A transmission electron microscopic study of icosahedral twins—II. A rapidly solidified Al-Cu-Fe alloy

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A(ta metalL mater. Vol. 43, No. 9, pp. 3553 3562, 1995

Pergamon

0956-7151(95)00025-9

Elsevier ScienceLtd Copyright ~" 1995Acta MetallurgieaInc. Printed in Great Britain.All rights reserved 0956-7151/95 $9.50+ 0.00

A T R A N S M I S S I O N E L E C T R O N M I C R O S C O P I C S T U D Y OF ICOSAHEDRAL TWINS--II. A RAPIDLY SOLIDIFIED AI-Cu-Fe ALLOY ALOK SINGH and S. RANGANATHANq, Centre for Advanced Study, Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India (Receiced 3 Noeember 1993: in r e v i s e d j b r m 16 October 1994)

A~traet--Twinning of the ordered icosahedral quasicrystal has been studied by transmission electron microscopy in a melt-spun A17,futzsFe~2~ alloy. Dendrites of about 10 #m of the icosahedral phase, formed near the wheel side of the melt spun ribbons, have been observed to twin extensively so that a multiple twinning of the grains is observed. Regions of about 1 i t m size are twin related through a common five-fold axis to several neighbouring regions. The possibility of different orientations of the twins formed by repeated twinning is infinite. Thus the multiple twinning gives rise to a random symmetry for the whole grain. Depending on the undercooling achieved across the melt-spun ribbons, several related phases like the decagonal quasicrystal and crystalline monoclinic AI3Fe phase in ten-fold multiply twinned form were also observed.

I. INTRODUCTION An interesting microstructure of the icosahcdral phase [1] was reported by Koskenmaki et al. [2] in an A I - M n Fe alloy where the icosahedral phase twins with a mirror plane perpendicular to a five-fold axis. Ranganathan e t al. [3] studied these icosahedral twins in an Alg0Mnl0 alloy and showed that the symmetry of the twinned grain is similar to that of a decagonal quasicrystal. Singh and Ranganathan [4] studied icosahedral twins in AI Mn--Fe alloys. Detailed studies on the icosahedral twins in the A I - M n Fe alloys has been reported in Part I [5]. Here in Part II we report investigations on icosahedral twins in an A I - C u - F e alloy. It is to be mentioned here that recently an icosahedral twin has been reported in an A162Cu25.sFe12.5 alloy [6] and deformation twins reported in an A16~Cu2~Fe~: alloy [7] in independent studies. After the discovery of the icosahedral [1] and the two-dimensional quasicrystal decagonal phase [8, 9], a major discovery has been that of an ordered and stable icosahedral phase in A1 C u - F e system by Tsai e t al. [10]. Ebalard and Spaepen [1 1] showed that this phase was face centered ordered in real space in six dimensions and the presence of anti-phase domains was demonstrated [12]. This phase reversibly transforms to ~i rhombohedral rational approximant phase at lower temperatures [13 17] with reports of a modulated quasicrystalline phase appearing during the transformation [18], shown to be an intermediate phase between the quasicrystal and the rhombohedral ;To whom all correspondence should be addressed.

phase [19]. A pentagonal phase is also reported in this system [20, 21]. Bancel [22] has reviewed the stability range of the quasicrystal in the A1 Cu Fe system and other phases which occur in its vicinity in the phase diagram. The composition of the stable icosahedral phase is close to AI62Cu25.5Fel, 5 [23]. This phase has now found a place on the stable ternary phase diagram [24]. The other ternary phases reported in this system are an orthorhombic AI23CuFe4 [25] and a tetragonal ALCu2Fe [26]. Apart from the stable icosahedral phase other quasicrystalline and related phases are found in the AI Cu Fe system. The decagonal phase formed on rapid solidification has also been reported in this system [27]. Liu and Koster [16] have shown that the icosahedral phase in a rapidly solidified alloy of composition AlTuCU2~,Fe~0decomposes to the tetragonal AL Cu2 Fe phase by a polymorphic reaction on heat treatment. The monoclinic AI~Fe [28] phase is often found to exist in AI~Cu-Fe alloys. This phase is known to be related to the decagonal phase [29 31]. Cheng e t al. [32, 33] have shown the AI3Fe phase in melt-spun AI6Cu z Fe alloy to be related to the decagonal as well as the icosahedral phase. They have discovered a phase intermediate between the decagonal and the AI 3Fe phase in melt-spun AlT~Cu~0Fe~3 [34]. They have discovered an incommensurate phase a" which appears to be an intermediate phase between a one-dimensional quasicrystal and a tetragonal cr phase [33, 35]. In this study an alloy of composition AIT~Cu~2~Fe~:~ has been taken up, which forms a metastable ordered icosahedral phase on rapid solidification, lcosahedral twinning occurs in this alloy in

