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Koichi Kitahara, Hiroyuki Takakura, [Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), [Kaoru Kimura](https://orcid.org/0000-0001-5050-4256)

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[Phase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 Kelvin](https://mdr.nims.go.jp/datasets/8383a6e0-33a6-4968-ae23-83ec93990042)

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Phase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 KelvinPhase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 KelvinKoichi Kitahara1,2,+1, Hiroyuki Takakura3, Yutaka Iwasaki2,4,+2 and Kaoru Kimura2,4,+31Department of Materials Science and Engineering, School of Electrical and Computer Engineering, National Defense Academy,Yokosuka 239-8686, Japan2Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan3Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan4National Institute for Materials Science (NIMS), Tsukuba 305-0047, JapanA narrow-gap semiconductor with a complex crystal structure was recently discovered in the Al–Ru–Si system. To determine thehomogeneity range of the semiconductor phase and further discover new phases, phase equilibria in the Al–Ru–Si system near 1200K wereinvestigated through prolonged-annealing experiments. Eleven new ternary phases including two incommensurate composite-crystalline and anicosahedral quasicrystalline phases were identified using powder and single-crystal X-ray diffraction, and their compositions at two-phase andthree-phase equilibria were evaluated by means of electron-probe X-ray microanalysis. On the basis of the data obtained in this study and thoseadopted from the literature, a tentative isothermal section of the Al–Ru–Si equilibrium phase diagram near 1200K was drawn.[doi:10.2320/matertrans.MT-M2023128](Received August 16, 2023; Accepted October 16, 2023; Published December 25, 2023)Keywords: aluminium–ruthenium–silicon system, phase equilibrium, crystal structure, composition, prolonged annealing, X-ray diffraction,electron-probe X-ray microanalysis, matrix correction, incommensurate composite crystal, quasicrystal1. IntroductionSemiconductors with complex crystal structures haveattracted interest primarily from thermoelectrics because anintrinsically low lattice thermal conductivity is expected fora complex-structure material.1–4) Recently, a narrow-gap[approximately 24 zJ (0.15 eV)] semiconductor with acomplex crystal structure (Pearson symbol ³cP31, i.e.approximately 31 atoms per unit cell) was discovered inthe Al–Ru–Si system near the composition Al67.6Ru23.5Si8.95)(referred to as the C phase following the nomenclature ofGrushko and Velikanova6)), and its thermoelectric propertieswere investigated through copper doping.7) The latticethermal conductivity of the C phase at temperatures aboveroom temperature is approximately 1Wm¹1 K¹1, which is aslow as that of glass.5,7) The carrier concentration in the Cphase can be optimized through copper doping, but thebandgap seems to be narrowed simultaneously, which leadsto a decrease in the thermopower compared to the oneexpected from theoretical calculations based on the rigid-band approximation.7) The carrier concentration may beoptimized without doping other elements, avoiding signifi-cant change in the bandgap, by changing the compositionwithin the Al–Ru–Si system, but the phase equilibriainvolving and the homogeneity range of the C phase shouldbe determined prior to such experiments.In the binary Al–Ru and Ru–Si systems, there also existnarrow-gap semiconductors, i.e. RuAl2 [Pearson symboloF24,8) bandgap (or pseudogap) of approximately 21 zJ(0.13 eV)9)], RuSi(cP8) [cP8,10) 42 zJ (0.26 eV)11)] andRu2Si3(o) [oP40,12) 0.1 aJ (0.7 eV)13)]. Given this fact,existence of other narrow-gap semiconductors in the Al–Ru–Si system is simply expected. However, information ofternary phases in this system was scarce. Only three ternaryphases were found in the literature as described below.Nowotny and coworkers14–16) mentioned the Ru(Al,Si)2¹xphase with the two compositions Ru(Al0.2Si0.8)2¹x andRu(Al0.5Si0.5)2¹x (the value of x is not reported). Althoughthe crystal structure (even the unit-cell parameters) was notdetermined completely, the Ru(Al,Si)2¹x phase is considereda variant of