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NEUTRON DIFFRACTION STUDY OF THE STRUCTURE OF SOME ALUMINIUM-
TRANSITION METAL NON PERIODIC CRYSTALS
R. Bellissent, F. Bouree-Vigneron, P. Sainfort
To cite this version:
R. Bellissent, F. Bouree-Vigneron, P. Sainfort. NEUTRON DIFFRACTION STUDY OF THE STRUCTURE OF SOME ALUMINIUM- TRANSITION METAL NON PERIODIC CRYSTALS.
Journal de Physique Colloques, 1986, 47 (C3), pp.C3-361-C3-369. �10.1051/jphyscol:1986337�. �jpa-
00225749�
NEUTRON DIFFRACTION STUDY OF THE STRUCTURE OF SOME ALUMINIUM- TRANSITION METAL NON PERIODIC CRYSTALS
R. BELLISSENT', F. BOUREE-VIGNERON*
and
P. SAINFORT*."~aboratoire Leon ~rillouin(l). CEN-Saclay, F-91191 Gif-Sur-Yvette Cedex, France
"'~egedur PBchiney, Centre de Recherches et D6veloppement.
BP. 27, F-38340 Voreppe, France
Abstract
A neutron scattering investigation of the structure of non periodic crystals A1-X, (X being Mn, Cr or MnCr mixture) has been performed. The negative coherent scattering length of Mn for thermal neutrons provided with a variable contrast with X. Our results are compared both with an X-Ray diffraction pattern and with a similar experiment performed on Al-(Mn,Fe) alloys using thermal neutron scattering.
The hypothesis of the isomorphic substitution will be discussed and our results qualitatively checked with various structural models in order to try to determine the location of the atoms in the quasi-lattice.
I. Introduction
Since the discovery of a five fold symmetry diffraction pattern /I/, several systems have been observed /2-51 exhibiting similar structural features and even different non periodic structures /4,6/. Moreover it had been proved for a long time that periodicity was not a necessary condition to obtain by a Fourier transformation a discrete set of diffraction lineq. In the case of icosahedral symmetry, an indexing mode, using the 6 five fold symmetry directions, has been used successfully to take into account an X-ray powder file / 7 / . However neither electron microscopy nor X-ray diffraction could answer the question of atomic positions within the quasilattice cell. Thus in order to try to determine the atomic positions, we have undertaken a neutron scattering study, which allows to change the scattering length ratio of the components and therefore the relative intensities of the diffraction lines.
11. Preparation of the samples
AlggMn14, Al86Cr14 and AlgsMn7Cr8 have been prepared by fast quenching on a rotating copper wheel. Each sample consisted of .ribbons of about 30 Um to 50 m thickness and 2.5 mm width. The A186Mnl4 structure has been checked by a preliminary X-ray experiment which proved the absence of any texture (regular Debye-Scherrer rings of both pure A1 matrix and icosahedral phase). The samples were then gently milled by hand and put in a very thin vanadium container for the neutron diffraction measurements.
111. Neutron diffraction
As far as neutrons are scattered by the nuclei, the coherent scattering lengths are quite different for X-rays and neutrons. Some elements and some isotopes even exhibit negative values of the scattering length. Fortunately, concerning the A16Mn
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986337
C3-362 JOURNAL DE PHYSIQUE
system, the coherent scattering length of manganese is negative, namely -0.373 10-12cm. Thus a strong intensity variation of the diffraction lines could be expected when going from X-rays to neutrons. Our diffraction experiments have been carried out on the 3T2 "high resolution" diffract~meter~ on a thermal source of the Orphde reactor at Saclay. The used wavelength was 1.227 A. The diffraction angle 2 8 ranged from 10' to 100° corresponding to momentum transfer values between 0.9 and 7.8 inverse angstroems. A Rietveld type analysis has been used to determine the positions and intensities of the diffraction peaks of both the aluminium matrix and the icosahedral phase.
The obtained diffraction pattern is reported on Figure 1, together with the recent results of P.A. Bancel and coworkers 171.
