Neutron diffraction analysis on FINEMET alloys

Neutron diffraction has been used to study in situ the nanocrystallization process of Fe73.5Cu1Nb3Si22.52xBx (x55, 9, and 12! amorphous alloys. Nanocrystallization results in a decrease of both the silicon content and the grain size of the Fe ~Si! phase with increasing value of x. By comparing the radial distribution function peak areas with those predicted for ideal bcc and DO3 structure, it can be concluded that the ordering in DO 3 Fe~Si! crystals increases with the silicon content. © 1998 American Institute of Physics. @S0021-8979 ~98!02424-4#


I. INTRODUCTION
2][3] The microstructure consists of a Fe͑Si͒ nanocrystalline phase about 10 nm in size and an amorphous matrix phase.The chemical composition of the Fe͑Si͒ grains depends on the initial amorphous composition and thermal history, [4][5][6] the silicon atoms are not randomly distributed in the Fe͑Si͒ phase, but mostly occupy the DO 3 superlattice sites. 7,8ome previous research about the short-range order ͑SRO͒ in FINEMET alloys by using x-ray diffraction 9 compares the interference function and the pair correlation function or radial distribution function ͑RDF͒ of initially amorphous samples with several compositions and after annealing at various temperatures, but a detailed discussion about the crystalline phase is still missing.
Neutron diffraction ͑ND͒ analysis is a good technique to extend the study of small structural changes not accessible in most other techniques.In this article, the ND is used as an effective tool to measure the influence of the chemical composition on the amorphous and crystallized FINEMET alloys.The SRO changes, especially the relationship between RDF and the ordered silicon distribution in Fe͑Si͒ crystalline phase, were investigated.

Amorphous
alloys of nominal composition Fe 73.5 Cu 1 Nb 3 Si 22.5Ϫx B x (xϭ5, 9, and 12͒ in the form of rib-bons of 15 mm width and about 20 m thickness were studied by ND.The sample ribbons, about 1.5 m long, were rolled up and inserted into a cylindrical vanadium sample can of ϳ7 mm diameter.The spectra of the amorphous samples were taken at 300 °C for 10 min, and those of the crystallized samples were carried out after annealing at 480 °C for 14 h. The ND experiments were carried out at the ISIS Pulsed Neutron Facility at the Rutherford Appleton Laboratory on the liquids and amorphous diffractometer, LAD, by in situ measurements of the diffraction patterns during the heat treatment. 10,11The diffraction patterns S(Q) are collected by seven groups of detectors with different scattering angles.The RDF are obtained by Fourier transformation of the S(Q), obtained after the usual corrections, using the program package ATLAS. 12

A. SRO of the amorphous samples
The ND patterns and the RDF for three different amorphous alloys ͑with xϭ5, 9, and 12͒ are shown in Figs. 1 and  2, respectively.The experimental RDF are indicated as black square symbols in Fig. 2, with the full lines showing the fitted results.The RDF indicate that the SRO of the amorphous phases are very similar to each other, with a split second peak, which is a form of behavior found for many amorphous metal-metalloid alloys, 13 and is in agreement with the dense random packing of hard spheres model.If we fit the RDF with Gaussian type peaks, small differences in the RDF can be seen. 14The position of the first coordination shell shifts from 2.59 to 2.60 Å and its relative area changes from 22.6% to 24.0% when the composition goes from x ϭ5 to xϭ12.The second shell splits into two peaks, except for alloy with xϭ12 which can be separated to three peaks, their distances also change from 4.25 to 4.28 Å and from 5.02 to 5.08 Å.In the third shell, the differences of the three alloys are clearer.The differences in peak position and relative area on changing nominal composition occur because the different atomic radii of boron and silicon influence the surrounding atomic arrangement.Also, in general, silicon substitutes iron in the network whereas boron modifies the topological SRO.

