Atomic structure of the binary icosahedral Yb Cd quasicrystal

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1 Atomi struture of the inry ioshedrl Y Cd qusirystl HIROYUKI TAKAKURA,2 *, CESAR PAY GÓMEZ, AKIJI YAMAMOTO 2,4, MARC DE OISSIEU 5 AND AN PANG TSAI 2, Division of Applied Physis, Grdute Shool of Engineering, Hokkido University, Spporo , Jpn 2 Solution Oriented Reserh for Siene nd Tehnology, Jpn Siene nd Tehnology Ageny, Kwguhi, Sitm 2-002, Jpn Institute of Multidisiplinry Reserh for Advned Mterils, Tohoku University, Sendi , Jpn 4 Ntionl Institute for Mterils Siene, Tsuku , Jpn 5 Lortoire de Thermodynmique et de Physio-Chimie Métllurgique, UMR CNRS 564, ENSEEG-INPG, P 75, 8402 Sint Mrtin d Hères, Frne *e-mil: tkkur@eng.hokudi..jp Pulished online: 0 Deemer 2006; doi:0.08/nmt799 Ioshedrl qusirystls (i-qcs) re long-rnge ordered solids tht show non-rystllogrphi symmetries suh s five-fold rottions. Their detiled tomi strutures re still fr from ompletely understood, euse most stle i-qcs form s ternry lloys suffering from hemil disorder. Here, we present the first detiled struture solution of i-ycd 5.7, one of the very few stle inry i-qcs, y mens of X-ry struture determintion. Three uilding units with unique tomi deortions rrnge qusiperiodilly nd fill the spe. These lso serve s uilding units in the periodi pproximnt rystls. The struture is not only hemilly fesile, ut lso provides semless struturl understnding of the i-ycd 5.7 phse nd its series of relted i-qcs nd pproximnt rystls, reveling hierrhi fetures tht re of onsiderle physil interest. Ioshedrl qusirystls (i-qcs) re the only lss to show qusiperiodiity in three dimensions,2. Oviously, struturl knowledge is essentil for understnding the physil properties, stility nd tiloring pplitions of these exoti mterils. However, in ontrst to other types of QCs tht show periodi order in t lest one diretion, i-qcs nnot mke effetive use of two-dimensionl (2D) imging tehniques suh s high-resolution eletron mirosopy or high-ngle nnulr drk-field snning trnsmission eletron mirosopy for their struturl hrteriztion 4. The i-qcs struture determintion is est hieved in the ontext of hyperspe rystllogrphy 5,6, where the struture n e desried s periodi rystl in higher dimensions. For i-qcs, the periodi spe is 6D nd deomposes into two orthogonl D suspes: the prllel (physil) spe nd the perpendiulr (omplementry) spe. The 6D unit ell is deorted y D ojets known s ouption domins (OD), the D QCs eing otined s setion of this deorted 6D lttie. This pproh llows modelling nd refinement of the struture ginst experimentl diffrtion dt in wy similr to tht hieved for D periodi rystls 6. Although muh progress hs een hieved reently, for instne in the i-alpdmn phse 7, the models proposed so fr re still eing deted 8. Indeed, the mount of oserved diffrtion dt is in generl rther limited, whih preludes detiled refinement of the hemil order in ternry QCs. Therefore, the tomi order in i-qcs remins hllenging nd outstnding question. The reent disovery of the first stle inry ioshedrl YCd 5.7 QCs 9,0 hs een rekthrough nd led to disoveries of whole series of relted ternry i-qcs. This i-qc offers unique opportunity for the struturl nlysis of i-qcs. Indeed, the i-ycd 5.7 phse n e otined s high-qulity single grins. Furthermore, it is inry nd exhiits very good X-ry ontrst etween Cd (Z = 48) nd Y (Z = 70) toms. Finlly, there is series of periodi pproximnt rystls (ACs) to the QC, hving lmost the sme hemil omposition nd for whih detiled struturl nlysis hs een hieved 2 5. These phses shre the sme lol environments tht in turn n e used for modelling the i-qc struture. The present struture nlysis of the i-ycd 