Structure and magnetic properties of Fe100-xSnx (3.2 < × < 62) alloys obtained by mechanical milling

~

ELSEVIER

Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

journal of magnetism and magnetic malerials

Structure and magnetic properties of Fel00_xSn ( 3.2 < x < 62) alloys obtained by mechanical milling E.P. Yelsukov a.*, E.V. Voronina u, G.N. Konygin a, V.A. Barinov °, S.K. Godovikov d, G.A. Dorofeev a, A.V. Zagainov a Physical-Technical Institute, Russian Academy of Sciences, Ural Branch, 426001 Izhecsk, Russia b Udmurt State University, 426037 Izhecsk, Russia Institute of Metal Physics, Russian Academy of Sciences, Ural Branch, 620219 Ekaterinburg, Russia d Moscow State UniversiO', bTstitute of Nuclear Physics, 119899 Moscow, Russia

Received 8 May 1996

Abstract

The structure and magnetic properties of mechanically ground Fe-Sn alIoys have been studied by X-ray diffraction, magnetic measurements, and 57Fe and 1198n M~Sssbauer spectroscopy. It has been shown that the alloys are nanocrystalline and have the disordered bcc structure with Sn concentrations x < 32.7 at%, and disordered hexagonal-like structures with x > 32.7. The concentration dependences of the magnetic ordering temperature, average magnetic moment per Fe atom, average hyperfine magnetic field and isomer shift, as well as those of the bcc lattice parameter and grain size are nonlinear and reveal a number of peculiarities at 12-15, 25 and 50 at% Sn. The fen'omagnetic state is shown to form in alloys with x < 50, the concentration range of cooperative magnetism existence being 0-72 at% Sn. We have compared the magnetic properties of nanocrystalline Fe-Sn alIoys with those of similar Fe-Si alloys and amorphous Fe-Sn films. We describe the essential differences between the Fe-Sn and Fe-Si systems, and assess the influence of the absence of topological disorder on the magnetic properties of non-ordered Fe-Sn alloys on the other. Keywords: NanocrystaIline alloys; Structure; Disorder

1. I n t r o d u c t i o n Binary alloys of Fe with C, A1, Si, P and Sn are the most appropriate model objects to study magnetism in non-ordered (disordered crystalline and amorphous) Fe systems with sp-elements. In the series ( F e - A 1 ) - ( F e - S i ) - ( F e - P ) with relatively small changes in the covalent radius of sp-atoms from

* Corresponding author. Email: [email protected];fax: + 7-3412-250614.

0.118 nm (A1) to 0.106 nm (P) the number of 3p-electrons changes from 1 (A1) to 3 (P). In the series ( F e - C ) - ( F e - S i ) - ( F e - S n ) with the same number of outer p-electrons in sp-atoms the covalent radii are 0.77(C), 0.11 l(Si) and 0.141 nm (Sn). Experimental studies of the above systems over the entire concentration range of cooperative magnetism allow us to determine the effect of the type (electron configuration, size) and concentration of sp-elements, topological and chemical disorder, local atomic environment parameters on such fundamental

0304-8853/97/$i7.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0304-8853(96)00537-9

E.P. Yelsukoc er al./ Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

magnetic properties as the average magnetic moment per Fe atom (7@e), the magnetic ordering temperature (Tc), the average hyperfine magnetic field (H---), etc. The results obtained in the Fe-A1, F e - S i and F e - P systems were reported in Refs. [1-5]. Three main conclusions were noted: (i) the electron configuration of sp-atoms influences the magnetic properties; (ii) a phenomenological description of the magnetic properties can be made in terms of local atomic environment parameters; and (iii) no influence of topological disorder on mFe, Tc, ~rze and the average isomer shift 6F~ was found in the Fe-Si system. This last conclusion resulted from a comparison of the experimental data for disordered crystalline F e - S i alloys obtained by mechanical grinding [2], and for amorphous F e - S i films produced by deposition from a gas medium onto cooled substrates [6-11]. So far there are still two unambiguous questions: (i) do the sizes of sp-atoms have any effect on the magnetic properties; and (ii) does topological disorder influence the magnetic properties only in the F e - S i alloys or in other systems as well? It is possible to determine the roles of these factors in magnetic properties by studying non-ordered F e - S n alloys. As well as the F e - S i system, amorphous F e - S n films with Sn concentrations 28-66 at% were obtained by deposition from a gas medium onto cooled substrates, and then complex studies were made of their structures and magnetic properties [12-15]. The possibility of obtaining disordered crystalline F e - S n alloys by mechanical alloying was shown in Refs. [16-20], and by mechanical grinding of originally multiphase melted alloys in Refs. [21,22]. Some preliminary data on the magnetic properties of the bcc disordered crystalline F e - S n alloys were presented in Refs. [23], where we showed different behaviours of the magnetic properties in F e - S n and F e - S i alloys versus concentration. In particular, we found a slight dependence of raze on Sn concentration in the range 0-25 at%, compared with 0 - 8 at% Si in the F e - S i system [24-26]. The aim of this work was: (i) to obtain disordered crystalline F e - S n alloys with Sn concentrations up to 60-70 at%, i.e. over the entire concentration range of cooperative magnetic phenomena; (ii) to perform a complex study of their structural peculiarities and magnetic properties by means of X-ray

335

diffraction, M/Sssbauer spectroscopy and magnetic measurements; and (iii) to compare the data obtained with those for similar types of F e - S i alloys and amorphous F e - S n films.

