Structural ordering and magnetic properties of arc-melted FeGa alloys

Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 1 Structural ordering and magnetic properties of arc-melted FeGa alloys J.M. Borrego, J.S. Blázquez, C.F. Conde and A. Conde Departamento de Física de la Materia Condensada, Instituto de Ciencia de Materiales, C.S.I.C., Universidad de Sevilla, P.O. Box 1065, 41080 Sevilla, Spain S. Roth Leibniz Institut für Metallische Werkstoffe, IFW Dresden, Postfach 270016, D-01171 Dresden, Germany Abstract X-ray diffraction, Mössbauer spectrometry and magnetic properties have been performed on FeGa arc-melted binary alloys in order to study the compositional dependence of the structural ordering and magnetic properties of these alloys. The average magnetic hyperfine field at 300 K decreases with increasing Ga content as does the average magnetic moment per Fe atom and a linear dependence between both quantities is found for Ga content up to 20 at. %. The substitution of Fe by Ga atoms increases the lattice parameter and causes a change in the order of the crystal structure that has been modelled using a binomial distribution method. The effect of Ga atoms as near neighbours of Fe on the average magnetic hyperfine field is evaluated. Keywords: A-Magnetic intermetallics, B-Magnetic properties, B-Order/disorder transformations, F-Mössbauer spectroscopy Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 2 1. Introduction FeGa alloys have attracted great attention in the last few years due to their superior magnetostrictive properties at low saturation field [1-4]. This quality associated with their high mechanical strengh, good ductility, negligible magnetic hysteresis and low cost [5] makes these materials very promising for sensor and actuator applications. Recent investigations include the study of the influence of the thermal history and the structural ordering on their magnetostriction [6,7], the phase equilibria and stability of ordered bcc phases in the Fe-rich portion of the FeGa system [8] and the structural transformations in quenched FeGa alloys [9]. Moreover, recently it was found that the addition of Cu to Fe65.5Cr4Mo4Ga4P12C5B5.5 amorphous alloy produces a nanocrystalline microstructure consistent of FeGa nanocrystals embedded in an amorphous matrix [10]. These nanocrystalline alloys are interesting since they would combine a large glassforming ability with good soft magnetic properties. However, a Mössbauer study of the FeGa alloy series is still missing. The importance of this study is double. On one hand, structure determination of FeGa alloys by X-ray diffraction is troublesome due to the similarity in the atomic scattering factors of Fe and Ga atoms which results in superlattice reflections of very low intensity. For example, the intensity of the strongest superlattice reflection associated with DO3 longrange order is calculated to be only 0.6% of the strongest primary reflection. Mössbauer spectrometry, as a short range order sensitive technique, does allow distinguishing between ordered and disordered atomic structures. For nanocrystalline alloys and due to the complexity of their magnetic hyperfine structure, the characterization of the hyperfine parameters of FeGa crystals becomes an essential information. In the present work, arc-melted polycrystalline Fe100-yGay (y=5, 10, 20 and 25) alloys were prepared in order to study variations in the atomic short range order at room Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 3 temperature with substitution of Fe by Ga. A local model based on a binomial distribution method [11] was used in order to correlate the magnetic hyperfine parameters with the structural ordering of these alloys. The influence of Ga substitution for Fe on the lattice parameter, saturation magnetization, magnetic moment and Curie temperature of these alloys is also reported. The interest of this study is focused in demonstrating that Mössbauer technique is able to supply detailed quantitative data for the structural ordering of such systems as Fe-Ga binary alloy where conventional X-ray diffraction techniques can not resolve an ordered structure due to the similarity between the scattering factors of its constituents. 