Charge and spin density on iron nuclei in the BCC Fe Ga alloys studied by Mössbauer spectroscopy

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1 Journal of Alloys and Compounds 455 (28) Charge and spin density on iron nuclei in the BCC Fe Ga alloys studied by Mössbauer spectroscopy A. Błachowski a, K. Ruebenbauer a,,j.żukrowski b, J. Przewoźnik b a Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, ul. Podchorążych 2, PL-3-84 Kraków, Poland b Solid State Physics Department, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 3, PL-3-59 Kraków, Poland Received 2 December 26; accepted 13 January 27 Available online 18 January 27 Abstract Random solutions of Ga atoms in BCC iron have been studied at room temperature by means of the Mössbauer spectroscopy versus Ga concentration ranging till 37 at.%. Contributions to the iron hyperfine field and isomer shift due to individual Ga impurity have been determined up to the third nearest neighbour shell. Contributions to the hyperfine field amount to 2.2 T,.2 T and +.44 T for the Ga impurity at subsequent shell, respectively. Corresponding contributions to the isomer shift are as follows: +.36 mm/s, +.76 mm/s and.2 mm/s. 27 Elsevier B.V. All rights reserved. PACS: 75.5.Bb; y Keywords: Charge and spin density; Hyperfine interactions; BCC alloys; Binary alloys 1. Introduction Mössbauer spectroscopy is sensitive to the perturbation of charge and spin density on the resonant nucleus via modification of the isomer shift and magnetic hyperfine coupling, respectively [1,2]. The latter coupling is described by the effective hyperfine magnetic field. Non-magnetic impurities dissolved randomly on the lattice sites of the ferromagnetic BCC iron structure perturb charge and spin density of the conduction electrons in their vicinity. These perturbations are transferred to the iron atoms on the regular sites causing modification of the isomer shift and hyperfine magnetic field on the iron nucleus [1,2]. Perturbations are additive in the algebraic sense and they are usually seen to the third co-ordination shell at most [3,4]. More distant impurities contribute to the average shift and field if at all, and cannot be distinguished one from another. Fe Ga alloys, the latter having the BCC structure and being rich in iron have been investigated by various methods including Mössbauer spectroscopy of the 14.4-keV transition in 57 Fe [5 9]. Newkirk and Tsuei [5] found that Ga substitutes iron at Corresponding author. Tel.: ; fax: address: sfrueben@cyf-kr.edu.pl (K. Ruebenbauer). random up to 25 at.% at least. They were able to identify particular Ga impurities up to the second co-ordination shell. Vincze and Cser [6] performed similar investigations and found individual contributions to the second shell too. They found that the magnetic transition temperature is almost independent of the Ga concentration for low Ga concentrations, and that the reduced magnetisation of the sample weakly depends on the Ga concentration as well. The Fe Ga system was recently investigated again [7]. Spectra were analysed in a phenomenological fashion similar to the Hesse Rübartsch method [1,11]. The present contribution reports on the more extended concentration range of Ga, and the concentration step from sample to sample is finer presently. On the other hand, the improved method of data fitting allowed us to distinguish individual impurities in the third shell. 2. Experimental Samples were prepared by the arc melting of the appropriate amounts of Ga, the latter having 5N purity, and Fe having >99.97 at.% purity. Pure argon protective atmosphere was used and approximately 1.5 g samples were melted three times to assure homogeneity. The mass loss during sample melting was very small in all cases. Hence, the sample composition could be estimated accurately from the initial amount of the components. The maximum composition error estimated as.1 at.% Ga is due to the iron loss, as gallium has negligible vapour pressure at all encountered temperatures. Samples were found to be /$ see front matter 27 Elsevier B.V. All rights reserved. doi:1.116/j.jallcom

