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STRUCTURE STUDIES OF ALUMINUM BASED QUASICRYSTALS
W. Malzfeldt, P. Horn, D. Divincenzo, B. Stephenson, R. Gambino, S. Herd
To cite this version:
W. Malzfeldt, P. Horn, D. Divincenzo, B. Stephenson, R. Gambino, et al.. STRUCTURE STUDIES
OF ALUMINUM BASED QUASICRYSTALS. Journal de Physique Colloques, 1986, 47 (C3), pp.C3-
379-C3-387. �10.1051/jphyscol:1986339�. �jpa-00225751�
STRUCTURE STUDIES OF ALUMINUM BASED QUASICRYSTALS
W. MALZFELDT, P.M. HORN, D.P. DIVINCENZO, B. STEPHENSON, R. GAMBINO and S. HERD
IBM, T h o m a s J. W a t s o n Research Center, P.O. B o x 218, Y o r k t o w n Heights, NY 10598, U.S.A.
Resume
Des experiences de diffraction de rayons x et de microscopie electronique en trans- mission (TEM) ont ete faites sur des echantillons de AlMn et AlMnSi presentant une structure icosahedre. L'ordre quasicristallin a ete obtenu par differentes techniques de preparation: trempe, recuit d' echantillons amorphes par laser ou dans un four. Dans un echantillon trempe d' AlMn, les grains A structure isosahedre se trouvent enfermes dans une matrice d' Aluminium cristallise. Celle-ci est reduite fortement ou rendue non cristalline par addition de Silicium. Les echantillons prepares par recuit laser et trempe presentent un grand desordre. Cela s' observe par une grande largeur de raie dans les spectres de diffraction de rayons x. Les ecllantillons recuits au four montrent apparament des grains homogenes en microscopie electronique par la methode du champ noir et des plus faibles largeurs de raies en rayons x. Cependant, les grains sont plus gros que la longueur de correlation obtenu par diffraction de rayons x. Les variations de largeur de raies et leurs valeures peuvent etre expliquees dans un modele Hendriks Teller comme une consequence des interferences entre differents espacements dans une sequence desordonnee.
Abstract
X-ray diffraction and transmission electron microscope (TEM) measurements were performed on icosahedral AlMn and AlMnSi samples. Quasicrystalline order was obtained via different sample treatments: quenching, laser annealing and furnace annealing of amorphous samples. In quenched bulk AlMn samples, the icosahedral grains are embed- ded in a crystalline Al matrix. The A1 matrix is strongly reduced or rendered noncrystalline by the addition of Si. Samples prepared by laser annealing and quenching show a high degree of disorder. This shows up, in x-ray diffraction, as a large average peak line width.
The furnace annealed samples show apparent homogenous grains by TEM darkfield methods, and the smallest peak widths in x-ray diffraction. However, the grain sizes are much larger than the x-ray correlation lengths. The variations of the line widths and their values can be understood in a Hendricks Teller model as a consequence of interferences between projected lattice spacings in a disordered sequence.
Introduction
Until two years ago, it was believed that all crystals in nature had only I-, 2-, 3-, 4- and 6-fold symmetry axes. It was therefore very surprising when Shechtman et al. /1/ observed, in a quenched AlMn alloy, a fivefold diffraction pattern by transmission electron microscope (TEM) Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986339
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measurements. This work stimulated extensive theoretical and experimental research. The electron diffraction patterns have sharp Bragg-like spots, with the point symmetry of an icosahedron with twofold,threefold and fivefold symmetry axes. Icosahedral bond orientational order had been predicted to occur in glasses by Steinhardt, Nelson and Ronchetti / 2 / . It was ex- pected, however, that the bond orientational order would be short ranged. Levine and Steinhardt /3/ proposed a model which is a three dimensional generalization of the ideas of Penrose /4/ to explain the sharp diffraction peaks. The latter found a fivefold symmetry by filling a two dimen- sional plane with two distinct building blocks. Levine and Steinhardt obtained perfect icosahedral order by arranging their two kinds of building blocks quasiperiodically according to specific math- ematical rules. The agreement of this model with experimentally observed electron diffraction patterns is good normal to the threefold and fivefold symmetry axes although the positions of the A1 and Mn atoms are not described.