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SINGH and RANGANATHAN:

STUDY OF ICOSAHEDRAL TWINS--II

an extensive fashion. Although an icosahedral twin in A1-Cu-Fe alloys has been already reported [6, 7], this is the first report of a detailed study of twinning in a face-centered icosahedral quasicrystal where repeated twinning of the icosahedral twinning during growth has been observed. The dccagonal phase and the A13Fe phase in a ten-fold multiply twinned form were also observed in this alloy. Presence of planar defects produces structures linking these phases.

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2. EXPERIMENTAL TECHNIQUES The alloy of composition Al7sCu~:sFel: s was prepared by induction melting high purity metals in appropriate quantities in an alumina crucible in an evacuated chamber backfilled with argon gas. The alloy was then melt spun by induction melting in a quartz tube and ejecting through a nozzle with 1 mm diameter, under argon pressure, on to a rotating copper wheel. The melt spun ribbons were thinned by ion milling for observation in a JEOL 2000FX-II transmission electron microscope (TEM). X-ray diffraction on powder samples was carried out on an Enraf-Nonius diffractometer with CoK~L radiation. Differential scanning calorimetry (DSC) was performed on a Perkin Elmer model C2.

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3.1. Phase ]brmation Figure 1 shows X-ray diffraclograms of the alloy in conventionally solidified, melt-spun and heat treated conditions. The phases identified in the as-cast alloy are AlvCu2Fe, Al~Fe, ALCu and aluminium. Figure 2 shows the DSC traces of the as-cast and the melt spun alloys. The as-cast alloy shows an

Fig, I, XRDs of A17sCul25Fet25 alloy in (a) conventionally cast; (b) melt-spun; and (c) melt-spun and aged at 437°C for lh.

endothermic peak beginning at about 565=C and ending at about 590(7. Another endothermic peak starts at about 620+C. Referring to the phase diagram

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Fig. 3. (a) T E M micrograph of an icosahedral grain in a two-fold zone axis orientation in melt-spun A175Cuz5 Fe~: 5 alloy showing three twin related subgrains A, B and C separated by boundaries seen as a set of fringes. (b) Selected area diffraction pattern from region A in (a); (c) selected area diffraction pattern from region A + B; (d) selected area diffraction pattern from region A + B + C; and (e) golden rectangles showing the orientation relationship between three twin variants.

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SlNGH and RANGANATHAN:

STUDY OF ICOSAHEDRAL TWINS II

[24] it is concluded that the reaction followed by the alloy is 590 C

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The phases identified in the melt-spun alloy are an icosahedral phase, A13Fe, AlzCu and aluminium. The TEM and SEM observations show that the phases near the contact side of the melt-spun foil are the icosahedral phase and AI 2Cu and near the free surface is the AI3Fe. The TEM observation of the melt-spun ribbons revealed a fine microstructure of icosahedral grains of average size of 0.5/xm near the contact side of the ribbons. These icosahedral grains were often surrounded by AI2Cu phase crystallites. The air side of the ribbons consisted entirely of highly defected A13Fe grains. This suggests that at a fast solidification rate the undercooling resulted in a solidification in the AITCu2Fe+AI2Cu phase field while at a lower undercooling it took place in the liquid+A13Fe region. The DSC trace of the melt spun alloy shows an exothermic peak at about 493cC and then an endothermic peak at about 622C. The X-ray diffractogram of Fig. l(c) shows and also from the TEM studies it was found that after an isothermal ageing for 1 h at 437"C the phases found are the AITCu2Fe, A13Fe and aluminium.

