Crystallographic orientations and interfaces of icosahedral quasicrystalline phase growing on cubic...

Materials Science and Engineering A 397 (2005) 22–34

Crystallographic orientations and interfaces of icosahedralquasicrystalline phase growing on cubic W phase in Mg–Zn–Y alloys

Alok Singha,∗, M. Watanabeb, A. Katob, A.P. Tsaia,c

a Materials Engineering Laboratory, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japanb Toyota Motor Corporation, 1, Toyota-cho, Toyota, Aichi 471-8572, Japan

c Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan

Received 15 October 2004; received in revised form 27 December 2004; accepted 10 February 2005

Abstract

Formation of icosahedral quasicrystalline phase on the W cubic phase in�-Mg matrix has been studied in a Mg97Zn2.5Y0.5 alloy. Theorientation relationship of the W phase with the matrix is determined to be [0 0 1]W‖[1 0 0]Mg, (1 1 0)W‖(0 0 1)Mg, equivalent to Burgersorientation relationship. The icosahedral phase forms curved interfaces with the W phase, but planar interfaces on five-fold and two-foldplanes with the matrix. The icosahedral phase shows its unique orientation relationship to the W phase, which results in two orientationr ecipitatesi ctures ared©

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elationships WOR1 and WOR2 with the matrix. WOR1 is a slight deviation of the orientation relation, OR1, of icosahedral phase prn the matrix. In WOR2, one of the five-fold axes occur along the hexagonal axis. The resulting morphology and the interface struescribed here. It is shown that WOR1 and WOR2 are related to each other by twinning of the icosahedral phase.2005 Elsevier B.V. All rights reserved.

eywords:Magnesium-alloys; Quasicrystals; Interfaces; Transmission electron microscopy (TEM)

. Introduction

In Mg–Zn–Y alloys, an icosahedral quasicrystalline phasexists in equilibrium with the magnesium matrix[1–3], dueo which stable two phase microstructures can be formed. Thecosahedral phase in such alloys can act as a strengtheninghase. In dilute alloys, the quasicrystalline phase solidifiess a eutectic phase in the interdendritic spaces. Thermome-hanical processing, such as hot rolling[4,5] and extrusion6,7], have been employed to distribute this phase finely in theatrix. The icosahedral phase also precipitates in the matrix

8]. The icosahedral phase has better stability among otherhases and pins grain boundaries and dislocations[7].

The icosahedral phase is a quasiperiodic phase with pointymmetrym3 5, which shows a five-fold symmetry and inhich the position of successive reciprocal spots is not peri-dic but scaled by an irrational number known as the Goldeneanτ = (1 + √

5)/2 = 1.618034. . . [9]. The symmetry in

∗ Corresponding author. Tel.: +81 298 59 2346; fax: +81 298 59 2301.E-mail address:[email protected] (A. Singh).

reciprocal space is that of the regular solid icosahedron, whas 20 isosceles triangular faces. Its 12 vertices possessfold symmetry. The major zone axes in the icosahedral pare 6 five-fold axes, 10 three-fold and 15 two-fold axes.cause of its quasiperiodicity, its diffraction patterns canbe indexed using schemes for the periodic crystals. Twdexing schemes in use are given by Elser[10] and Cahn eal. [11], both using six integer indices. These two scheare complimentary to each other[12]. The Elser indices aused in this paper, in which the nearest diffraction spot aa five-fold reciprocal vector in indexed{100000}. Two mosintense reciprocal spots are the{211111} which occur alongfive-fold vectors and{221001} which occur along two-folvectors (the Mg–Zn–Y icosahedral phase is ordered F[2] in which the indices are doubled; however, in thisper only primitive indices are used). Diffraction alongtwo-fold axes is most informative because this zonetains all the important reciprocal vectors—five-fold, thrfold and two-fold. In the two-fold diffraction pattern, a reangle drawn by joining the five-fold vector spots{211111} iscalled a Golden rectangle, because the ratio of the length

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.02.036

A. Singh et al. / Materials Science and Engineering A 397 (2005) 22–34 23

sides is the Golden meanτ. The Mg–Zn–Y icosahedral phaseshows a pentagonal dodecahedral morphology[2], whichsuggests that five-fold planes form low energy surfaces. Twin-ning of the icosahedral phase is observed to occur on five-fold planes, the matrix and the twin sharing a five-fold axis[13,14].