5.7 phse hs thus een rried out under the most fvourle onditions. In ddition, stte-of-the-rt omputtionl methods on the sis of hyperspe rystllogrphy 6 hve een pplied to high-qulity synhrotron X-ry dt. This hs resulted in the most detiled struture solution of n i-qc hieved to dte. The tomi struture of periodi pproximnt rystl n e generted from the 6D representtion of the prent i-qc y tilting the ut spe until it rehes rtionl slope 6. For the Y Cd system, two suessive ui ACs hve een synthesized, the / ui pproximnt YCd 6 nd the 2/ ui pproximnt Y Cd 76 (YCd 5.8 ). Detiled X-ry struture determintion shows tht oth periodi pproximnts n e desried s pking of lrge rhomi trionthedrl (RTH) units presenting very well-defined hemil order (Fig.,). The RTH is uilt up of five suessive tomi shells, s seen in Fig. d,g. These tomi shells re the sme in oth ACs, differing only in the oupny of some of the tomi positions loted t the three-fold verties of the RTH units, nd the pperne of the disorder of the entrl Cd 4 tetrhedron 5. In oth ACs, the RTH units re linked to eh other long two-fold (-linkge, length = ) diretions y shring fe, nd three-fold diretions (-linkge, length = ( /2)) sillustrted in Fig.. The ell prmeters of / nd 2/ ACs re relted to eh other s =.566 nm nd τ = 2.5 nm (τ = golden rtio,.68) respetively. The RTH units interpenetrte long the three-fold -diretion, defining t the intersetion n otuse 58 nture mterils VOL 6 JANUARY

2 d e f g Figure Approximnts, uilding units nd linkges., The ody-entred-ui pking of RTH units in the / ui pproximnt., The pking of RTH units in the 2/ ui pproximnt., The two different types of linkges etween the RTH units. The - nd -linkge ours long the two- nd three-fold diretions, respetively. d f, The three fundmentl uilding units: RTH (d), AR (e) nd OR(f), nd their orresponding tomi deortions. All rhomi fes of these three uilding units re deorted with Cd toms on the verties nd mid-edges. g, Atomi su-shells inside the RTH unit (92 toms, R = 0.78 nm long its two-fold diretion). From left to right: Cd iosidodehedron (0 toms, R = 0.65 nm), Y ioshedron (2 toms, R = 0.56 nm), Cd dodehedron (20 toms, R = 0.46 nm), nd the inner Cd tetrhedron (4 toms, ourring in different orienttions). All Cd toms re shown in grey nd Y toms in yellow. The red rrows indite where in the pproximnt strutures the orresponding uilding units n e found. rhomohedron (OR) with deortion of Cd toms, s seen in Fig.,f. As expeted from the rtionl ut proedure 6, the lttie onstnt = (4 + 8/ 5) /2,where orresponds to the edge length of the RTH s surfe rhomi, nd to the dimeter of the RTH unit long its two-fold xis. The 6D QC lttie prmeter is equl to 2. The two ACs differ in the wy the RTH units re pked 5. The / AC is defined y ody-entred-ui pking of RTH units, tht is, ll toms elong to the RTH. The 2/ AC hs different pking of RTH units (Fig. ), whih requires the introdution of yet nother uilding lok to fill the gps reted etween the RTH units. This is the ute rhomohedron (AR) with edge length. The AR, with the exeption of two pping toms, is ompletely defined y doule Friuf polyhedron 7. The AR ontins two Y toms long its long digonl nd Cd toms on verties nd edges 4,5 (Fig. e). The only known AC tht ontins ARs is the 2/, whih points to the importne of the 2/ pproximnt struture when identifying the uilding units for n i-qc struture. Thus, we now hve in hnd three uilding units (RTH, OR, AR, Fig. d f) with their lmost-perfet hemil deortion nd linkges, whih n e used for the QC s modelling. To nlyse the struture of the i-ycd 5.7 phse, we hve rried out dt olletion using synhrotron X-ry diffrtion. This ws done on single grin of very high struturl qulity nd nrrow mosi spred. The spe group ws determined to e Pm5 with n ioshedrl lttie onstnt = nm. We olleted over five thousnd unique rgg refletions, with lrge dynmil rnge (8 orders of mgnitude in intensity). The dt set ontins lrge numer of refletions hving lrge Q perp omponent of their wvevetor; those refletions re prtiulrly sensitive to the detils of the struture nd re importnt for ny omprison with model. nture mterils VOL 6 JANUARY