2 48 A. Błachowski et al. / Journal of Alloys and Compounds 455 (28) homogeneous by means of the electron micro-probe. Powder X-ray diffraction patterns for high Ga concentration samples were obtained at room temperature by means of the Cu K radiation with the pyrolytic graphite monochromator on the detector side. The Siemens D5 diffractometer was used, and the data were analysed by Rietveld method using FULLPROF programme [12]. Mössbauer absorbers were made as fine powders using diamond file. Powder was mixed with the epoxy resin and discs having 25 mm diameter with 3 mg/cm 2 of alloy were prepared. Resonantly thin commercial 57 Co(Rh) source was used. Source and absorber were kept at room temperature and 14.4-keV transition was used. Data were collected in round-corner triangular mode by means of the MsAa-3 spectrometer in 496 channels prior to folding [13]. Spectral shifts are reported versus room temperature -Fe. ray diffraction patterns are shown in Fig. 1. No ordering to the D 3 phase was found at least for the sample with 29 at.% Ga [14]. Mössbauer data were analysed within transmission integral approach using Gmbernz programme of MOSGRAF [15]. A model described in [3,4] was used. It relies on the assumption 3. Data evaluation and discussion of results X-ray diffraction patterns indicate that the single BCC phase is present up to 29 at.% Ga. Reflections for the sample with 29 at.% Ga are still narrow indicating good gallium solubility on all scales down to the atomic scale. On the other hand, lattice constant for this sample amounts to a =.2921(2) nm in comparison with the pure BCC iron, the latter having lattice constant a =.28665(2) nm. For higher Ga concentration some other phases appear. However, they are quite spurious even for the Ga concentration of 37 at.%. Lattice constant of the BCC phase with 37 at.% Ga equals a =.2924(2) nm. Relevant X- Fig. 1. Powder X-ray diffraction patterns obtained vs. scattering angle 2θ. Very weak reflections due to the sample holder are seen. The inset shows behaviour of the strongest reflection vicinity for the sample with 37 at.% of gallium. Fig. 2. Mössbauer spectra fitted by the transmission integral method to the σ =3 model. Subsequent gallium concentrations are shown adjacent to the corresponding spectrum.

3 Table 1 Essential results obtained within the σ = 2 model A. Błachowski et al. / Journal of Alloys and Compounds 455 (28) c [at.%], ±.1 B 2 [T], B (2) [T], B 1 [T], B 2 [T], S 2 [mm/s], S (2) [mm/s], S 1 [T], S 2 [T] The last row shows respective averages, where appropriate. The average values are calculated for samples with Ga concentration varying between 2 at.% and 21 at.%. that perturbations either to the charge or spin density are algebraically additive and depend solely on the distance from the resonant nucleus ( 57 Fe) to the impurity (Ga). It is assumed that impurities are randomly distributed on the lattice sites. Individual impurities are treated to the outermost co-ordination shell being either the second neighbour shell (σ = 2 model) or the third neighbour shell (σ = 3 model). More distant impurities contribute to the remainder of the hyperfine field B (σ) and/or to the remainder of the shift S (σ). Individual contributions depend on the co-ordination shell and could be expressed as B s or S s, respectively. The index s =1,..., σ enumerates subsequent co-ordination shells around the resonant atom. Mössbauer spectra for samples containing up to 29 at.% Ga are shown in Fig. 2. Essential results for σ = 2 model are listed in Table 1, while the corresponding results for σ = 3 model are shown in Table 2. The symbol c stands for the Ga concentration, while symbols B σ and S σ denote average hyperfine field and average shift, respectively. The model with two co-ordinate shells (σ = 2) seems insufficient to describe accurately enough results, as the remainders B (2) and S (2) evolve significantly with the Ga concentration. Model with three shells (σ = 3) is basically sufficient to account for the impurity effects. It works well till 21 at.% Ga. Evolution of the essential model parameters versus Ga concentration is shown in Fig. 3. It is interesting to note that Ga as the nearest neighbour of iron decreases hyperfine field on the iron nucleus, it has almost no effect as the second neighbour, and it causes increase of the field as the third neighbour. On the other hand, the nearest neighbour Ga decreases electron density on the iron nucleus, the second Ga neighbour acts in the same way, but more than twice as strong, and the third neighbour has almost no effect on the electron density. Contributions to either hyperfine field or isomer shift determined by us remain in excellent agreement with the results of Vincze and Cser [6] up to the second shell, the latter considered as the outermost relevant shell in the paper [6]. Distributions of the hyperfine fields produced by means of σ = 2 and 3 models are compared with the distributions obtained by the Hesse Rübartsch method [1,11] in Fig. 4. The Hesse Rübartsch data fits were made in the thin absorber approximation with the smoothing parameter set as 1. One has Table 2 Essential results obtained within the σ = 3 model c [at.%], ±.1 B 3 [T], B (3) [T], B 1 [T], B 2 [T], B 3 [T], S 3 [mm/s], S (3) [mm/s], S 1 [mm/s], S 2 [mm/s], S 3 [mm/s], The last row shows respective averages, where appropriate. The average values are calculated for samples with Ga concentration varying between 2 at.% and 21 at.%.