An orientation relationship (OR) occurs between theicosahedral phase and magnesium, called OR1 here, which isdescribed by Singh et al.[8]. In this orientation relationship,three mutually perpendicular icosahedral two-fold zone axesoccur along the hexagonal, [1 0 0] and [1 2 0] axes. A set oficosahedral two-fold planes is parallel to the hexagonal basalplanes. A variant of this relationship, called OR2, also occur[7]. Observed occasionally, in this variant too, three of theicosahedral two-fold axes, which are mutually perpendicu-lar, occur parallel to hexagonal, [1 0 0] and [1 2 0] axes, butin this case the icosahedral lattice is rotated 90◦ with respectto the hexagonal lattice around the hexagonal axis. In bothOR1 and OR2, two of the icosahedral two-fold reciprocalvectors are parallel to matrix (0 1 0) and (21 0), but while inOR1, two of the five-fold vectors correspond to{1 0 0} andin OR2, they correspond to{1 1 0}. Singh et al.[15] havefurther shown that even more ORs are possible. In an orien-tation relationship called OR3, a five-fold axis occurs alongthe matrix hexagonal axis. These three orientation relation-ships are shown to be related to each other by twinning of them

ei istsi lib-r nta-t se isd

dralp iluteM ei nter-f d ont ma-t eent d theo thei

2

asp reat-m d at4 izedsw ans-m EMo monds OL

2000FX-II equipped with EDS and a 4000EX-II TEMs wereused for observation.

3. Results

On solutionizing at 460◦C, the grain boundary icosahe-dral phase transformed to a hexagonal phase H with lat-tice parametersa= 0.918 nm andc= 0.95 nm[17]. Simul-taneous with this, started dissolution of the grain boundaryphase. The composition of the H phase was determined tobe Mg–60 at%Zn–20 at%Y. Rod-like precipitatesβ1, bear-ing the structure of MgZn2 and oriented parallel to the matrixhexagonal axis, occurred in the matrix.

Fig. 1. (a) W phase on a grain boundary and (b) the composite diffractionpattern from the W phase as well as the matrix, recorded off-zone axis todistinguish between the W phase and the matrix spots. The W phase is in a〈1 1 1〉 orientation while the matrix is in〈1 0 0〉. The W spots are marked bya hexagon.

atrix or the icosahedral phase.A cubic W phase Mg3Zn3Y2 competes strongly with th

cosahedral phase in dilute Mg–Zn–Y alloys. It also exn equilibrium with the matrix, and can also exist in equiium with the icosahedral phase. A crystallographic orieion relationship between the icosahedral and the W phaescribed by Singh and Tsai[16].

Here, we present studies of interfaces of icosahehase formed by solid state reactions in solutionized dg–Zn–Y alloys on annealing at 400◦C. Formation of th

cosahedral phase occur in the matrix and the W–Mg iaces. The orientation of the icosahedral phase formehe W phase is dictated by the W phase, rather than therix. This leads to two new orientation relationships betwhe icosahedral phase and the matrix. We have studierientation relationships, the resulting morphology and

nterfaces.

. Experimental

Alloy with composition Mg–2.5 at%Zn–0.5 at%Y wrepared in an electric furnace. Isothermal annealing tents were performed on the alloy. It was solutionize60◦C (the eutectic temperature) for 15 h. The solutionamples were annealed at 400◦C for 30 min, followed byater quenching. The microstructure was studied by trission electron microscopy (TEM). For preparing for Tbservations, samples were sliced by a low speed diaaw, thinned mechanically and finally ion milled. A JE

24 A. Singh et al. / Materials Science and Engineering A 397 (2005) 22–34

On annealing at 400◦C, the grain boundary phase trans-formed to the W phase, while precipitation of the H phaseand the icosahedral phase occurred in the matrix. The Hphase precipitation was in form of rods growing along its[0 0 1] direction but with no apparent orientation relation-ship with the matrix. The icosahedral phase precipitation oc-curred by heterogeneous nucleation in form of plates in thebasal planes of the matrix, showing the orientation relation-ship OR1. The icosahedral phase also nucleated on the Wphase at the grain boundaries. Icosahedral phase was alwaysfound on the W–Mg interface.