The aluminium Bragg peaks (111, 200, 220, 311, 222, 400, 331, 420, 422, 333 and 511, some of them not represented in the diagram of figure 1) have been analysed (isotropic intensity refinement) to test the occurence of preferential orientations of the matrix. The only parameter in the refinement was a Debye-Waller temperature factor. As the reliability factor R = ( C I I
-
~Iobsl/~~obs) ~ ~ ~ is less than 4.10-~, we can affirm that no texture is present in our sample. This result confirms in a more quantitative way the X-ray result of part 11.As for the quasi-crystalline diffraction peaks, one can see at a first glance on Figure 1, that their relative intensities vary in a drastic way from the X-ray to the neutron diagram : the two first quasi-crystalline reflections, 110001 and 111010, are much stronger for neutrons and moreover have similar intensities whereas the corresponding intensity ratio is about 5 for X-rays. On the contrary the two main X-ray lines, 100000 and 110000 are much weaker for neutron scattering. A more detailed comparison can be done using table 1, in which have been reported all the measured diffraction lines for both X-ray and neutron scattering. This table shows a fairly good agreement concerning the location of the diffraction lines.
On the contrary the scattered intensity ratio are quite different.
2. AlggCrl4 AlggMn7Cr8 : isomorphic substitution.
In order to try to determine the basis of the AlMn quasi-lattice, Cr has been chosen to perform isomorphic substitution. Such a choice seemed to be a priori reasonable owing to the great similarity between Mn and Cr which are nearest neighbour transition metals and have an almost identical valence band. Thus either Cr or Mn could be assumed to be bounded in the same way to A1 atoms. Concerning the scattering of thermal neutrons by the systems, Cr is again a good choice, for its coherent scattering length is quite comparable to the Mn coherent scattering length but with the opposite sign (bNn = -0.373 1 0 - ~ ~ c m and bCr = +0.363 10-12cm).
Therefore by using a system the Mn versus Cr composition of which has been conveniently chosen and assuming a random occurence of Mn and Cr atoms, it has been possible to vanish the coherent scattering amplitude of the transition metal atoms. Our neutron scattering experiments have been performed on three quasi-crystalline samples :
i) AlggMn14
ii) AlggCrl4 x
and iii) A185(~nxCrl-x)15 with
I-x rn bcr (x = 0.465) .
The diffraction patterns of the 3 samples are shown in Figure 2. As expected, several diffraction lines vanish when going from AlMn to AlMnCr. Thus, the two first quasi-crystalline diffraction peaks, 110001 and 111010, seem to correspond to scattering from "quasi-planes" made of transition metal atoms only. The 2 positions (or Q values) of the remaining diffracted lines in AlMnCr approximatively correspond to those of AlMn. Thus one can expect that the structure has not been too much changed by the isomorphic substitution.
scattering lengths, this fact could be explained by a term bA1
-
bCr in the structure factor of the lines, which is contradictory with our previous assumption of scattering by transition metal atoms only.We have reported on table 2 the positions and intensities of the diffraction lines in order to put into light the evolution of the quasi-crystalline structure when going from AlMn to AlCr.
In order to check what kind of structural change occurs then, we have calculated (tahle 3) the theoretical values for the six diffraction lines which are present in the AlCr and AlMnCr neutron diffraction spectra. The six five-fold symmetry axis of the icosahedra used by P.A. Bancel et a1 /7/ have been used for indexation and the variation of the lattice parameter from one quasi-crystal to the other has been assumed to be given by the variation of the (100000) diffraction peak position. When comparing the experimental (table 2) to the calculated Q values (table 3 ) , a rather good agreement is observed, especially when all the indexes are low (equal to 0 or 1). An increase of the quasi-lattice parameter is obtained from AlggMnl4 to
~~~~~~~~~8
(relative value : 1%) and again from AlggMn7Crg to AlggCr14 (0.8%). This result is consistentowith the xariation of the atomic radii from Mn to Cr, the values of which are 1.26 A and 1.27 A /8/ (0.8% relative variation). Thus, as a first approximation, the structural change obtained with Mn to Cr isomorphic can be described as an homothetic transformation.If we consider now the intensity changes in the diffraction lines a straighfonvard hypothesis should be to assume that the vanishing peaks correspond :
i) for AlMnCr to a diffraction by MnCr "quasi-planes".
ii) for AlCr to a diffraction with a (bAl-bCr) dependent structure factor.
Moreover the (221011) and (310011) peaks only appear in AlMnCr and AlCr.
This should be consistent with a (bAl+bfi) term in the structure factor but would not explain the vanishing of these lines in the X-ray diffraction pattern /7/.