4 5 A. Błachowski et al. / Journal of Alloys and Compounds 455 (28) Fig. 3. Essential model parameters plotted vs. gallium concentration. to note that the envelope of these three distributions is very similar for each Ga concentration. The average fields and spectral shifts obtained by means of the Hesse Rübartsch method are shown in Table 3. The model described above fails gradually above 21 at.% Ga. Some extra lines are seen in the Mössbauer spectra of the 33 at.% and 37 at.% Ga samples as shown in Fig. 5. Such behaviour is consistent with the X-ray diffraction data. The reason for that does not necessarily means that some Ga ordering occurs [7,8]. One has to remember that the model depends on the algebraic addition of the contributions to the hyperfine field, and this Table 3 Average hyperfine field B and average spectral shift S vs. Ga concentration as obtained by means of the Hesse Rübartsch method c [at.%], ±.1 B [T], S [mm/s], Fig. 4. Hyperfine field distributions obtained in the σ = 2 and 3 models and by means of the Hesse Rübartsch method (H.R.) with the smoothing parameter set as 1. Gallium concentrations are indicated for each set of distributions. assumption might be invalid at high formally diamagnetic impurity concentration. It is clear that none Ga pairing occurs up to 21 at.% Ga at least, as the model works fine in this concentration range. Spectra for Ga concentrations measured by Dunlap et al. [7] up to about 2 at.% are similar to our spectra, while the spectrum for 23.3 at.% of Ga reported by these authors is vastly different from the spectrum of the random sample. We found no electric quadrupole interaction on iron nuclei in agreement with the results of Ref. [5]. On the other hand, some quadrupole interaction has been reported for the Fe Ga alloy with the FCC structure [9]. Ga impurities have relatively strong influence on the charge and spin density transfer to the iron nucleus in the BCC iron,

5 A. Błachowski et al. / Journal of Alloys and Compounds 455 (28) Fig. 5. Hesse Rübartsch fits to the data obtained for the samples with the highest gallium concentrations reported here. Gallium concentrations are indicated for each spectrum, and the corresponding distribution of the hyperfine fields is shown as well. These data were processed in the thin sample limit. however weaker than, e.g. osmium [16]. Some oscillations in the charge and spin density transfer versus distance from the impurity could be seen in our data in similarity to the more pronounced oscillations in the Fe Ru BCC alloys [17]. One has to remember that Ga is non-transition metal in contrast to Ru. However, oscillations are still present provided the sufficient number of co-ordination shells is taken into account in contrast to the previous works [18]. Acknowledgement Dr. Jakub Cieślak, Medical Physics Department, Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków, Poland, is warmly thanked for supplying us with the computer programme based on the modified Hesse Rübartsch method and designed to extract hyperfine magnetic field distributions from the Mössbauer spectra. References [1] I. Vincze, I.A. Campbell, J. Phys. F: Met. Phys. 3 (1973) 647. [2] J. Cieślak, S.M. Dubiel, J. Alloys Compd. 35 (23) 17. [3] A. Błachowski, K. Ruebenbauer, J. Żukrowski, Phys. Stat. Sol (b) 242 (25) 321. [4] A. Błachowski, K. Ruebenbauer, J. Żukrowski, Phys. Scr. 7 (24) 368. [5] L.R. Newkirk, C.C. Tsuei, Phys. Rev. B 4 (1971) 446. [6] I. Vincze, L. Cser, Phys. Stat. Sol (b) 5 (1972) 79. [7] R.A. Dunlap, J.D. McGraw, S.P. Farrell, J. Magn. Magn. Mater. 35 (26) 315. [8] R.A. Dunlap, N.C. Deschamps, R.E. Mar, S.P. Farrell, J. Phys.: Condens. Matter 18 (26) 497. [9] N. Kawamiya, K. Adachi, Y. Nakamura, J. Phys. Soc. Jpn. 33 (1972) [1] J. Hesse, A. Rübartsch, J. Phys. E: Sci. Instrum. 7 (1974) 526. [11] G. Le Caër, J.M. Dubois, J. Phys. E: Sci. Instrum. 12 (1979) 183. [12] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [13] R. Górnicki, RENON, [14] T.B. Massalski, Binary Alloy Phase Diagrams, vol. 1, second ed., ASM International, Materials Park, OH, 199, p [15] K. Ruebenbauer, [16] A. Błachowski, K. Ruebenbauer, J. Żukrowski, Nukleonika 49 (24) S67. [17] A. Błachowski, K. Ruebenbauer, J. Żukrowski, Phys. Rev. B 73 (26) [18] I. Vincze, A.T. Aldred, Phys. Rev. B 9 (1974) 3845.