3.1. Orientation relationships and morphology

Fig. 1shows an example of a grain boundary W phase anda composite diffraction pattern with one of the grains. The Wphase precipitates are oriented along a〈1 1 1〉 zone axis (thisdiffraction pattern is recorded off-zone to show the spots fromthe two phases separately). The streaking is from the rod-likeβ1 precipitates in the matrix. From this composite diffractionpattern, it can be seen that this orientation relationship isthe Burgers OR, which can be written as [1 1 1]W‖[1 0 0]Mg,(1 1 0)W‖(0 0 1)Mg. The orientation relationship is depictedon a stereogram inFig. 2, which is drawn such that [1 1 0]Wand [0 0 1]Mg are coincident in the center, and [0 0 1]W and[1 0 0] are also coincident.

Fig. 3shows an idiomorph of a W phase several microm-eters long and about half a micron thick. Icosahedral phaseoccur on its surface. A composite diffraction from the Wphase and an icosahedral phase precipitate on its surface isshown, where the icosahedral phase is in a two-fold zoneaxis orientation, while the W phase is along a [0 1 1] zoneaxis. The matrix orientation is near [1 2 1]. The orientationrelationship between the icosahedral phase and the W phasefollows that described by Singh and Tsai[16]. The five-foldvectors are along the W phase{2 2 0} and{1 1 3}, while thetwo-fold vectors are along{1 1 1} and{1 1 3}.

In the orientation relationship between the matrix and theW phase, along the unique hexagonal axis of the matrix occura 〈1 1 0〉W axis. At the same time, along a〈1 1 0〉 axis of theW phase would occur either a five-fold or a two-fold axis ofthe icosahedral phase[16]. Thus, an icosahedral precipitategrowing on a W phase will have a five-fold or a two-foldaxis along the matrix hexagonal axis. This will result in twoorientation relationships between the icosahedral phase andthe matrix. These two orientation relationships are depictedon stereograms inFig. 4and will be referred to as WOR1 andWOR2. Both of these orientation relationships were found tooccur. The relationship between the axes and planes of theicosahedral phase, the W phase and the matrix is listed inTable 1. Because of the lowering of symmetry in the hexago-nal lattice, each icosahedral–W relationship is split into two.

Fm

Mg

ig. 2. Stereogram showing the orientation relationship between the W phasatrix phase (Mg), drawn in lighter ink, along the hexagonal axis.

e and the matrix. The W phase stereogram is oriented along [1 1 0] axis while the


Fig. 3. (a) Icosahedral phase grown on W phase. (b) A composite diffractionfrom the icosahedral phase and the W phase. The icosahedral phase is in atwo-fold zone axis orientation while the W phase is oriented along a〈1 1 0〉axis.

The icosahedral two-fold-〈1 1 0〉W axis pair occur along threeof the hexagonal-Mg lattice—one [1 2 0] and two

⟨1 2 1

⟩.

The example ofFig. 3 occurs close to a⟨1 2 1

⟩Mg ma-

trix zone axis and corresponds to the orientation relationshipWOR2. The icosahedral phase is in contact with the W phasethrough one of its five-fold facets, which matches with a setof {1 1 0} planes of the W phase, but this interface is not pla-nar. In the matrix, the icosahedral phase shows faceting on afive-fold and two-fold planes. The facetted five-fold plane isalong a{1 0 1} low-index matrix planes, while the two-foldplane is along a{11 3} matrix plane, which is also observedin the stereogram ofFig. 4(b). Interplanar spacings acrossthese interfaces are listed inTable 2. In case of the WOR1too, a W[1 0 1] axis and an icosahedral two-fold axis occurat an equivalent matrix axis [3 2 1], but the orientation of theicosahedral phase with respect to the matrix is different.

Fig. 5shows an example of WOR1 under various tilt con-ditions.Fig. 5(a) and its diffractionFig. 5(b) are along a two-

Table 1Axes and planes correspondence between matrix and the icosahedral phasewith respect to the W phase

I phase W phase No. WOR1 No. WOR2 No.