B. LRO of the crystallized state
The neutron diffraction spectra of amorphous alloys annealed at 480 °C for 14 h are shown in Fig. 3.The intensity of the peaks of the crystalline phase increases with the composition of silicon.The remaining amorphous pattern is also seen, as expected, producing broad peaks in the boron rich alloys diffraction patterns.To look for the trends, the fitting of the diffraction pattern was performed assuming the crystalline peaks of Lorentz type and the amorphous of a Gaussian type.The fitting results of S(Q) in the range of 2.5-6 Å Ϫ1 for alloy with xϭ5 are shown in Fig. 4.There are some small peaks which belong to the superlattice DO 3 ordered structure.
In Fig. 3 the relative intensity of the DO 3 peaks indicates that the LRO of the crystalline phase is altered by the change of composition.For alloy with xϭ5 ͑silicon rich͒, a Fe͑Si͒ phase close to the ideal DO 3 super lattice structure is obtained.In this case, the DO 3 peaks appear completely developed.The fitting results shown in Fig. 4 give their position and relative area.But for alloy with xϭ12 ͑silicon poor͒ no clear DO 3 superlattice peaks appear in the S(Q) pattern.][17] In Table I are listed the fitted results of S(Q) patterns for the three different alloys.The position of the peaks depends on composition, for instance, the one with Miller index ͑220͒, decreases from 3.087 to 3.075 Å Ϫ1 when the composition changes from xϭ5 to xϭ12.It is due to the silicon content changing in the crystalline Fe͑Si͒ phase.The full width at half maximum ͑FWHM͒ of the peaks is attributed to the mean grain size of the Fe͑Si͒ crystals.The value of FWHM of peak ͑220͒ increases from 0.048 (xϭ5) to 0.063 Å Ϫ1 (xϭ12).This effect indicates that the average grain size in the alloy with xϭ12 is smaller than that in the alloy with xϭ5.
Further important information obtained from the fitted results is the relative intensity of the diffraction peaks belonging to crystals and to the remaining amorphous phase.The relative area is related to the transformed fraction.After 14 h annealing at 480 °C, for the alloy with xϭ5, the transformation is nearly completed ͑crystalline fraction around 97%͒, for the alloy xϭ9 it is about 77% and for the alloy with xϭ12 it is only about 56%.The TTT ͑timetemperature-transformation͒ diagram for these three FINEMET alloys has been constructed from the calorimetric results by DSC.The TTT diagrams obtained are presented in Fig. 5, it shows that the crystallization of Fe͑Si͒ in the three alloys occurs at different temperature ranges.In the alloy with xϭ5, the temperature range is lower than for the other two alloys.The annealing temperature selected for neutron diffraction measurement was already over the end line of the transformation for alloy with xϭ5, this is the reason why the crystalline fraction was rather high.For the other two alloys, the annealing temperature was in between the onset line and the end line.Therefore, the transformed fractions obtained from neutron diffraction pattern are in good agreement with the TTT diagram.

C. SRO of the crystallized state
The SRO of the annealed alloys are presented as RDF in Fig. 6 for the three alloys and the calculated RDF for the bcc and DO 3 Fe͑Si͒ phases are shown as a series of delta functions.The SRO are different from the amorphous state shown in Fig. 2. The crystallized fraction effects in the RDF curves are seen in the intensity changes from the amorphous state.The first and third peaks are enhanced as the crystallized fraction increase.
In order to get the RDF of ideal bcc and DO 3 structures, we assume them to have the same silicon content and the same lattice parameter.For a binary system, the atomic density can be written as 18 ͑r ͒ϭ ͚ i, j w i, j i, j ͑ r ͒, ͑1͒ where w i, j is the effective scattering length of the binary system.i, j is the average number of j atoms in unit volume at a distance r around an atom i.
͑2͒ f i is the scattering length of element i, normalized to mean scattering length ͗ f ͘ϭ͚ c i f i .Here c i is the content of ele- ment i.In our case the scattering length of Fe and Si are 0.954 and 0.415, respectively.The RDF is so that we obtain the relation for the apparent coordination number N(r) in terms of the partial coordination number Z i, j .