2. Experimental Fe100-yGay (y = 5, 10, 20 and 25 at. %) alloys were prepared by arc-melting from pure Fe (99.95%) and Ga (99.999%) in an Edmund-Bühler high vacuum arc-melting system. The arc-melted bottoms (~2 cm diameter and ~0.8 mm thick) were remelted several times to get homogeneous samples. X-ray diffraction (XRD) patterns were recorded at room temperature using a Brucker AXS D8-Advance diffractometer with Cu K radiation on slices ~100 m thick cut from the bulk samples. For thermomagnetic (TMG) experiments, the magnetic field of a small magnet (20 mT) was applied to the sample and the temperature variation of the magnetic force was recorded in a thermobalance (Perkin-Elmer TGA-7) as an apparent weight change of the sample. The Curie temperature, TC, was determined from low field magnetization curves, by the “kink point” method. Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 4 The saturation magnetization, Ms, was measured on samples ~5 mg at room temperature with a Lakeshore 7407 vibrating sample magnetometer (VSM), using a maximum applied field of 15 kOe. Mössbauer spectra on the same samples studied by XRD were taken at 300 K in a transmission geometry using a 57Co(Rh) source, with the -beam perpendicular to the ribbon plane. The values of the hyperfine parameters were refined using NORMOS [12] and MOSFIT programs [13]. The isomer shift values are quoted relative to -Fe at 300 K. 3. Results 3.1 X-ray diffraction X-ray diffractograms of as-cast samples show that the substitution of Fe by Ga shifts the position of diffraction lines corresponding to bcc phase of pure -Fe to smaller values of 2. Figure 1a shows, as an example, the XRD pattern of Fe75Ga25 alloy. The increase of the lattice parameter, a, caused by Ga addition can be expressed by (Fig. 1b): ya )1(00020.0)2(2869.0   [nm] (1) where y is the Ga content (at. %) of the alloy. Additional weak reflections due to the possible occurrence of DO3 ordering of the structure are not detected. In fact, as it was said above, the similarity between the atomic scattering factors of Fe and Ga makes this detection difficult, unlike for FeSi alloys. 3.2 Magnetic properties The saturation magnetization, MS, at 300 K, shows a linear dependence with the Ga content, y, up to 20 at. % Ga (see Fig. 2a.), that can be expressed by: Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 5 yM S)5(0.3)6(223  [emu/g] (2) The average magnetic moment per Fe atom, <  Fe>, decreases as the Fe content decreases (Fig. 2b). A linear dependence of <  Fe> with y is observed for Ga content up to 20 %, that can be given by: y Fe )3(004.0)3(24.2   [  B] (3) The different behaviour of MS and <  Fe> below and above y = 20 at. % suggests a change in the structural ordering of the binary alloy. The Curie temperature, TC, of the arc-melted alloys decreases monotonously with the Ga content of the alloy as can be observed in Fig. 2c. 3.3 Mössbauer spectrometry Fig. 3 shows Mössbauer spectra of the studied alloys recorded at room temperature. The hyperfine structure is strongly dependent on Ga content. For y ≤ 20 at. % a six line pattern is observed, with increasing line widths as the Ga content of the alloy increases. The Mössbauer spectrum corresponding to Fe75Ga25 alloy is qualitatively different to those of alloys with lower Ga content, exhibiting additional and sharper lines that suggest some structural change. The fitting of the spectra was first tried using several independent sextets with free width but only the spectrum corresponding to the alloy with 5 at.% Ga could be satisfactorily fitted using this model. Neither the spectrum of the 25 at.