3 r [00000] r E Eletron density (.u.) V 0 0. nm d f [0] 0 r 2f y f d f e e r 2f x Eletron density (.u.) 0. nm 0 Cd Y Figure 2 Reonstruted 6D eletron densities for the i-ycd 5.7 QCndoservedtomishells., The 2D ut of the eletron density ontining five-fold xis oth in the physil (r ) nd perpendiulr (r ) spe. Ellipses with red dotted lines show the independent prts of the eletron densities. The lels V, nd E show high-symmetry positions in the 6D unit ell (indited y the inner lk retngle). These positions hve the 6D frtionl oordintes (0,0,0,0,0,0), (,,,,,)/2 nd (,0,0,0,0,0)/2 respetively. The thik red r shows the dimeter of the rhetype OD long its five-fold diretion (see Fig. )., The 2D ut of the eletron density ontining five-, three- nd two-fold xes in the physil spe (right), nd oserved trionthedrl tomi su-shells (left). The polygons lelled () to (f) orrespond to the tomi shells of the RTH unit. In the first step, phse reonstrution for Fourier synthesis ws hieved y pplying the low-density elimintion method diret phsing method in rystllogrphy tht hs een shown to pply for QCs (ref. 8). The otined phses nd Fourier mplitudes were used to generte the eletron densities within the 6D unit ell of i-ycd 5.7. Figure 2 shows rtionl setion of the 6D eletrondensity mp, ontining five-fold xis oth in the prllel nd the perpendiulr spe. The eletron densities lerly onentrte t three high-symmetry positions in the unit ell, entred t V, nd E (Fig. 2) s previously indited y preliminry study 9. Furthermore, euse there is good ontrst etween Cd nd Y, the hemil deortion n lso e identified. For instne the higher eletron density oserved round the position, n unmiguously e ttriuted to Y toms. The resulting D qusirystlline struture is diretly relted to the rrngement of the ODs tht orrespond to the 6D eletron densities seen in Fig. 2. From detiled nlysis of this mp we find tht the RTH units, whih inlude the previously identified iosidodehedrl shell 20, re lso present in the QC. This is demonstrted if we fous ttention on the ody-entre position t (,,,,,)/2. Exept for the inner disordered tetrhedron, whih hs insuffiient eletron density to e seen in the mp, we 60 nture mterils VOL 6 JANUARY

4 f 2 2f V 7 0 2f Cd (in RTHs) Cd (prtilly oupied) Cd (not in RTHs) Y (in RTHs) Y (in ARs) Vnies Figure Ouption domins of the i-ycd 5.7 QC model., The rhetype OD tht selets the suset of 2-fold verties from DPT. The dimeter of the OD orresponds to the thik red line in Fig. 2., The ODs of the i-ycd 5.7 QC model, projeted onto the perpendiulr spe, whih re onstruted on the sis of the rhetype OD in. The lels V, nd E indite their positions in the 6D unit ell, sshowninfig.2., The symmetri prts of the ODs loted t V nd. The numers nd olour odes explin whih prts of the ODs generte orresponding tomi positions in D physil spe. genertes the Cd dodehedr inside the RTH units. 2 nd 7, The different prtilly oupied vertex positions of the disordered Cd 4 tetrhedron. nd, AR nd OR Cd positions of verties nd mid-edges respetively, whih re not shred with the RTH units. 4 nd 5, Vertex positions of RTH units. 2 Mid-edge positions of RTH units. 6, Vnt entres of stellte polyhedr. 8, Cd iosidodehedr inside the RTH units. 9, Y ioshedr inside RTH units. 