2. Experimental F e - S n ingots of 200 g were melted in an induction furnace in Ar from high-purity Sn (99.99) and Fe (99.95) components. The ingots were ground by hand in a hardened steel mortar. Particles with sizes not more than 300 txm were sieved from the powder. After sieving the powder was ground in a planetary ball mill 'Pulverizette' using grinding vials of 80 cm 3 and tungsten carbide balls (10 mm diameter). Each vial was loaded with 10 g of powder and 25 balls. The grinding was done in an inert atmosphere by rotating the supporting disk at a velocity of 450 rpm, and rotating the grinding vials in relation to the supporting disk at 955 rpm; this corresponds to an absolute velocity of the vial rotation of 504.9 rpm. Under these mechanical treatment conditions the time of grinding of 30 h was enough to produce homogeneous disordered crystalline Fe100_,.Sn x powder [21,221. After grinding, the Sn and tungsten carbide contents in the samples were determined. In the series of 15 samples, the minimal Sn concentration was 3.2 at%, and the maximal 62 at%. The error in the determination of the Sn concentrations in the alloys did not exceed _ 1 at%. The admixture of tungsten carbide incorporated into the samples during grinding was estimated from the weight increments, chemical analyses and X-ray diffraction measurements. The maximum WC content of 5 mass% was found in the alloy with 3.2 at% Sn. In all other samples this value was about 1 mass%. To determine the sizes of particles in the ground powders a laser interferometer 'Analizette 22' was used. It was found that the average particle size was 4 txm, with the entire particle size distribution being in the interval 0 . 5 - 1 5 b~m. X-ray patterns were taken in Fe K s filtered radiation at room temperature. The phase type, bcc lattice parameters (a) and the powder particles grain sizes (L) were determined. In calculating the bcc lattice

336

E.P. gelsukovet al.~Journal of Magnetismand MagneticMaterials166 (1997) 334-348

parameter, we made use of the line (211) and the wavelength of the K~ radiation h a = (2h~t + h < ) / 3 .

(1)

To estimate L, the method of line profile analysis [27] was used, taking into account two peaks in the samples with x = 3.2-19.2 at% Sn. For samples with higher Sn concentrations the calculations were carried out taking into account only one peak (110), since the rest of the lines were blurred. However, a comparison of the calculated results for the samples with 3.2-19.2 at% Sn with two lines of different orders of reflection and with one line showed good agreement. In the calculations of L, X-ray patterns of annealed powders of a-Fe and DO 3 ordered F%Si alloy were taken as standards to single out the profiles of physical broadening. M~Sssbauer spectra on 57Fe and 119Sn nuclei were taken at 77 K using 57Co(Cr) and llgrnsn (CaSnO 3) sources. A generalized regular algorithm of the inverse problem solution of M~Sssbauer spectroscopy [28,29] was used to determine the functions of the hyperfine magnetic field distribution P(H). For a number of alloys with high Sn concentrations, M~Sssbauer measurements were made to determine the magnetic ordering temperatures. The magnetization curves were obtained at 4.2 K using a vibrating sample magnetometer under external magnetic fields as high as 15 kOe. The temperature dependence of the magnetic susceptibility was determined from measurements in an alternating sinusoidal field with amplitude 80 A / m and frequency 120 Hz, the samples being placed in silicon ampoules filled with argon.

3. Results

3.1. Structure Fig. t shows the X-ray patterns of the ground alloys, tn the samples with Sn concentrations x_< 32.7 at% a bcc structure formed. The new peaks in the X-ray patterns of samples with 36.4 and 42 at% Sn at the angles 2 0 close to 38 and 42 ° provided evidence of the appearance of a new structure type. A comparison of these data with known data from