3.2. h'osahedral multiple twins A detailed study of the icosahedral phase revealed that the ~'grains" of about 1 #m are twin related to each other with a common five-fold axis between each other. Figure 3(a) shows a bright field micrograph of an icosahedral grain in a two-fold zone axis orientation and the diffraction patterns associated with it. The bright-field micrograph has a mottled contrast. Three regions marked TA, TB and TC can be recognized in the grain. These regions are separated by boundaries seen as two sets of fringes. Figure 3(b) is a two-fold zone axis diffraction pattern from the region of the grain marked TA in the bright-field micrograph. The diffraction pattern has weak superlattice spots indicating a weak face-centered ordering. Figure 3(c) shows a composite diffraction pattern from regions TA and TB. The two superimposed patterns have a common five-fold axis between them, as in the case of an icosahedral twin [2-6]. The icosahedral twin can also be expressed as a rotation of 63.43 or 116.57° around this axis [5]. Figure 3(d) is a composite diffraction pattern from the areas marked TA, TB and TC, i.e. from the whole area in Fig. 3(a) included. The diffraction pattern from the region TB has a five-fold axis common with each of regions TA and TC. Thus, region TB is twin related to both the regions TA and TC. This phenomenon is called here an icosahedral "multiple" twin. This relationship is expressed in Fig. 3(e) where the golden rectangles for each variant are shown. The golden rectangle, with sides in the ratio of the golden mean z, is obtained by joining the vertex vector spots in a two-fold zone axis pattern. The golden rectangle of

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Fig. 4a. (Caption on [acing page.)

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SINGH and RANGANATHAN:

STUDY OF ICOSAHEDRAL TWINS--It

3557

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Fig. 4. (b-k.) Fig. 4. (a) Stereogram showing three variants A, B and C of an icosahedral multiple twin. (b)~g) are diffraction patterns from an icosahedral multiple twin in orientations ~ g , respectively, marked on the stereogram. (h)~j) are bright-field micrographs of the twinned icosahedral grain corresponding to the orientations ofb. fand g respectively. (k) is an enlargement of the diffraction pattern in (g) to show details.

the twin variant TB is shown by full lines. It shares a diagonal each with the golden rectangle of the twin T A (dot dashed lines) and with TC (dashed lines). A stereogram has been constructed to show the orientation relationship between the three twin related regions of the icosahedral multiple twin [Fig. 4(a)]. It has the common two-fold zone axis of all three twins in its centre. The zone axes of different twins TA, TB and TC are shown by open, hatched and solid symbols respectively. The zone axis relationship between different twins shown in the stereogram was verified by tilting vari-

ous twinned grains. Figure 4(b-g) is a series of zone axis patterns obtained by tilting a grain through the zone axes marked correspondingly b-g in the stereogram. Bright-field micrographs [Fig. 4(h-j)] are provided for some of the orientations to show the shape of the twinned regions. The twin regions have an irregular shape. At position " b " in the stereogram occurs the two-fold zone axes of twins T A and TC with a c o m m o n five-fold axis. The diffraction pattern from this zone [Fig. 4(b)] can easily be recognized to be an icosahedral twin. A bright-field micrograph in this

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SINGH and RANGANATHAN:

STUDY OF ICOSAHEDRAL TWINS

orientation is shown in Fig. 4(h). Part of the twin boundary can be observed between T A and TC domains. A little away from this orientation, at " c " is the five-fold zone axis of the TB variant. On tilting around the c o m m o n five-fold axis of the two-fold zone axes of T A and TB at " b " the D zone axis (notation of Singh and Ranganathan [36]) is arrived at for both these twins coinciding at " d " in the stereogram. The twin variants are rotated by 180" about this axis [5]. Tilting further along the same axis leads to the unique orientation " e " where the twofold zone axes of all the three twins occur [Fig. 4(e)], sharing two five-fold axes between them, as demonstrated in Fig. 3. Tilting about a two-fold axis of the region TC, its five-fold zone axis is arrived at in orientation " f " . Its corresponding bright-field micrograph in Fig. 4(i) shows a slice of an irregular shaped region. The regions T A and TC are inter-twined with each other. Further tilting leads to two-fold zone axis of TC at "g". A bright field micrograph of TB in a two-fold zone axis orientation at " g " in Fig. 4(j) shows a highly curved boundary of a twin about half a micron in length. The vertex vector strong spots in the two-fold zone axis pattern from the twin TC in Fig. 4(g) are not well defined and some weak spots are seen adjacent to them. This pattern is shown enlarged in Fig. 4(k) for a detailed examination. It is observed that this pattern also shows multiple twinning, the twinning spots being weak as only small portions of the other two twin regions may have been left in the thinned foil. It is thus concluded that the twinning is not limited to three regions, but is propagated through several boundaries. Due to the limited dimensions of the foil this relationship may not be very apparent. An idea of the real grain size of the icosahedral phase can be had from SEM observation of the contact size of the melt-spun ribbons, where the icosahedral phase occurs. The SEM micrograph of the contact side of the melt-spun ribbon, Fig. 5, shows large grains about 10/~m across with a sub-

Fig. 5. SEM micrograph of the contact side of the melt-spun A175Cu125Fel-_5 ribbon.