the Ru2Si3(o) phase and hence falls into so-calledNowotny chimney ladder (NCL) phases,17) which alsoinclude the RuAl2 phase mentioned above. Since manyNCL phases including the RuAl2 and Ru2Si3(o) phases aresemiconducting,9,13,18,19) and the crystal structure of someNCL phases are complex,20–22) Ru(Al,Si)2¹x may also be asemiconductor with a complex crystal structure.The C phase mentioned above was first discovered nearthe composition Al69Ru23Si8 by Koshikawa et al.,23) but onlya powder X-ray diffraction (XRD) pattern was reported atthat time. This phase was recently rediscovered in the courseof searching for semiconducting quasicrystals and relatedcrystals (so-called crystalline approximants) employing aband-engineering technique and confirmed to be a semi-conductor.5) The C phase is regarded as a cubic 1/0 rationalcrystalline approximant24) to an icosahedral quasicrystal.23)Since a quasicrystal and its approximants often exist in aclose compositional region6) and show similar transportproperties,25–27) there may exist semiconducting quasicrystal-line and other approximant crystalline phases near thecomposition of the C phase.Morrison et al.28) grew some single crystals ofRu23(Al,Si)97 with compositions approximately ranging fromAl73Ru20Si7 to Al68Ru19Si13 and determined its complexcrystal structure (Pearson symbol hP240) using single-crystalXRD. Here, this phase is referred to as the χA phase becausethe crystal structure is quite similar to that of the Ir9Al28 phase(Pearson symbol ³hP22229)), which is referred to as the χphase in the nomenclature of Grushko and Velikanova.6) The+1Present address: National Defense Academy, Yokosuka 239-8686, Japan+2Graduate Student, The University of Tokyo. Present address: NationalInstitute for Materials Science (NIMS), Tsukuba 305-0047, Japan+3Present address: National Institute for Materials Science (NIMS),Tsukuba 305-0047, JapanMaterials Transactions, Vol. 65, No. 1 (2024) pp. 18 to 26©2023 The Japan Institute of Metals and Materialshttps://doi.org/10.2320/matertrans.MT-M2023128χA phase may be regarded as an approximant to a decagonalquasicrystal similarly to the χ phase.29)Although the majority of the Al–Ru–Si system wasunexplored, some phases with interesting characteristicshad already been discovered as described above. In thisstudy, phase equilibria in the Al–Ru–Si system near 1200Kwere thoroughly investigated through prolonged-annealingexperiments. The choice of 1200K is a compromise betweena lower annealing temperature and a shorter annealing time.2. MethodsAlloy samples of desired nominal compositions wereprepared from powders of aluminium (Kojundo ChemicalLab. Co., Ltd., Japan, 99.9%), ruthenium (Tanaka KikinzokuKogyo K.K., Japan, 99.90% or purer) and silicon (KojundoChemical Lab. Co., Ltd., Japan, 99.99% or purer) usingarc melting in an argon atmosphere (NEV-ACD-05, NissinGiken Corporation, Japan). Each sample was then wrapped ina tantalum or graphite sheet, sealed in a silica tube filled withargon and annealed in a furnace at 1200K for approximatelyfrom 114 h to 331 h, followed by water quenching. As thisstudy was a long-term study spanning approximately a year(for annealing experiments only), the thermocouples of thefurnaces could be deteriorated and damaged. During thisstudy period, we repeatedly evaluated temperature deviationsfrom the set temperature and temperature differences amongdifferent positions for each furnace using the Referthermoreference materials (Japan Fine Ceramics Center, Japan), andan uncertainty of at most 50K or larger should be assumedfor the annealing temperature. Samples that partly meltbelow 1200K were placed in aluminium nitride cruciblesinstead of tantalum and graphite sheets. Samples forinvestigating phase equilibria were annealed at least twiceto check for any significant changes in constituent phases andtheir unit-cell parameters by comparing powder XRD peakpositions. This condition should imply equilibrium for mostcases, but some samples remained nonequilibrium even inthis condition, particularly for ruthenium-rich samples (seeSecs. 