The structure of decagonal Al7(Mn1-xFe x)2 alloys

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The structure of decagonal Al7(Mn1-xFe x)2 alloys

P.J. Schurer, T.J. van Netten, L. Niesen

To cite this version:

P.J. Schurer, T.J. van Netten, L. Niesen. The structure of decagonal Al7(Mn1-xFe x)2 alloys. Journal

de Physique, 1988, 49 (2), pp.237-241. �10.1051/jphys:01988004902023700�. �jpa-00210689�

The structure of decagonal Al7(Mn1-xFex)2 alloys

P. J. Schurer (1, *), ^{T. J. van Netten} (2) and L. Niesen (2)

(1) Laboratorium voor Vaste Stof Fysica, Materials Science Centre, University ^of Groningen, Groningen, The Netherlands

(2) Laboratorium voor Algemene Natuurkunde, Materials Science Centre, University ^of Groningen, Groningen, The Netherlands

(Reçu le 18 aout 1987, accepté le 13 octobre 1987)

Résumé.

Les fonctions de distribution radiales autour de l’atome Mn ont été déduites de mesures EXAFS dans Al7(Mn1-xFex)2 décagonal, ^{avec x}

^{0 et x}

0,3. ^Cette analyse ^montre que les mêmes unités structurales existent dans la phase icosahédrique ^{et la} phase décagonale ^des alliages Al-Mn ^et 03B1-AlMnSi. Ces unités structurales avec symétrie ^locale icosahédrique ^{forment un réseau avec une} _symétrie décagonale ^à longue portée.

Abstract.

Radial distribution functions around the Mn atom have been derived from EXAFS measurements on decagonal Al7(Mn1-xFex)2, x

^{0 and x}

^0.3. Analysis indicates that the same structural units exist in

decagonal ^as in icosahedral Al-Mn alloys and 03B1-AlMnSi. These structural units with local icosahedral symmetry ^{form a} framework with long range decagonal symmetry.

Classification

Physics ^Abstracts

61.55H

1. Introduction.

Several rapidly quenched Al-Transition Metal (TM) alloys ^{have been} discovered that possess the icosahe- dral point group symmetry m35 with six 5-fold symmetry ^axes [1, 2]. ^Another type ^{of «} quasi-crys-

tal » has the point group symmetry ^{10/m or 10/mmm.}

For this so-called decagonal phase only ^{one 10 fold}

rotation axis exists that points ^{in the same direction}

as the one dimensional translational symmetry [2-5].

The decagonal and icosahedral phases ^are closely

related and in Al-Mn alloys generally ^coexist together. A pure decagonal phase ^{can be obtai-} ned [5] by rapid solidification of AI7(Mnl-xFex)2,

x

0 and x

0.3. Mossbauer effect measure- ments [5] show that a distribution of Quadrupole Splittings (QS) ^{exists at 57 Fe nuclei in} A17(Mno.7FeO.3)2. ^{The QS} distribution is slightly

different from that found in the icosahedral Al- (Mnl _ xFex ) alloys. ^The magnitude of the Isomer Shift (IS) indicates that the Fe atoms and presumably

also the Mn atoms have only ^{Al nearest} neighbours.

The purpose ^{of the} present study ^{is to obtain more}

information about the local structure in decagonal Ah (Mnl _ xFex )2 by performing ^Extended X-ray Absorption Fine Structure (EXAFS) measurements.

Such a study ^can give information about the number and lengths ^{of the Mn nearest} neighbour (Inn)

bonds and in principle ^{also of the next} neighbour (2nn) ^bonds.

2. Experimental.

Molten alloys ^of composition AhMn2 ^and A17(Mno.7FeO.3)2 ^were rapidly quenched ⁱⁿ Argon atmosphere ^{onto the outer} surface of a rotating

copper wheel. Pure decagonal ^{ribbons were pro-}

duced _up to the highest ^wheel speed ^{of 45 m/s. No}

fcc Al ^or icosahedral phase ^{could be} distinguished ⁱⁿ X-ray diffractograms. The ribbons ^were annealed at about 550 K to reduce strain and lattice defects.

Subsequently, Transition Electron Microscopy (TEM) ^{studies showed that the} diffraction patterns satisfied the decagonal symmetry.

Crystalline c-Al6Mn ^was prepared by annealing ^a

ribbon containing icosahedral Al-Mn and fcc Al.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01988004902023700

238

The crystalline sample ^{was used as a known structu-}

ral standard for the EXAFS investigation.

EXAFS samples ^{were made} by sticking ^{a number}

of ribbons ^on scotch tape. ^The samples ^were placed

with their surface normal at 45° with respect ^{to the} X-ray ^{beam. The EXAFS} experiments ^were perfor-

med on station 7.1 at the Daresbury S.R.S. The K-

absorption edges ^{of Mn were} scanned with a

Si 111> channel-cut monochromator. Since the structural part ^of the disorder is far more important

than the thermal part [6], ^{the EXAFS} measurements were performed only ^{at room} temperature.