Refs. [30-32] for the most intensive peaks of equilibrium stoichiometric intermetallic compounds shown in Fig. 1, allows us to conclude that in the ground samples with 36.4 and 42 at% Sn a hexagonal structure FesSn 3 (B8 z) type forms. In the alloys with Sn concentrations x > 46 at%, the X-ray patterns show complicated structures of broadened peaks that can not be unambiguously connected with any of the known compounds in the equilibrium state diagram of the Fe-Sn system [33]. Such a case is most vividly revealed for the ground F%4Sn46 alloy (Fig. 1), whose X-ray pattern can be represented by the superposition of peaks from different types of intermetallic compounds, i.e. the structure of the Fe54Sn46 sample can be interpreted as being multiphase. However, this conception is not confirmed by the shape of the temperature dependence the of magnetic susceptibility. Fig. 2 shows the temperature dependence of the magnetic susceptibility reduced to that at room temperature, X/Xar(T), for the ground Fe54Sn46 alloy; it can be seen that there is only one magnetic phase. As will be shown below, from the concentration dependence of the magnetic ordering temperature, T¢(x), of the ground Fe-Sn alloys with x > 25 at%, we can determine the sample composition with an accuracy of + 1 at%. Thus, the absence of any additional peaks or bends in X/Xaz(T) for the Fe54Sn46 sample points to the fact that its structure is a monophase state. The analogous case was also observed for other samples with x > 46 at% Sn. The concentration dependence of the bcc lattice parameter a(x) is shown in Fig. 3, curve 1. The a values increase to as high as 0.2995 nm with x = 33 at% Sn, whereas in the bcc disordered Fe-Si alloys a decreases to 0.2814 nm with x = 33 at% Si [5]. The a(x) dependence is nonlinear and in its approximation by two linear sections the intersection point coincides with x = 12 at% Sn. The data on grain sizes L are given in Fig. 3, curve 2. The L(x) dependence is presented only in the concentration range 0 - 4 0 at% Sn, since the average grain size decreases from 19 nm for the sample with x - - 3.2, to 6 - 7 nm with x = 25; beyond this, L does not depend on the Sn concentration. These estimates of grain sizes agree well with analogous data for the Fe-Sn alloy obtained by mechanical alloying [19,20], where the approximation of the L(x) dependence by two linear sections gives an intersection point at

E.P. Yelsukou et al. / Journal of Magnetism and Magnetic Materials 155 (1997) 334-348

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Fig. I. X-ray diffraction patterns of the ground Fe-Sn alloys. Tmeas= 300 K. Top: (in parentheses) indices of the bcc structure lines; the [ denote the positions of the most intensive WC lines. Bottom: vertical lines show the positions of the most intensive lines of intermetallic compounds in the Fe-Sn system.

338

E.P. Yelsukov et aL / Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

1.5o~-

on the 57Fe nucleus for samples with Sn concentrations x > 4 6 at%. Fig. 7 shows the spectra and P(H) functions of the Fe4sSn55 alloy at different temperatures. Calculating H according to

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-H= foH'~:"~P(H) HdH, Fe54Sn.,~

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300

400

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600

T (K) Fig. 2. Temperaturedependenceof the reduced magneticsusceptibility of the ground Fes~Sn46 alloy.

x = 13 at% Sn. These L values emphasize the fact that the ground F e - S n alloys are nanocrystalline. Additional data on the structure of the alloys were obtained from M6ssbauer measurements. Figs. 4 and 5 present the MSssbauer spectra and the evaluated functions of the hyperfine magnetic field distribution, P(H), on the 57Fe and 119Sn nuclei, respectively. The shapes of the spectra and P(H) functions are characteristic of alloys with chemical disorder. With increasing Sn concentrations, i.e. with increasing numbers of Fe atoms non-equivalent positions in a disordered structure, there occurs a considerable regular broadening of P(H). It should be noted that there is similarity between the P(H) functions of the ground alloys obtained in this work and those of thin amorphous F e - S n films with similar concentrations [13]. Besides, in the P(H) functions we found no pronounced components from equilibrium stoichiometric phases Fe3Sn, Fe:Sn 3, Fe3Sn 2, FeSn and FeSn 2 with well known MtSssbauer parameters [32,34-39].

(2)

we have to determine the range of fields from 0 to Hp which should be taken equal to 0 as the nonmagnetic part of the spectrum was also described in terms of the hyperfine magnetic field distribution. From the M~Sssbauer spectrum at T = 300 K (Fig. 7) we estimated Hp = 35 kOe. Fig. 6(a), curves 2 and 3, shows the H(T) dependences of the Fe45Sn55 and F%sSn62 alloys, respectively. It can be seen that the Tc values for the Fe45Snes alloy found from the magnetic and Mbssbauer measurements differ by no more than 10 K. The ~r(T) dependence of the Fe3sSn62 sample shows that magnetic hyperfine splitting takes place up to 150 K. For the low-concentration F e - S n alloys with x < 8 at% Sn the magnetic ordering temperatures were determined from the magnetic measurements by the following procedure. First, the sample was rapidly heated to the temperature corresponding to the equilibrium bcc phase [33] and was kept at this temperature for about 1 h. Then the sample was relatively slowly heated or cooled in the vicinity of Tc. The error in Tc was + 3 K for the low-concentration alloys and _+20 K for the high-concentration

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3.2. Magnetic ordering temperature 0.290 The values of Tc were determined by cross-sections of tangent lines on the temperature dependence of the magnetic susceptibility, as shown in Fig. 6(a), curve 1, for Fe45Sn55. It should be noted that for the F%sSn62 alloy the magnetic susceptibility was not registered because its value was very small. We therefore performed temperature Mbssbauer studies

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Fig. 3. Curve 1, the bcc lattice parameter a(x); curve 2, grain size

L(x).