II

Fig. 6. An icosahedral twin in melt-spun A175Cu12.sFe125 showing planar faults normal to the twin axis. (a) Selected area diffraction pattern; and (b) bright-field micrograph.

structure of 0.2-1 # m size. The morphology of the grain is dendritic. A high density of the dendrite arms is observed. Some irregular boundaries are seen where the dendrite arms growing from two different directions impinge on each other.

3.3. Other related phases In between the region of icosahedral phase and A12Cu at the contact side of the melt spun ribbon, and the AI3Fe near the air side a decagonal phase as well as some defect structures, which can be considered as intermediate structures between these phases, were discovered. Figure 6 shows an icosahedral twin with planar faults on the five-fold planes c o m m o n to the matrix and the twin. This results in the streaking of reciprocal spots parallel to the twin axis, seen in the selected area electron diffraction pattern of the Fig. 6(a). The corresponding bright field micrograph exhibits faults perpendicular to this axis. Figure 7 shows the decagonal phase found in this alloy. A two-fold " G " zone axis of this decagonal phase is shown in Fig. 7(a). This zone axis occurs at 9ff to the ten-fold axis and therefore contains the decagonal axis, marked in the figure. The reciprocal spots along the decagonal axis are periodic while the spots in the rows perpendicular to the decagonal axis are arranged quasiperiodically. It shows a periodicity of eight along the decagonal axis and resembles the corresponding zone axis from an A I - F e decagonal

SINGH and RANGANATHAN: STUDY OF ICOSAHEDRAL TWINS--II

3559

Fig. 8. AI3Fe phase in the melt-spun A175Cul2 sFel2 5 (a) and (b) selected area diffraction pattern and the corresponding TEM bright-field micrograph, respectively.

Fig. 7. Decagonal phase in melt-spun AlvsCul2.sFe~2.~. (a) "G" zone axis diffraction pattern; (b) bright field micrograph of the grain in G zone axis orientation; (c) "'I" zone axis pattern: and (d) "J" zone axis pattern.

phase [37] with streaking parallel to the decagonal axis. The corresponding bright-field micrograph clearly shows planar faults normal to this axis. A good correspondence between the features of this pattern and that of the icosahedral twin in Fig. 6(a) can be made. In addition to the streaking parallel to the decagonal axis, streaking perpendicular to it is also noticed in the " G " zone axis pattern of Fig. 7(a). Although Fung e t al. [37] ignored this streaking in the case of the AI-Fe decagonal phase, it is nevertheless present in their diffraction patterns too. A tilting to the other zone axes which do not contain the decagonal axis [the pseudo five- and three-folds, Fig. 7(d and c) respectively] causes the streaking parallel to the decagonal axis to disappear while that perpendicular to it remains. This shows that while the former kind is due to planar faults, the latter are sheets of intensity produced by "pencil" defects [38]. These sheets of intensity are characteristic of the decagonal phase. Figure 8 shows a diffraction pattern frequently obtained in this alloy. This diffraction pattern can be indexed on the basis of superimposed [100] and [001] zone axes of the AI3Fe phase with a coincident [010] axis. This suggests that this phase is ten-fold multiply twinned around [010] axis, since the [100] and [001] zone axes lie about 72 ~ apart and here they are observed to coincide with a c o m m o n [010] axis.