AxesTwo-fold 〈1 1 0〉 3 [0 0 1] 1 [1 2 0] 1

[3 2 1] 2 [1 2 1] 2

〈1 1 1〉 3 ∼[1 1 0] 1 ∼[1 1 0] 2[1 0 1] 2 [1 0 1] 1

〈1 1 2〉 3 [2 3 0] 1 [3 0 1] 1∼[1 5 1] 2 [2 1 2] 2

〈1 1 3〉 6 [5 0 1] 2 [1 3 3] 2[2 3 1] 2 [5 6 2] 2[0 1 1] 2 [4 1 0] 2

Five-fold 〈1 0 1〉 3 [1 2 0]–[3 5 0] 1 [0 0 1] 1[1 2 1] 2 [3 2 1]–[4 2 1] 2

〈1 1 3〉 3 [1 1 1] 2 [3 0 1] 1[5 2 0] 1 [1 4 1] 2

PlanesTwo-fold 1 1 0 3 0 0 1 1 0 1 0 1

5 1 6 2 5 6 6 (1 1 1) 2

1 1 1 3 ∼1 1 0 1 215 12 1 5 2 3 2 0 2

1 1 2 3 1 1 0 1 21 2 13 8 4 2 1 0 3 2

1 1 3 6 ∼1 3 3 2 1 2 3 22 1 1 2 41 0 21 2 5 2 1 2 5 2

Five-fold 1 0 1 3 ∼0 1 0 1 0 0 1 15 6 6 (1 1 1) 2 1 0 1 2

1 1 3 3 1 1 5 2 2 7 6 (1 3 3) 2∼1 0 0 1 6 3 5 1

fold axis of the icosahedral phase, which is along a [1 1 0]axis of W and close to the hexagonal axis of the matrix. Theorientation of the icosahedral phase diffraction is shown bythe Golden rectangle drawn by joining the five-fold vectors{211111}. Thus, vectors through its vertices are five-fold,and through its sides are two-fold. In this case, one of theicosahedral five-fold vectors is almost coincident with ma-trix (0 1 0) vector, but the hexagonal axis is shifted by a fewdegrees with respect to the icosahedral two-fold axis. Theapproximate directions of the prismatic vectors are markedin the diffraction pattern.

The morphology along another two-fold, along W[1 0 1],close to matrix [3 2 1] is shown inFig. 5(c and d). Here,facets on one set of icosahedral two-fold planes match ma-

Table 2Interplanar spacings of some of the matching planes of the icosahedral phase,the W phase and the matrix inFig. 3(a)

Phase Plane Spacing I-plane I-spacing

W 2 2 0 2.41 5-f{211111} 2.435

Mg 11 3 1.47 2-f{221001} 2.342-f {322002} 2.34/τ = 1.4462

1 0 1 2.45 5-f{211111} 2.435


trix (2 1 4) (∼ 21 5). The other set of two-fold planes corre-spond to matrix (1 2 1) and the five-fold planes correspond tomatrix (11 1) and (1 1 5). Another two-fold axis correspondsto W[1 1 1] and matrix [1 0 1] axis. Details of interfaces inthis orientation are shown inFig. 6. Fig. 5(e) shows the mor-phology when viewed close to the matrix [1 0 0] axis. Thereare facets on the basal and a{1 0 1} planes of the matrix.The sharpest facet is on an icosahedral five-fold plane, whichmatches with a matrix (0 1 0) plane. The (0 0 1) facet corre-sponds to an icosahedral two-fold.

Fig. 7 shows an example of WOR2 viewed along thehexagonal axis of the matrix. The ordered form of W, W′,is observed, whose lattice parameter is about three times thatof the W phase[18]. The zone axes of the three phases do notcoincide exactly; therefore, two separate diffraction patternsare shown. In one (Fig. 7(b)), it is seen a five-fold pattern ofthe icosahedral phase is close to the matrix hexagonal axis.Ten concentric spots making the five-fold pattern are markedby circles. InFig. 7(c), diffraction spots from all phases areobserved, where the W′ phase is in [1 1 0] zone axis. Twoof the five two-fold axes in the icosahedral five-fold patternare observed, with the expected OR with the W phase. TheOR between the matrix and the W phase is a variation ofstereogram inFig. 2, by a rotation of 90◦ about each other.Therefore, a{1 1 0}W plane is parallel to a{2 1 0}Mg plane,

instead of{0 1 0}Mg plane. This, however, keeps the orien-tation relationship between icosahedral phase and the matrixnearly unchanged. A rotation of 36◦ about a five-fold axis inan icosahedral phase is equivalent a 90◦ rotation. In a hexag-onal lattice, a rotation of 30◦ about the hexagonal axis isequivalent to a rotation of 90◦.