E.P. Yelsukou et al./Journal of Magnetism and Magnetic Materials ]d5 (1997) 334-348

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Fig. 4. 57Fe MSssbauer spectra of the ground F e - S n alloys and the distribution functions of hyperfine magnetic field P(H). Tin,as = 77 K.

E.P. gelsukoc et aL / Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

340

alloys due to a relatively large error in the Sn concentration of _+ 1% and the smeared temperature dependence of the magnetic susceptibility. The Tc of nanocrystalline Fe-Sn alloys, thin amorphous Fe-Sn films [13,15], and those of disordered crystalline and amorphous Fe-Si are shown in Fig. 8. For the Fe-Si

system Tc(x) is shown by solid lines, approximating the results of Refs. [2,5,7-I0,24-26]. From a compalison of the given Tc(x) dependences, we find: (i) As in the Fe-Si alloys, there is a concentration range in which it is impossible to measure Tc in the non-ordered Fe-Sn alloys even at high sample heatFe + at. % Sn I

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Fig. 5. I19Sn Mbssbauer spectra and the functions P(H) of the ground F e - S n alloys. Tmeas = 77 K.

200

E.P. Yelsukoc et al./Journal of Magnetism and Magnetic Materials 166 (]997) 334-348

ing rates because of phase transformations during heating; (ii) With F e - S n alloys with low Sn concentrations, the Tc values are close to those of F e - S i alloys and depend slightly on x. With high values, x > 25 at%, the Tc(X) of both F e - S i and F e - S n alloys change sharply, although the Tc values for the F e - S n alloys exceed those of the Fe-Si alloys considerably; (iii) Tc(x) of the nanocrystalline and amorphous F e - S n alloys differ considerably. This conclusion does not agree with the results for the Fe-Si system, in which the Tc values for disordered crystalline and amorphous alloys are the same within experimental error.

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Fig. 6. (a) Temperature dependence of the reduced magnetic succeptibility .~/XRT(T). Curve I, Fej~Sns5 alloy; curve 2, the average hyperfine magnetic field on Fe nuclei H(T) of the Fe4sSn55 alloy; curve 3, of the Fe3sSn62 alloy. (b) Temperature dependence of the magnetization of the Fe,,sSn55 alloy in an applied magnetic field He×t = 100 Oe. Curve 1, amorphous thin film on heating and cooling [14,15]; curve 2, ground samples on heating; curve 3, and on cooling. TcF and Tg, magnetic ordering temperatures, derived according to the technique described in Refs. [I4,I5].

341

To find out the reason %r the differences found in the F e - S n system we studied the temperature dependence of the magnetization of the Fe45Sn55 alloy under an external magnetic field Hext = i00 Oe, similar to the procedure used in Refs. [i4,15]. Prior to the measurements, each powder sample was demagnetized and cooled to 77 K, and then the external magnetic field He~~ was applied. In the applied field the sample was heated from 77 to 300 K and then cooled. Fig. 6(b), curve 1, presents the temperature dependence of the magnetization of the Fe45Sn55 amorphous film [14,15], as well as the method used by the authors to determine the magnetic ordering temperature (TcF) by the tangents crossing. Fig. 6(b), curve 2, shows the cr(T) obtained in this work after heating the powder crystalline sample. Using the same method to determine the magnetic ordering temperature as in Refs. [14,15], we obtained T° value. This way of determining the difference T° - TF does not exceed 20 K, whereas the difference between Tc values found from the X/XRT(T) and H ( x ) dependences (Fig. 6a) and TcF is 120 K for the Fe45Sn55 alloy. It can also be seen from Fig. 6(b) that in the temperature range 200-300 K, curves 1 and 2 actually coincide. These results emphasize that there is no difference in the magnetic ordering temperatures for the nanocrystalline and amorphous states of F e Sn alloys. There are several practical ways to determine the magnetic ordering temperature; we consider it to be the temperature at which any cooperative magnetic phenomena disappear. Extrapolating the dependence Tc(X) to T = 0 we evaluate the concentration range of cooperative magnetic phenomena of 0 - 7 0 at% Sn. It should also be noted that from Ref. [14] it follows that the heating and cooling of the amorphous Fe45Sn55 film have almost no effect on the shape of dependence or(T) (Fig. 6b, curve 1), whereas for the nanocrystalline powder sample of the same composition heating and cooling at T < 200 K result in considerable hysteresis (Fig. 6b, curves 2 and 3, respectiveIy). 3.3. Magnetic moment and hyperfine interaction parameters

Fig. 9 shows typical magnetization curves of nanocrystalline F e - S n alloys measured at 4.2 K. For

E.P. Yelsukoc, et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

342

the samples with Sn contents x < 50 at% saturation was achieved under external magnetic fields of 5 - 6 kOe, whereas with x > 50 the maximum value /:rext = 15 kOe was not enough to magnetize the samples to saturation. This is most clearly seen in Fig. 9 for the F%,Sns2 alloy. Analogous behaviour of the magnetization curves was observed earlier in thin amorphous films [15].