͑4͒
where Z i, j (r) is the number of j atoms arround i atoms at r distance.In our case, we only consider Fe and Si atoms in the crystalline sites of a Fe͑Si͒ phase.In the bcc structure, all sites in the lattice have the same probability for the occupation by Fe or Si atom.For the DO 3 structure, only the four sites in the center of the cubic cell with symmetry Fm3 ¯m can be occupied by Si atoms.Therefore, for each near neighborhood, the Z i, j are calculated considering the probability of Fe or Si occupation in the order of DO 3 .
As shown in Fig. 6, the interatomic distances and the corresponding number of ideal bcc and DO 3 structures of near ͑in direction of ͓111͔͒ and next near neighbor ͑in direction of ͓100͔͒ have no significant differences, but the third nearest neighbor has different values because at this distance ͑in ͓110͔ direction͒ the effect of the term in Z Si,Si becomes important.
The first peak occurs with a shoulder, due to the existence of two peaks corresponding to the first and second nearest neighbors.We fit the RDF with the peak position as bcc or DO 3 structure distribution with a Gaussian shape to take into account the thermal vibrations.The fitted results are shown in Fig. 7 in the range from 2 to 10 Å.It seems that all the peaks fitted can be associated with the different near neighbor distances of bcc or DO 3 crystalline phase.Even for the alloy with a lot of remaining amorphous phase ͑45% in alloy with xϭ12), the crystalline SRO character is rather clearly visible.
The main results of the fitting are listed in Table II.These are the peak distances between first, second, and third near neighbors, their FWHM and relative area.In agreement with the S(Q), the peak distances increase with the composition of B, because of the Fe͑Si͒ crystalline phase changes; the lattice parameter increases and the silicon content decreases with the increase of B composition.
The FWHM of each peak also changes with composition.It increases for the first and second near neighbor but decreases for the third one.These changes are attributed to both the distribution of interatomic distances and the effects of the remaining amorphous phase.The last effect seems to be more important than the first one in the first and second neighbor peak broadening on increasing B composition since, as shown in Fig. 5, the amount of amorphous phase after 14 h at 480 °C is larger for alloys with xϭ9 and 12 than in alloy with xϭ5.
Most interesting for the present purpose is the consideration of the ratio between the area of the third (A 3 ) and first (A 1 ) near neighbor peaks.The calculated value of this ratio for the ideal DO 3 structure is A 3 /A 1 ϭ0.668, higher than the corresponding one ͑0.562͒for the ideal bcc structure.There- fore, this value may be considered as a measure of the SRO in the DO 3 superlattice.The value of ratio A 3 /A 1 obtained for the three alloys, also shown in Table II, indicates that for the alloy with xϭ5, the SRO of the crystalline Fe͑Si͒ phase is closer to the ideal DO 3 one than for the other two alloys.

IV. CONCLUSIONS
In this article, the SRO in amorphous and crystallized FeCuNbSiB alloys was investigated by neutron diffraction.In the amorphous phase, the radial distribution functions are very similar in all the alloys studied.The small differences encountered are considered to be due to the changes of chemical composition.
The differences between the neutron diffraction patterns of the crystallized alloys result from the changes of both the silicon content and the grain size of the Fe͑Si͒ phase.
The analysis of the relative area of the diffraction peaks was performed in terms of the degree of crystalline phase achieved after annealing at 480 °C for 14 h.
The transformed fraction obtained from the analysis agrees with that deduced from the TTT diagrams.
The degree of DO 3 ordering in the Fe͑Si͒ crystals was deduced by comparing the RDF peak areas with those predicted for the ideal bcc and DO 3 structures for the same crystalline composition.
The results indicate that the Fe͑Si͒ crystals obtained after annealing are closer to the ordered DO 3 structure for the sample with lower B content in the initial amorphous phase.

TABLE I .
Fitted results of S(Q) of alloys annealed at 480 °C for 14 h with the diffraction peak position Q, the FWHM and relative fraction of crystalline phase.Error estimates: Ϯ0.004 Å Ϫ1 ͑Q͒ and Ϯ0.001 Å Ϫ1 ͑FWHM͒.
FIG. 5. TTT diagram of crystallization process of three amorphous alloys.FIG. 6. RDF of three FINEMET alloys after annealing at 480 °C for 14 h, together with RDF of bcc and DO 3 structure.

TABLE II .
Fitted results of G(r) obtained from Fourier transformation of S(Q) of alloys annealed at 480 °C for 14 h with values of first, second, and third near neighbor distance r i , the FWHM i and relative area A i .Error estimates: Ϯ0.005 Å (r i ) and Ϯ0.002 Å (FWHM i ).
FIG.7.RDF fitted results of three FINEMET alloys after annealing at 480 °C for 14 h.