We have performed x-ray diffraction and transmission electron microscopy (TEM) on quasicrystalline AlMn material. The interpretation of electron diffraction data is complicated by the occurrence of electron multiple diffraction. The combination of both methods is a powerful tool to get information about the structure of quasicrystals. X-ray diffraction data, especially, yield information about the correlation lengths and the nature of the disorder in quasicrystals. An earlier work by one of us /5/ showed that all major peaks observed in electron diffraction are found in x-ray diffraction too. The apparent correlation lengths in quenched A16Mn ribbons, obtained from the width of the x-ray diffraction peaks, are on the order of 100-300 A. This is in contrast to the results from TEM; the icosahedral grain sizes for these material are on the order of 0.1-1 ym.
Broad peaks are in disagreement with model calculations of three dimensional Penrose tilings which yield sharp Bragg peaks. In this paper we discuss the origin of these broad peaks.
Experimental
X-ray diffraction and TEM measurements were performed on ribbons of quenched Als6Mn,,, AlssMnly A175Mn21Si and on AlMnSi films prepared on glass and Si substrates with thicknesses of 5000 A. The Mn composition varied between 14-at.% and 30-at.% and the Si composition between 5-at.% and 20-at.%. The ribbons were made by quenching a molten alloy on a 9-in. Cu wheel rotating at 3250 rpm. The films of AlMnSi were prepared by three source electron beam evaporation. The elements were evaporated from individual electron beam heated sources. The rate of deposition of each element was controlled with an automatic rate controller using a quartz crystal rate monitor as a feedback device. The vacuum system used a turbomolecular pump in conjunction with a titanium getter pump and cryopump to achieve a base pressure of Torr.
The pressure during evaporation typically increased to about Torr. The Si and glass substrates were mounted on a massive metal block for heat sinking but were not otherwise cooled during evaporation. The films were always found to be amorphous after preparation. The ribbon speci- mens for electron microscopy were thinned by standard ion-milling techniques. The AlMnSi films were prepared for electron microscopy by mechanically polishing and grinding the substrates down to 1 ym and finally by ion-milling. Some films were furnace annealed and showed a transition to a quasicrystalline structure when heated to more than 365' C. The heating was performed in a special furnace in which the annealing could be done during the x-ray diffraction measurements.
The base pressure in the furnace was Torr. The pressure increased during the annealing pro- ceduroe to Torr. A depth profile of such a film after two hour annealing showed that the first 100 A below the surface was oxidized. The composition of deeper layers was not influenced by the heating process. One sample, a film with the composition A1 81-at.%, Mn 14-at.%, Si 5-at.%
on a glass substrate, was laser annealed with a ruby laser with an energy density of approximately 1 J ~ m - ~ and a pulse length of 2 ns. The areas hit by the laser became very rough and flaky and showed icosahedral order in TEM. Due to the large diffuse scattering background of the glass substrate, only the strongest icosahedral peaks were observable in x-ray diffraction. The x-ray
and the scattered intensity from the strongest quasicrystalline peaks was 10000 counts/100 s and 3000 counts/100 s for the ribbons and the films, respectively. Some of the x-ray diffraction ex- periments of AlMnSi films were performed with Synchrotron radiation at the Brookhaven National Laboratory using a Ge (1 11) double crystal monochromator and a Ge (1 11) analyzer. The inci-
<ent X-rays had an energy of 8.93keV and the momentum resolution was approximately 0.0002 A-l.
Results
and
DiscussionA variety of samples were studied including quenched Als6Mn,, ribbons which were more A1 rich than those originally studied /5/. All the earlier results were confirmed and no additional peaks were found. Some of the low intensity x-ray diffraction spots at low q values were not al- ways detectable because of the large diffuse background due to small angle scattering from the sample's microstructure. Our TEM measurements of the quenched bulk AlMn show 0.5-3 pm large icosahedral grains embedded in crystalline A1 (Fig. 1).
Figure 1. Darkfield TEM picture of an icosahedral grain in a quenched bulk A16Mn ribbon. It consists of smaller subunits with seizes of approximately 0.3 pm.
The grains are divided into smaller units with sizes between 0.1 pm and 0.3 pm. All subgrains have the same orientational order (to within 5O) but areoseparated by Al. Furthermore, the icosahedral subgrains can contain A1 inclusions of up to 300 A in size. The intensity of the Al(111) peak is
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more than 3 times larger than the most intense icosahedral one. This implies that the concentration of Mn in the icosahedral phase is far more than 17%. This high Mn/Al ratio has been confirmed by microprobe analysis of the sample. The average Mn concentration was measured to be 12 %.