Thus howsoever promissing when considering the location of the peaks, the isomorphic substitution appears to be much dubious concerning their intensities.
Therefore we have tried to compare our results to a similar study /9/, using substitution of Mn by Fe.
IV. Discussion
In order to compare our data to the similar neutron measurements done on the Alg5(Mn.72Fe.2g)14Si system by Dubois and coworkers /9/ we have reported the later results in table 4. Owin to the larger coherent scattering length for thermal neutrons of Fe (0.952 10-52cm) compared to Cr (0.363 10-12cm), this substitution can be assumed to result in smaller changes in the structure of the icosahedral phase (x = .72 compared to x = .465 and to x = 1, when no substitution is present).
Moreover, the atomic radii of Mn and Fe are quite similar /8/.
As a first approximation, the two systems : AlggMn7Crg and A185 (Mn. 72Fe. 28)14Si exhibit a similar behaviour : when using a "zero-scattering" transition metal alloy, the quasi-crystalline (110001), (111010) and (211000) nearly disappear. But a quantitative intensity agreement between the two systems is not really found (see table 2 and table 4).
A comparison with a structural model based on the a-phase of AlMnSi /9/presents similar limits. The agreement is quite reasonable concerning the position of the diffraction lines but cannot also take into account the corresponding values of the observed intensities.
Several EXAFS experiments have been performed at the Mn K-edge /lo-11/ to find the Mn environment in the icosahedral phase. They confirm that the local order around Mn atoms is in good agreement with the model proposed by Guyot and
C3-364 JOURNAL
DE
PHYSIQUEAudier /l2-13/. However the attempts to use these results to find a basis from which the described intensities of the neutron diffraction patterns could be reproduced have been still now unsuccessfull.
v.
ConclusionNeutron scattering experiments have been performed using a high-resolution diffractometer on A186Mnl4, AlegMn7Crg and AlggCrl4 quasi-crystalline samples. The assumption that Cr can be isomorphically substituted to Mn has been a posteriori shown to be reasonable when indexing the quasi-crystalline diffraction peaks. The A186Cr14 lattice seems to be deduced from the AlggMnlq one by an homothetic transformation, the order of magnitude of which is in good agreement with the atomic radius change when going from Mn to Cr. Neutron scattering has been shown to be a very sensitive probe in order to test the possible location of the atoms in the unit cell. However a detailed intensity calculation for diffraction patterns has not yet been obtained and the question : where are the atoms ? the difficulty of which has been underlined in a recent paper /14/ has not yet been solved.
The problem which has been raised by the vanishing of several diffraction lines in both "zero scattering" transition metal and Cr alloys, may be due to different kinds of structure for these two samples. Therefore a better substitution method would be to use isotopic instead of isomorphic substitution for further neutron structural studies.
Acknwledgments.
We are grateful to Marcel Pinot for his help in the neutron experiments and to Pierre Guyot and Denis Gratias for stimulating discussions on structural models.
/I/ D. Shechtman, I. Blech, D. Gratias and J.W. Cahn., Phys. Rev. Lett. 53, 1951 (1984).
/2/ Z. Zhang and K.H. Kuo, Phil. Mag. A52, L49 (1985).
/3/ S.J. Poon, A.J. Drehman and K.R. Lawless, Phys. Rev. Lett. 55, 2324 (1985) /4/ H.U. Nissen, International Workshop on Aperiodic Crystals,
Les Houches, France, 11-20 March 1986 (to be published in J. Physique).
/5/ P. Sainfort, B. Dubost, (Les Houches, 1986, see ref ./4/) 161 L. Bendersky, Phys. Rev. Lett. 5 5 , 1461 (1985).
/7/ P.A. Bancel, P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, Phys. Rev. Lett. 54, 2422 (1985)
/8/ L. Pauling, The Nature of the Chemical Bond./9/ J.M. Dubois, C. Janot, J.
Pannetier, to be published in Physics Lett. A.
/lo/ E.A. Stern, Y. Ma, C.E. Bouldin, Phys. Rev. Lett. 55, 2172 (1985) /11/ A. Sadoc, A.M. Flank, P. Lagarde, P. Sainfort, R. Bellissent,
to be published in J. Physique, mai 1986.