3.2. Interfaces

Fig. 6is an example of WOR1 in which the W phase is in〈1 1 1〉 orientation, the icosahedral phase grown on its sidesare oriented along two-fold axes, and the matrix along [1 0 1]axis. The composite diffraction pattern from all the threephases shows a five-fold reciprocal vector along (22 0) of Wand (01 0) of the matrix. Another five-fold vector is along(2 02) of W and (11 1) of the matrix. An icosahedral two-foldvector is close to (02 2) of W and (1 01) of the matrix. An-other two-fold is along (21 1) of W and (12 1) of the matrix.While the interfaces between the icosahedral phase and thematrix are planar, those between the icosahedral phase andthe W phase are curved. The interfaces with the matrix aremainly on five-fold and two-fold planes of the icosahedralphase, which are on{0 1 0} and{1 0 1} planes of the matrix.In the multi-beam micrograph ofFig. 6(a), interfaces marked‘c’ and ‘d’ are whose lattice images are shown.

Fl

ig. 4. Two possible orientation relationships of the matrix with icosahedralighter ink, W in dark ink and icosahedral phase in black.

phase nucleated on a W phase (a) WOR1 and (b) WOR2. Matrix stereogram in


Fig. 4. (Continued).

Fig. 6(c) is a lattice image from the region marked ‘c’ inFig. 6(a). This interface is close to a set of two-fold planes.Matching between the planes on either sides of the interfaceis clearly seen. In this orientation, a set of (11 1) matrix and aset of five-fold planes are clearly imaged. These planes appearto be continuous across the interface, with a few degrees bentat the interface.

Fig. 6(d) is from a thicker part of this interface, at locationmarked ‘d’ inFig. 6(a). This interface makes about 10◦ with aset of two-fold planes. At intervals, marked by arrows, ledgesare noticed. These ledges are on matrix (0 1 0) and a set offive-fold planes. Interfaces on five-fold planes, however, arequite planar. The interface at ‘f’ is sharply on the five-foldplane, parallel with (11 1) matrix plane.

In the case of interface between the icosahedral phase andthe W phase in region marked ‘e’ inFig. 6(a), very littlecontrast difference across the interface was observed. Theinterface was very irregular and difficult to distinguish. A setof five-fold planes were almost perfectly parallel to W phase(11 0) planes, which appear to be quite continuous across theinterface. Another set of five-fold planes were nearly parallelto W phase (1 01).

3.3. Twin orientations

The growth of the icosahedral phase on the W phase canr

phase is in [1 1 0] orientation, the icosahedral phase on eithersides, marked ‘m’ and ‘n’ of the W phase are in two-foldorientations, but are twin related. This W zone axis containsonly one{2 2 0} reciprocal vector, along which occurs a five-fold vector each of the icosahedral phase on two sides of theW phase. The other five-fold vector in each of the icosahe-dral phase grains are on two different vectors of kind{1 1 3}.Thus, the icosahedral phase on the two sides are twin re-lated with a common five-fold vector. The diffraction patternfrom the region ‘m’ is shown inFig. 8(b) while that fromthe region ‘n’ inFig. 8(c). The spots from the W phase arecommon in these two regions, but the icosahedral two-folddiffraction patterns are oriented differently. The orientationof the icosahedral two-fold patterns is shown by drawing aGolden rectangle. In each case, one of the diagonals of therectangle is parallel to the (2 2 0)W vector. This diagonal iscommon to the icosahedral phase at ‘m’ and ‘n’, and corre-sponds to a twin axis.