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4. DISCUSSION

4.1. Icosahedral multiple twinning The icosahedral phase studied here is ordered and shows weak face centred ordering superlattice spots. The grains of this phase show a dendritic morphology and although it has low stability, its grain size extends to 10 pm (Fig. 5), comparable to the grain size of the stable Al~sCu20Fel5 icosahedral phase [10]. But although the grain size is large here, the size of the twinned regions is very small, making selected area diffraction patterns difficult to obtain. However, the occurrence of icosahedral multiple twinning and related structures makes a study of this alloy very interesting. The twin boundaries in the icosahedral phase has been observed to be curved in the previous studies [2-4]. In the present study the twin regions are observed to be highly irregular in shape. However, as in Fig. 3(a), it is observed that the boundaries between twin related regions (seen as fringes) are fairly straight. As each region is twin related to several regions, it is possible to have an irregular shape while maintaining a planar interface with the neighbouring regions. These boundaries appear to be perpendicular to the twin axis. Thus the two boundaries are at about 116: to each other in Fig. 3(a). A similar observation about the orientation of the twin boundary with respect to the twin axis has been made by Dai and Urban [6] for a slowly cooled AI62Cu255Fel2s alloy. In Fig. 6 numerous twin boundaries are observed to occur closely, giving rise to diffuse streaks in the diffraction pattern. In case of the AI-Mn-Fe alloys [2, 4, 5] the observation that the twin boundary is curved may be due to a confusion between the dendrite shape and the twin boundary. As the different dendrite arms having different twin orientations are joined in a very small region, the twin boundary will be difficult to see. When the grain is tilted, its three-dimensional form may obscure the twin boundary [5]. On twinning, the structure at the twin boundary becomes decagonal due to a ten-fold symmetry. Since the decagonal quasicrystal forms at a lower undercooling than required for an icosahedral quasicrystal. it can be considered more stable than the icosahedral quasicrystal. Thus the twinning would produce a low energy configuration at the boundary. A number of twin boundaries close together will produce a decagonal structure. While in the AI-Mn [3] and AI M n - F e [2,4, 5] alloys the icosahedral twinning occurred in the earliest stages of growth, or possibly during nucleation, the twinning takes place at regular intervals during the growth of the icosahedral phase in A175Cu125Fel2.~. Multiple twinning of the icosahedral phase has been observed in the Alg0Mn5 Fe5 alloy too [5] but in the smaller grain size only the primary dendrite arms are observed and so the multiple twinning is not so apparent. If these grains could

grow further the secondary dendrite arms formed may be twin related to the primary arms. Due to the incommensurability of the icosahedral phase, the icosahedral twinning is not a closed operation. This also results from a high symmetry of the icosahedral phase. If an icosahedral quasicrystal matrix TM forms a twin TT, then TT can again twin to produce TM again, as observed in the twin bands observed by Dai and Urban [6] and on deformation by Shield and Kramer [7]. The twin band observed by Dai and Urban [6] may also be formed due to thermal stress [7]. Since in the present study the twins appear to have formed during growth, the twin TT has five more ways of producing twins with the other five five-fold axes. These twins do not have a simple orientation relationship to TM. As the icosahedral symmetry has six five-fold symmetry axes, when a twin TT is formed from matrix TM, five more five-fold axes are generated. This is shown in the stereogram of Fig. 9 where only the five-fold axes are marked for simplicity. The five-fold axes of the matrix TM are shown as solid pentagons and those of the twin TT as open ones. Some of these five-fold axes are twinned again to form twins denoted by A, B, C . . . . for twins formed from TM and by 1, 2, 3. . . . for twins formed from TT. With formation of each of these new twins, five more five-fold axes are created. Thus infinite twin orientations are possible. A grain containing these twins will not have a definite total symmetry. Further inspection of the stereogram of Fig. 9 shows, for example, that two five-fold axes of the twin I are close to two such axes of the twin D. A five-fold axis of twin 2 also lies close to one of such axis of twin D. The difference between these axes close to each other is 3 - 4 . Thus if these twinned regions lie close to each other, they will each have a five-fold axis nearly parallel, but not exactly parallel. When TM and TT are twinned along all of their five-fold axes, the twin D (a twin of TM) has two five-fold axes nearly parallel to ones from the twin 1, and one each to twins 2 and 5. The remaining five-fold axis does not lie close to another from a different variant. A twinning on this axis will produce another five fivefold axes. It is expected that with further twinnings the stereogram will be densely filled with five-fold axes. Generation of quasicrystalline symmetries by the multiple twinning of the crystals is known. An example is the AI 3Fe phase in the present study which shows pseudo ten-fold symmetry by such a twinning. Twinned aggregate of some cubic crystals display an icosahedral symmetry [39-42]. In these cases the twinned crystals have a limited number of orientations, for example five in case of the cubic crystals wilh icosahedral motifs. In case of the icosahedral quasicrystal, the number of possible orientations of the twins is infinite. Thus the twinned aggregate will have a symmetry like that of an amorphous material. In a diffraction from large aggregates the reciprocal

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spots would form discrete spheres, whose rotational symmetry can be considered as infinite. 4.2. Other related phases