0, Y positions inside ARs., Vnt entres of RTH units. find extly the sme suessive ioshedrl shells with the sme rdii s in the ACs 5 (Fig. d,g). The shells lso hve the sme hemil deortion (the Y ioshedron, nd the deortion of Cd toms on the verties nd edges of the trionthedron re prtiulrly pprent), s illustrted in Fig. 2, where the densities orresponding to toms in the different ioshedrl shells re lelled () to (f). The undne of RTH units in the QC struture n e estimted from the size of the hole t the position in Fig. 2, whih orresponds to the OD tht determines the rrngement of the RTH entres. The density mp is not detiled enough to give omplete desription of the struture similr to those hieved for D periodi rystls. It is thus neessry to design struture model, with resonle numer of prmeters, whih n then e refined ginst experimentl dt. This is omplex prolem whih is gretly simplified here y the knowledge gined from the AC strutures nd from the 6D density mp. The size of the hole t the position in Fig. 2 fits very well with the size expeted for RTH units entred t the so-lled 2-fold sphere-pking sites 2. These sites onstitute restrited suset of verties in the threedimensionl generliztion 22 of the Penrose tiling (DPT), with the edge length, nd re onneted only y - nd -linkges. The E DPT is generted y n OD with the shpe of trionthedron. The OD for generting the 2-fold sphere-pking verties is otined y mking the edge length τ 2 times smller nd utting wy its five-fold tips (Fig. ). This OD ensures similr RTH onnetivity s tht oserved in the ACs, nd hs een used s n rhetype OD in our modelling of the i-ycd 5.7 phse, s previously done 2,24 for other i-qcs. This OD is not suffiient to generte ll toms, ut it n e shown tht the remining spe etween the RTH units n e filled y different rrngements of ORs nd ARs 25. A nturl ssumption is to deorte these two units in wy similr to tht oserved in the pproximnt phses. This gives the resulting 6D model of the ODs shown in Fig.,. Some prts of these ODs re shifted long the prllel spe to otin the hrteristi tomi shell struture seen in Fig. d,g. However, this is not shown in Fig. for the ske of simpliity. The model ensures tht there re no unresonly short tomi distnes, exept for the disordered Cd 4 tetrhedron sites. Using n pproh similr to tht used for the i-alpdmn phse 7, the 6D model is then sudivided into smller frgments, eh of whih is ssigned omposition, prllel shift prmeter nd so on. These prmeters re ll refinle, nd would orrespond to the struturl prmeters in D periodi rystls. This results in 25 prmeters, whih were refined ginst 5,024 unique refletions. The resulting R-ftor is 9.4%, whih demonstrtes the vlidity of the proposed model, prtiulrly in view of the lrge numer of mesured refletions. (Plots of oserved nd lulted struture ftors re provided in the Supplementry Informtion.) The lulted density nd omposition is 8.88gm nd Y 6. Cd 8.7,whihisinexellent greement with the ville experimentl dt 0. One the 6D model is refined, it is possile to provide omplete nlysis of the resulting D qusiperiodi struture. A detiled nlysis will e provided elsewhere nd we give here only the min fetures. The first prominent feture is tht the hemil order n e well determined in the qusirystlline phse. The seond prominent feture is tht lmost ll the QC struture is desried y the interpenetrting RTH units s 9.8% of the toms elong to these RTH units. The third feture is tht smll distortions of the tomi shells, espeilly the iosidodehedrl shell, resulting from the -linkges nd oserved in the pproximnts, re lso reprodued in the QC model. In ontrst to the herein proposed model of the i-ycd 5.7 phse, ll previous models