SIGN DETERMINATION OF THE 57Fe ELECTRIC FIELD GRADIENT IN AMORPHOUS Al70Si17Fe13

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SIGN DETERMINATION OF THE 57Fe ELECTRIC

FIELD GRADIENT IN AMORPHOUS Al70Si17Fe13

Gérard Le Caër, R. Brand, K. Dehghan

To cite this version:

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SIGN DETERMINATION OF THE 5 7 ~ e

ELECTRIC FIELD GRADIENT IN AMORPHOUS

A170Si17Fe13

G. Le Caer, R.A.

rand'

and K. Dehghan

Laboratoire de Me'taZZurgie, Associe' au C. N.R.S. U.A. 159, EcoZe des Mines, 54042 Nancy Cedex, France

' ~ a b o r a t o r i u m fur Angewandte Physik, U n i v e r s i t d t Duisburg 0-4100 Duisburg 1,

F.R.G.

RBsumd

-

Dans A170Si,7Fe13 amorphe, une fraction p+ 2. 0.50 des atomes de fer

ont un gradient de champ 6lectrique ( ~ ~ ~ ) ~ o s i t i f . AprEs cristal- lisation, pf augmente fortement alors que les effet quadrupolaire et d6pla- cement isomdrique moyens ne changent pratiquement pas. Les rdsultats sont in- terprdtds 2 l'aide de modSles de GCE.

Abstract

-

In amorphous A170Si17Fe13, a fraction p+ 2. 0.50 of iron atoms have a positive electric field gradient (EFG), After crystallization, p+ increases strongly while the mean quadrupole splitting and isomer shift show almost no change. The results are interpreted with the help of EFG models.

I

-

INTRODUCTION

Melt-spun aluminium-based amorphous alloys have been recently described in Al-transition metal systems and in A1 Si Fe 11, 2, 31. The latter alloy is particularly suited for neutron inve~ti~aS?on!~ l3 which show the existence of a strong chemical order around Fe atoms

141.

As A170Si17Fe13 is essentially non-magnetic, we have per- formed a 5 7 ~ e Msssbauer study in applied fields in order to determine if the electric field gradient (EFG) distribution disagrees with the Czjzek et al. model /5,6/ which was shown to correspond to random packed structures without chemical order. Before discussing the experimental results, we describe the main assumptions used to derive functional forms of EFG distributions in disordered solids.

2

-

EFG DISTRIBUTIONS IN AMORPHOUS SOLIDS

Two main methods are used to describe the functional forms of EFG and quadrupole splitting distributions (QSD) in amorphous solids :

1

-

one method considers the distribution D5 of the EFG tensor

Y,

that is the distribution of a 5-dimensional random variable T /7/ (called U in 151) which is directly deduced from the irreducible spherical tensor associated with

z.

is a symmetric zero-trace tensor.

2

-

another method considers the distribution D2 of the EFG principal values that is of a 2-dimensional random variable

181.

If some D5 distribution is assumed, a D2 distribution can be deduced. However, if some D2 distribution is assumed, one must make a second assumption on the distribution of the principal axes systems (PAS) in order to calculate D5. Independent assumptions cannot be done simultaneously on both D5 and D2 as was done, all things consi- dered, by Egami and Srolovitz (appendix 2 of / 9 c s e e figure 2 of /7/ for the correct distributions of a, and 0 2 ) .

-

In order to characterize EFG distributions in disordered systems, the first problem is to choose the best method with respect to the available information. The compo-

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C8-170 JOURNAL DE PHYSIQUE

packings, this condition is fulfilled for the first neighbour shell only for a point charge EFG /5/ while, in general, we expect it to be influenced by screening as already emphasized by Egami /lo/. For a Gaussian D5, two cases only are possible :

a) - the mean of the 5-dimensional random variable T (see 1) is zero and its variance-covariance matrix is proportional to a unit matrix of order 5 171. b)

-

one of the two conditions given in a) is not satisfied.

In case a) the EFG tensor is statistically isotropic : the distribution D5 is inva- riant under orthogonal transformations /5,7,12/. The corresponding model

(6

= 0 in /5,6/) has therefore been named the Gaussian isotropic model (GIM) in 171. Such distributions have been deduced analytically and numerically for a point charge EFG (and atomic level stresses /7,9/) in disordered cubic systems with a large concen- tration of defects or for models of amorphous solids /5,13,14/. Conditions a) have also been checked numerically in a model of amorphous metal-metalloid alloys (Ta- kacs and Le CaBr, to be published). They lead unevitably to a chi distribution with five degrees of freedom for the QS

A

/5,7/ :

p5(A)a

n4

exp { - ~ ~ 1 2 5 ~ 1 (1)

For a statistically isotropic sample, MSssbauer spectra are independent of correla- tions between the PAS from atom to atom. This is one reason why an EFG distribution agreeing with the GIM is not in a one-to-one correspondance with a given disordered structure (see also sectiqn 4). Moreover, the central limit theorem holds under very general conditions. Finally, it must be emphasized that the distribution D2 is not Gaussian (see equations (8) and (9) of 171).

