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Diffraction approach to the structure of decagonal quasi-crystals
Volume 117, number 8
PHYSICS LETTERS A
8 September 1986
DIFFRACTION APPROACH TO THE STRUCTURE OF DECAGONAL Q U A S I - C R Y S T A L S J.-M. D U B O I S a, Chr. J A N O T b, j. P A N N E T I E R b and A. P I A N E L L I a Laboratoire de Science et G$nie des Matbriaux Mbtalliques ( C N R S U,4 159), Ecole des Mines, Pare de Saurupt, 54042 Nancy Cedex, France b Institut Laue-Langevin, 156 X, Centre de Tri, 38042 Grenoble Cedex, France
Received 6 May 1986; accepted for publication 9 July 1986
Neutron and X-ray diffraction data measured on A14Mn decagonal quasi-crystals, with a non-crystallographicpoint group 10/m, are reported. Contrast variations were produced by Fe/Mn isomorphous substitution on the transition metal sites. The independent measurements on the peak intensities allow suggestions about atomic correlations and lead to fruitful comparisons with icosahedral m35 material and/or the crystalline modifications of related composition.
1. Introduction Since the first experimental evidence for the possible existence of an icosahedral phase (iphase), with point group symmetry m35, in A16Mn melt-spun alloys [1], the same kind of rather exotic structure has been also obtained in several rapidly solidified A1-T alloys (with T a 3d transition metal) [2] and also by solid state reactions in metallic glasses [3] or in A 1 - L i - C u - M g crystalline solid solution [4]. The now famous A1-Mn i-phase forms in alloys with M n concentration ranging from 14 to 22 at%. The quenched .samples exhibit a coexistence of fcc A1 with the icosahedral phase, the latter having a m a x i m u m volume fraction at x = 0.20; a superstructure has been reported for alloys lying in the upper limit of the Mn concentration [5]. Despite the stoichiometry of the i-phase being obviously in the vicinity of A14Mn [6-8] it is far from easy to produce samples of pure i-phase at or near to this ideal A14Mn composition. It requires quite high solidification rates [9]. Currently, a so-called T-phase forms in competition with the i-one [9]. This T-phase grows in heavily faulted cylindrical domains rather than in the coral-like dendrites morphology typical of the i-phase [9]. Electron diffraction patterns of the T-phase show one ten-fold and ten equivalent two-fold
axes in consistency with a 1 0 / m point group symmetry [10]. A one-dimensional periodicity along the ten-fold axis is associated with a planar quasi-periodicity perpendicular to this axis. According to Bendersky [10], it will be referred to as the decagonal phase, or d-phase, in the following. Icosahedral and decagonal A14Mn quasicrystals have shown symmetry relationships [11,12] and strong similarities in reciprocal space, though being supposedly different in real space [13]. The purpose of the present work was to extend to the d-phase the contrast variation method previously applied in a diffraction study of the i-phase [14]. Thus, positions and intensities of the diffractions peaks have been measured with neutrons and X-rays on d-A14Mn and d-A14(Mno.v2Fe0.28 ) alloys, the latter having a M n / F e mixture with a zero average scattering length for neutrons. This so-called "zero T M " alloy was intended to provide direct information on the A1-A1 correlations in the quasi-lattice of the d-phase.
2. Sample preparation and experiments Preparation of the master alloys and quenching procedure have been described elsewhere [14]. A critical parameter is the quenching rate which has
0375-9601/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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to be ajusted at a low enough value to avoid the formation of the i-phase but must be sufficiently rapid to bypass crystallization. The samples were obtained in the form of brittle ribbons 15 to 20 ~m thick and 1 to 2 m m wide. As is well known, the reliability of a contrast variation method in neutron diffraction studies strongly depends on the randomness of the isomorphous substitution. The effectiveness of a proper M n / F e substitution has indeed been care-
X-rogs
8 September 1986
fully tested as explained elsewhere [14,15] and is further supported by the X-ray diffraction patterns shown in fig. 1 which are identical for dAlnMn and d-A14(Mn0.72Fe0.28 ) alloys. Incidentally, these X-ray patterns do not exhibit any resolved Bragg peaks at the positions expected for the (111) and (200) reflections in fcc aluminium. Thus, the amount of fcc A1 retained in the samples can be considered as negligible with the consequence that the d-phase has indeed the A14Mn (or A14(Mn, Fe)) nominal composition. The typical morphology of the d-phase grains, as observed on electron micrographs in fig. 2 together with corresponding diffraction patterns, allows to rule out a possible presence of i-phase (within a few percent) in the samples. (M. Foos and J.P. Houin, data to be published). Neutron diffraction experiments were mainly performed on the D1B two-axis diffractometer at the I L L (Grenoble), with a wavelength 2, = 2.515
neufrons
d-Al/. Mn X-rctLJS
2
3
q(~-l)
Fig. 1. Neutron and X-ray diffraction patterns of the decagonal phase of the A14 Mn system (intensities in arbitrary units).
422
Fig. 2. Typical electron micrographsand associated 2-fold zone axis diffraction patterns as observed on the decagonal AI4Mn phase.
,~;
its 400
cell multidetector
covers
range 20 = 80 ° and was positioned with
a resolution
an
angular
in such a way
that scattering vectors q were explored 3.9 ,~-1
of about
from 0.9 to 0.01 to 0.02
,~-1. The ribbon-shaped alloys were ground to powder and packed into cylindrical vanadium cans (~
=10mm,
8 September 1986
PHYSICS LETTERS A
Volume 117, number 8
for the X-ray at
20
Ktx 1 radiation fraction
from
patterns
especially around Gaussian neutron
and
data being collected
o f 0 . 0 3 2 °. T h e
1 . 7 8 8 9 ,~) i n d u c e s
h=50mm).