/12/ P. Guyot, M. Audier, Phil. Mag. B52, L15 (1985).
/13/ M. Audier, P. Guyot, Phil. Mag. B53,1, L43 (1985).
/14/ P. Bak, Phys. Rev. Lett. 56, 861 (1986).
Table 1. Comparison between X-ray and n e u t r o n d i f f r a c t i o n peaks f o r q u a s i - c r y s t a l l i n e AlggMnl4
The e r r o r on t h e p o s i t i o n of t h e peaks i s about 5 10-~1-l f o r n e u t r o n s .
The 100000 l i n e which a p p e a r s t o b e t h e most i n t e n s e f o r X-ray s c a t t e r i n g h a s been given a 100 i n t e n s i t y a s r e f e r e n c e . The same r e f e r e n c e h a s been used f o r n e u t r o n s i n o r d e r t o make e a s i e r i n t e n s i t y comparisons.
Index
110001
{ ---
321112 l l l 0 i 0 221050
---
311111
? 2 i i o o i 2 i i i o i 100000 321002
i -
110000 220002 { 2 2 1 1 i 1 111101 210001 3 2 o o i i 220001 2 2 i o i o 111000
{
330071111100
n i i o i o
2110i1 320002 101000 221101
Q ( i - l )
1.632
1.876 2.00 2.20
-
2.49 2.64 2.896
3.043 3.24
3.44 3.576 3.63 3.92 4.04 4.20
4.307 4.60 4.70
-
4.928 4.99
I (A.U)
22
8
-
1.5
-
3
-
100
78 1
-
1.5
-
.5
-
11
3 .5 - 5
-
20 . 5
Q ( I )
1.630
1.884
- -
2.396 2.486
2.900
3.038 3.286
3.458 3.581
-
3.924
4.209
4.319 4.607
-
4.765 4.932 4.99
I (A.U)
202
114
- -
38 163
100
69 24
5 5 54
-
33
5 2
12 106
-
44 54 10
JOURNAL DE PHYSIQUE
Table 2.Neutron diffraction from AlggMnl4, AlggMn7Crg and AlggCrl4 quasi-crystalline alloys. As well as in table 1, the intensity of (100000) is taken equal to 100 as a reference for intensity comparisons. Such a choice must not withhold the fact that the total intensity scattered from the quasi-crystalline phase is much higher compared to the A1 matrix, in the AlggCrl4 than in the AlggMn7Crg sample.
the consecutive error on the calculated oositions is then about 5.10-~;-1
T a b l e 4 . Neutron diffraction from AlggMnl4Si and Alg5(Mno72Fe.28)14Si 191.
The 100000 has been still taken as an intensity reference for comparison to the patterns of table 1 and table 2.
Index 110001 {32iii2
iiioio
-
211001
--
211101 100000 110000 220002 {zziiii
111101 210001 320011 222020 220001
AlggMnlhSi
Q 1.628 1.876 2.493 2.652 2.894 3.038 3.254
-
3.450 3.574 3.632 3.751 3.927
A185(~n. 72~e28)14~i I(A.u.)
390 300 280 6 8 100 138 85
-
85 9 7 54 10 80
Q(i-l)
%-
1.875 2.485 2.649 2.902 3.044
-
-
-
3.570
-
-
-
I(A.u. )
*
12 23 12 100 150
- - -
*
-
-
-
JOURNAL DE PHYSIQUE
Figure 1. AlggMnl4 diffraction patterns : X-ray determination ( P . A . Bancel et a1
/ 7 / ) and neutrog experiment (this work). The diagrams are
lotted
as a functionof Q = 4?rsine/h(~-l). The quasi-crystallines line are indexed on the six following five-fold symmetry directions : ql = (l,-r,O) ; qg = (1,-T,O) ; qg = (0,1,T) ; 94 = (0,1,--r) ; q g = h ,0,1) ; qg = (-~,0,1), where T is the golden mean, (1+/5)/2.
8
12' 5 1
8g
;1g gpz g
- = 1-
- t
= =
2$
2 g S K --
L
II
b
Figure 2. AlggMnl4 ; A185Mr17Cr8 and A186Crl4 neutron diffraction spectra. For thermal neutrons, the respective scattering lengths of Al, Mn and Cr are 0.345, -0.373 and 0.363 in 10-~*cm units.