In case b) the PAS are not isotropical.ly distributed. There is a PAS texture which may, in principle, be observed with 5 7 ~ e MSssbauer spectroscopy by following the changes in intensities as a function of sample orientation with respect to the gamma beam /15/. No such changes can be detected in an amorphous Fe24Zr76 alloy (Le Cagr, unpublished). The QSD is, in the simplest cases, given by a non-central chi distribution q (A) with n (( 5) degrees of freedom (equations (3) of /11/ and (12) of /7/). It wouldnalso be interesting to consider the QSD resulting from a

a

distribution in

(1).

The main problem with method 2 is that the central limit theorem cannot be applied directly to the principal values Vxx, Vyy, Vzz which are not linear with respect to the components of

y.

The choice of a D2 distribution is therefore arbitrary. In such conditions, it is aifficult to give a structural interpretation to such a distribution as the derived QSD have not yet been deduced from the structure of an amorphous solid with or without short-range order. A distribution p2 (A)hasbeen proposed by Coey, as explained in /8/ :

2 2 p2(A)a

A

exp

C-

A

125

I

Distributions p (A) have been calculated from some MSssbauer spectra but the uncer- 2

tainties in the isomer shift distributions prevent one of being sure of the validi- ty of such results. Moreover, it has never been demonstrated that the fitted p (A) is the unique solution and not an approximation of some other unknown distribugion. Finally, why wouid there be a unique functional form characteristic of all amorphous systems (covalent, ionic or metallic) if the central limit theorem, that is the GIM, does not hold ? To summarize, either

.i) the GIM is valid as a zeroth order approximation (f3 = 0 /5,7/). Only one parameter 5 is needed to characterize completely the

y

and (Vzz,

n)

distributions, where q is the asymmetry parameter (0 ( q (

I),

but-no precise conclusion can be drawn about the structure (section 4).

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crystallized state. The latter alloy mainly c o n s ~ s s

A2

a mixture of iron-free aluminium and the intermetallic compound @-A1 Fe Si

141.

Table 1 shows that similar quadrupole parameters are obtained from bo?h gtages. The spectra of the amorphous sample recorded in an applied field H = 50 kG, are almost perfectly symmetric (figure 2), as also observed for H = 70 kG. They are inconsistent with

n

= 1 and a gaussian distribution of Vzz ( ~ 2 = 4.63), the central part of the calculated spec- trum being too flat and too deep. More technical details about the various calculations will be published later. As obviously p+ (Vzz > 0)

2

p- (Vzz < O), we are led to investigate if the spectra are consistent with the GIM. A normal distribution of the isomer shift IS, N(<IS>, ofS), distributed independently of Vzz and

n ,

has been used to fit the spectra. This assumption is also a natural consequence of the GIM.

r

-2 1 0 *1 +2

- 2 - 1 0 .I . - .2 V I T E S S E 1)0M/SI

Tabie 1

Experimental results in the non magnetic state (mm s-l

,

+

0.01, linewidth

r

= 0.24 mm s-l) and reduced chi-square X2 2

The same model has been used to fit the spectra of figure 2. The best fits (x2=1 .OO

(a), X2=1 .32 (b)) are obtained for H = 49 kG, a Lorentz width

r

= 0.21 mm s-l, a = 0.08 mm s-I and aGIM =2~.21 mm s-1 in

agreement with the results of table 1. Clear asymmetries are observed for the crystallized alloy (figure 3). Calculations with gaussian distributions of Vzz and a fixed <rp value give <r)> % 0.4 to 0.7 with a frac-

Alloy 4

Amorphous

Crystal11ine0.41

tion p+(~zz)

2

0.8 t o 1. In the amorphous Fig.1 - MGssbauer spectra of

state, the experimental results are consis- A1 OSi17Fe13 at 4.2 K a) amorphous

alloy b) crystallized alloy. tent with the G I 3 although other models with P+

2

0.50 may also agree with them, as ex- pected more generally for symmetric 5 7 ~ e spectra of amorphous systems in applied fields. It is therefore important to justify the use of a given model. The long range oscillating potential in such aluminium-based alloys allows the effect of long-range disorder to overcome the effect of short-range order as shown in the next section.