A linear position sensitive detector set up to m e a s u r e i n t e n s i t i e s i n ~ 0 / 2 0 s c a n s [16] w a s u s e d
measurements,
intervals
a cobalt
monochromated anode
Mn fluorescence cannot
tube
(X=
which the dif-
be easily corrected
for,
the weakest peaks measured.
shapes were fitted in 20-space X-ray
diffraction
of the lines, when observed,
to the
peaks. Asymmetry
was accounted
for by
Table 1 Measured intensities I and positions q of the diffraction peaks in the d-phase, along with d spacings ( - not observed; * : too weak to be fitted; {: unresolved doublet). Peak
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
d-A1 a (Mn 0.72Fe0.zs)
d-A14 M n
neutrons
X-rays
q (£-x)
d (A)
0.994
6.32
1.415
4.44
1.540 1.605 1.642 1.688
4.08 3.92 3.83 3.72
1.876 1.905
3.35 3.30
2.025 2.150 2.214 2.259 2.322 2.370 2.510 2.592 2.658 2.686 2.790 2.910 3.017
3.10 2.92 2.84 2.78 2.71 2.65 2.50 2.42 2.36 2.34 2.25 2.16 2.08
3.069
2.05
3.197 3.270
1.97 1.92
3.49 3.58
1.80 1.76
I (%)
neutrons
q (£-~)
d (A)
3.5 * 1.0
0.964 1.008
6.52 6.23
[, ~ 2.4 4.4 [ 6.2 \ 4.4 * • 2.5 7.7 6.0 9.2 4.8 0.8 0.5 4.5 3.5 27.7 31.8 4.9 9.5 14.0 [ 100.0 \f\ 0 5 .0 * 4.1 2.0 • 4.1 9.0 * *
1.430
4.39
1.609
3.90
1.682 1.805 1.841 1.891
3.74 3.48 3.41 3.32
2.587 2.648 2.686 2.788 2.902 3.005 3.032 3.058
2.43 2.37 2.34 2.25 2.17 2.09 2.07 2.05
3.210
1.96
I (%)
q (£-1)
d (£)
I (%)
1.4 5.6 • 5.3
0.970 1.008 1.409 1.438
6.48 6.23 4.46 4.37
[ 12.6 ~ 11.5 5.9 1.4 4.5 5.7 4.1 3.2 34.5 2.5 100.0 19.3 42.0 5.0 -
1.616 1.667 1.692 1.803 1.819 1.891 1.906 1.958 2.024 2.129 2.197 2.249 2.337 2.389 2.570 2.587 2.643 2.684 2.789 2.901 3.004 3.031 3.067 3.108 3.196 3.240 3.436 3.515 3.582 3.669 3.699
3.89 3.77 3.71 3.48 3.45 3.32 3.30 3.21 3.10 2.95 2.86 2.79 2.69 2.63 2.44 2.43 2.38 2.34 2.25 2.17 2.09 2.07 2.05 2.02 1.97 1.94 1.83 1.79 1.75 1.71 1.70
1.7 7.2 8.4 •2.7 ~ * 11.9 26.9 10.9 11.0 35.2 51.8 19.0 2.2 37.1 15.1 22.9 1.1 5.2 7.1 25.3 81.1 100.0 22.8 7.0 8,2 20.0 6,1 27.4 1.2 19.4 6.8 16.2 0.9 51.3 11.1 2.3
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fitting individual experimental peaks to the sum of two gaussians. The integrated line intensities were normalized to the strongest peak of each pattern. The fitted intensities, along with positions in the reciprocal space (q=(4-~/?Q sin O) and interplanar spacings ( d = 2v/q) are given in table 1. These data correspond to the diffraction patterns presented in fig. 1. Intensities given in table I have typical standard deviations of about 1 to 3%. Some lines with vanishingly small intensity have not been fitted (see for instance wavy features around 1.05 to 2.4 ,~-1 in pattern (a) of fig. 1). Clearly enough, the structure of this decagonal phase is not affected by the F e / M n substitution, except perhaps for a very slight shift in the peak positions (as illustrated in fig. 3 on an enlarged fraction of the diffraction patterns). Similar position shifts can be observed when comparing crystalline orthorhombic A16Mn [17] to metastable A16Fe [18] compounds; they may be attributed to the A1-Fe interaction distances being shorter than
8 September 1986
Table 2 Average weighting factors of the atomic pairs.
Alloys
Radiation Pairs A1-AI A 1 - T M T M - T M
a A14(Mn0.72Feo.28 ) neutrons b AI4Mn X-rays c A14Mn neutrons
1 0.433 1.878
0 0 0.450 0.117 - 1 . 0 1 6 0.137
the A1-Mn ones. It is also clear that the observed intensity changes due to contrast variation induced by the isomorphous substitution method a n d / o r the use of two different radiations, appear as drastic as expected (see figs. 1 and 3, and table 1) from the weighting factors associated with the different atomic pairs given in table 2: the largest contribution obviously arises from the A1-A1 and A1-TM correlations, the T M - T M ones being much smaller.
3. Discussion and conclusion
d-Al~ (MnazFe.m)
L
neutrons
I
!
!
2.8
I
2.'9
3.0
Fig. 3. Enlarged presentation of a part of the diffraction patterns shown in fig. 1, around the peaks labelled 24 to 28 in table 3. Arrows point to line 27.