of i-qcs using RTH units to speify the struture, fil to give unique tomi deortions for ertin uilding units 25,26. Figure 4 shows sl of the resulting spe-filling QC struture perpendiulr to five-fold xis. The struture is mostly omposed of RTH units following the previously desried linking sheme (Fig. ). The spes etween the RTH units re filled y different rrngements of ARs nd ORs. These rrngements n e lssified into two min tegories: we ll the first the ogwheel omplex (Fig. 4, top left inset) nd the seond the stellte polyhedron (Fig. 4, top right inset). The ltter forms ergmn luster 26 in its interior (Fig. 4, top right inset, A D). Frgments of these two min rrngements (inomplete og-wheel omplexes nd stellte polyhedr lking severl ARs nd ORs) re lso seen in Fig. 4. Another interesting wy to desrie the struture is in terms of infltion nd hierrhil pking of lusters 27. Here, infltion mens the property when suset of speil points from the originl struture re found in n identil rrngement when inresed in sle y prtiulr ftor; τ in this se. This is shown in Fig. 5, whih shows the RTH entre positions nd their onnetions in five-fold plne. Strting from the entre, it n e shown tht luster of RTH units (iosidodehedron) is formed. This luster of RTH units is t the entre of lrger luster of nture mterils VOL 6 JANUARY

5 D C A Figure 4 Idel struture of the i-ycd 5.7 QC. Aslofi-YCd 5.7 in D physil spe with its norml vetor prllel to five-fold xis. The uilding units nd toms re shown using the sme olour odes s in Fig.. The og wheel omplex is seen ner the entre of the min imge. This is lrge rrngement of ARs tht serves s host for stellr rrngement of ten ORs, s seen in the top left inset, where the ontents of the og wheel omplex re shown. The stellte polyhedron omposed of twenty ARs is lso reurring rrngement in the struture. A omplete stellte polyhedron is seen in the top right inset; the first four tomi su-shells (lelled A to D) of this rrngement orrespond to ergmn luster. The RTH units re shown in green, s seen in the ottom left inset. τ Figure 5 Infltion properties of the i-ycd 5.7 QC., A dense plne of RTH units is seen long the five-fold xis. Only the entres of the RTH units re shown s oloured spheres. The dense plne is slightly pukered; the ornge spheres re ove the idel plne, green spheres re elow nd drk grey (nd lue) spheres re in the plne. The onds onneting the drk grey spheres re two-fold -linkges (see Fig. ). In the entre of the imge yellow degon outlined y lue RTH entres nd -linkges is seen. This represents luster of RTH units. A lrge τ -inflted degon luster omposed of lusters of RTH units t its verties is outlined y thik red onds., A D perspetive view of the τ -inflted luster; its rdius is out 2 nm. It is seen tht the τ -inflted luster nd its onstituent lusters of RTH units form n iosidodehedron. The lue irle nd degons in nd indite the position of the ut plne. RTH entres seen in ornge, green nd drk grey hve een omitted in for lrity. lusters, whih is lso n iosidodehedron ut τ times inresed in sle s shown y the red onnetions. Other uthors hve reently rried out first-priniples lultions on the ACs nd the hexgonl Lves phse CCd 2 in the relted C Cd system sed on nonil ells 28. The Lves phse, whih lso exists in the Y Cd system, is of prtiulr interest euse it is omposed entirely of fe-shring ARs. The results re in ordne with the lol tomi rrngements in the herein 62 nture mterils VOL 6 JANUARY