4. Discussion

The W phase is a competing phase with the icosahedralphase. Phase diagrams[3] show that both these phases canexist in equilibrium with the matrix. The W phase forms athigher temperatures. According to the ternary phase diagram[ ctic
esult in twin orientations. An example is inFig. 8. The W 19], the W phase can form directly from the melt by a eute


Fig. 5. An icosahedral phase growing on a W phase, showing orientation relationship WOR1 with the matrix, observed under different tilt conditions. (a) Abright field image and (b) a composite diffraction pattern along the matrix hexagonal axis. The orientation of the icosahedral two-fold pattern is marked by arectangle where the five-fold vectors pass through the vertices. (c and d) Bright field image and composite diffraction pattern along an icosahedral two-foldaxis along W[1 0 1] close to matrix [3 2 1] axis. (e) A bright field image close to matrix [1 0 0] axis. Images and diffraction patterns along the two-fold axisalong W [1 1 1] and matrix [1 0 1] are shown inFig. 6.


Fig. 6. (a) A multibeam micrograph showing the morphology of icosahedral phase (IQC) growing on a W phase (W) in the matrix (Mg). (b) A compositediffraction pattern of the three phases—the icosahedral phase along a two-fold axis, the W phase along〈1 1 1〉 and the matrix along [1 0 1]. (c and d) Latticeimages of the interfaces in region ‘c’ (c) and region ‘d’ (d) marked in (a).

reaction

L = Mg + W; 550◦C (1)

The W phase and the icosahedral phaseI are in equilibriumby the reaction

L + W = Mg + I; 448◦C (2)

The primary eutectic phase has been mentioned in theternary phase diagrams[19] as hexagonal Mg85Zn6Y9 withlattice parametersa= 3.224A andc= 46.985A. This phaseis reported in quaternary alloys containing Zr[20]. In theternary Mg–Zn–Y alloys, the primary eutectic phase has been

identified[17] to be a hexagonal H phase with a compositioncomposition Mg24Zn59Y17, lattice parametersa= 9.18A andc= 9.5A, and structure similar to Zn5RE [21]. The icosa-hedral phase transforms to this phase on annealing abovethe eutectic temperature. The H phase can also transformto the W phase, according to the phase diagram by Tsaiet al.[3].

4.1. Orientation relationships and the relationshipbetween them

WOR1 is almost like the orientation relationship OR1,which is the most commonly found between and icosahedral


phase and the magnesium matrix. It can be seen that WOR2 isthe same as the orientation relationship OR3 between icosa-hedral phase and magnesium, described by Singh et al.[15],where OR1 and OR3 are shown to be related to each otherby a twinning of the matrix or a twinning of the icosahedralphase.

Tilting sequences showed that the two-fold axis in caseof WOR1 (Figs. 5 and 6) and the five-fold axis in case ofWOR2 (Fig. 7) are not coincident with the hexagonal axis.Thus, in case of WOR1, the adjustment of the orientationand interfaces of the icosahedral phase with the matrix is notreally as shown inFig. 4(a), in which the icosahedral two-foldaxis is slightly disoriented about the matrix hexagonal axis.Instead, the matrix [1 0 1] and W phase [1 11] axes coincidewith an icosahedral two-fold axis, and a five-fold plane isparallel to matrix (0 1 0) (Figs. 5 and 6). For this reason, theorientation relationships WOR1 and WOR2 are drawn again,Fig. 9(a and b). In both of these, an icosahedral two-fold axisis shown to occur along [1 0 1]Mg–[1 11]W in the centre ofthe stereogram. The icosahedral phase is oriented differentlyin these two ORs about this two-fold axis, such that anothertwo-fold axis nearly coincides with [1 1 0]W along the matrixhexagonal axis in WOR1 (marked A) and a five-fold axis incase of WOR2 (marked B′).

The important difference between WOR1 and WOR2 isthat the orientation of the icosahedral phase in these twoO ec-ttt e isa ent -foldp o-f seo n-t theW hases anes,efi hipW ari-a sameg dralp R1a

F gr . (b)A rkedw entricsm e Wp ill bet

Rs is twin related. An icosahedral twin occurs by reflion across a five-fold plane[13,14]. The two-fold axis inhe center of the stereogram in WOR1 inFig. 9(a) containsraces of two five-fold reciprocal vectors. One of theslong the matrix (1 1 1) and is marked in the figure. Wh

he icosahedral stereogram is reflected across this fivelane, the five-fold axis at B now coincides with the tw

old axis A. This new OR is equivalent to WOR2. In caf WOR2 inFig. 9(b), the two-fold zone at the centre co

ains two five-fold planes which are approximately alongphase (1 0 1) and (0 1 1) planes. If the icosahedral p

tereogram is reflected across one of these five-fold plither a two-fold at A′ or the one at A′′ coincides with theve-fold axis at B′. This produces an orientation relationsOR1. In this context, the observation of twin related v

nts growing on the W phase assume importance. In therain of matrix, two twin related variants of the icosahehase can hold two different ORs with the matrix, WOnd WOR2.