% Ga could be clearly decomposed into two components with proportions 3:1, as could be expected for a stoichiometric Fe3Ga with a DO3 structure. The best fitting of the spectra was attained using a discrete magnetic hyperfine field distribution (HFD) with a linear correlation between the magnetic hyperfine field and the isomer shift of the components of the distribution in order to reproduce the Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 6 asymmetrical shape of the spectra [14]. The quadrupolar splitting was averaged to zero. The obtained HFDs are shown in Fig. 3 (right hand side). HFDs corresponding to y = 5 and 10 at. % Ga range from 25 to 36 T and show no significant differences: only a small shift of the maximum from 32 T to 31.5 T and a small increase in the width of the distribution from 3.5 T to 4.6 T (for a Gaussian fitting) with increasing Ga content. For y = 20 at. % Ga alloy, the HFD corresponds to a much broader six-line pattern spectrum and ranges from 18 to 36 T with a main maximum at 30.5 T and a shoulder at 21.5 T. The magnetic hyperfine field distribution of Fe75Ga25 alloy, that ranges from 16 to 36 T, consists of two clear maxima, labelled as “a” and “b” in Fig. 3, centred at 20 T and 30.5 T and with fraction areas of 0.54 and 0.46, respectively. For a correct fitting of the spectrum it was necessary to add a number of components with magnetic hyperfine fields ranging from 1.5 to 16 T (~ 4 % of the total Fe atoms). The average magnetic hyperfine field at 300 K decreases with increasing Ga content (Fig. 4a) as does the average magnetic moment per Fe atom, and a linear dependence between these two quantities is found for Ga content  20 at. % (Fig. 4c). The decrease of <Bhf> with y, for y up to 20 at. %, can be expressed by a linear relation: yBhf )2(23.0)3(1.33  [T] (4) The value of <Bhf> at y = 0 at. % of Ga is in agreement with the expected value of Bhf for pure -Fe phase at room temperature, 33.0 T. For comparison, Fig.4a also shows the compositional dependence of <Bhf> for FeAl [15] and FeSi [16] alloys. A discontinuous jump at 20 at.% metalloid is encountered for FeGa and FeAl alloys, but this jump is not so clear for FeSi alloys. Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 7 The average isomer shift (Fig. 4b) increases linearly with Ga content up to 20 at.% Ga following the relation: yIS )5(0070.0)5(003.0     [mm/s] (5) The angle , defined by the direction of the magnetic hyperfine field and the propagation direction of the  rays, can be obtained from the intensities of the second and the third absorption lines of the spectra. For the present alloys, a value of around 55 º reveals the absence of texture of magnetic moments for all alloys. 4. Local order modelling Using a binomial distribution, the probability, Pnm, of a bcc environment with n Ga atoms as near neighbours (NN), in the first shell, and m Ga atoms as next near neighbours (NNN), in the second shell is given by the expression: 8 6 ( ) ( ) ( ) ( ) n m n m NN NNN NN NNN nm Ga Ga Fe Fe P M x x x x                   (6) where )(NN U xand )(NNN U xare the concentration of U atoms (Ga or Fe) in the set of 8 NN atoms of the first shell and in the set of 6 NNN atoms of the second shell, respectively, that surrounds the central Fe atom. The multiplicity, M, can be calculated as: !)!6( !6 !)!8( !8 mmnn M    (7) However, the composition of the neighbourhood of the Fe atoms must be strongly affected, not only by the global composition, but also by the ordering of the crystalline structure. In a fully disordered A2 structure, the Ga and Fe positions are indistinguishable and their distribution would be random. Therefore, the atomic composition of the first and second shells is the same, xFe and xGa, for Fe and Ga atoms, respectively. However, it is important to note that using Mössbauer spectrometry (MS), from the 15 atoms (one central surrounded by 8 as NN and 6 as NNN) which are probed Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 8 and form the cluster unit, the central one is forced to be a Fe atom. Therefore, the probabilities for finding a Fe atom or a Ga atom in the neighbourhood of the probe are