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

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 performed 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 considered, by Egami and Srolovitz (appendix 2 of /9csee 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 components of the EFCi tensor are sums of random terms. This is also true for atomic level stresses /7,9/. If the range of the interactions are long enough /5,7/, the central limit theorem will hold and D5 will have a Gaussian distribution. In random atomic Article published online by EDP Sciences and available at http://dx.doi. org/10.1051/jphyscol:1985823 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 invariant 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 concentration 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 (Takacs 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 correlations 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 CA 125 I Distributions p (A) have been calculated from some MSssbauer spectra but the uncer2 tainties in the isomer shift distributions prevent one of being sure of the validity 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). ii) the GIM is not valid. More must be known about the structure, its local order and the physical contributions to the EFG before obtaining a trustworthy mathematical model. 3 EXPERIMENTAL RESULTS IN A170Si17Fe13 Figure 1 shows the paramagnetic spectra of A1 Si . lIFe in the amorphous and in the crystallized state. The latter alloy mainly cons~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 spectrum 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