single-crystal XRD analysis on La4Si3AlN9, Si and Alatoms were assumed to share the same sites with random distri-bution, since it is difficult to distinguish these two elements byXRD. However, the two sites have considerably different distancesto the coordinating N atoms: 1.71–1.76 Å of the Si/Al1 site, whereas1.79–1.84 Å of the Si/Al2 site. This implies that the Si and Al distri-bution is not random and the larger Al ions preferentially occupythe Si/Al2 site. Therefore, DFT calculations on La4Si3AlN9 wereconducted to analyze the distribution of Si and Al atoms.There are ten symmetrically distinct configurations of Si andAl atoms within the unit cell of La4Si3AlN9. Figure 3(a) illustratesthe DFT total energies of these configurations with respect to thenumber of Al atoms at the Si/Al1 site. As more Al atoms occupy theSi/Al1 site, the energy becomes higher. Therefore, Al atoms likelyoccupy the Si/Al2 site only. This is consistent with the distances tothe coordinating N atoms as mentioned above.Among the three configurations in which all Al atoms occupythe Si/Al2 site, two of them have almost the same energy, whereasthe other has considerably high energy. Hence, the Si and Al con-figurations at the Si/Al2 site was additionally investigated using2 × 1 × 1 and 1 × 2 × 1 supercells. There are 11 and 10 symmetri-cally distinct irreducible configurations for the 2× 1× 1 and 1× 2× 1supercells, respectively, assuming that all Al atoms occupy the Si/Al2site. (Si/Al)N4 tetrahedra at the Si/Al2 site are one-dimensionallylinked to each other via common corners of the N4 site along theb-axis direction [see Fig. 2(b)]. Figure 3(b) illustrates the DFT totalenergies of all the configurations with respect to the number ofAlN4–AlN4 links at the Si/Al2 site, which is equal to the num-ber of SiN4–SiN4 links at the Si/Al2 site. Configurations with noAlN4–AlN4 link are in the lowest energy group and have almostthe same energies. As the number of AlN4–AlN4 links increases, theenergy becomes higher. These calculation results suggest that Si andAl atoms alternately occupy the Si/Al2 site on the one-dimensionallinks along the b-axis direction. In contrast to this one-dimensionalordering, the configuration of Si and Al atoms on different links isprobably random.Harmonic phonon calculations were conducted on La4Si3AlN9with the lowest energy configuration of Si and Al atoms within theFIG. 3. (a) DFT total energy of La4Si3AlN9 with a variety of configurations of Si andAl atoms within the unit cell with respect to the number of Al atoms at the Si/Al1site, and (b) DFT total energy within the unit cell, 2× 1× 1 supercell, and 1× 2× 1supercell with respect to the number of AlN4–AlN4 links at the Si/Al2 site per unitcell assuming that all Al atoms occupy the Si/Al2 site. The marks are jittered inthe horizontal axes to avoid overlaps. Energies are relative to the lowest energyconfiguration.J. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-5Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcpThe Journalof Chemical Physics ARTICLE scitation.org/journal/jcpunit cell, which is also lower in energy than the other configura-tions within the 2 × 1 × 1 and 1 × 2 × 1 supercells. The structureof La4Si3AlN9 optimized by the DFT calculation with the lowestenergy configuration of Si and Al atoms is supplied as a crystallo-graphic information file (CIF) of the supplementary material (S3).The phonon dispersion curves exhibit no phonon mode with imag-inary frequency, as shown in Fig. S1 in the supplementary material,indicating that La4Si3AlN9 is dynamically stable.E. Discussion15 compositions in the LaN–Si3N4–AlN pseudo-ternary sys-tem by the machine learning prediction were experimentally val-idated. As a result, four new compounds, La4Si3AlN9, La7Si6N15,La4Si5N10O, and La26Si41N80O, have been discovered. They mightform solid solutions in which Al and O atoms substitute for Si andN atoms, respectively, although the solubility has not been ana-lyzed in detail in this study. La7Si6N15 and La4Si5N10O are vari-ants (isostructural substitutions) of already registered compoundsin ICSD, whereas La4Si3AlN9 and La26Si41N80O have no similar-structural compounds in ICSD. The yield to discover new com-pounds is notably high. The success of this study demonstratespowerfulness of the proposed approach.The new compound La4Si3AlN9 discovered by the experimen-tal validation has the exact composition by the machine learningprediction. The chemical compositions of AB3C4X9 are quite rare inICSD. They can be found