424
The diffraction data reported in the present work cover only a restricted range of scattering vectors. However they provide three independent sets of intensity and position values on the same material. Obviously enough this information is still too limited to achieve a determination of atomic locations. Nonetheless a semi-quantitative analysis of the data and comparison to the i-phase or the crystalline c~-phase may suggest interesting structural features. For this purpose data are presented in table 3 in such a way that it is possible to compare directly the relative intensity of the diffraction peaks measured in the present work to those obtained with neutron [14] and X-rays [19] for the i-phase, along to those calculated for the cubic c~-phase using atom positions from ref. [20]. For the sake of examplifying the way data of table 3 can be used, let us consider the subset of peaks labelled 12 to 19. The corresponding intensities in the d-phase are zero or vanishingly small when measured with X-rays, and significantly larger when measured with neutrons on d-A14Mn than when measured on d-A14(Mn0.72Fe0.28). As the X-ray scattering factors of Mn and A1 are
Volume 117, number 8
PHYSICS LETTERS A
8 September 1986
Table 3 Atomic phase spacings d (A) and intensities I (%) of the diffraction peaks in the decagonal phase (d) compared to those measured in the icosahedral phase (i) and in the cubic e~-phase (a, b a n d c refer respectively to neutron data of the "zero T M " alloy, X-rays and neutron data of A14Mn ) (symbols are the same as in table 1). Peak
Decagonal phase l(a)
1 2 3 4 5 6
l(b)
3.5 • 1.0 (.
1.4 5.6 • (
2.4 4,4
5.3 12.6
Cubic a-phase l(c) 1,7 7.2 8.4 2,7 • 11.9
Icosahedral phase
l(a)
hkl
200
0.7
310
6
1.2
29
7 8 9 10 11 12 13 14 15
6.2 [ 4.4 \ • • 2.5 7.7 6.0 9.2
16 17 18 19 20
4.8 0.8 0.5 4,5 3.5
21
27.7
5,7
22 23 24 25
31.8 4.9 9.5 14.0
4.1 3.2 34,5 2.5
100,0 22.8 7.0 8.2
520/432
13
4
441/522 530/333
5 76
2.4 65
26 27 28 29
[ 100,0 ~f\ 0 5 .0 *
100.0 19.3 42.0 -
20,0 6.1 27.4 1.2
600 532/611 620
21.8 100 22
28.5 100 10
30 31 32 33 34 35 36
4.1 2.0 * 4.1 9.0 * *
5.0 -
19.4 6.8 16.2 0.9 51.3 11.1 2.3
11.5 5.9 1.4 4.5
-
26.9 10.9 11.0 35.2 51.8 321 19.0 2.2 410 37.1 400 15.1 [ 430 ~, 411 22.9 420 1.1 5.2 332 7.1 25.3 [ 510 431 81.1 511/333
l(b)
444 640 633/552 642
14
10
signs (bMn = --bAl), these reflections associated
to
"reticular
planes"
index
l(a)
Atomic spacings l(b)
l(c)
d-
100
6,50 6.23 4.45 4.37 4.08 3.90
6.4
56
f 110001 32i~i2
•
22
61
1110]0
8
8
77
0 2.4 0.3
0.4 0.6 3.0
0.5 14.9 5.0
221010
0.6
•
0.9
860263
1,0
3.0
5
7,0
5.0
18
311111
-
1.5
2.9
0.8
0,03
3300]2
-
-
2.2
[ 211001 [ 331021 1.9 [ 441041 \ 430022 14 211101
15
3
0,5
-
8
4 60
* 66
66,0
11.0
5.5
1.4
3,0 100
8.9 34 20
220132 / 100000 321002
110000 { 220002 2211~1
100 -
4.01
3.86
3.39
3,35
3.07 3.17 2,99
3.14 3.01
•2.70
2,72
2.49
2.52
1.1
2.43
2,44
2,42
-
17.5
2.35
2.37
100
2 25.7
2.37 2.34 2.25 2.17
2,21 2,17
2~20 2.17
35.6 22
2.09 2.07 2.05 2.02
2.11 2,06 2.00
2.07 1.94
1.83
1.83
1.76 1.73 1.69
1.76 1.73 1.67
78 1
72
11110I
-
*
22
17.5 10.0 16.8
3.3 1,4 0.4
25.0 34 34
210001 320071 222020
* -
1,5 * -
25 14 2,7
containing
6,34
2.85
5.5
12 to 19 can
3,80 3.71 3.48 3.45 3.32 3.30 3.21 3.10 2.95
i-
2,83
0.8
about
a-
2.85 2.79 2.70 2.64 2,47
4.5
obviously positive (fMn is about twice fA0 whereas their neutron scattering lengths are of opposite be
l(c)
twice as much
A1 a s M n
1,97 1.94 1.83 1.79 1.75 1.71 1.70
atoms
with phase
shift between the two species approaching or. A s a f u r t h e r e x a m p l e t h e p e a k l a b d l e d 2 6 i n t a b l e 3, which has strong intensities with X-rays
and with 425
Volume 117, number 8
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neutrons on the "zero TM" alloy but a weaker one with neutrons on the d-A14Mn sample, may arise from "reticular planes" containing A1 and Mn atoms interfering in a "constructive way" (i.e. with a phase shift close to zero). It is also worth noticing that the similarity between the i- and d-phases is certainly not restricted to orientation relationships as suggested by electron microscopy and diffraction data [11,12]. Intensities are also quite strongly correlated. Let us consider for instance the peaks of the i-phase labelled with the six-integer indices 110001 and 111010; they correspond to groups of peaks of the d-phase close to the reflexions labelled 6 and 11 respectively in table 3. The total relative intensities of these groups of peaks are affected by contrast changes as if these groups of peaks were simply resulting from some sort of splitting of the i-phase peaks. This analysis extends easily to all the other peaks of the i-phase. Thus, we may conclude that, probably, a common structure building principle operates in both i- and d-phases. However, at variance from what is observed for the i-phase [14], it is not possible to conclude that some "atomic planes" of the d-phase are populated only by transition metal atoms, since no peak intensity reduces to zero when the relevant F e / M n substitution is used in neutron diffraction. An even more quantitative conclusion can be gained from the fact that the d-phase exhibits some very sharp diffraction peaks, whose width is close to the diffractometer resolution. These lines, which have no counterparts in the i-phase diffraction patterns #1, have been labelled 2, 14 and 27 in table 3. The latter is reasonably separated from the neighbour peaks 26 and 28 in the X-ray patterns and also in the neutron pattern-measured on d-Al4Mn, but is not really visible in the neutron pattern of the d-Ala(Mn0.72Fe0.28 ) alloy (fig. 3) because of the peak shift induced by the F e / M n substitution as already mentioned in section 2.