It increases in the icosahedral areas up to 30 % and drops inside the crystalline Al regions to 2.8
%. These results are consistent with similar measurements published by Krishnan et al. / 6 / . The high Mn concentration suggests that the Mn atoms are positioned outside of the icosahedra instead of their centers. This is in agreement with conclusions by Henley and Elser /7/ and Koskenmaki et al. /8/. They suggest that the Mn atoms are positioned on the second shells of the icosahedra.
Another quenched A1 alloy was investigated with some Si added into the melt. The idea was to reduce the internal strain and stabilize the icosahedral order. These ribbons were composed of 21-at% Mn and 4-at.% Si. All the icosahedral x-ray diffraction peaks observed in the pure AlMn alloy also occur in the Si doped sample. However, there is a huge reduction in the peak intensity of the fcc Al peaks; The intensity of the strongest Al peak, from the (1 11) plane, is approximately only 8 % of the strongest icosahedral peak. Thus, only small amounts of Si are sufficient to destroy the structure of the fcc Al matrix. The icosahedral peak positions are shifted on average by 0.2%
to slightly larger q values. This suggests substitution of Si into the icosahedral structure and that the Si alloy has somewhat better structural order than does pure AlMn. Another manifestation of this order is the existence of narrower x-ray peak widths.
I I I I I I I I I I
AlMnSi (FURNACE ANNEALED)
Figure 2. X-ray diffraction pattern of furnace annealed A160Mn zoSi20. The icosahedral peaks are labeled in the notation of Elser /9/.
In the laser annealed quasicrystalline sample, (A18,Mn,,SiS) the peak intensities are in exactly the same ratio as those from the quenched AlMn ribbons. The peak widths are, however, slightly larger. In these samples the Si content is similar to that found in quenched A175Mn21Si4 ribbons.
the quenched AlMn ribbon.
Amorphous films on Si of the composition Mn20Si20 did not show a phase transition after laser annealing. The surface still looks macroscopically smooth in contrast t o the above sample with a glass substrate. After laser annealing the x-ray diffraction pattern is amorphous as before. We believe that the quenching process for films on Si was too fast for the icosahedral phase t o form. Furnace annealing of such an amorphous film doesn't change anything until a temperature of about 36S0 C. Th? amorphous samples A160Mn20 Si20 show a huge broad liquid-like diffraction peak a t q ~ 3 A-'. The films contain a substantial degree of short range positional order. A t 365 C or above, the icosahedral peaks start t o grow. Their amplitudes are a function of the temperature and annealing time. Fig. 2 shows the x-ray diffraction pattern of such a film with icosahedral order. The intensity of the liquid structure decreases with annealing time and increasing temperature but it doesn't vanish completely. Fig. 3 d e m y - strates this by showing a detailed comparison of the x-ray diffraction structure around 3 A - ~ between the amorphous and the icosahedral phase. A weak crystalline A1 phase occurs in ad- dition t o the icosahedral one.
AlMnSi (amorph)
"
88
Figure 3. Superposition of x-ray diffraction data for amorehous and icosahedral A1,Mn,oSi20 films. The liquid structure around 3 A-' has been converted mostly into an icosahedral structure after annealing. A small amorphous background is still present.
Our TEM results (Fig. 4) confirm the amorphous phase b z a general lack of contrast in brightfield images and by strong out-of-focus contrast of a 200-300 A sized void network structure common in amorphous materials. This is not observed in quenched bulk AlMn ribbon samples. The
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icosahedral phase is macroscopically uniform with amorphous material separating icosahedral grains. In addition, the transmission electron diffraction pattern looks different from that of the AlMn ribbon in that a distinct broad halo indicative of an amorphous phase is superimposed on the strongest reflections of the icosahedral phase.
Figure 4. TEM darkfield image of a furnace annealed icosahedral A160Mn20Si20 sample.
Grains with similar orientation have seizes between .05 pm and 0.3 pm.
It i s clear that the annealed samples look very uniform with a high density of icosahedral grains.
The grain sizes vary and are comparable to the subgrains of the quenched AlMn bulk ribbon sam- ples. No irregularities inside the icosahedra can be observed.