3.1 and 3.4).Depending on the alloy composition, samples can becomehighly inhomogeneous during solidification. To improvehomogeneity, the following processes were used for somesamples before annealing. Some samples were crushed intopowders after melting and then compacted using pulsedelectric current sintering with a uniaxial pressure ofapproximately 90MPa in an argon atmosphere (SPS-515S,Sumitomo Coal Mining Co., Ltd., Japan). The maximumtemperature during a sintering was approximately 1230K orlower. Some other samples were prepared by just mechan-ically compacting powders without melting. Note that theseprocesses were not always sufficient for improving homoge-neity, and some samples remained inhomogeneous even afterthese processes (see Sec. 3.1 for examples).Phases in the samples were identified using powder XRD(SmartLab, Rigaku Corporation, Japan; D8 ADVANCE,Bruker Corporation, USA; Cu K–L2,3 radiation), and thecomposition of each phase was analysed by means ofelectron-probe X-ray microanalysis using the energy-dispersive spectrometer (EDS) equipped in a scanningelectron microscope (SEM) (JSM-6010LA, JEOL Ltd.,Japan). For the composition analyses, pure elementalsubstances (JEOL Ltd., Japan) were used as standardmaterials, and the Armstrong/Love–Scott model30–32) wasused to correct for the matrix effects, which gives reasonablecompositions for stoichiometric phases in the Al–Ru andRu–Si systems (see Sec. 3.1 and Table 3). The unit-cellparameters were evaluated using the Le Bail method33) withthe Jana2006 software34) for selected samples.The crystal structure was determined using single-crystalXRD (XtaLAB Synergy-R, Rigaku Corporation, Japan;Mo K–L2,3 radiation) if a sufficiently large single crystalcould be obtained. Single crystals were either selected fromcrushed fragments of the samples described above or grownusing the self-flux method. For the flux growth, alloy samplesof desired compositions were prepared from ingots ofaluminium (The Nilaco Corporation, Japan, 99.999%),ruthenium (Rare Metallic Co., Ltd., Japan, 99.95%) andsilicon (Rare Metallic Co., Ltd., Japan, 99.9999%) using arcmelting in an argon atmosphere (NEV-AD03, Nissin GikenCorporation, Japan). Each sample was then placed in analumina crucible and sealed in a silica tube in an argonatmosphere. The tube was then heated to 1473K in a furnace,then cooled at ¹2K/h to a desired temperature (1223K,1273K or 1323K), then kept at the desired temperature for10 h and then centrifuged, followed by water quenching. Datacollection, cell refinement and data reduction were performedusing CrysAlis PRO software (Rigaku Oxford Diffraction).35)Initial structural models were obtained using SHELXTsoftware,36) and subsequent structure refinement wasperformed using SHELXL software.37)3. Results and DiscussionAfter investigating several tens of samples, compositionalregions of three-phase equilibria in the Al–Ru–Si system near1200K were preliminarily determined. Samples that wouldfall into desired phase equilibria were then prepared toevaluate the composition and unit-cell parameters of eachphase involved in each equilibrium. Eight two-phase and 23three-phase equilibria (from one to three samples for eachequilibrium) were investigated. Figure 1 shows the tentativeisothermal section of the Al–Ru–Si equilibrium phasediagram near 1200K drawn on the basis of the data obtainedin this study and those adopted from the literature. Thenominal compositions of the samples are also shown inFig. 1. They are basically on the tie lines for two-phaseequilibria and inside the tie triangles for three-phaseequilibria. For some aluminium-rich samples, they were setat compositions out or on the boundary of the tie trianglesto compensate for possible evaporation loss of aluminium (orsilicon) during arc melting and annealing. Crystallographicdata of the solid phases observed in this study throughpowder XRD are summarized in Table 1. The compositionand unit-cell parameters evaluated for each phase involvedin each equilibrium are summarized in Table 2.3.1 Phase equilibria in the binary systemsThree two-phase equilibria (No. 1–3 in Table 2) wereinvestigated in the binary Al–Ru system, which involve thePhase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 Kelvin 19Ru4Al13, RuAl2, Ru2Al3 and RuAl(cP2) phases (referred to asthe β1, β2, β3 and β4 phases, respectively). According to therecent Al–Ru equilibrium phase diagrams,43–45) there existthe liquid and Ru phases [referred to as the L and (Ru)phases, respectively] at 1200K in addition to the abovephases. In the samples for the β2–β3 equilibrium (No. 2), aFig. 1 Tentative isothermal section of the Al–Ru–Si equilibrium phase diagram near 1200K. Provisional single-phase regions are shownas the black regions with the boundaries shown as the white dotted lines. Tie lines are shown as either solid (confirmed) or dashed(provisional) lines. Three-phase regions are shown as the grey regions (confirmed or provisional in accordance with the surrounding tielines). The numbers written either inside or near two-phase and three-phase regions correspond to those defined in Table 2. The nominalcompositions of the samples are shown as the open circles.Table 1 Symbols, prototypes (if available), Pearson symbols, (super)space groups of the solid phases in the Al–Ru–Si system observed inthis study through powder XRD.K. Kitahara, H. Takakura, Y. Iwasaki and K. Kimura20minor β4 phase was observed in powder XRD and SEM,which may have primarily crystallized from melt duringsolidification and remained even after a long-time annealing.The existence of the primary β4 phase indicates that thesesamples are inhomogeneous and not fully in equilibrium, andthe homogeneity could not be improved even after sinteringprocesses. The compositions of the β2 and β3 phases wereanalysed at regions far from the β4 phase in these samples.The compositions of the β1, β2 and β3 phases are consistentwith their stoichiometry and those reported in the recentphase diagrams.43–45) The composition of the β4 phase atthe β3–β4 equilibrium (No. 3) is consistent with that givenin Gobran et al.44) The composition of the β4 phase at theβ4–(Ru) equilibrium (not investigated in this study) wastherefore adopted from Gobran et al.44) in drawing Fig. 1.The other compositions [L at L–β1 and (Ru) at β4–(Ru)] wereadopted from Liu et al.45)Three two-phase equilibria (No. 4–6 in Table 2) wereinvestigated in the binary Ru–Si system, which involve theRu, RuSi(cP2), RuSi(cP8), Ru2Si3(o) and Si phases [referredto as the (Ru), β4, β5, β6 and (Si) phases, respectively]. Thephase equilibria and the associated compositions in the Ru–Sisystem are essentially consistent with those reported byPerring et al.46) although the reported compositions aresystematically deficient in silicon. They attributed thisdeficiency to the PAP model,47) which they used for thematrix correction. Table 3 shows the compositions of thestoichiometric phases in the Al–Ru and Ru–Si systems (β1,β2, β3, β5 and β6) evaluated using different matrix correctionmodels. While the compositions evaluated using the PAPmodel are systematically deficient in aluminium or silicon,those evaluated using the Armstrong/Love–Scott model(adopted in this study) are consistent with the stoichiometry.The reason why the Armstrong/Love–Scott model givesbetter compositions for these phases than the PAP model isunder investigation.In the sample for the (Ru)–β4 equilibrium (No. 4), a minorphase with the composition Ru57(2)Si43(2) was observed onlyin SEM; thus, this sample is not fully in equilibrium. Theminor phase may be identified as the Ru4Si3 phase from thecomposition. According to Perring et al.,46) existence ofthe Ru4Si3 phase below 1473K is questionable. Possibleexistence of the Ru4Si3 phase near 1200K is indicated inFig. 1 by “Ru4Si3?”. Note that Liu et al.48) and Du et al.49)also reported phase diagrams of the Ru–Si system, and theRu4Si3 phase exists at 1200K as an equilibrium phase intheir phase diagrams. However, their phase diagrams werederived in terms of thermodynamic assessment of availableexperimental data, mainly those given by Perring et al.;46)Table 2 Composition and unit-cell parameters (a, b, c, ¢ and £ = c/cA) ofeach phase at each equilibrium.Continued on next column:Continued:a Not fully in equilibrium.b Analysable grains could not be found in SEM.c Probably crystallized from the L phase during cooling.d Not determined.e Probably transformed from the P phase during cooling.f The P and I phases could not be distinguished in SEM.Phase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 Kelvin 21thus, the existence of the Ru4Si3 phase at 1200K in theirphase diagrams has not been justified experimentally.Solution of silicon in the (Ru) phase of 2.6(3)% wasobserved in this