~1 A possible contamination of the samples studied in ref. [14] by a small amount of d-phase may have led to a wrong assignment of some of the very weak narrow lines observed by neutron diffraction and not detected by X-ray diffraction [20].
426
8 September 1986
Consequently, peak 27 has not been individually fitted in AI4(Mn, Fe) data. Sharp peaks may be thought of as coming from a pollution of the d-phase by hexagonal A14Mn crystals formed during quenching; but the strongest reflections of the hexagonal phase [22] do not coincide with the sharp peak observed here. According to electron diffraction patterns (fig. 2) these sharp peaks may be rather assigned to interferences between "atomic planes" perpendicular to the ten-fold axis and spaced respectively boy distances D / 2 , D / 4 and D / 6 with D = 12.43 A being the one-dimensional translation parameter. This result is in fair agreement with values reported in the literature [10-12]. It is also interesting to note that: (i) D is not too far from 12.69 A which is the lattice parameter of the cubic a-phase (about 2% misfits). (ii) Changes of integrated intensities with contrast variations and positions of the three sharp peaks o f the d-phase compare quite nicely with those calculated for the (200), (400) and (600) reflections of the same cubic a-phase (see table 3). For instance, peak 14 corresponds to a d-spacing of 3.10 ,~ and intensity ratios I c / I a = 6.18 and I J I a = 0 while the a-(400) reflection occurs at d = 3.17 ,~ with I c / I a = 6.20 and I b / I a = 0.25. (iii) Odd one-dimensional translation peaks, that would correspond to D, D / 3 or D / 5 spacings, are not observed in the d-phase, in correspondance with the very weak intensities of the (100), (300), (500) reflections of the cubic a-phase. Such a symmetry relationship between a [100] row of the cubic a-phase and the ten-fold axis of the decagonal phase was not expected actually and must be thereby considered very cautiously. It has been indeed established [12] that symmetry relationships would rather correspond to the a-[100] row being parallel to a two-fold axis of the i-phase whose 5-fold axis matches very well the 10-fold axis of the d-phase. Thus, the observed correspondances between a- and d-phases might be fortuitous since occurring along non-equivalent crystallographic directions. At this stage, it is probably not worth pushing further a detailed comparison between the icosahedral, decagonal and cubic phases. A sensible structure analysis obviously relies on the dif-
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fracted intensities being determined on an abs o l u t e s c a l e o v e r a l a r g e r r a n g e o f s c a t t e r i n g vectors and with a proper angular resolution. The r e l e v a n t w o r k is i n p r o g r e s s .
Acknowledgement I t is o u r p l e a s u r e t o e m p h a s i z e t h e d e t e r m i n i n g c o n t r i b u t i o n t o t h i s w o r k o f P. W e i n l a n d a n d J.P. Houin who prepared the samples. We also gratefully thank the Institut Laue-Langevin for the allocation of beam time.
References [1] D. Schechtman, I.A. Blech, D. Gratias and J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] R.A. Dunlap and K. Dini, Can. J. Phys. 63 (1985) 1267. [3] D.A. Lilienfeld, M. Nastasi, H.H. Johnson, D.G. Ast and J.W. Mayer, Phys. Rev. Lett. 55 (1985) 1587. [4] P. Sainford, B. Dubost and A. Dubus, C.R. Acad. Sci. II 301 (1985) 689. [5] T. Rajasekharan and J.A. Sekhar, Scr. Metall. 20 (1986) 235.
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[6] P. Guyot and M. Audier, Philos. Mag. B 52 (1985) L15. [7] K. Kimura, T. Hashimoto, K. Suzuki, K. Nagayama, H. Ino and S. Takeuchi, J. Phys. Soc. Japan 54 (1985) 3217. [8] G.A. Dixit and V.S. Raghunathan, Scr. Metall. 20 (1986) 235. [9] R.J. Schaefer, L.A. Bendersky, D. Schechtman, W.J. Boettinger and F.S. Biancaniello, Metallurgy of phase relationships of icosahedral AI-Mn, preprint. [10] L. Bendersky, Phys. Rev. Lett. 55 (1985) 1461. [11] L. Bendersky, R.J. Schaefer, F.S. Biancaniello, W.J. Boettinger, M.J. Kaufman and D. Schechtman, Scr. Metall. 19 (1985) 909. [12] P. Guyot and M. Audier, J. Microsc. Spectrom. Elect. 10 (1985) 575. [13] Tin-Lun Ho, Phys. Rev. Lett. 56 (1986) 468. [14] J.M. Dubois, Chr. Janot and J. Pannetier, Phys. Lett. A 115 (1986) 177. [15] Chr. Janot, B. George, C. Tete, A. Chamberod and J. Laugier, J. Phys. 46 (1985) 1233. [16] A. Pianelli, Chem. Scr. Suppl. A 26, to be published. [17] A.D.I. Nicol, Acta Crystallogr. 6 (1953) 285. [18] L.K. Walford, Acta Crystallogr. 18 (1965) 287. [19] P.A. Bancel, P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, Phys. Rev. Lett. 54 (1985) 2422. [20] M. Cooper and K. Robinson, Acta Crystallogr. 20 (1966) 614. [21] K. Kimura, T. Hashimoto, K. Suzuki, K. Nagayama, H. Ino and S. Takeuchi, J. Phys. Soc. Japan 55 (1986) 534.