Because the samples ^were quite inhomogeneous

in thickness, fluorescence detection was used. For this purpose a NaI scintillation detector ^was positio-

ned at 90° with respect ^to the beam. A Z-1 filter was

put ^between sample ^and detector ; its thickness was

chosen in such a way that the maximum ^{count rate}

was between 3 x 105 and 4 x 105 p/s.

3. Analysis.

For the calculations ^we used programs developed ⁱⁿ Daresbury, ^U.K. [7], using ^a curved-wave version of the EXAFS formula. After background subtraction

a model containing one or more Gaussian distribu- tions of near neighbours is fitted to the k3-weighted

EXAFS spectrum. ^Shell dependent ^fit parameters

are N, Rand u 2, where N is the coordination

number, ^{R is the mean distance} and o- 2 is the mean

square variation in bond length ^{of the} distribution, taking ^{into account} both thermal vibrations and a

static distribution of bond lengths.

Phase functions and some other non-shell-depen-

dent parameters ^were fixed with the help ^{of the}

model compound c-MnA16. The best fit of this

crystalline sample with well known structure is shown in figure 1. Table I compares the EXAFS distances with those obtained from X-ray ^diffrac-

tion [8].

Decagonal spectra ^were fitted with _one, two or

three Al shells around a central Mn atom. As a

second possibility ^the spectra ^were also fitted with

one Al shell and one Mn shell. In these fits only ^the

coordination number N, the distance R and the

mean square variation in bond length u2 of ^each

shell are varied. All other parameters ^were kept

Table I.

Nearest neighbour ^{distances as derived} from X-ray diffraction ^{and EXAFS} for ^the crystalline alloy c-MnA6 ^{used as standard.}

Fig. ^1.

Results of EXAFS experiments ^{on the} Mn-edge

of the crystalline compound MnAlb. Top : k3 X (k) ^as

derived experimentally ^without filtering (full line) ^and

fitted with the parameters in table I and optimized phase

functions (dashed line). Middle : Fourier transform (abso-

lute value and imaginary part). Bottom : radial distribution function derived from fit.

constant. If the energy Eo at ^{which k}

^{0 was left} free, variations in this parameter ^were observed up to 0.3 eV. Such variations did not lead to significant changes ^{in the} quality of the fit and in the parameters derived for the various shells.

The results of fits by different models are sum-

marized in table II. Figure ^{2 shows as an} example ^a

Table II.

Structural parameters for decagonal ^Al-

Mn alloys ^{with Mn as central atom.}

,

-

NPT loo

r * 3 ²

FI (fit index)

_{i=1 NPT} 1: - * (r * k

where : r is the residual of point ^{i :} X (k )cal -

X (k )cxp

k is the wave number at point ^i.

typical ^{errors :}

coordination numbers (N) : ^{10 %}

distances (R ) ^{: 0.03 A}

fit of k3 X (k) ^for AhMn2 together with the Fourier transform (corrected for the Al phase function) ^and

the radial distribution function derived from the fit parameters. ^The quality ^of the one-shell fit is

definitely ^worse than of the other fits with ^more than one-shell. A fit with two Al shells and the mean

square bond length variations u 2 ^{left as} free par- ameters gives N2 > N1 ^{1 and} af « a 2 2for ^{both deca-}

gonal samples. However the values of Ntot ^are

different for the ^two samples. ^{A two Al} shell fit with

a2 1 and o- 2 2 constrained to an average value demons- trates that small adjustments in the model of analysis

can affect the values of parameters N1 ^{1 and} NZ

without affecting ^the quality of the fit. For this fit

Fig. ^2.

EXAFS results on the Mn-edge ^of decagonal A17Mn2l fitted with two Al nearest neighbour ^{shells, and}

two next nearest neighbour shells. The various curves have the same meaning ^{as in} figure ^1.

N1, N2 ^and Ntot ^are about the same for the two

samples. The values of R1 ^and R2 remain the same.

The quality of the three Al shell fit is slightly ^better

than the two Al shell fit. Ntot ^{=10 for both} alloys

and the values of o, 2 ^are of the same order of

magnitude ^as those found for the Inn shells in

c-Al6Mn. However, the values shown in table II for

Nl, N2 ^and N3 ^{have an} uncertainty ^much larger ^than

the 10 % uncertainty usually ^{found for the N-values}

in the other models. We conclude that values for the

240

distributions of Al atoms in the three shells are not reliable. An analysis of EXAFS data with one Al and one Mn Inn shell gives fits of the same quality ^as

that obtained with only ^{Al nearest} neighbours. ^In

this fit the - 7 Al and - 2 Mn nearest neighbours ^are

all at the same distance from the central Mn atom.