4

- MODEL AND NUMERICAL CALCULATIONS IN SYSTEMS WITH SHORT-RANGE ORDER We consider the following EFG tensor :

T=295 K

< A > <IS> 0 ~ 4 2 0.17

0.19

where corresponds to a well defined neighbourhood of a given atomic species and

YGI

to-: gaussian isotropic part related to disorder of more remote atomic shells

while x allows changing the influence of the latter part. To analyse the 05 distribution in an isotropic system, it is necessary to rotate inall directions using correct weights (to be published). Whitout loss of general%ty, we assume that

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C8-172 JOURNAL

DE

PHYSIQUE

Fig. 2

-

Massbauer spectra of amor- Fig. 3

-

MGssbauer spectra of crystallized phous A170Si17Fe13 at 4.2 K in an A170Si17Fe13 at 4.2 K in an applied field of

applled field of 50 kG 50 kG a) H / / y b ) H ~ . y a) H

/I

y b) H l y 2 2 : nef ining 2 2 2 m = T 1 0 + T 2 0 -1 0 +l +2 VlTESSE ( M M / S ) -1 0 +l + 2 VlTESSE IMM/S)

where the Tio correspond to (section 1 and (1) of /7/), and o = x uGI, we obtain in a straightforward manner-O:

9~

&+

t

f i

a

3 4

*

t +

s

'

-2 -1 0 +I +2 VITESSE (MM/S) 2 2 2

[(mA/u ) cosh (mA/a )

-

sinh (mA/u )

1

/m 3 The mean QS, <A> and the standard deviation uA are given by :

2 2 2 4 3

<A> = (21~) 1/2u(l

+

02/m) exp (- m /2a )

+

(m + 20 /m

-

0 /m )erf(m/(oJ2)) (6)

and = 5a2

+

m2

-

<A> 2

OA (7)

The parameter z = x <A> I/Ao is very close to the ratio of the modulus of the two parts of (3) (% 1.015 z y . Two normalized quantities which are characteristic of the QSD shape are plotted in figure 4 (q5(A) is maximum for A =

A

) . The QSD change very rapidly from 0 to z

2

1 and show almost no change for max z

2

1.5 as con- firmed by direct plots (tobe published). This simple model demonstrates that the random term rapidly dominates the short-range order term. It may be applied to systems such as amorphous gallium.

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long-range disorder i s c l e a r . Table 2

EFG calculations in a model of NiR B„ /16/

symbols explained in text.

Atom Ni Ni GIM B B R (A) 2 . 6 4 . 4 -4 . -4 2 . 6 <A>/0A 3 . 1 4 3.21 3.09 3.17 2 . 6 8 + P 0 . 4 4 0 . 4 4 0 . 5 0 0 . 4 9 0 . 2 8

<n>

0 . 4 7 0 . 6 0 0 . 6 1 0 . 6 6 0 . 5 8 a

n

0 . 2 9 0 . 2 4 0 . 2 4 0 . 2 4 0 . 2 4

The present results show that there is not a one - to - one correspondance between the GIM and a random packing without short-range order. Long-range disorder and the central limit theorem are enough to explain the observations. In Al Si.-Fe ,, only the constancy of <A> and <IS> may be used to suggest the pre-sence of a similar short-range order in the amorphous and crystalline states. The long-range disorder associated to the long-range potential may explain that p+ ^ p_ in the amorphous state while the disappearance of long-range disorder upon crystallization would involve the strong increase of p+. It is therefore

tem-pting to assume the existence of a short-range icosahedral order in both states (see also /4/) consistent with recent descriptions of the structures of many Al-transition metal crystals /17/, /18/.

Acknowledgements : We thank Dr. J.M. DUBOIS for numerous and very helpful discus-sions. We also thank Pechiney for the financial support of K. Dehghan.

REFERENCES

/l/ DUBOIS J.M., LE CAER G., pli cachete du 07-06-1982, C.R. Ac. Sci 301, II n° 2 (1985) 73.

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/3/ SUZUKI R.O., K0MATSU Y., KOBAYASHI K.F., SHINGU P.H., J. Mat. Sci. _[8 (1983) 1195.

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/6/ CZJZEK G., Nucl. Instrum. and Methods jj>£ (1982) 37.

Ill LE CAER G., DUBOIS J.M., BRAND R.A., Amorphous Metals and Non-equilibrium pro-cessing, VON ALLMEN M. Ed. (Les Editions de Physique, 1984) 249.

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/12/ AVERBUCH P., C.R. Ac. Sci. 253_ (1961) 2674.

/13/ BILLARD L., LANCON F., RODMACQ B., CHAMBEROD A., J. Phys. F : Met. Phys. lh_ (1984) 555.

/14/ STOCKMANN H.J., J. Magn. Reson. 44 (1981) 145. /15/ PFANNES H.D., GONSER U., Appl. Phys. l_ (1973) 93.

/16/ DUBOIS J.M., GASKELL P.H., LE CAER G., Proc.Roy.Soc. Lond., to be published /17/ HENLEY C.L., J. Non-Cryst. Sol., to be published.