EXAFS STUDIES OF AlMnSi AND AlMn PERIODIC AND APERIODIC ALLOYS

In a recent extended x-ray absorption fine structure (EXAFS) analysis of icosahedral and a-phases of AlMnSi it was shown frgm the Mn-Mn scattering that an icosahedron cage of Mn atoms with edge length 2 5 A is the structural unit in the icosahedral phase. In this paper we present results on the radial distribution function (RDF) of the first shell A1 atoms yielded by a direct Fourier transform method from the EXAFS. This method yields a RDF with higher resolution and lessbias than the usual method of fitting by a model. The results are consistent with the Mn-Mn analysis of similar icosahedrar units interconnected differently in the iphase than in the a-phase. In a recent EXAFS study [I] of icosahedral and a-phases of AlMnSi alloys it is concluded, zrom analysis of the Mn-Mn scattering, that a Mn icosahedron of edge length ?, 5 A is the structural unit in the icosahedral phase and that the connection between these units are different from those in the a-phase. These results are consistent with the random connection icosahedra model [Z-41 for the icosahedral phase. The conclusion was possible because of the similarity in the EXAFS between the icosahedral phase and the a-phase and the fact that the EXAFS contributions from the Mn on the same icosahedron as the central Mn atoms and from Mn on neighboring Mn icosahedra separate. It was pointed out that analysis of the first shell EXAFS will not permit such unambiguous conclusions because it is not possible to uniquely separate the above two kinds of contributions. However, the analysis of the first shell EXAFS is interesting because it provides information about the locations of the A1 atoms and it can provide further evidence for the conclusion reached in the earlier analysis. In our discussion we do not distinguish between A1 and Si since their EXAFS backscatterings are so similar. There have been many EXAFS studies of the first shell [5-91. However, most of the analyses involve using a model for fitting to the data, giving bias to the final answer. In addition, the resolution in the radial distribution function (RDF) is poor. We have obtained the RDF for the first shell A1 atoms around Mn atoms in the icosahedral AlMnSi and AlMn using a new method. We have checked the method against the known RDF of the a-phase of AlMnSi obtaining a satisfactory agreement. This method was discussed briefly by Bouldin and Stern [lo]. . Starting with the single shell EXAFS ~(k), Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868197 C8-1026 JOURNAL DE PHYSIQUE we can obtain the normalized ~'(k), 2 X' (k) = r p (r) sin(2kr)dr = Im(A' (k)exp(i@' (k) ) , (2) which contains only the geometrical information by using suitable standards. The RDF is easily obtained by inverse transforming Eq. (2) and correcting for the r2 factor. We use crystalline [ll] MnA16 as our standard for determining B(k) and 6(k). All the measurements and the method used to extract EXAFS ~(k) from the measurements were described before [I]. The first shell EXAFS were obtained by the usual method of Fourier filtering. In the following analysis the R window from 1.4 A to 2.7 i is used. This covers the R range in the RDF from 2 1.9 to 3.2 1. To get the amplitudes and phases of the normalized ~'(k), we take the ratio of the EXAFS amplitudes and the differences in phase between the unknowns and MnA16 and then correct for the structure of MnA16. We have neglected the contribution due to the mean free path term in the EXAFS formula in the analysis because we expect that A will be roughly the same in the icosahedral phase as in MnA16 and the ratio between the two amplitudes will cancel out the mean free path contribution to the normalized ~'(k). However, due to the finite data range available from the EXAFS, the normalized ~'(k) are available only for 2.3 < k < 13 k'. We extrapolate the data down to k=O by using the cumulant expansion, i.e., Log A' (k) = a,, + a k2 + a,k4 for the amplitude and @'(k) = alk + a,k3 for the phase. A high k(k > 13 f-') extrapolation was done by a regular polynomial expansion to about k=16 ;i -' . Figure 1 shows the X' (k) so obtained for the a-phase A173Mn16Sill. By taking the imaginary part of the Fourier transform of the xl(k)'s and correcting for the r-2 factor, we obtained RDF's for the icosahedral A184 6Mn15 4, A179Mn15.4Si5.6, the i(A1MnSi) sample annealed for 44 hours at 500°C i; vacu;m which forms a defected or-phase, and the a(A1MnSi). The results are shown in Fig. 2. The transforms were over 0.0 < k < $6 0 1-1. The RDF's are broadened by including an artificial disorder factor e-2k Q~ in the transform, and a Hanning function from 12.0 to 16.0 i-' to reduce the cutoff wiggles due to the finite range of the data. Due to the cutoffs the high k data above 10 i-' contribute relatively little to the RDF's, so that our high k extrapolation does not contribute to the final result. On the other hand, theoretically the low k behavior of the amplitude and phase is well