To calculate the average magnetic moment per Fe atom 0"~ve) we used the value of the specific saturation magnetization or0, obtained by extrapolation of the linear high-field part of the magnetization curve to He~t = 0 , as shown in Fig. 9 by dashed lines. While determining rove the magnetic moment on the Sn atoms was considered to be equal to 0. The calculated tnFe values and published data for il,ii,~J}tllEilllljllltilill

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100 200 300 H(kOe)

Fig. 7.57Fe M~Sssbauer spectra and P(H) functions of the Fe4sSnss alloy at various temperatures.

343

E.P. Yelsukou et aL /Journal of Magnetism and Magnetic Materials 166 (2997) 334-348

Tc(K) ~ .......

2.5 ~

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20 30 40 50 60 Sn (Si) concentration, x (at.%)

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Fig. 8. Concentrationdependences of the magnetic ordering temperature of ground (@ this work) and amorphous (o, [] Refs. [i3,i5]) Fe-Sn alloys, ground and amorphous Fe-Si alloys according to the data in Refs. [2, 5, 7-10, 24-26].

I=

~

j Fe-

i00 \

the low-concentration ( x < 8 ) bcc F e - S n alloys [24,36] and amorphous F e - S n films [12,13] are given in Fig. 10(a), together with the concentration dependence mz~(X) of disordered crystalline and amorphous F e - S i alloys; the solid lines approximate the experimental results of Refs. [2,5,7,9,1 1,24,25]. With an increase in Sn concentration from 0 to 5 at%, rnz~ increases from 2.22 to 2.3 /.t B. In the range 5 < x < 25 at% Sn rose actually remains constant, but with further increases in x falls sharply with the I

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g t~

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=__ .....

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5

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t4~

25

,

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0

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20 30 40 50 60 Sn (Si) concentration (at.%)

70

Fig. 10. Concentration dependence of (a) the average magnetic moment per Fe atom mFe(x); (b) mean hyperfine magnetic field EFt(x); (c) Hsn(X). (zx [24]; × [36]; • [41]; + [42]) low-concentration Fe-Sn alloys; (rT, o [12,13]) amorphous Fe-Sn films; (. this work) ground Fe-Sn alloys. Solid lines for the Fe-Si alloys are plotted according to the data from Refs. [2,5,7,9,11,24,25].

==

4O 20

do)

==

i

15

Fig. 9. Magnetization curves of Fe-Sn alloys. T~as = 4.2 K. Dashed lines show the extrapolation to Hext = 0 for determining cro.

slope change of mFe(x) dependence in the vicinity of 50 at% Sn. The comparison of the results for nanocrystalline and amorphous F e - S n alloys with x > 28 at% Sn shows absence of any differences for these two structure states. In both cases r o s e ( x ) = 0 with xc~--63% Sn, which differs from the value xc~ = 70 at% obtained from Tc(X). This behaviour of the raze(x) dependence in F e Sn alloys leads to considerable differences in the magnetic moments per Fe atom in the F e - S n and F e - S i systems, reaching 1 /z B for high x values.

344

E.P. Yelsukov etal./Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

We can note in Fig. 10(a) that for the bcc disordered F e - S i alloys the condition m F e ( x ) = const, is fulfilled in a much smaller concentration range, 0 - 8 at% Si. In contrast with mFe(x), the concentration dependences of the average hyperfine magnetic fields on 57Fe nuclei, ~rFe(X) (Fig. 10b), and on Hgsn nuclei, Hs~(X) (Fig. 10c) decrease linearly with increasing x from 0 to 13-15 at% Sn. The published data for this concentration range [36,40,41] agree well with these results. It is interesting to note that the changes in and Hs~ are similar, 25 and 30 kOe, respectively. In the Sn concentration range 15-50 at%, the slope of the HFe(X) dependence increases, as can be seen from a comparison with the dashed line in Fig. 10(b), where firs~ is actually independent of x. Extrapolating the HF~ and HSn values with x > 50 to zero, we obtain X~r = 72 at% Sn, which is in good agreement with X0r obtained from increasing Tc(x). The HF~(x) dependences of the F e - S n and F e - S i alloys [2,7,9,11] presented in Fig. 10(b) differ considerably. Comparing the average hyperfine magnetic fields HF~ and HSn for nanocrystalline and amorphous states in the F e - S n system, we find that in the range 23 < x < 45 there are rio differences at all. With x > 45 for amorphous thin films, much lower values of ~r [13] are typical in comparison with nanocrystalline alloys, resulting in lower values of Xcr in Ref. [13]. We believe that these differences are due to the methodologies employed. In the present work, calculating H by expression (2) we used the value H = 0 in the interval 0 < H < HI,, with the normalization condition

0.5 =-- (a)

"~ 0'4--

= I.