ig. 7. An example of icosahedral phase growing on W′ phase exhibitinelationship WOR2. (a) A bright field image showing the morphology

composite diffraction pattern of the matrix along hexagonal axis (maith a hexagon) and the icosahedral phase in five-fold zone (ten concpots are marked with circles). A reciprocal direction of the W′ phase isarked. (c) A composite diffraction pattern of all three phases. Th′hase is in [1 1 0] zone axis. Indices marked are for W phase and w

ripled for the W′ phase.


Fig. 8. Icosahedral phase grown on two sides of the W phase are twin related. (a) A bright field micrograph; (b) and (c) are diffractions from regions marked‘m’ and ‘n’, respectively, in (a). The icosahedral phases are in two-fold orientations while the W phase is in a〈1 1 0〉 orientation. Golden rectangles are drawnfor the icosahedral two-fold patterns. In both the diffraction patterns, a five-fold reciprocal vector is along the W phase{2 2 0} (shown by a diagonal of theGolden rectangle drawn with a full line) while the other five-fold vector is along a different W phase{1 1 3} reciprocal vector.

4.2. Orientation and shape

The equilibrium shape of a Mg–Zn–Y icosahedral singlephase is known to be a pentagonal dodecahedron[2]; thus,its faces are five-fold planes and growth direction three-foldaxes. The edges are two-fold directions. The low energy facesare thus five-fold and two-fold planes, in that order.

In the orientation relationship between the icosahedralphase and the W phase[16], the intersection symmetry is3m, whose order is 12. Since the order of the icosahedralpoint group symmetrym 3 5 is 120, W phase growing on anicosahedral phase can have 10 variants. In the transformation

studied here, the icosahedral phase nucleates on the W phase,which possesses the point group symmetrym 3m. Icosahe-dral phase growing on it can have four variants.

In case of the WOR1, the intersection symmetry would benearly 2m, while in case of WOR2 it is justm. Therefore, theorder of the intersection symmetry in case of former is 4 andlatter is 2. If the icosahedral phase were growing freely in thematrix, in case of WOR1 there would be 6 variants while incase of OR2 there could be 12.

It is observed that the icosahedral phase does not formsharp interfaces with the W phase. Crystallographically, thetwo phases have a very good match, as shown by diffraction


patterns by Singh and Tsai[16]. They may share commonstructural units, even though W is not a rational approximantto the icosahedral quasicrystal in a strict sense[16]. Thus, thechemical part of the interfacial energy would be low.

The morphology of the icosahedral phase in magnesiumis dominated by low energy planes – the five-fold and thetwo-fold planes – of the icosahedral phase, and the basal andprismatic planes of the matrix. Prominent facets are formedby a match of the matrix basal planes with the icosahedraltwo-fold (WOR1) and five-fold (WOR2). Other prominentfacets are by match of matrix prismatic planes with icosahe-dral two-fold or five-fold planes.

4.3. Quasicrystal–crystal interface

In case of the icosahedral phase precipitates in magne-sium, the interfaces are on two-fold planes, which interfaceswith {1 0 0} and (0 0 1) matrix planes, the low energy planesof the hexagonal phase. Taking the quasilattice parameter ofthe Mg–Zn–Y icosahedral phase as 0.52 nm[2], the interpla-nar distance of the two-fold{221001} planes are 0.234 nm.Considering the matrix as pure magnesium, the misfit with the{1 0 0} planes is 10.17% while that with the (0 0 1) planes is15.77%. This explains the broader interface with the{1 0 0}planes, and minimizing the width along the hexagonal axis.

The misfit of the five-fold planes{211111} is about 12.35%with (1 0 0) and just 6.5% with the (0 0 1) planes. The in-terfaces with the matrix are, however, predominantly on thetwo-fold planes. That an icosahedron has sets of three mu-tually perpendicular two-fold planes will help matching themutually perpendicular low energy faces of the hexagonalphase.

