VOLUME 53, NUMBER 20 PHYSICAL REVIE%' LETTERS 12 NOVEMBER 1984

Metallic Phase with Long-Range Orientational Order and NoTranslational SymmetryD. Shechtman and I. Blech

Department ofMaterials Engineering, Israel Institute of Technology T-echnion, 3200 Haifa, Israel

and

D. GratiasCentre d'Etudes de Chimie Metallurgique, Centre National de la Recherche Scientiftque, F 94400-Vi try, France

and

J. W. CahnCenter for Materials Science, National Bureau ofStandards, Gaithersburg, Maryland 20760

(Received 9 October 1984)

We have observed a metallic solid (Al—14-at. /o-Mn) with long-range orientationai order,but with icosahedral point group symmetry, which is inconsistent with lattice translations. Itsdiffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice.The solid is metastable and forms from the melt by a first-order transition.

PACS numbers: 61.50.Em, 61.55.Hg, 64.70.Ew

We report herein the existence of a metallic solidwhich diffracts electrons like a single crystal but haspoint group symmetery rn35 (icosahedral) which isinconsistent with lattice translations. If the speci-men is rotated through the angles of this pointgroup (Fig. 1), selected-area electron diffractionpatterns clearly display the six fivefold, ten three-fold, and fifteen twofold axes characteristic' oficosahedral symmetry (Fig. 2). Grains up to 2 p, min size with this structure form in rapidly cooled al-loys of Al with 10—14 at. '/0 Mn, Fe, or Cr. We willrefer to the phase as the icosahedral phase. Micro-diffraction from many different volume elements ofa grain and dark-field imaging from various diffrac-tion spots confirm that entire grains have long-range orientational order. If the orientational orderdecays with distance, its correlation length is fargreater than the grain size. We have thus a solidmetallic phase with no translational order and withwith long-range orientational order.The remarkable sharpness of the diffraction spots

(Fig. 2) indicates a high coherency in the spatial in-terference, comparable to the one usually encoun-tered in crystals. The diffraction data are qualita-tively well fitted by a model consisting of a randompacking of nonoverlapping parallel icosahedra at-tached by edges. The invariance of the local orien-tational symmetry from site to site and the finitenumber of possible translations between two adja-cent icosahedra seem to be sufficient for insuringhighly coherent interferences. Icosahedra are acommon packing unit in intermetallic crystals withthe smaller transition element at the center sur-

rounded by twelve larger atoms arranged like thecorners of an icosahedron. The symmetries of thecrystals dictate that the several icosqhedra in a unitcell have different orientations and allow them tobe distorted, leaving the overall crystal consistentwith the well-known crystallographic point andspace groups. Even though icosahedral symmetry isof great importance as an approximate site sym-metry in crystals, it cannot survive the impositionof lattice translations: Crystals cannot and do notexhibit the icosahedral point group symmetry.Elementary crystallography indicates that fivefold

FIG. 1. Stereographic projection of the symmetry ele-ments of the icosahedral group m35.

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VOLUME 53, NUMBER 20 PHYSICAL REVIEW LETTERS 12 NOVEMBER 1984

63.43

t»» EI 'll' *

Ie s:»

31.72 36

79.2 58.29 37.38:KR

FIG. 2. Selected-area electron diffraction patterns taken from a single grain of the icosahedral phase. Rotations matchthose in Fig. 1.

axes are inconsistent with translational order.Crystals with an apparent fivefold axis do occur asmultiple twins. 5 Icosahedral symmetry could con-ceivably occur by multiple t~inning, but at leastfive twins are required in order to obtain anicosahedral diffraction set from a conventional crys-tal. Experiments in the electron microscope andwith x-ray diffraction contradict the twin hypoth-esis:(I) A set of dark-field images taken from any re-

flection reveals no twins and in all cases the wholegrain is illuminated.(2) A convergent-beam diffraction pattern along

the fivefold zone taken from an area 20 nm in di-arneter at any point of the grain displays all the re-flections that appear in the selected-area diffractionpattern. This is also true when the thickness of thespecimen is of the order of 10 nm.(3) An x-ray diffraction pattern (Cu Ka source)

was taken from a single-phase sample of the materi-al containing many grains of various orientations.Had the phase consisted of a multiply twinned crys-talline structure, it should have been possible to in-dex the powder pattern regardless of the twins. Thepattern obtained from the icosahedral phase could