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8 September 1986
DIFFRACTION APPROACH TO THE STRUCTURE OF DECAGONAL Q U A S I - C R Y S T A L S J.-M. D U B O I S a, Chr. J A N O T b, j. P A N N E T I E R b and A. P I A N E L L I a Laboratoire de Science et G$nie des Matbriaux Mbtalliques ( C N R S U,4 159), Ecole des Mines, Pare de Saurupt, 54042 Nancy Cedex, France b Institut Laue-Langevin, 156 X, Centre de Tri, 38042 Grenoble Cedex, France
Received 6 May 1986; accepted for publication 9 July 1986
Neutron and X-ray diffraction data measured on A14Mn decagonal quasi-crystals, with a non-crystallographicpoint group 10/m, are reported. Contrast variations were produced by Fe/Mn isomorphous substitution on the transition metal sites. The independent measurements on the peak intensities allow suggestions about atomic correlations and lead to fruitful comparisons with icosahedral m35 material and/or the crystalline modifications of related composition.
1. Introduction Since the first experimental evidence for the possible existence of an icosahedral phase (iphase), with point group symmetry m35, in A16Mn melt-spun alloys [1], the same kind of rather exotic structure has been also obtained in several rapidly solidified A1-T alloys (with T a 3d transition metal) [2] and also by solid state reactions in metallic glasses [3] or in A 1 - L i - C u - M g crystalline solid solution [4]. The now famous A1-Mn i-phase forms in alloys with M n concentration ranging from 14 to 22 at%. The quenched .samples exhibit a coexistence of fcc A1 with the icosahedral phase, the latter having a m a x i m u m volume fraction at x = 0.20; a superstructure has been reported for alloys lying in the upper limit of the Mn concentration [5]. Despite the stoichiometry of the i-phase being obviously in the vicinity of A14Mn [6-8] it is far from easy to produce samples of pure i-phase at or near to this ideal A14Mn composition. It requires quite high solidification rates [9]. Currently, a so-called T-phase forms in competition with the i-one [9]. This T-phase grows in heavily faulted cylindrical domains rather than in the coral-like dendrites morphology typical of the i-phase [9]. Electron diffraction patterns of the T-phase show one ten-fold and ten equivalent two-fold
axes in consistency with a 1 0 / m point group symmetry [10]. A one-dimensional periodicity along the ten-fold axis is associated with a planar quasi-periodicity perpendicular to this axis. According to Bendersky [10], it will be referred to as the decagonal phase, or d-phase, in the following. Icosahedral and decagonal A14Mn quasicrystals have shown symmetry relationships [11,12] and strong similarities in reciprocal space, though being supposedly different in real space [13]. The purpose of the present work was to extend to the d-phase the contrast variation method previously applied in a diffraction study of the i-phase [14]. Thus, positions and intensities of the diffractions peaks have been measured with neutrons and X-rays on d-A14Mn and d-A14(Mno.v2Fe0.28 ) alloys, the latter having a M n / F e mixture with a zero average scattering length for neutrons. This so-called "zero T M " alloy was intended to provide direct information on the A1-A1 correlations in the quasi-lattice of the d-phase.
2. Sample preparation and experiments Preparation of the master alloys and quenching procedure have been described elsewhere [14]. A critical parameter is the quenching rate which has
0375-9601/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
421
Volume 117, number 8
PHYSICS LETTERSA
to be ajusted at a low enough value to avoid the formation of the i-phase but must be sufficiently rapid to bypass crystallization. The samples were obtained in the form of brittle ribbons 15 to 20 ~m thick and 1 to 2 m m wide. As is well known, the reliability of a contrast variation method in neutron diffraction studies strongly depends on the randomness of the isomorphous substitution. The effectiveness of a proper M n / F e substitution has indeed been care-
X-rogs
8 September 1986
fully tested as explained elsewhere [14,15] and is further supported by the X-ray diffraction patterns shown in fig. 1 which are identical for dAlnMn and d-A14(Mn0.72Fe0.28 ) alloys. Incidentally, these X-ray patterns do not exhibit any resolved Bragg peaks at the positions expected for the (111) and (200) reflections in fcc aluminium. Thus, the amount of fcc A1 retained in the samples can be considered as negligible with the consequence that the d-phase has indeed the A14Mn (or A14(Mn, Fe)) nominal composition. The typical morphology of the d-phase grains, as observed on electron micrographs in fig. 2 together with corresponding diffraction patterns, allows to rule out a possible presence of i-phase (within a few percent) in the samples. (M. Foos and J.P. Houin, data to be published). Neutron diffraction experiments were mainly performed on the D1B two-axis diffractometer at the I L L (Grenoble), with a wavelength 2, = 2.515
neufrons
d-Al/. Mn X-rctLJS
2
3
q(~-l)
Fig. 1. Neutron and X-ray diffraction patterns of the decagonal phase of the A14 Mn system (intensities in arbitrary units).
422
Fig. 2. Typical electron micrographsand associated 2-fold zone axis diffraction patterns as observed on the decagonal AI4Mn phase.
,~;
its 400
cell multidetector
covers
range 20 = 80 ° and was positioned with
a resolution
an
angular
in such a way
that scattering vectors q were explored 3.9 ,~-1
of about
from 0.9 to 0.01 to 0.02
,~-1. The ribbon-shaped alloys were ground to powder and packed into cylindrical vanadium cans (~
=10mm,
8 September 1986
PHYSICS LETTERS A
Volume 117, number 8
for the X-ray at
20
Ktx 1 radiation fraction
from
patterns
especially around Gaussian neutron
and
data being collected
o f 0 . 0 3 2 °. T h e
1 . 7 8 8 9 ,~) i n d u c e s
h=50mm).