(4)

From the temperature M/Sssbauer measurements on the 57Fe nucleus (Fig. 7) and the [3-Sn spectrum on the 119Sn nucleus (Fig. 4) we estimated Her e = 35 kOe and H sn = 15 kOe. The authors of Ref. [13] used Hp = I00 kOe for 57Fe nuclei, which is almost three times the value of H F e = 35 kOe accepted in this work. With relatively low Sn concentrations x < 45 the fraction of with is small, which results in a good coincidence of Hve and HSn values for nanocrystalline and amorphous samples. For x >

P(H)

H<_Hp

Fe-Sn

Itz~ 0._~ ^ 1~

"~/"~ "L'/"

f'""

"

Fe-si

00~ m ~ , H , i , , , ¢ ' ~ , , -0.2 ~

Hz~

foHm~P(H)d H

÷

-0.4 ~ CO)

,~

a 4.8 ~ -1,0

.

Fe3$Sn2 2
.

~'~

.

-1.2 -1.4 ~

~-.M.

"~

t

,~

Fe3Sr~ FesSn3 FeSrt

t

FeSn2

-1.6 0

10 20 30 40 50 60 Sn (A1, Si, P) concentration (at%)

70

Fig. 11. Concentration dependences of the average isomer shifts 6F~(x) in (a) Fe-AI, Fe-Si, Fe-P, Fe-Sn alloys, and (b) ~sn(X) in Fe-Sn alloys. (× [36], [] [40], z~ [42]) low-concentration Fe-Sn alloys; (× [36], * [38], + [39])Fe-Sn intermetallic compounds; (. this work) ground Fe-Sn alloys; solid lines for Fe-A1, Fe-Si and Fe-P alloys are plotted according to the data in Refs. [1-3,5].

45, with an increasing contribution of the non-magnetic part in the spectrum, different techniques lead to different average hyperfine fields. In evaIuating the functions from the M~Sssbauer spectra of nanocrystalline F e - S n alloys, we also obtained the average isomer shifts on 57Fe (~e) and ltgsn (-3sn) nuclei. The values of "3Fe relative to c~-Fe and 8sn relative to [3-Sn are shown in Fig. l l(a,b), respectively. Unfortunately, due to the lack of published data on isomer shifts for amorphous F e - S n alloys we were unable to determine the influence of the structure state on ~F~ and 8sn' However, the published results for bcc alloys with low Sn concentrations [36,40,42] and Sn intermetallic compounds [36,38,39] agree well with the -3z, and "3sn values for the nanocrystalline F e - S n alloys of similar concentrations. Thus, one can assume that there

P(H)

E.P. Yelsukoe et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 334-348

are no differences in isomer shifts for nanocwstalline and amorphous samples. Considering the 6Fe(X) and 6s~(X) dependences in general, we can note peculiarities at 12-15 at% for both dependences and at 25 at% for 6s:(X). For comparison, Fig. 1 l(a) presents the concentration dependence ~F~(X) of disordered crystalline and amorphous Fe-A1 [1], F e - S i [2] and F e - P [3] alloys. It should be noted that 6F~ for F e - S n alloys with 0 < x < 15 are in the vicinity of 6F~ for F e - P alloys and at x > 15 6F~ in non-ordered systems F e - S n and Fe-A1 are practically the same.

4. Discussion The results presented in this work and in Refs. [12-23] show that in the F e - S n system, depending on the method of production, two types of nonordered structures can form: amorphous and disordered crystalline. The latter, according to the grain size evaluated, is a nanocrystalline structure. The ground nanostructured alloys with Sn concentrations x = 3.2-42 at% are disordered monophase ones, and the alloys with x > 42 at% Sn, according to the X-ray patterns, are multiphase ones. However, they can be regarded as quasi-monophase structures for two reasons: (a) each alloy has only one value of the magnetic ordering temperature; and (b) the local atomic structures of the ground alloys are similar to those of the amorphous films. The contradiction between the results of X-ray diffraction and magnetic measurements can be explained by the same chemical composition and the close local atomic environment parameters in all phases available in the given sample due to the mixing Fe and Sn atoms during mechanical milling. We designated the structure of such alloys as a disordered 'hexagonal' type. The range of the different phases is displayed in Fig. 12 (1 and 2). First, it should be noted that analogous non-equilibrium phase diagrams with similar concentration ranges form in the F e - S i system [5]. One can also see in Fig. 12 that the ranges of the amorphous and nanostructured F e - S n alloys overlap. All of these indicate the validity of a comparative analysis of the magnetic properties of F e - S n and Fe-Si alloys, as well as of amorphous and nanos-

345

I . . . . . . . . . . . . . . . . . . . .

[i~",

,

i::;;',

O. CoCo

2~e~'FOK~lagH e t ~ C state 0

lO

20

[

:l ~

Amorphous tl, it~fitms ;Bs, I'~exagonal" 'OTe structures : 1

30 40 50 x (at % Sn)

I

2

Nott-collbtear magnetic[ 3 structure

_J

60

70

Fig. 12. Non-equilibrium structural and magnetic phase diagrams of ground and amorphous F e - S n alloys. 1, Refs. [ I 2 - i 5 ] ; 2, this work. The dashed part shows the range of existence of equilibrium bcc structure at 600°C [33]; 3, this work and Ref. [14].