A transition from an amorphous to an icosahedral phase was also seen in Pd60U20Si20 by Poon et al. /9/ in a narrow compositional range. The furnace annealed films have the best structural order of all samples investigated, as indicated by their narrow x-ray line widths. The smallest linewidth was only 0.005 A"HWHV obtained by deconvoluting the measured half widths with the experimental resolution of 0.01 A-l These results were c o n f i i e d by high resolution measure- ments made at the x-ray synchrotron source in Brookhaven. In the films, the x-ray peak positions are shifted approximately 1% to larger q values. Annealing of an amorphous sample to 650 C leads to the crystalline P-phase of AlMnSi.
In the following section, we try to explain the origin of the x-ray line widths. The details of these ideas will be presented elsewhere/lO/. In Fig. 5 we plot the x-ray peak half widths versus the momentum transfer G II for a quenched AlMn sample and a furnace annealed sample.
It is clear from Fig. 5 that there is a wide point-to-point variation in the peak width and that there is no obvious relationship between the widths and G I I . Similar results were observed in all samples.
It is convenient to discuss these results in the context of the projection techniques introduced by Elser
/
11/ and others/ 12,13,14/ in which a quasicrystal is obtained by projection of a crystal from 6-dimensional space. The components of the 6-dimensional reciprocal space are G (the physical momentum) and GL (the three orthogonal phason components). The intensity of a Bragg peak decreases rapidly with GL /1 l/. GL values can be determined by indexing the Bragg peaks ac- cording to icosahedral lattice vectors as described by Bancel et. al. /5/ and by Elser /1 l/. The Bancel et. al. notation is more convenient when using the density wave language whereas here, we use the Elser indexing scheme which is more microscopically physical. Fig. 6 shows the de- pendence of the half widths at half maximum (HWHM) of various samples versus GkC3-386 JOURNAL DE PHYSIQUE
Figure 6. Plot of the x-ray HWHM versus G, for various icosahedral samples.
There is no obvious relationship between peak widths and G, for the laser annealed sample and the quenched ribbons. However, the furnace annealed samples show a strong positive correlation between width and Gk It is clear, therefore, that in these samples, G, is the correct parameter to systematize the data. Differences between the rapidly quenched and the furnace annealed samples are also quite obvious from the TEM pictures. In the former, the icosahedral grains are surrounded by and presumably strained by FCC Al. In the latter case, the pattern looks quite homogeneous without any recognizable disruption of the icosahedral or$er. There is no evidence for strain. Still, even the sharpest pcaks have a HWHM of 6q=0.005 A, corresponding to a length L=a/Gq of approximately 600 A, much smaller than the grain size. One simple and elegant mechanism to generate broadened x-ray lines without strain was proposed by Stephens and Goidman
/
15/ and is based on an old model by Hendricks and Teller /16/. The detailed application of the Hendricks-Teller model to icosahedral material will be discussed elsewhere /10,17/. Briefly Stephens and Goldman argue that AlMn can be thought of as a collection of randomly packed vertex sharing icosahedra. To insure orientational order, the icosahedra are oriented such that their centers and common vertex are colinear. Perhaps the most interesting feature of this "icosahedral glass" is that, if there is no lattice relaxation, the disorder is purely of phason character /10,17/.That is, since there is no strain, the peak widths will depend only on Gk The most obvious one- dimensional application of the Hendricks-Teller model yields peak widths which are proportional to G?. More generally (i.e., in three dimensions), one expects the width to scale as GLX; clearly, the data is not good enough to obtain x. However, it is clear that there is a systematic trend of the data with GL and not with G
,, . In general, any model of a quasicrystal which has primarily phason disorder will yield similar results.
References
/1/ D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Phys. Rev. Lett. 53,1951 (1984);
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/4/ R. Penrose, Bull. Inst. Math. Appl. 10,266 (1974);
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/8/ D.C. Koskenmaki, H.S. Chen, and K.V. Rao, AT&T preprint;
/9/ S.J. Poon, A.J. Drehman, and K.R. Lawless, Phys. Rev. Lett., 55,2324 (1985) /10/P.M. Horn, W. Malzfeldt, D. P. DiVincenzo, John Toner and R. Gambino,
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/11/V. Elser, Phys. Rev. B 32,4892 (1985); Acta Cryst. A42, 36 (1986);
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