A linear position sensitive detector set up to m e a s u r e i n t e n s i t i e s i n ~ 0 / 2 0 s c a n s [16] w a s u s e d
measurements,
intervals
a cobalt
monochromated anode
Mn fluorescence cannot
tube
(X=
which the dif-
be easily corrected
for,
the weakest peaks measured.
shapes were fitted in 20-space X-ray
diffraction
of the lines, when observed,
to the
peaks. Asymmetry
was accounted
for by
Table 1 Measured intensities I and positions q of the diffraction peaks in the d-phase, along with d spacings ( - not observed; * : too weak to be fitted; {: unresolved doublet). Peak
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
d-A1 a (Mn 0.72Fe0.zs)
d-A14 M n
neutrons
X-rays
q (£-x)
d (A)
0.994
6.32
1.415
4.44
1.540 1.605 1.642 1.688
4.08 3.92 3.83 3.72
1.876 1.905
3.35 3.30
2.025 2.150 2.214 2.259 2.322 2.370 2.510 2.592 2.658 2.686 2.790 2.910 3.017
3.10 2.92 2.84 2.78 2.71 2.65 2.50 2.42 2.36 2.34 2.25 2.16 2.08
3.069
2.05
3.197 3.270
1.97 1.92
3.49 3.58
1.80 1.76
I (%)
neutrons
q (£-~)
d (A)
3.5 * 1.0
0.964 1.008
6.52 6.23
[, ~ 2.4 4.4 [ 6.2 \ 4.4 * • 2.5 7.7 6.0 9.2 4.8 0.8 0.5 4.5 3.5 27.7 31.8 4.9 9.5 14.0 [ 100.0 \f\ 0 5 .0 * 4.1 2.0 • 4.1 9.0 * *
1.430
4.39
1.609
3.90
1.682 1.805 1.841 1.891
3.74 3.48 3.41 3.32
2.587 2.648 2.686 2.788 2.902 3.005 3.032 3.058
2.43 2.37 2.34 2.25 2.17 2.09 2.07 2.05
3.210
1.96
I (%)
q (£-1)
d (£)
I (%)
1.4 5.6 • 5.3
0.970 1.008 1.409 1.438
6.48 6.23 4.46 4.37
[ 12.6 ~ 11.5 5.9 1.4 4.5 5.7 4.1 3.2 34.5 2.5 100.0 19.3 42.0 5.0 -
1.616 1.667 1.692 1.803 1.819 1.891 1.906 1.958 2.024 2.129 2.197 2.249 2.337 2.389 2.570 2.587 2.643 2.684 2.789 2.901 3.004 3.031 3.067 3.108 3.196 3.240 3.436 3.515 3.582 3.669 3.699
3.89 3.77 3.71 3.48 3.45 3.32 3.30 3.21 3.10 2.95 2.86 2.79 2.69 2.63 2.44 2.43 2.38 2.34 2.25 2.17 2.09 2.07 2.05 2.02 1.97 1.94 1.83 1.79 1.75 1.71 1.70
1.7 7.2 8.4 •2.7 ~ * 11.9 26.9 10.9 11.0 35.2 51.8 19.0 2.2 37.1 15.1 22.9 1.1 5.2 7.1 25.3 81.1 100.0 22.8 7.0 8,2 20.0 6,1 27.4 1.2 19.4 6.8 16.2 0.9 51.3 11.1 2.3
423
Volume 117, number 8
PHYSICS LETTERS A
fitting individual experimental peaks to the sum of two gaussians. The integrated line intensities were normalized to the strongest peak of each pattern. The fitted intensities, along with positions in the reciprocal space (q=(4-~/?Q sin O) and interplanar spacings ( d = 2v/q) are given in table 1. These data correspond to the diffraction patterns presented in fig. 1. Intensities given in table I have typical standard deviations of about 1 to 3%. Some lines with vanishingly small intensity have not been fitted (see for instance wavy features around 1.05 to 2.4 ,~-1 in pattern (a) of fig. 1). Clearly enough, the structure of this decagonal phase is not affected by the F e / M n substitution, except perhaps for a very slight shift in the peak positions (as illustrated in fig. 3 on an enlarged fraction of the diffraction patterns). Similar position shifts can be observed when comparing crystalline orthorhombic A16Mn [17] to metastable A16Fe [18] compounds; they may be attributed to the A1-Fe interaction distances being shorter than
8 September 1986
Table 2 Average weighting factors of the atomic pairs.
Alloys
Radiation Pairs A1-AI A 1 - T M T M - T M
a A14(Mn0.72Feo.28 ) neutrons b AI4Mn X-rays c A14Mn neutrons
1 0.433 1.878
0 0 0.450 0.117 - 1 . 0 1 6 0.137
the A1-Mn ones. It is also clear that the observed intensity changes due to contrast variation induced by the isomorphous substitution method a n d / o r the use of two different radiations, appear as drastic as expected (see figs. 1 and 3, and table 1) from the weighting factors associated with the different atomic pairs given in table 2: the largest contribution obviously arises from the A1-A1 and A1-TM correlations, the T M - T M ones being much smaller.
3. Discussion and conclusion
d-Al~ (MnazFe.m)
L
neutrons
I
!
!
2.8
I
2.'9
3.0
Fig. 3. Enlarged presentation of a part of the diffraction patterns shown in fig. 1, around the peaks labelled 24 to 28 in table 3. Arrows point to line 27.