sample. By comparing this to the solubilitydata given by Perring et al.,46) the actual annealing temper-ature may be estimated to be near 1473K. However, thismuch higher temperature than 1200K is unrealisticconsidering our experimental set-up. Instead, it may beanother evidence that this sample is not fully in equilibrium.The RuSi2 phase reported by Ivanenko et al.50) was notobserved in this study. Note that occurrence of the twoRuSi phases (β4 and β5) at different compositions, which isconsistent with Perring et al.’s observation,46) is not reflectedin the recent thermodynamic assessments48,49) and compila-tion51) of the Ru–Si system.No phase equilibria were investigated in the binary Al–Sisystem. According to Murray and McAlister,52) there existonly the L and (Si) phases at 1200K. Compositions adoptedfrom Murray and McAlister52) were used in drawing Fig. 1.3.2 Ternary solid solutions in the binary phasesSolution of silicon in the Al–Ru binary phases (β1, β2,β3 and β4) were observed in ten equilibria (No. 7–16 inTable 2). From the compositions, these solutions seem to besubstitutional (silicon for aluminium) with small variation inthe ruthenium fraction for the β4 phase. The solubility limitsof silicon in the β1, β2 and β3 phases are approximately 2%,5% and 22%, respectively. The β4 phase seems to be acomplete solid solution between RuAl(cP2) and RuSi(cP2).The unit-cell lengths in these phases basically decreasewith increasing silicon fraction (see Table 2). An obviousexception is the length b in the β1 phase, which roughlyincreases with increasing silicon fraction. Solution ofaluminium in the β5 phase was observed in one equilibrium(No. 16 in Table 2) with a low solubility limit ofapproximately 0.5%.An extension of the β6 phase (referred to as �06 or �006depending on the composition) in the Al–Ru–Si system wasobserved in eight equilibria (No. 11, 12, 15–20 in Table 2).The crystal structure of the β6 phase is of the Ru2Ge3 type(see Table 1), and the Ru2Ge3 type with the space-groupsetting Pnca is a 1 © 2 © 1 superstructure of the Ru2Sn3type.53) For the β6 phase, an XRD peak indexed as hkl withk = 2n + 1 (n is an integer) corresponds to a superstructurereflection. Figure 2 shows powder XRD patterns taken fromsamples at the β6–(Si), �06–(Si) and β3–β4–�006 equilibria(No. 6, 17 and 15, respectively). The aluminium fractionin the β6, �06 and �006 phases increases in this order. Whilesuperstructure reflections were observed for the β6 and �06phases, no such reflections were observed for the �006 phase.Most of the peaks due to the �06 and �006 phases shift towardlower angles compared to the β6 phase, which can beattributed to increase in the unit-cell lengths (in terms ofthe basic Ru2Sn3-type structure) with increasing aluminiumfraction. Some peaks, however, shift toward higher angles,and another length parameter is required to account for thisbehaviour.Powder XRD peaks from the �006 phase can be indexedassuming the MnSi£ type20) (see Table 1). The MnSi£ phase(£ µ 1.74) is an NCL phase with an incommensuratecomposite-crystalline structure characterized by two lengthsalong the c axis, c for the [Mn] subsystem and cA for the[Si] subsystem, and £ = c/cA is the ratio of the two lengths.The MnSi£ type can be regarded as an incommensuratelymodulated variant of the Ru2Sn3 type. In a similar way,powder XRD peaks from the �06 phase can be indexedassuming a superstructure of the MnSi£ type (or anincommensurately modulated variant of the Ru2Ge3 type)(see Table 1). The space group P �4c2 of the Ru2Sn3 type canFig. 2 Powder XRD patterns taken from samples at the β6–(Si), �06–(Si)and β3–β4–�006 equilibria (No. 6, 17 and 15, respectively, in Table 2).Table 3 Compositions of the stoichiometric phases in the Al–Ru and Ru–Si systems evaluated using different matrix correction models.K. Kitahara, H. Takakura, Y. Iwasaki and K. Kimura22be deduced from the superspace group I41/amd(00£)00ss ofthe MnSi£ type with £ = 3/2 (i.e. commensurate case).54) Thesuperspace group Pbma(00£)ss0 was chosen for the �06 phaseso that a similar relation holds with the Ru2Ge3 type.The combined composition range of the β6, �06 and�006 phases is approximately from Al33Ru36Si31[Ru(Al0.51Si0.49)1.7] to Ru67Si33 (RuSi1.5), which may containthe compositions