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not be indexed to any Bravais lattice.On the basis of these experiments we conclude

that the icosahedral phase does not consist of multi-ply t~inned regular crystal structures.The icosahedral phase forms during rapid cooling

of the melt by a nucleation and growth mechanism.This mechanism is characteristic of a first-ordertransition because the two phases coexist along amoving interface. Each particle nucleates at acenter and grows out from there. The atomic rear-rangements that result in the orientational order ofthe icosahedral phase occur at this interface, andthe two adjoining phases differ in entropy and, forsome alloys, in composition. If the transition werehigher order, ordering would occur everywhere inthe liquid instead of being confined to interfaces.Our evidence for the first-order character is mor-phological. We examined alloys with 10—14 at.%Mn. Samples with 10% to 12% Mn showed manynodular grains separated from each other by crystal-line films of fcc Al. The grains were approximatelyspherical in shape but were deeply indented with ra-dial streaks composed of fcc Al crystals. The mor-phology is similar to a commonly observed one inrapid solidification in which crystals nucleate at

VOLUME 53, NUMBER 20 PHYSICAL REVIEW LETTERS 12 NOVEMBER 1984

many centers and grow until the remaining liquidsolidifies, except that instead of isolated crystals wehave isolated icosahedral grains embedded in solidi-fied Al.Another aspect of the first-order character of the

transition is that segregation accompanies thegrowth of the icosahedral phase. In the 10%- and12%-Mn samples the growing phase rejects Al intothe liquid. The indentations in the nodules arecharacteristic of the cellular morphology caused byan instability in the diffusion layer surrounding thesolid resulting from segregation during growth. Inthe 14%-Mn alloys the icosahedral grains occupy al-most all of the volume of the specimen. Only smallamounts of fcc A1 occur along some grain boun-daries where the grains grew to impingement.Some radial streaking still points to the nucleationcenters from which the grains grew. We concludethat little segregation occurs in this alloy and thatthe icosahedral phase contains 14'/o Mn.The obvious cellular morphology indicates that

the growth of the icosahedral phase is slow enoughto permit diffusional segregation on the scale of 1p,m. With the diffusion coefficient in the liqud oforder 10 m /s this indicates interface velocities oforder 10 m/s and formation times of 10 s.This is 2 to 3 orders of magnitude slower than thefastest known crystallization velocities of a metallicliquid during rapid cooling, but it is a typical upperlimit of velocity of crystallization with compositionchanges. 7 There is thus plenty of time for atomicrearrangements to occur at the interface betweenthe melt and the icosahedral phase.The icosahedral phase in rapidly solidified Al-Mn

alloys is remarkably resistant to crystallization. Pro-longed heating of 6 h at 300 C and 1 h at 350'Cproduced no detectable crystallization, but 1 h at400'C caused crystallization to the stable A16Mnphase. We conclude that the icosahedral phase is atruly metastable phase which nucleates and growsfor a range of cooling rates which are slow enoughto permit its formation but rapid enough to preventcrystallization, either from the melt or from the

icosahedral phase after its formation.The icosahedral phase has symmetries intermedi-

ate between those of a crystal and a liquid. Itdiffers from other intermediate phases in that it isboth solid, like a metallic glass, and that it haslong-range orientational order. Many intermediatephases do have orientational order, but usually it isonly local, and the transition to such phases is con-tinuous. s 9 The possibility of an icosahedral phasewith long range order was inferred from a computersimulation, ' " and a first-order liquid-to-icosa-hedral phase transition has been predicted from amean-field theory. "'We thank F. S. Biancaniello for spinning the al-

loys, C. R. Hubbard for x-ray experiments, andB. Burton for a critical review of the manuscript.This work was sponsored by the Defense AdvancedResearch Projects Agency and the National ScienceFoundation. This work was performed while one ofus {D.S.) was a guest worker at the National Bureauof Standards and while another of us (D.G.) was atthe Institute for Theoretical Physics, University ofCalifornia at Santa Barbara.

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(1958), and 12, 483 (1959).4M. J. Buerger, Elementary Crystallography (MIT Press,

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J. W. Cahn, in Rapid Solidification Processing Il, edited byR. Mehrabian et al. (Claitors, Baton Rouge, 1980), p. 50.SD. R. Nelson, Phys. Rev. B 2&, 5515 (1983).sJ. Sadoc, J. Phys. (Paris), Colloq. 41, C8-326 (1980).&OP. J. Steinhardt, D. R. Nelson and M. Rouchetti,Phys. Rev. Lett. 47, 1297 (1981).»P. J. Steinhardt, D. R. Nelson and M. Rouchetti,Phys. Rev. B 28, 784 (1983).t2A. D. J. Haymet, Phys. Rev. B 27, 1725 (1983).

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