tructured Fe-Sn alloys, in order to determine the sp-atom size and the influence of topological disorder on the magnetism of non-ordered transition metal-metalloid systems. From the shapes of the magnetization curves (Fig. 9) and the hysteresis of the magnetization temperature dependence of the Fe45Sn55 alloy on heating and cooling (Fig. 6b, curves 2 and 3), it follows that high-concentration F e - S n alloys are not ferromagnetics. We can suppose that a noncollinear magnetic structure forms in them. The concentration range of ferromagnetic alloys can be more precisely found from the 0-0/o-is(x) dependence, where o-15 is the saturation magnetization in H ~ t = 15 kOe. The 0-o/0-15(x) dependence presented in Fig. 13, curve 1, shows that nanocrystalline F e - S n alloys are fen'o-

•

~

18o 17o ~

1.0

t

E" I40 'Y" 130

Z

120 ~

- :

'~ %//

Z

:

~.

1 1 0 ~K 0

1 I0

20 30 40 50 Sn concentration (at.%)

60

Fig. i3. Concentration dependence: curve 1, cr0 / o t i s ( x ) ; curve 2, HF,(x). o'0, magnetisation of the ground F e - S n alloys extrapolated to H~t = 0; cr~s, the value in a field H~x~= i5 kOe.

346

E,P. Yelsukou et al. / Journal of Magnetism and Maglzetic Materials 166 (1997) 334-348

magnetics with x < 50 at%. This estimate of the range of ferromagnetic order agrees we11 with that of amorphous thin Fe-Sn films [14]. Thus, the nonequilibrium magnetic phase diagram 3 in Fig. 12 is characteristic of both types of non-ordered structure. Taking into account the methodological peculiarities in obtaining Tc, ~rFo and ~rsn, we conclude that there are no differences in the magnetic properties of disordered nanostructured and amorphous Fe-Sn alloys. Thus, the topological disorder does not matter in the magnetism of non-ordered transition metalmetalloid systems. The Tc(x), HFe(x) and ~rSn(X) dependences show that the concentration range of any cooperative magnetic phenomenon is from 0 to Xcr = 70-72 at% Sn, while from the ~Fe (X) dependence, X:r = 63 at% Sn. This lower value of xc~ results from the fact that the mF° values from the magnetization curves of alloys with x > 50 at% Sn do not correspond to the real magnetic moments on the Fe atom. As can be seen from Fig. 9, next = 15 kOe is not sufficient for the complete magnetization of samples with a noncollinear magnetic structure. This is confirmed by the concentration dependence ~rFe//-~Fe(X) shown in Fig. 13, curve 2, which rises sharply with x > 50, reaching the value of 1185 kOe//* B with x = 6 2 at% Sn. Assuming that at x > 25 the contribution from the conduction electrons to the hyperfine field HFo may be ignored, we used the mean ratio ~rFe/mFo = 120 k O e / / z B in the range x = 25-50 to calculate the real value of mFe in the Fe3sSn62 sample, for which HFe = 84 kOe. The calculated mFe = 0.7 /.% is ten times the value of mFe obtained from the magnetization curve of the Fe3sSn62 sample, showing that despite the approximate estimate of mFe values from the MtSssbauer spectroscopy data, the range x¢~ = 70-72 at% Sn should be accepted. The concentration dependences of structural and magnetic parameters of nanocrystatline F e - S n alloys presented in the work are nonlinear, as in the Fe-Si system. However, there are considerable differences in the properties of these alloys. At any given concentration the following inequality is valid: so >

The ranges with boundaries at x = 12-15, 25 and 50 at% Sn, in which the concentration dependences of the magnetic properties change their behaviour, dif-

fer from those of the non-ordered Fe-Si alloys [2,5]. Hence, although Si and Sn atoms have equal electron configurations of the outer shell 3sZp 2 and 5s2p 2, the difference in their atomic radii (0.03 rim) affects considerably the magnetic properties of non-ordered alloys. Earlier, the concentration dependences of the magnetic properties of microcrystalline and amorphous Fe-A1, Fe-Si, F e - P alloys were explained in the terms of local atomic environment parameters [1-5]. It was therefore of interest also to verify the possibility of using such an approximation in nonordered Fe-Sn alloys. The estimates of local magnetic fields H~ e for Sn atom numbers k = 0 - 4 in the Fe atom nearest environment were made from the P(H) functions of low-concentration Fe-Sn alloys (Fig. 4). The average concentration value 7z= H~.~ 1 - HFe = 24 kOe agrees well with the value given in Ref. [40] for changing of the hyperfine magnetic field 22 kOe per Sn atom in the first coordination shell. Assuming that these changes for k = 0 - 4 are caused by decreasing numbers of 4s-like conduction electrons, the local magnetic moments on the Fe atom m~e with k _< 4 must remain unchanged and equal to 2.22 /'~B" The growth of the isomer shift 6F~ with increasing Sn concentrations (Fig. 1 l a) and the value of the magnetic moment per Fe atom mFe = 2.27 /.% for the intermetallic Fe3Sn compound [36] in which there is a single local Fe atom configuration with four Sn atoms in the nearest environment are to a certain extent the basis of the H I ° and m~.~ estimates for k = 0-4. Further, we assumed the proportionality of H I e and m Fe with k > 4 and the condition Hkv~ [mve ] = 0 with k = 7, as well as in the Fe-Si system [2]. The dependences H~.e(k) and m~.°(k) obtained in this way are presented in Fig. 14, curves 1 and 2, respectively. Then we calculated mFe(X) and ~rFo(x) according to the expression