Ru(Al0.2Si0.8)2¹x and Ru(Al0.5Si0.5)2¹xmentioned by Nowotny and coworkers14–16) although itcannot be confirmed as the value of x is not reported. Thereason why Nowotny and coworkers could not determine theunit-cell parameters of Ru(Al0.2Si0.8)2¹x and Ru(Al0.5Si0.5)2¹xmight be that they are incommensurate composite crystals,which were probably not common at that time. The phaseboundaries between the β6, �06 and �006 phases are notclear from our data. The unit-cell lengths in these phasesbasically increase with increasing aluminium fraction exceptfor cA, which decreases with increasing aluminium fraction(see Table 2).3.3 C and related phasesThe C phase was observed in five equilibria (No. 7, 8,13, 21 and 22 in Table 2). The homogeneity range of the Cphase was found to be approximately from Al72Ru23Si5 toAl69Ru24Si7. Near the composition of the C phase, two newphases (referred to as the C1 and C4 phases) were discovered(see Fig. 1). The C1 phase was observed in three equilibria(No. 13, 14 and 21) near the composition Al66Ru25Si9, andthe C4 phase was observed in one equilibrium (No. 9) nearthe composition Al73Ru23Si4.Single crystals of the C and C4 phases could begrown using the self-flux method from alloy sampleswith the nominal compositions Al66.5Ru10.0Si23.5 andAl79.0Ru10.0Si11.0, respectively. Crystal data, data collectionand structure refinement details are summarized in theCrystallographic Information File (CIF) format and availableonline.55) For the C phase, weak 2 © 2 © 2 face-centred cubicsuperstructure reflections were observed in single-crystalXRD, but only an approximate average structure could besolved as a 1 © 1 © 1 simple cubic basic structure as shownin Fig. 3(a). The structure can be viewed as a CsCl-typepacking of icosahedral and so-called pseudo-Mackayclusters, and the inner-shell structure of the pseudo-Mackaycluster is highly disordered similarly to the other knownstructures of the C phases in other systems.56–58) Note that nosignificant XRD peaks corresponding to the superstructurereflections are found in the powder XRD patterns probablybecause of the weak intensities, and the Le Bail analysescould be done assuming the basic structure without difficulty.The structure of the C4 phase was found to be a 2 © 2 © 2side-face-centred orthorhombic superstructure of the C phaseas shown in Fig. 3(b). Two types of pseudo-Mackay clusterswith different inner-shell configurations constitute the super-structure ordering. Distinction between aluminium andsilicon is rather ambiguous from the structure refinementfor these two phases, particularly at partially occupied sites.Superstructures of the C phase (not necessarily in the Al–Ru–Si system) had been found in three forms, 2 © 2 © 2body-centred cubic, 2 © 2 © 2 face-centred cubic andffiffiffi2p�ffiffiffi2p�ffiffiffi3phexagonal, and they are referred to as the C1, C2and C3 phases, respectively, in the nomenclature of Grushkoand Velikanova.6) The name C4 was chosen because it is thefourth form of the superstructures of the C phase. PowderXRD peaks from the C1 phase can be indexed assuming a2 © 2 © 2 body-centred cubic superstructure of the C phase,and that is why this phase is referred to as the C1 phase.The unit-cell lengths in the C, C1 and C4 phases (in terms ofthe basic structure of the C phase and on average over a, band c for the C4 phase) decrease with increasing siliconfraction.3.4 Other ternary phasesThe χA phase was observed in seven equilibria (No. 9, 10,22–26 in Table 2). The homogeneity range of the χA phasewas found to be approximately from Al74Ru19Si7 toAl66Ru19Si15, which is 2% wider on the silicon-rich sidethan that deduced from the compositions of single crystalsreported by Morrison et al.28) The unit-cell lengths basicallydecrease with increasing silicon fraction as is mentioned inMorrison et al.28) A large single crystal of the χA phase wasobtained as a by-product of growing single crystals of the Cphase using the self-flux method from an alloy sample withthe nominal composition Al74.0Ru10.0Si16.0. Crystal data, datacollection and structure refinement details are summarized inthe CIF format and available online.60) The structure of theχA phase determined in this study is quite similar to that ofRu23(Al,Si)97 reported by Morrison et al.,28) but there