424
The diffraction data reported in the present work cover only a restricted range of scattering vectors. However they provide three independent sets of intensity and position values on the same material. Obviously enough this information is still too limited to achieve a determination of atomic locations. Nonetheless a semi-quantitative analysis of the data and comparison to the i-phase or the crystalline c~-phase may suggest interesting structural features. For this purpose data are presented in table 3 in such a way that it is possible to compare directly the relative intensity of the diffraction peaks measured in the present work to those obtained with neutron [14] and X-rays [19] for the i-phase, along to those calculated for the cubic c~-phase using atom positions from ref. [20]. For the sake of examplifying the way data of table 3 can be used, let us consider the subset of peaks labelled 12 to 19. The corresponding intensities in the d-phase are zero or vanishingly small when measured with X-rays, and significantly larger when measured with neutrons on d-A14Mn than when measured on d-A14(Mn0.72Fe0.28). As the X-ray scattering factors of Mn and A1 are
Volume 117, number 8
PHYSICS LETTERS A
8 September 1986
Table 3 Atomic phase spacings d (A) and intensities I (%) of the diffraction peaks in the decagonal phase (d) compared to those measured in the icosahedral phase (i) and in the cubic e~-phase (a, b a n d c refer respectively to neutron data of the "zero T M " alloy, X-rays and neutron data of A14Mn ) (symbols are the same as in table 1). Peak
Decagonal phase l(a)
1 2 3 4 5 6
l(b)
3.5 • 1.0 (.
1.4 5.6 • (
2.4 4,4
5.3 12.6
Cubic a-phase l(c) 1,7 7.2 8.4 2,7 • 11.9
Icosahedral phase
l(a)
hkl
200
0.7
310
6
1.2
29
7 8 9 10 11 12 13 14 15
6.2 [ 4.4 \ • • 2.5 7.7 6.0 9.2
16 17 18 19 20
4.8 0.8 0.5 4,5 3.5
21
27.7
5,7
22 23 24 25
31.8 4.9 9.5 14.0
4.1 3.2 34,5 2.5
100,0 22.8 7.0 8.2
520/432
13
4
441/522 530/333
5 76
2.4 65
26 27 28 29
[ 100,0 ~f\ 0 5 .0 *
100.0 19.3 42.0 -
20,0 6.1 27.4 1.2
600 532/611 620
21.8 100 22
28.5 100 10
30 31 32 33 34 35 36
4.1 2.0 * 4.1 9.0 * *
5.0 -
19.4 6.8 16.2 0.9 51.3 11.1 2.3
11.5 5.9 1.4 4.5
-
26.9 10.9 11.0 35.2 51.8 321 19.0 2.2 410 37.1 400 15.1 [ 430 ~, 411 22.9 420 1.1 5.2 332 7.1 25.3 [ 510 431 81.1 511/333
l(b)
444 640 633/552 642
14
10
signs (bMn = --bAl), these reflections associated
to
"reticular
planes"
index
l(a)
Atomic spacings l(b)
l(c)
d-
100
6,50 6.23 4.45 4.37 4.08 3.90
6.4
56
f 110001 32i~i2
•
22
61
1110]0
8
8
77
0 2.4 0.3
0.4 0.6 3.0
0.5 14.9 5.0
221010
0.6
•
0.9
860263
1,0
3.0
5
7,0
5.0
18
311111
-
1.5
2.9
0.8
0,03
3300]2
-
-
2.2
[ 211001 [ 331021 1.9 [ 441041 \ 430022 14 211101
15
3
0,5
-
8
4 60
* 66
66,0
11.0
5.5
1.4
3,0 100
8.9 34 20
220132 / 100000 321002
110000 { 220002 2211~1
100 -
4.01
3.86
3.39
3,35
3.07 3.17 2,99
3.14 3.01
•2.70
2,72
2.49
2.52
1.1
2.43
2,44
2,42
-
17.5
2.35
2.37
100
2 25.7
2.37 2.34 2.25 2.17
2,21 2,17
2~20 2.17
35.6 22
2.09 2.07 2.05 2.02
2.11 2,06 2.00
2.07 1.94
1.83
1.83
1.76 1.73 1.69
1.76 1.73 1.67
78 1
72
11110I
-
*
22
17.5 10.0 16.8
3.3 1,4 0.4
25.0 34 34
210001 320071 222020
* -
1,5 * -
25 14 2,7
containing
6,34
2.85
5.5
12 to 19 can
3,80 3.71 3.48 3.45 3.32 3.30 3.21 3.10 2.95
i-
2,83
0.8
about
a-
2.85 2.79 2.70 2.64 2,47
4.5
obviously positive (fMn is about twice fA0 whereas their neutron scattering lengths are of opposite be
l(c)
twice as much
A1 a s M n
1,97 1.94 1.83 1.79 1.75 1.71 1.70
atoms
with phase
shift between the two species approaching or. A s a f u r t h e r e x a m p l e t h e p e a k l a b d l e d 2 6 i n t a b l e 3, which has strong intensities with X-rays
and with 425
Volume 117, number 8
PHYSICS LETTERS A
neutrons on the "zero TM" alloy but a weaker one with neutrons on the d-A14Mn sample, may arise from "reticular planes" containing A1 and Mn atoms interfering in a "constructive way" (i.e. with a phase shift close to zero). It is also worth noticing that the similarity between the i- and d-phases is certainly not restricted to orientation relationships as suggested by electron microscopy and diffraction data [11,12]. Intensities are also quite strongly correlated. Let us consider for instance the peaks of the i-phase labelled with the six-integer indices 110001 and 111010; they correspond to groups of peaks of the d-phase close to the reflexions labelled 6 and 11 respectively in table 3. The total relative intensities of these groups of peaks are affected by contrast changes as if these groups of peaks were simply resulting from some sort of splitting of the i-phase peaks. This analysis extends easily to all the other peaks of the i-phase. Thus, we may conclude that, probably, a common structure building principle operates in both i- and d-phases. However, at variance from what is observed for the i-phase [14], it is not possible to conclude that some "atomic planes" of the d-phase are populated only by transition metal atoms, since no peak intensity reduces to zero when the relevant F e / M n substitution is used in neutron diffraction. An even more quantitative conclusion can be gained from the fact that the d-phase exhibits some very sharp diffraction peaks, whose width is close to the diffractometer resolution. These lines, which have no counterparts in the i-phase diffraction patterns #1, have been labelled 2, 14 and 27 in table 3. The latter is reasonably separated from the neighbour peaks 26 and 28 in the X-ray patterns and also in the neutron pattern-measured on d-Al4Mn, but is not really visible in the neutron pattern of the d-Ala(Mn0.72Fe0.28 ) alloy (fig. 3) because of the peak shift induced by the F e / M n substitution as already mentioned in section 2.