Diffuse streaks parallel to the decagonal axis have been observed in the AI Fe decagonal phase [37]. Fung et al. [37] have taken this to be evidence in support of the theory that a decagonal phase can be obtained from the icosahedral phase by an addition of a mirror plane to a five-fold axis. This is equivalent of producing an icosahedral twin [2, 3]. Introduction of mirror plane at different sites will produce stacking of planar slabs along the five-fold axis and thus produce streaking parallel to this axis. This kind of structure is observed in Fig. 6. The decagonal phase periodicity of eight is observed in the AI Mn-Pd alloys, too, where the corresponding icosahedral phase is a face-centered ordered one [43-45] just as the AI-Cu- Fe icosahedral phase. Tsai et al. [44, 45] point out that this decagonal periodicity resembles the five-fold direction of the ordered icosahedral phase better. This is because in case of the ordered icosabedral phase the reciprocal spots are closer due to the presence of the superlattice spots. The relationship between the icosahedral, the decagonal and the AI~Fe phases has been shown by A M 43 9

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Cheng et al. [32] who studied the orientation relationship of the AI3Fe phase coexisting with the icosahedral phase in Al6CuzFe alloy. The threedimensional Penrose tiling, which is a projection of a six-dimensional hypercubic lattice onto the physical space, turns into a superposition of a series of two-dimensional Penrose tiling by a rotation of the physical space with respect to the six-dimensional space. All the rhombohedra then turn into rhombic prisms. In addition to this, when the atomic decoration is ignored, the calculated five-dimensional pattern of the icosahedral phase turns into [010] pattern of the AI~Fe phase. In addition to these three phases, intermediate defect structures have also been observed in the present study. The [100] zone axis of the A13Fe (Fig. 8) is analogous to a two-fold pattern of the decagonal phase. Due to the multiple twinning, normal to the [010]* axis in this diffraction pattern the ratio of distances of spots (200) and (001), (003) and (002), and (005) and (003) are about 1.6, close to the value of the golden mean, making almost a quasiperiodic arrangement of spots. The rows containing (kl0) with k odd spots are rather diffuse. Although the AI3Fe phase in the A175Cu12.sFe12.5 alloy shows multiple twinning, in the A 1 - M ~ F e alloys [5] it did not. Equal quantities of manganese

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SINGH and RANGANATHAN:

STUDY OF ICOSAHEDRAL TWINS--II

and iron produced the icosahedral twins in the Al90MnsFe 5 alloy. On increasing the alloying elements the icosahedral a n d the A13Fe phases formed in the A186MnTFe7 and AlsoMnmFe~o alloys. However, the decagonal phase did not form. The presence of copper in the AI75CuI2.sFe~2 5 alloy is observed to p r o m o t e the f o r m a t i o n of b o t h the icosahedral a n d the decagonal quasicrystal and therefore it is not surprising to find a multiple twinning of the AI 3Fe phase in the same alloy. 5. CONCLUSIONS The melt-spun AI75Cu12.sFeI25 alloy showed presence of multiply twinned icosahedral phase and related structures. A study of this alloy led to the following conclusions: 1. Melt-spinning produces large (10 p m ) dendritic icosahedral grains near the contact side of the wheel, containing regions of 1 p m which occur due to a multiple twinning of the icosahedral phase. This icosahedral phase transforms to the tetragonal AITCu2Fe phase on ageing above 493°C. 2. The twins in the multiply twinned icosahedral phase are related to each other by a c o m m o n five-fold axis as the twin axis. The twin b o u n d a r i e s a p p e a r to be fairly straight a n d perpendicular to the five-fold twin axis. Twin b o u n d a r i e s close to each other were also observed, resulting in streaking o f reciprocal spots. 3. Twins with infinite possible orientations can occur in a grain. Thus the multiple twinning o f the icosahedral phase does not lead to any particular symmetry for the whole grain. 4. A decagonal phase occurs in a small region at the middle thickness of the ribbons. P l a n a r faults occur perpendicular to the ten-fold axis of the decagonal phase. 5. The air side of the melt-spun ribbons c o n t a i n e d ten-fold multiply twinned A13Fe phase. Acknowledgements The authors are grateful to Professor K. Chattopadhyay and Mr A. K. Srivastava for stimulating discussions. Financial support from the Department of Science and Technology, New Delhi, and the Office of the Naval Research under the Indo U.S. Cooperation project is gratefully acknowledged. One of the authors (S. Ranganathan) is grateful to the Karnataka State Industrial Investment Development Corporation endowed chair.

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