6 presented struture of i-ycd 5.7 in terms of pkings of RTH units nd frgments omposed of severl fe-shring ARs ontining Y Y pirs 29. We thus otin omplete desription of the tomi struture for the i-ycd phse. Note tht, lthough the entres of the RTH units re loted on suset of verties in DPT, the struture nnot e desried with two uniquely deorted rhomohedr in DPT 6. It is lso seen tht the struture nnot e desried using only four types of nonil ells, without leving lrge gps in the tiling 28. A hrteristi of the present i-ycd model is tht there is ertin degree of freedom regrding the rrngement of the fundmentl uilding units while mintining the linkges, the undne of RTH units nd the ioshedrl symmetry unhnged. Indeed, some vritions on detils of the externl shpe of the OD re possile (see Fig. ), nd might e relted to the phson degrees of freedom 0. We hve proposed model for the inry i-ycd 5.7 phse tht is in very good greement with ll ville dt nd shres the sme luster nd onnetivity s the orresponding pproximnt strutures. A very good R-ftor is hieved with hemilly ordered struture, whih points to the rther unique properties of the inry Y Cd system. This is most likely relted to the reltive tomi size of Cd nd Y toms on one hnd, nd to the eletroni hyridiztion, s shown y lultions, on the other hnd. The present model n thus redily e used for lulting physil properties nd shed some light on the stility of these mterils. Although the proposed 6D model is rther omplex, its uilding priniple is reltively simple. Indeed, the use of the lrge interpenetrting RTH units lrgely redues the numer of toms involved in the intersties ( glue toms ). Furthermore, the tomi deortion of the intersties is ompletely defined y the OR nd AR units. This uilding priniple n redily e pplied to other types of i-qcs 25,26,2,,ifpropertomideortionsre onsidered, thus giving generl frme for desriing ioshedrl strutures nd understnding their physil properties s well s the universlity of qusiperiodi order. The ft tht the struture is suessfully desried with uilding units hving unique tomi deortions, nd tht the prolem of unspeified glue toms hs een effetively eliminted is unique feture of the present model nd n unpreedented event in the history of ioshedrl QCs. METHODS DATA COLLECTION Mesurements hve een rried out on the D2AM em line t the Europen Synhrotron Rdition Fility. A single grin of the i-ycd phse, with ui size of pproximtely 0. mm, ws extrted from n ingot slowly ooled from the liquid. It ws seled under inert gs in glss pillry to void oxidtion. The inoming X-ry energy ws seleted y doule Si monohromtor nd set to 20.6 kev to minimize sorption orretions. We used sintilltor detetor, ontinuous sn proedure nd n utomti ttenutor set-up llowing for the mesurement of intensities with lrge dynmil rnge (8 orders of mgnitude). The smple mosi spred ws found to e 0.0.A stndrd refletion ws mesured regulrly nd showed very smooth vrition s funtion of time. 5,500 refletions hve een mesured in the symmetri unit with Q perp vetorsvryingfrom0to(2π/ unit). A few equivlent refletions were mesured nd were found to gree within 4% fter sorption orretion. Dt re ville on request. Reeived 28 July 2006; epted 6 Novemer 2006; pulished 0 Deemer Referenes. Shehtmn, D., leh, I., Grtis, D. & Chn, J. W. Metlli phse with long-rnge orienttionl order nd no trnsltionl symmetry. Phys.Rev.Lett.5, (984). 2. Jnot, C. Qusirystls: A Primer (Oxford Univ. Press, New York, 992).. Stdnik, Z. M. (ed.) Physil Properties of Qusirystls (Springer, erlin, 999). 4. Ae, E., Yn, Y. & Pennyook, S. J. Qusirystls s luster ggregtes. Nture Mter., (2004). 5. Jnssen, T. Crystllogrphy of qusi-rystls. At Crystllogr. A 42, (986). 6. Ymmoto, A. Crystllogrphy of qusiperiodi rystls. At Crystllogr. A 52, (996). 7. Ymmoto, A., Tkkur, H. & Tsi, A. P. Six-dimensionl model of ioshedrl Al-Pd-Mn qusirystls. Phys.Rev.68, (200). 