only for borates, such as NaCa4B3O9; sil-icates and germanates, such as K4CaSi3O9; and copper oxides, suchas YBa4Cu3O9. It is therefore hard to imagine the unusual compo-sition of La4Si3AlN9 to be chemically relevant without the machinelearning prediction.FIG. 4. Phase diagram of the LaN–Si3N4–AlN pseudo-ternary system based onthe DFT total energies, which is overlaid on the chemically relevant compositionmap shown in Fig. 1.In the experimental validation, the poor fitting of the powderXRD patterns only with known compounds in a pattern library is apromising indication of the presence of new compounds, as in sam-ple No. 5 and No. 6. Fortunately, we have obtained almost single-phase products in these samples. It is, however, hard to know, ingeneral, whether the sample is a single phase or not, unless the com-position and crystal structure of the new compound are known. Thishas been a dilemma in the search of new compounds. The single-particle diagnosis is extremely helpful in such a situation, since thisapproach does not require single-phase products in contrast to theconventional powder XRD analysis.From the DFT total energies of La4Si3AlN9 and other nitridesin the LaN–Si3N4–AlN pseudo-ternary system, the phase diagramof this pseudo-ternary system is illustrated in Fig. 4. Computed for-mation energies of La4Si3AlN9 and the known nitrides are listed inTable S1 in the supplementary material. La4Si3AlN9 is located onthe energy convex hull, indicating that it is energetically stable evenwithout consideration of configurational entropy associated with themixture of Si and Al atoms.IV. CONCLUSIONWe have proposed a new approach to search new com-pounds, in which chemical relevance of compositions is predictedby machine learning and the prediction is validated by experi-ments using the single-particle diagnosis. The proposed approachhas been adopted to the LaN–Si3N4–AlN pseudo-ternary system,and four new compounds, La4Si3AlN9, La7Si6N15, La4Si5N10O, andLa26Si41N80O, have been discovered. They might form solid solu-tions in which Al and O atoms substitute for Si and N atoms, respec-tively. The yield to discover new compounds in this study is notablyhigh. The success of this study demonstrates the powerfulness of theproposed approach to search new compounds.The new compound, La4Si3AlN9, was found to be energeticallyand dynamically stable by the DFT calculations. It was suggestedthat Al atoms preferentially occupy the Si/Al2 site and that Si andAl atoms are arranged alternately.SUPPLEMENTARY MATERIALSee the supplementary material for the detailed crystallographicdata and two CIFs for La4Si3AlN9 that are determined by the exper-imental analysis and optimized by the DFT calculation with thelowest energy configuration of Si and Al atoms within the unit cell.Phonon dispersion curves of La4Si3AlN9 with the lowest energyconfiguration by the DFT calculation and formation energies ofLa4Si3AlN9 and the known nitrides in the LaN–Si3N4–AlN pseudo-ternary system by the DFT calculation are also included in thesupplementary material.ACKNOWLEDGMENTSThis work was supported, in part, by the Japan Science andTechnology Agency (JST), CREST Grant No. JPMJCR19J2, and the“Materials Research by Information Integration” Initiative (MI2I)of the Support Program for Starting Up Innovation Hub. Y.K.acknowledges financial support from the Japan Society for theJ. Chem. Phys. 154, 224117 (2021); doi: 10.1063/5.0049981 154, 224117-6Published under an exclusive license by AIP Publishinghttps://scitation.org/journal/jcphttps://www.scitation.org/doi/suppl/10.1063/5.0049981https://www.scitation.org/doi/suppl/10.1063/5.0049981https://www.scitation.org/doi/suppl/10.1063/5.0049981https://www.scitation.org/doi/suppl/10.1063/5.0049981https://www.scitation.org/doi/suppl/10.1063/5.0049981The Journalof Chemical Physics ARTICLE scitation.org/journal/jcpPromotion of Science (JSPS) KAKENHI (Grant No. JP18K04716).The DFT calculations in this study were performed on theNumerical Materials Simulator at National Institute for MaterialsScience.DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1Inorganic Crystal Structure Database (ICSD), FIZ Karlsruhe GmbH, Germany.2International Centre for Diffraction Data Powder Diffraction File (ICDD-PDF),JCPDS-International Centre for Diffraction Data, USA.3SpringerMaterials, Springer Nature Switzerland AG, Switzerland.4Pearson’s Crystal Data: Crystal Structure Database for Inorganic Compounds,ASM International, USA.5S. 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