aresome remarkable differences. First of all, the positions ofsome atoms given in Table 1 in Morrison et al.28) areinconsistent with the structure shown in their Fig. 2 probablybecause of severe typos. They stated that the structure ofRu23(Al,Si)97 is similar to that of ³Fe23(Al,Si)9761,62) with thedifference being that there are neither positionally disorderednor partially occupied sites in Ru23(Al,Si)97. In this study,however, positionally disordered and partially occupied sitesas seen in ³Fe23(Al,Si)97 were deduced from the structurerefinement, and thus the formula ³Ru23(Al,Si)97 should bemore suitable than Ru23(Al,Si)97 for the χA phase. In addition,aluminium and silicon could be distinguished to some extentFig. 3 Crystal structures of the (a) C and (b) C4 phases visualized usingVESTA 3 software.59) Colour codes: grey spheres for aluminium andsilicon, black spheres for ruthenium, black polyhedra for icosahedralclusters and white and grey polyhedra for pseudo-Mackay clusters.Phase Equilibria in Aluminium–Ruthenium–Silicon System near 1200 Kelvin 23from the structure refinement in this study, while thedistinction was completely ignored in Morrison et al.28)Five new crystalline phases (referred to as the τ1, τ2, τ3, τ4and τ5 phases) were observed in 16 equilibria (No. 12, 14, 18–31 in Table 2) and identified as follows. Small single crystalsof these phases could be obtained from nearly single-phasesamples. Results of the single-crystal XRD analyses werereported elsewhere.42) Powder XRD peaks from these phasescan be indexed assuming the structures deduced from thesingle-crystal XRD analyses (see Table 1). The homogeneityranges of these phases are approximately from Al62Ru25Si13to Al56Ru26Si18 for τ1, from Al57Ru22Si21 to Al54Ru22Si24for τ2, from Al55Ru20Si25 to Al54Ru20Si26 for τ3, fromAl49Ru17Si34 to Al47Ru17Si36 for τ4 and from Al41Ru18Si41 toAl37Ru18Si45 for τ5. The unit-cell lengths in these phasesbasically decrease with increasing silicon fraction. Obviousexceptions are the length c in the τ4 and τ5 phases, whichroughly increase with increasing silicon fraction.The other two new phases (referred to as the I and Pphases) were observed in four equilibria (No. 18, 19, 27 and29 in Table 2) and identified as follows. The I phase was firstidentified as an icosahedral quasicrystal employing anautomated identification system based on machine learningat an early stage of this study. The details of the identificationwill be reported elsewhere.63) A rather systematic way ofidentification of the I phase employing the Le Bail method isshown here. Figure 4(a) shows results of the Le Bail analysisfor a sample of the τ1–τ2–I equilibrium (No. 27) with only theτ1 and τ2 phases taken into account. It was found thatsignificant peaks in the absolute residual can be indexedassuming a primitive icosahedral quasicrystal (the indexingscheme of Elser64) is used in this study). Le Bail analysiswas then performed taking into account the icosahedralquasicrystal. The icosahedral quasicrystal was treated asa six-dimensional modulated structure in the Jana2006software with only twelve typically strong reflections takeninto account. Note that this phase was identified as a face-centred icosahedral quasicrystal via electron diffraction,63)but no significant XRD peaks corresponding to face-centredsuperstructure reflections are found in the powder XRDpatterns probably because of very weak intensities in XRD.A primitive icosahedral quasicrystal is therefore assumed tosimplify the indexing and Le Bail analysis. Results of theLe Bail analysis are shown in Fig. 4(b), and no significantpeaks are found in the absolute residual in this case. In asimilar way, the P phase was identified as a cubic 2/1 rationalcrystalline approximant24) to the I phase from the Le Bailanalysis for a sample of the �006–τ5–P equilibrium (No. 19).Samples with the other two conditions (No. 18 and 29)consist of four phases including both I and P. In ourpreliminary annealing experiments at 1000K, the P phasehas never been observed. Probably, the above samples werein equilibrium near 1200K without the I phase, but a partof the P phase transformed into the I phase during cooling.The combined composition range of the I and P phases isapproximately from Al46Ru23Si31 to Al43Ru24Si33. On thebasis of the above results and discussion, we tentativelyassigned the aluminium-rich and silicon-rich sides to the Iand P phases, respectively. However, equilibrium involvingthese two phases should be investigated in more detail, takinginto account temperature dependence. The unit-cell lengths inthese phases decrease with increasing silicon fraction.It was found unlikely to achieve equilibrium in theruthenium-rich region (the amount fraction of rutheniumhigher than 50%) near 1200K within a reasonable time. Asfar as investigated (up to approximately 2000 h), only the(Ru) and β4 phases (and possibly the Ru4Si3 phase, seeSec. 