modified with respect to the global composition (Fe100-yGay, with xFe = (100-y)/100, xGa = y/100). In fact, the average number of Fe atoms in a group of 15 is 15xFe and the average number of Ga atoms is 15xGa. Taking into account that the central probe is a Fe atom, the average number of Fe atoms in the 8 NN plus 6 NNN will be 15xFe-1 and, thus, the corrected Fe concentration, 14/)115(  Fe cor Fe xx , in the NN plus NNN environment is decreased with respect to the global value, and the corrected Ga concentration, 15 /14 cor Ga Ga x x, is enhanced with respect to its global concentration in the alloy. In the case of ordered structures, the positions of Ga and Fe atoms in the elementary cell are distinguishable. For a perfect ordered DO3 structure, only possible for an alloy composition of Fe75Ga25, a Ga atom is always surrounded by 8 Fe atoms as NN and 6 Fe atoms as NNN, but for Fe atoms, two different sites are present; namely, 1/3 of the Fe atoms have 8 Fe atoms as NN and 6 Ga atoms as NNN (D site) and 2/3 have 4 Fe and 4 Ga atoms as NN and 6 Fe atoms as NNN (A site). (Table 1). For alloy compositions Fe100-yGay with y < 25 at. %, there is no possibility for a perfect ordered structure as the number of Fe atoms is in excess and the number of Ga atoms is less than the needed. Therefore, we assume a “maximum ordered” structure in which Ga atoms will be always located in their correct sites and the Ga sites which can not be occupied by Ga atoms will be filled with the exceeding Fe atoms. Thus, “maximum ordered” structure implies that a Fe site will never be occupied by a Ga atom but some Ga sites will be occupied by Fe atoms, resulting three different sites for Fe (Table 1): A and D sites, which are correct Fe sites, and Ga sites occupied by Fe Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 9 atoms. The distribution of the 100-y Fe atoms will be as follows: 50 will be in A sites, 25 in D sites and 25-y Fe atoms will be substituting Ga atoms. Each Fe atom in an A site in a perfect ordered DO3 structure has 4 Ga atoms as NN but for a Ga content lower than 25 at. %, a Fe atom in an A site could have 4, 3, 2, 1 or 0 Ga atoms as NN. Analogously, the possible configurations for a Fe atom in a D site ranges from 6 to 0 Ga atoms as NNN. Finally, a Fe atom in a “Ga atom-site” will always have 0 Ga atoms as NN and 0 Ga atoms as NNN (Table 1). Taking into account the previous considerations to obtain the concentration of Fe and Ga atoms in the NN and NNN sets of atoms, the probabilities of the different configurations can be calculated using equation (6). The results for disordered and ordered structures are shown in figures 5 and 6, respectively. 5. Discussion (a) Alloys with low Ga content (10 at. %) Assuming the effect of the Ga atoms on the magnetic hyperfine field to be proportional to the number of Ga atoms in the first shell, n, and the number of Ga atoms in the second shell, m, the average magnetic hyperfine field can be expressed by:    mn nm mn nmhf rmPqnPB ,, 33 [T] (8) where q and r are the reduction of Bhf per Ga atom in the first and the second shell, respectively. The linearity between the reduction of Bhf and the number of Ga atoms as NN (or NNN) yielding to q (or r) is not a strong hypothesis for low Ga containing alloys (expected to be in a disordered structure) as the most probable configurations are those of 0, 1 or 2 Ga atoms as NN or NNN (Fig. 5). For fully disordered systems, the relationships between both Pnmn and Pnmm with y are linear (Fig. 7). Therefore, from equations (4) and (8) it is possible to obtain: Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 16 [15] D.S. Schmool, E. Araujo, M.M. Amado, M. Alegria Feio, D. Martín Rodríguez, J.S. Garitaonandia and F. Plazaola, J. Magn. Mag. Mater. 272-276 (2004) 1342. [16] M.B. Stearns, Phys. Rev. 129 (1963) 1136. [17] G. Inden and W. Pitsch, Z. Metallkde, 62 (1971) 627. Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 17 Table 1. Definition of the different Fe sites in a perfect ordered DO3 structure and in a “maximum ordered” structure for Fe100-yGay alloys. Structure Site NN Fe atoms NN Ga atoms (n) NNN Fe atoms NNN Ga atoms (m) Perfect ordered DO3 y=25 at.% Fe atom in D site 8 0 0 6 Fe atom in A site 4 4 6 0 Ga atom site 8 0 6 0 “Maximum ordered” y<25 at. % Fe atom in D site 8 0  6  6 Fe atom in A site 4  4 6 0 Fe atom in a Ga atom site 8 0 6 0 Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 18 Figure captions FIG. 1. (a) XRD pattern corresponding to Fe75Ga25 alloy and (b) lattice parameter, a, of the bcc phase of FeGa alloys as a function of the Ga content of the alloy. FIG.2. (a) Compositional dependence of the saturation magnetization, MS; (b) average magnetic moment per Fe atom, <  Fe>, at 300 K and (c) Curie temperature, TC, of Fe100-yGay alloys. FIG. 3. Transmission Mössbauer spectra at 300 K and their corresponding fitting (solid line) and magnetic hyperfine field distributions of Fe100-yGay alloys. FIG. 4. (a) Compositional dependence of the average magnetic hyperfine field, <Bhf>; (b) average isomer shift, <IS>, of FeGa alloys. For comparison, it is also shown the compositional dependence of <Bhf> for FeAl [12] and FeSi [13] binary alloys on (a). (c) Average magnetic hyperfine field, <Bhf>, as a function of the average magnetic moment per Fe atom, <  Fe>, at 300 K. FIG. 5. Probabilities, Pnm, of a Fe site to have n Ga atoms as NN, in the first shell, and m Ga atoms as NNN, in the second shell for a fully disordered A2 structure, calculated using equation (6), for the different studied alloys. FIG. 6. Probabilities, Pnm, of a Fe site to have n Ga atoms as NN, in the first shell, and m Ga atoms as NNN, in the second shell for a “maximum ordered” DO3 structure, calculated using equation (6), for the different studied alloys. FIG. 7. Summatories of the products Pnm  n and Pnm  m, as a function of the Ga content for Fe100-yGay alloys. FIG. 8. <Bhf> dependence on the average number of Ga atoms as near neighbours, <n>, for both fully disordered and “maximum ordered” structures. The experimental Bhf Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 19 values corresponding to maxima “a” and “b” of the HFD of Fe75Ga25 alloy are also shown. Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 20 FIGURE 1 20 40 60 80 100 0 5 10 15 20 25 2.86 2.88 2.90 2.92 (a) (220) (211) (200) Intensity (a.u.) 2 Theta (º) (110) (b) a (A) Ga content (at.%) o Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 21 FIGURE 2 0 5 10 15 20 25 700 800 900 1000 1100 0 5 10 15 20 25 120 160 200 240 0 5 10 15 20 25 1.8 2.0 2.2 Ga content (at. %) (c) (b) T c (K) (a) M s (emu/g) < Fe > ( B ) Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 22 FIGURE 3 0 10 20 0 10 20 30 0 10 -8 -4 0 4 8 0 10 20 30 40 0 10 20 P(B hf ) x=20 x=10 x=5 x=25 v (mm/s) Relative transmission b Bhf (T) a Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 23 FIGURE 4 0 5 10 15 20 25 0.00 0.06 0.12 0.18 0.24 0 5 10 15 20 25 24 28 32 2.3 2.2 2.1 2.0 1.9 1.8 24 28 32 <IS> (mm/s) Ga content (at. %) (b) (a) FeGa FeAl FeSi <B hf > (T) (c) <B hf > (T) <Fe> (B) Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 24 FIGURE 5 0 2 4 6 8 0.00 0.05 0.10 0 2 4 6 Fe80Ga20 disordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.0 0.1 0.2 0 2 4 6 Fe90Ga10 disordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.0 0.2 0.4 0 2 4 6 Fe95Ga5 disordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.00 0.05 0.10 0 2 4 6 Fe75Ga25 disordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) Intermetallics. Vol. 15. Núm. 2. 2007. Pag. 193-200 http://dx.doi.org/10.1016/j.intermet.2006.05.007 25 FIGURE 6 0 2 4 6 8 0.0 0.2 0.4 0 2 4 6 Fe95Ga5 ordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.0 0.1 0.2 0 2 4 6 Fe80Ga20 ordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.0 0.1 0.2 0 2 4 6 Fe90Ga10 ordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN) 0 2 4 6 8 0.0 0.3 0.6 0 2 4 6 Fe75Ga25 ordered Probability Ga atoms in 2nd shell (NNN) Ga atoms in 1st shell (NN)