VFo(X)[aFo(X)] =

ee(x),

(5)

k

where Pfi~(x) are the probabilities of local atomic configurations with k Sn atoms in the Fe atom nearest environment calculated for random distribu-

E.P. YeIsukou et al./ JoutT~al of Magnetism and Magnetic Materials 166 (1997) 334-348

3.0 250

,

200

l 2 0 . Lz.~ ="

I50

_j_ d

°°I0 0 r

~

0

I

I

i

1

~

'~

1 2 3 4 5 6 7 Number of Sn nearest neighbours K

Jo.o

8

Fig. 14. Models of local hyperfine magnetic fields H~ and magnetic moments m~e for different numbers k of Sn atoms in the surrounding the Fe atom. tions of the atoms in the lattice with the coordination number z = 8. Fig. 15(a,b) illustrates the experimental results (curves 1) and those calculated by the expressions raze(x) and TrFe(X) dependences (curves 2) [4]. We can see that the calculation results account qualitatively for the nonlinear behaviour of the experimental dependences, emphasizing the possibility

2.0 ~

I~ 1.0 0.5 1.5!

(a)

,,,I .... , .... I .... I .... I ....

350 ~~'& 300

~250 2OO

(b) 150

~-F~,*!:,p~l~,iillr,~Ir1111,,llli,iiIi,l,ll,,,lIi~r

0

I0

20 30 40 Sn concentration (at.%)

50

Fig. 15. Experimental and calculated dependences (a) mFe(x); (b) HFe(x). i, experiment; 2, calculation. Dashed lines: extrapolation of the initial part of the calculated curve.

347

of using the Jaccarino-WaIker models for nonordered F e - S n alloys. However, the suggested models of H [ ~ and m~e do not explain a number of results even qualitatively: (i) the increase in mFe to 2.3 /.% with increasing Sn concentration up to 5 at%; and (ii) the peculiarities in the concentration dependences with x = 12-15 at% Sn. At present there is no explanation of the constancy of ~rsn (52 kOe) over the wide Sn concentration range x = 13-50 at% (Fig. 10c). According to Refs. [41,43] there are two contributions to the hyperfine magnetic field on the 119Sn nucleus, one of which is directly connected with the magnetic moment on the Fe atom. In this case the question arises as to why the reduction in mFe with x > 25 at% Sn did not affect the Trsn(X) dependence in any way. It is quite clear that for a complete qualitative and quantitative description of the concentration dependences of the magnetic properties in non-ordered F e - S n alloys further detailed investigations of their electron structure and local atomic environment parameters are necessary. Such studies are now in progress.

5. Conclusions Mechanical grinding of originally multiphase F e Sn ingots forms disordered nanocrystalline powders of homogeneous compositions with average particle sizes of 4 txm and grain sizes in the particles changing from 19 to 6 nm with increasing Sn concentration. The samples with Sn concentrations x = 3 . 2 32.7 at% have a bcc structure; whereas those with x > 32.7 at% form disordered states of a hexagonal type. The measured concentration dependences of the magnetic properties Tc(x), mFe(X), ~rV~(X) and ~rsn(X) are nonlinear and show a number of peculiarities with 12-15, 25 and 50 at% Sn. One of the most interesting features is the weak dependence of mFe on Sn concentration in the range x = 0 - 2 5 at%. It was found that a ferromagnetic state forms in the alloys with x < 50 at% Sn. A noncollinear structure forms for x > 50 at%. The concentration range of cooperative magnetic phenomena was estimated to be x = 0 - 7 2 at% Sn. From a comparison of the magnetic properties of

348

E.P. Yelsukov et al. / Journal of Magnetism and Mczglwtic Materials 166 (1997) 334-348

nanocrystalline F e - S n alloys with those of amorphous F e - S n films and F e - S i alloys of a similar type, it follows that the topological disorder does not essentially influence t h e m in non-ordered systems. On the other hand, the fact that Sn atoms are larger (by 0.03 nm) than Si atoms results in essential differences in the m a g n e t i c properties of non-ordered F e - S n and F e - S i alloys. For any concentration of sp-elements the f o l l o w i n g inequality is valid:

(rc,,,,Fe, HFo,)Fo so > (re, ; Fe, HFe)Fe-S, The calculations of the concentration dependences mFe(x) and ~rFe(x) with suggested models of local m a g n e t i c m o m e n t s and hyperfine magnetic fields e m p h a s i z e the possibility o f describing the magnetic properties of non-ordered F e - S n alloys in terms of local atomic e n v i r o n m e n t parameters.

Acknowledgements This work was particularly supported by the Russian F u n d of Fundamental Research.

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