3.1) were observed in the ruthenium-rich region.Therefore no other phases are expected in this region.4. ConclusionPhase equilibria in the Al–Ru–Si system near 1200K werethoroughly investigated through prolonged-annealing experi-ments. The composition and unit-cell parameters of eachphase involved in each equilibrium were evaluated at eighttwo-phase and 23 three-phase equilibria, and a tentativeisothermal section of the Al–Ru–Si equilibrium phasediagram near 1200K was drawn on the basis of those dataand the data adopted from the literature. In the course ofthe investigation, eleven new ternary phases including twoincommensurate composite-crystalline (�06 and �006) and anicosahedral quasicrystalline (I) phases were identified. Inaddition, single crystals of some ternary phases could beFig. 4 (a) Results of the Le Bail analysis for a sample of the τ1–τ2–Iequilibrium (No. 27 in Table 2) with only the τ1 and τ2 phases taken intoaccount. Io and Ic are the observed and calculated intensities, respectively.· is the standard deviation of Io and was estimated to be equal toffiffiffiffiIop.(b) Similar to (a) but with the I phase taken into account.K. Kitahara, H. Takakura, Y. Iwasaki and K. Kimura24obtained, and their crystal structures were determined usingsingle-crystal XRD.Note that the existence of the quasicrystalline (I) phasein the Al–Ru–Si system was not predicted by the recentlydeveloped machine-learning model for predicting composi-tions of quasicrystals,65) which was trained using knowncompositions of known quasicrystals and successfully usedfor discovering three new quasicrystals.66) This may indicatethat the I phase in the Al–Ru–Si system has somewhatdifferent characteristics from previously known quasicrystals,by which the machine-learning model could not predictthe existence from the training data. Two obvious differencesare the amount fraction of aluminium of approximately46% and unit-cell parameter of approximately 435.8 pm (seeTable 2), which are from 65% to 72% and from 446.5 pmto 461.7 pm, respectively, for previously known stableicosahedral quasicrystals composed of aluminium and latetransition elements.67)As a final remark, single-phase boundaries drawn in Fig. 1should be considered provisional. These boundaries weredrawn with straight line segments so that the compositionsat the investigated equilibria and those adopted from theliterature are reasonably covered by the single-phase regions.However, segments of the boundaries are not necessarilystraight, i.e. they are curved in general. In contrast, there isno such ambiguity in the three-phase regions. In any case, thephase diagram shown in Fig. 1 should be a good startingpoint for further investigations in the Al–Ru–Si system.AcknowledgementsMost of the sample preparations, powder XRD measure-ments and SEM–EDS measurements were performed withthe help of Ms Itaya and Ms Nakamura at The University ofTokyo. Single-crystal growth using the self-flux method andpreliminary single-crystal XRD analyses for the C, C4 and χAphases were performed with the help of Mr Shibata atHokkaido University. This work was supported by JSPSKAKENHI Grant number JP19H05818, JP19H05819 andJP19K15274.REFERENCES1) G.J. Snyder and E.S. Toberer: Nat. Mater. 7 (2008) 105–114.2) X. Zhang and L.-D. Zhao: J. Materiomics 1 (2015) 92–105.3) W. Liu, J. Hu, S. Zhang, M. Deng, C.-G. Han and Y. Liu: Mater. TodayPhys. 1 (2017) 50–60.4) Y. Shiota, H. Muta, K. Yamamoto, Y. Ohishi, K. Kurosaki and S.Yamanaka: Intermetallics 89 (2017) 51–56.5) Y. Iwasaki, K. Kitahara and K. Kimura: Phys. Rev. Mater. 3 (2019)061601(R).6) B. 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