Next we made an attempt ^to obtain information in the range R > 3 A from the central Mn atom. First

we note that for crystalline Al6Mn ^no peaks ^{can be} distinguished in the Fourier transform, although

6 Mn and 34 Al atoms are present between 4 and 6 A. _{This many} atoms over varying distances appa-

rently ^causes interference that effectively inhibits the appearance of significant peaks between 4 and 6 A.

Because the SIN - ^{1 not a} good ^{fit can} be obtained

even though ^{the structure of} c-Al6Mn ^determined

from X-ray diffraction can be used as model.

For the decagonal phase ^on the other hand, ^a

distinct peak is visible for both samples ^{at the same} position in the Fourier transform. Considering ^the

interference effect mentioned above, it is difficult to

interpret this result without some structural model in mind. Comparing experimental results, ^{the 2nn shell} in the decagonal sample ^{seems to} be different from the 2nn shell in c-Al6Mn. It has been suggested ^that

the quasi-crystalline ^Al-Mn alloys ^{have the same}

structural units as in a-AlMnSi [9, 10]. ^{In this} crystalline material the structure is a periodic ^ar- rangement ^of Mackay [11] icosahedra, ^{where the}

Mn atoms are placed ^at the vertices of icosahedra.

The average distance between ^a Mn atom and the 5 Mn nearest neighbours ^{on the same} icosahedron is about 5.1 A. The average distance between ^a Mn atom and 5 Mn atoms on the neighbouring ^icosahed-

ra is about 4.4 A. In total there are 10 Mn atoms and 35 Al atoms between 4 and 6 A from a central Mn atom. A theoretical EXAFS spectrum ^{for the a-} AlMnSi alloys shows that distinct peaks ^{can be} expected between 4 and 6 A. Further analysis ^shows

that the major contribution to the peaks originates

from Mn atoms. For this reason we have fitted only

two shells of 5 Mn atoms each in the region ^of

interest neglecting the contribution of Al atoms. The result of this fit is shown in figure 2. For both

decagonal samples the fit is consistent with 5 Mn atoms at 4.51 A (2 (T2 ^{= 0.05} A ) ^{and 5 Mn atoms at}

4.94 A (2 C, 2 =0.04 A2). This result is similar to that obtained for icosahedral Al-Mn alloys [12] ^and

Al-Cr alloys [13].

4. Discussion.

Inspection of table II shows that fits of similar

quality ^can be obtained with different models, indicating that the EXAFS results are model biased.

For the fits with only ^{Al nearest} neighbours, ^the

values obtained however are generally ^{the same}

within the experimental ^error. The total number of

nearest Al neighbours Ntot = ^{9 ± 1. The} asymmetry of the radial distribution function in the decagonal alloys is similar to that found for icosahedral Al-Mn

alloys that have been analysed ^{with the same}

model [13]. ^{For both} types ^of quasi-crystalline ^ma-

terial N 1 N2 ^and o, 2- 012. Furthermore, ^{the values}

of R1 ^and R2 ^are very similar.

Most authors assume that Mn atoms in icosahedral

alloys ^are completely surrounded by Al in the Inn shell. We note however, that there is no direct evidence for this from the EXAFS results neither for the decagonal alloys (Tab. II) ^nor for the icosahedral

alloys [6, 13]. ^The assumption ^of only ^{Al nearest} neighbours ⁱⁿ quasi-crystalline materials is based on

the fact that in crystalline ^{Al-Mn and Al-Fe} alloys ^of

similar composition the transition metal atoms are

completely surrounded by ^{Al atoms.} On the other hand this is not the case for crystalline Al13Cr4Si4 [14]. ^A Monte Carlo Simulations of a Lennard-Jones system, indicating ^10-fold symmetry ^{in two dimen-} sions, shows many small ^atoms that have other small atoms as nearest neighbour [15]. However this result does not seem applicable immediately ^to our case as

the size of atoms and variations in bond lengths ^is

much different from that found in Al-Mn based

alloys. ^The assumption ^of only ^{Al nearest} neighbours

is supported by the results of Mossbauer effect measurements [5, 16].