One side of the interface being quasiperiodic, has planesarranged quasiperiodically, all of which cannot match theperiodically arranged planes of the crystalline phase. It isdifficult to thus classify the interface as a coherent or an in-coherent one. In the reciprocal space, the most intense spotsin the whole lattice are the{211111}, which are along five-fold reciprocal directions, and{221001}, along two-fold.These spots also correspond to usual interatomic spacingsof about 2.5A. Thus, these two interplanar distances mustcorrespond to the dominant coordination in the lattice. Mostoften the quasicrystals make interfaces on their five-fold ortwo-fold planes, in which the{211111} or {221001} planesmatch with the crystal planes. Aτ inflation or deflation pro-duces other interplanar spacings of the quasiperiodic planes.This inflation/deflation can produce numbers, which mightmatch spacings of the other planes in the neighboring crys-tal. For example, in the example ofFig. 3(a), followingWOR2, an icosahedral two-fold plane makes an interface

Fr

ig. 9. Modified orientation relationships WOR1 and WOR2 drawn with [1 0 1elated by reflection (twinning) across five-fold planes marked with lines.

] of the matrix and the [1 11] axis of the W phase in center. These two ORs are


Fig. 9. (Continued).

with a (11 3) plane of the matrix. Looking up the interplanarspacing inTable 2, it is noticed that the interplanar spacingof the (11 3)Mg plane is 1.47A. In the matching icosahedraltwo-fold plane, the interplanar spacing corresponding to the{221001} spot is 2.34A. However, the spacings correspond-ing to the next inflated reciprocal spot,{332002} is 1.4462A,which is close to the interpalanar spacing of (11 3)Mg. Thus,the {332002} planes would match the (11 3)Mg across theinterface. It brings the possibility that icosahedral planes canform interfaces with a variety of planes in a crystalline phase.

It can be concluded that the icosahedral phase can formlow energy interfaces with a crystalline phase because of its(a) high rotational symmetry, which gives large possibilitythat a low energy icosahedral plane will be parallel to a lowenergy crystalline phase plane and (b) quasiperiodicity givingrise to a variable interplanar spacing, increasing the chancesof an atomic match across the interface.

5. Conclusions

A Mg97Zn2.5Y0.5 alloy containing icosahedral quasicrys-talline phase was solutionized at 460◦C. Upon this treatment,the icosahedral phase dissolved or transformed to a hexago-nal H phase. On annealing again at 400◦C, icosahedral phase

formed by nucleating heterogeneously. The crystallographicorientation, morphology and interfaces with the matrix of theicosahedral phase formed on W phase by the reaction of theW phase and the matrix are studied here.

(1) The W phase exhibits and orientation relationshipwith the matrix, such that [0 0 1]W‖[1 0 0]Mg, (1 1 0)W‖(0 0 1)Mg, equivalent to Burgers orientation relationship.

(2) It is shown that growth of icosahedral phase on W phaseresults in two more orientation relationships betweenthe icosahedral phase and the magnesium matrix, calledWOR1 and WOR2 here.

(3) The WOR1 is a slight deviation of the orientation rela-tionship OR1 of an icosahedral precipitate with the ma-trix.

(4) The WOR2 is significantly different, in which a five-foldaxis is along the matrix hexagonal axis. This orientationrelationship is equivalent to an orientation relationshipOR3 between an icosahedral phase and�-Mg matrix.

(5) The two orientation relationships are related to each otherby a twinning of the icosahedral phase.

(6) The interfaces of the icosahedral phase with the matrixare facetted, but with W phase are not. The facets are onfive-fold and two-fold planes of the icosahedral phase.These facets match mainly the basal and the prismatic


planes of the matrix, but also higher index planes to ac-commodate asymmetry in the orientation.

(7) The lattice images show a good matching of the planesacross interfaces. The interfaces often contain ledges onhigh-symmetry/low-index planes.

(8) It is argued that the high symmetry and the quasiperiod-icity of the icosahedral phase raise the possibilities of amatched interface with a crystalline phase.

Acknowledgement

This work is partially supported by Japan Science andTechnology Corporation.

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