8. Henley, C. L., de oissieu, M. & Steurer, W. Disussion on lusters, phsons nd qusirystl stilistion. Phil. Mg. 86, 5 (2006). 9. Tsi, A. P., Guo, J. Q., Ae, E., Tkkur, H. & Sto, T. J. A stle inry qusirystl. Nture 408, (2000). 0. Guo, J. Q., Ae, E. & Tsi, A. P. Stle ioshedrl qusirystls in inry Cd-C nd Cd-Y systems. Phys.Rev.62, R4605 R4608 (2000).. Mezw, R., Kshimoto, S. & Ishims, T. Ioshedrl qusirystls in Zn-T-S (T= Mn, Fe, Co or Ni) lloys. Phil. Mg. Lett. 84, (2004). 2. Plenzon, A. The ytterium-dmium system. J. Less-Common Met. 25, (97).. Gómez, C. P. & Lidin, S. Comprtive struturl study of the disordered MCd 6 qusirystl pproximnts. Phys.Rev.68, (200). 4. Gómez, C. P. & Lidin, S. Struture of C Cd 76: A novel pproximnt to the MCd 5.7 qusirystls (M = C, Y). Angew. Chem. Int. Edn Engl. 40, (200). 5. Gómez, C. P. Order nd Disorder in the RE-Cd nd Relted Systems (Stokholm Univ., Stokholm, 200). 6. Elser, V. & Henley, C. L. Crystl nd qusirystl strutures in Al-Mn-Si lloys. Phys.Rev.Lett.55, (985). 7. Smson, S. in Struturl Chemistry nd Moleulr iology (eds Rih, A. & Dvidson, N.) (Freemn, Sn Frniso, 968). 8. Tkkur, H., Shiono, M., Sto, T. J., Ymmoto, A. & Tsi, A. P. A Initio struture determintion of ioshedrl Zn-Mg-Ho qusirystls y density modifition method. Phys.Rev.Lett.86, (200). 9. Tkkur, H., Ymmoto, A., Shiono, M., Sto, T. J. & Tsi, A. P. A initio struture determintion of qusirystls y density modifition method. J. Alloys Compounds 42, (2002). 20. Tkkur, H., Ymmoto, A., de oissieu, M. & Tsi, A. P. A initio struture solution of ioshedrl Cd-Y qusirystls y density modifition method. Ferroeletris 05, (2004). 2. Henley, C. L. Sphere pkings nd lol environments in Penrose tilings. Phys.Rev.4, (986). 22. Krmer, P. & Neri, R. On Periodi nd non-periodi spe fillings of E m otined y projetion. At Crystllogr. A 40, (984). 2. Ymmoto, A. Struture of n ioshedrl Al-Mn qusirystl. Phys.Rev.7, (988). 24. Duneu, M. & Oguey, C. Idel AlMnSi qusirystl: struturl model with ioshedrl lusters. J. Phys. (Pris) 50, 5 46 (989). 25. Mihlkovič, M., Zhu, W.-J., Henley, C. L. & Oxorrow, M. Ioshedrl qusirystl deortion models. I. geometril priniples. Phys.Rev.5, (996). 26. Audier, M. & Guyot, P. in Extended Ioshedrl Strutures (eds Jrić, M. V. & Grtis, D.) 5 (Ademi, New York, 989). 27. Jnot, C. & de oissieu, M. Qusirystls s hierrhy of lusters. Phys.Rev.Lett.72, (994). 28. Henley, C. L. Cell geometry for luster-sed qusirystl models. Phys.Rev.4, (99). 29. Mihlkovič, M. & Widom, M. Cnonil ell model of dmium-sed ioshedrl lloys. Phil. Mg. 86, (2006). 0. Luensky, T. C., Rmswmy, S. & Toner, J. Hydrodynmis of ioshedrl qusirystls. Phys.Rev. 2, (985).. Ishii, Y. & Fujiwr, T. Hyridiztion mehnism for ohesion of Cd-sed qusirystls. Phys. Rev. Lett. 87, (200). 2. Yng, Q.. Qusirystl model sed on series of superui rystl strutures onsisting of trionthedr or Mky ioshedr. Phil. Mg. 6, (990).. Fowler, H. A., Mozer,. & Sims, J. Triple-shell symmetry in α-(al,si)-mn. Phys.Rev.7, (988). Aknowledgements We knowledge the Europen Synhrotron Rdition Fility nd the Frenh Coopertive Reserh Group for the llotion of em time on the D2AM em line. We thnk N. oudet nd J. F. err for their ssistne on D2AM during the experiment. C.P.G. hs een finnilly supported y the Jpn Soiety for the Promotion of Siene (JSPS). Correspondene nd requests for mterils should e ddressed to H.T. Supplementry Informtion ompnies this pper on Author ontriutions All uthors disussed the results nd ommented on the mnusript. H.T. nd C.P.G. ontriuted eqully to the finl form of the mnusript. Competing finnil interests The uthors delre tht they hve no ompeting finnil interests. Reprints nd permission informtion is ville online t nture mterils VOL 6 JANUARY