A previous analysis of EXAFS data obtained by

Stern et al. [12, 17] for icosahedral AlMnSi alloys presents the first direct evidence that the ^structure of Al-Mn based icosahedral alloys is very similar ^to that of crystalline a-AlMnSi. For both alloys ^{the EXAFS}

transform shows a peak corresponding ^{to 5 Mn} neighbours ^{at about 5.1} A. This is consistent with the idea that in both the icosahedral and the

crystalline ^{structure the same} basic structural unit exists. This unit is an icosahedron with Mn atoms at the vertices. The vertices are separated by ^{5.1 A}

from the nearest neighbour vertices. A second peak

at about 4.5 A that is also present ^{for both} alloys presumably corresponds ^to the distance between a

central Mn and Mn atoms located at neighbouring

Mn icosahedra. The results obtained for our deca-

gonal samples ^are consistent with this. The peak ^at

4.94 A _may correspond ^{to the nearest} neighbour

distances between Mn atoms located at the vertex

positions ^{of Mn} icosahedron. The 4.94 A value is

slightly smaller than the 5.1 A found in the AlMnSi

alloys, ^but equal ^to the value 4.94 A found by ^Stern

et al. [12] for icosahedral Al-Mn. The 4.51 A dis- tance, interpreted ^as the distance between Mn ^atoms

belonging ^{to different} icosahedral basic units, ^{is the}

same as that found in the AlMnSi alloys [12]. ^The

existence of the same structural unit with icosahedral symmetry ⁱⁿ crystalline ^and quasi-crystalline ^mate-

rials suggests ^that they already ^{exists above the}

melting point. Depending ^on cooling ^{rate and}

composition, the units connect together ^{into an} icosahedral, decagonal ^or crystalline structure. We note that most quasi-crystalline alloys ^{seem to be}

associated with crystalline ^{« cousin »} alloys ^{in which} regular ^or distorted icosahedral structural units dominate.

In conclusion, the results of EXAFS measure- ments on decagonal A’7(Mnl-.,Fe,,)2 ^{are consistent}

with the ideas first formulated by Elser and Hen-

ley [9] ^and Guyot ^{and Audier} [10] ^for icosahedral

alloys. ^{The EXAFS} analysis presents evidence that icosahedral structural units, such e.g. ^as Mackay Icosahedra, ^{are connected} together ^{in a framework}

that has the decagonal symmetry.

Acknowledgments.

It is a pleasure ^{to thank B.} Koopmans for assistance in sample preparation. We thank the scientific and technical staff of the SRS in Daresbury ^{for the use of}

their facilities and the provision ^of computer pro- grams for the analyses.

This work is part of the research program of the

Stichting ^voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on

Matter) ^{and was made} possible by ^financial support from the Nederlandse Organisatie ^{voor Zuiver-} Wetenschappelijk ^Onderzoek (Netherlands Organi-

zation for the Advancement of Pure Research).

References

[1] SHECHTMAN, D., BLECH, I., GRATIAS, ^{D. and} CAHN, J. W., Phys. Rev. Lett. 53 (1984) ^1951.

[2] BANCEL, ^{P. A. and} HEINEY, ^P. A., Phys. ^{Rev. B 33} (1986) ^7917.

[3] BENDERSKY, L., Phys. Rev. Lett. 55 (1985) ^1461.

[4] FUNG, K. K., YANG, C. Y., ZHAO, Y. Q., ZHAN, W. S. and SHEN, B. G., Phys. Rev. Lett. 56

(1986) ^2060.

[5] KOOPMANS, B., SCHURER, ^P. J., ^{VAN DER} WOUDE, F., BRONSVELD, P., Phys. Rev. B 35 (1987)

3005.

[6] SADOC, A., FLANK, ^A. M., LAGARDE, P., SAINFORT, P. and BELLISSENT, R., ^J. Phys. ^{France 47} (1986) ^873.

[7] GURMAN, ^S. J., BINSTEAD, N. and Ross, I., ^J. Phys.

C 17 (1984) ^143.

[8] ^{NICOL, A. D., Acta} Crystallogr. ⁶ (1953) ^285.

[9] ELSER, ^{V. and} HENLEY, C., Phys. Rev. Lett. 26

(1985) ^2883.

[10] ^{GUYOT, P. and AUDIER,} M., ^Philos. Mag. ^{B 52} (1985) ^L15 (1985) ;

AUDIER, M. and GUYOT, P., ^Philos. Mag. ^{B 53} (1986) ^L43.

[11] ^{MACKAY, A. L., Acta} Crystallogr. ¹⁵ (1962) ^916.

[12] STERN, E. A., MA, Y., BAUER, ^{K. and} BOULDIN, C. E., ^J. Phys. Colloq. ^{France 47} (1986) ^C3-371.

[13] ^VAN NETTEN, ^T. J., SCHURER, ^{P. J. and} NIESEN, L.,

to be published ^{in J.} Phys. ^F.

[14] ROBINSON, K., ^Acta Crystallogr. ⁶ (1953) ^854.

[15] WIDOM, M., STRANDBURG, K. J. and SWENDSEN, R. H., Phys. Rev. Lett. 58 (1987) ^706.

[16] SCHURER, P. J., KOOPMANS, ^{B. and VAN DER} WOUDE, F., Phys. ^Rev. B, in press.

[17] ^{MA, Y. and} STERN, ^E. A., J. Phys. Colloq. ^{France 47}

(1986) ^C8-1025.