~1 A possible contamination of the samples studied in ref. [14] by a small amount of d-phase may have led to a wrong assignment of some of the very weak narrow lines observed by neutron diffraction and not detected by X-ray diffraction [20].
426
8 September 1986
Consequently, peak 27 has not been individually fitted in AI4(Mn, Fe) data. Sharp peaks may be thought of as coming from a pollution of the d-phase by hexagonal A14Mn crystals formed during quenching; but the strongest reflections of the hexagonal phase [22] do not coincide with the sharp peak observed here. According to electron diffraction patterns (fig. 2) these sharp peaks may be rather assigned to interferences between "atomic planes" perpendicular to the ten-fold axis and spaced respectively boy distances D / 2 , D / 4 and D / 6 with D = 12.43 A being the one-dimensional translation parameter. This result is in fair agreement with values reported in the literature [10-12]. It is also interesting to note that: (i) D is not too far from 12.69 A which is the lattice parameter of the cubic a-phase (about 2% misfits). (ii) Changes of integrated intensities with contrast variations and positions of the three sharp peaks o f the d-phase compare quite nicely with those calculated for the (200), (400) and (600) reflections of the same cubic a-phase (see table 3). For instance, peak 14 corresponds to a d-spacing of 3.10 ,~ and intensity ratios I c / I a = 6.18 and I J I a = 0 while the a-(400) reflection occurs at d = 3.17 ,~ with I c / I a = 6.20 and I b / I a = 0.25. (iii) Odd one-dimensional translation peaks, that would correspond to D, D / 3 or D / 5 spacings, are not observed in the d-phase, in correspondance with the very weak intensities of the (100), (300), (500) reflections of the cubic a-phase. Such a symmetry relationship between a [100] row of the cubic a-phase and the ten-fold axis of the decagonal phase was not expected actually and must be thereby considered very cautiously. It has been indeed established [12] that symmetry relationships would rather correspond to the a-[100] row being parallel to a two-fold axis of the i-phase whose 5-fold axis matches very well the 10-fold axis of the d-phase. Thus, the observed correspondances between a- and d-phases might be fortuitous since occurring along non-equivalent crystallographic directions. At this stage, it is probably not worth pushing further a detailed comparison between the icosahedral, decagonal and cubic phases. A sensible structure analysis obviously relies on the dif-
Volume 117, number 8
PHYSICS LETTERS A
fracted intensities being determined on an abs o l u t e s c a l e o v e r a l a r g e r r a n g e o f s c a t t e r i n g vectors and with a proper angular resolution. The r e l e v a n t w o r k is i n p r o g r e s s .
Acknowledgement I t is o u r p l e a s u r e t o e m p h a s i z e t h e d e t e r m i n i n g c o n t r i b u t i o n t o t h i s w o r k o f P. W e i n l a n d a n d J.P. Houin who prepared the samples. We also gratefully thank the Institut Laue-Langevin for the allocation of beam time.
References [1] D. Schechtman, I.A. Blech, D. Gratias and J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] R.A. Dunlap and K. Dini, Can. J. Phys. 63 (1985) 1267. [3] D.A. Lilienfeld, M. Nastasi, H.H. Johnson, D.G. Ast and J.W. Mayer, Phys. Rev. Lett. 55 (1985) 1587. [4] P. Sainford, B. Dubost and A. Dubus, C.R. Acad. Sci. II 301 (1985) 689. [5] T. Rajasekharan and J.A. Sekhar, Scr. Metall. 20 (1986) 235.
8 September 1986
[6] P. Guyot and M. Audier, Philos. Mag. B 52 (1985) L15. [7] K. Kimura, T. Hashimoto, K. Suzuki, K. Nagayama, H. Ino and S. Takeuchi, J. Phys. Soc. Japan 54 (1985) 3217. [8] G.A. Dixit and V.S. Raghunathan, Scr. Metall. 20 (1986) 235. [9] R.J. Schaefer, L.A. Bendersky, D. Schechtman, W.J. Boettinger and F.S. Biancaniello, Metallurgy of phase relationships of icosahedral AI-Mn, preprint. [10] L. Bendersky, Phys. Rev. Lett. 55 (1985) 1461. [11] L. Bendersky, R.J. Schaefer, F.S. Biancaniello, W.J. Boettinger, M.J. Kaufman and D. Schechtman, Scr. Metall. 19 (1985) 909. [12] P. Guyot and M. Audier, J. Microsc. Spectrom. Elect. 10 (1985) 575. [13] Tin-Lun Ho, Phys. Rev. Lett. 56 (1986) 468. [14] J.M. Dubois, Chr. Janot and J. Pannetier, Phys. Lett. A 115 (1986) 177. [15] Chr. Janot, B. George, C. Tete, A. Chamberod and J. Laugier, J. Phys. 46 (1985) 1233. [16] A. Pianelli, Chem. Scr. Suppl. A 26, to be published. [17] A.D.I. Nicol, Acta Crystallogr. 6 (1953) 285. [18] L.K. Walford, Acta Crystallogr. 18 (1965) 287. [19] P.A. Bancel, P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, Phys. Rev. Lett. 54 (1985) 2422. [20] M. Cooper and K. Robinson, Acta Crystallogr. 20 (1966) 614. [21] K. Kimura, T. Hashimoto, K. Suzuki, K. Nagayama, H. Ino and S. Takeuchi, J. Phys. Soc. Japan 55 (1986) 534.
427