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Mössbauer studies and some magnetic properties of amorphous and nanocrystalline Fe87−xZr7B6Cux alloys
Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
MoK ssbauer studies and some magnetic properties of amorphous and nanocrystalline Fe Zr B Cu alloys 87~x 7 6 x W.H. CiurzynH ska!,*, L.K. Varga", J. Olszewski!, J. Zbroszczyk!, M. Hasiak! !Institute of Physics, Technical University of Cze9 stochowa, Al. Armii Krajowej 19, 42-200 Cze9 stochowa, Poland "Research Institute for Solid State Physics, Budapest, Hungary Received 1 April 1999; received in revised form 11 August 1999
Abstract The structure and low-"eld magnetic properties (i.e. the magnetic susceptibility and its disaccommodation) for the Fe Zr B and Fe Zr B Cu alloys in the amorphous and nanocrystalline states are investigated. It was stated that 87 7 6 86 7 6 1 the replacement of 1 at% iron atoms by Cu atoms in Fe Zr B leads to the decrease of the crystallization temperature. 87 7 6 Moreover, the results obtained indicate that in the nanocrystalline alloys, besides the amorphous matrix and a-Fe grains, the interfacial zone consisting of two components may be distinguished. The volume fraction of the interfacial zone is higher for the nanocrystalline Fe Zr B Cu alloy. From studies on the magnetic susceptibility disaccommodation in 86 7 6 1 investigated alloys, it is evident that the relaxation processes occurring in the amorphous phase are the main source of this phenomenon. From the analysis of the isochronal disaccommodation curves (applying a Gaussian distribution of relaxation times) the values of activation energy of the individual processes are found. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 7680; 7560L Keywords: Alloys } amorphous; Alloys } nanocrystalline; MoK ssbauer e!ect; Magnetic permeability disaccommodation
1. Introduction Fe-Zr-based nanocrystalline materials are obtained by a controlled crystallization of melt-spun amorphous ribbons. These nanocrystalline alloys consist of a-Fe grains of about 10}20 nm in size surrounded by an intergranual amorphous layer [1] with highly disordered structure [2,3]. The magnetic properties of the nanocrystalline materials were usually described taking into account
* Corresponding author. Fax: #48-34-3250791. E-mail address: [email protected] (W.H. CiurzynH ska)
these two phases [4]. However, the additional structural component consisting of iron atoms at the grain surfaces is also considered [5,6]. The structure of the amorphous matrix and phase composition of the nanocrystalline alloys in#uence their magnetic properties. The magnetic susceptibility disaccommodation, one of the magnetic after-e!ect phenomena, is very sensitive to the structural changes in these materials [7]. In this paper we study the structure, magnetic susceptibility and its disaccommodation for the asquenched, stress relieved and nanocrystalline Fe Zr B Cu (x"0 or 1) alloys. 87~x 7 6 x
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 5 6 9 - 7
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W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
2. Experimental procedure
cording to the expression:
The amorphous ribbons of Fe Zr B and 87 7 6 Fe Zr B Cu alloys were obtained by the rapid 86 7 6 1 quenching method. The ribbons were 1 mm wide and 0.022 mm thick. The microstructure of the samples was studied by MoK ssbauer spectroscopy and X-ray di!ractometry. From MoK ssbauer spectroscopy investigations the average hyper"ne "eld, distribution of the magnetization and phase composition were determined. The average hyper"ne "eld was obtained from hyper"ne "eld distributions which were evaluated according to the Hesse}RuK barsch method [8]. Assuming that the crystalline grains consist of a-Fe phase, the volume fraction of that phase was estimated from the expression:
*
C R < " F% #3 , #3 R 505
(1)
where C is the fractional iron concentration in F% the as-quenched alloys, R and R are relative #3 505 areas of MoK ssbauer subspectra corresponding to the crystalline phase and total area of the spectrum, respectively. The volume fraction of the amorphous matrix (< ) and the iron content in it (Fe ) were calculated m m from < "1!< m #3
AB
1 1 1 " ! "f (¹), s s s 2 1
(4)
where s and s are susceptibilities at times 1 2 t "2 s and t "120 s after demagnetization, re1 2 spectively. All investigations were carried out for the samples of the Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys in the as-quenched state and after annealing at 725 K for 30 min and 820 K for 1 h.
3. Results The MoK ssbauer spectra obtained at room temperature and corresponding hyper"ne "eld distributions obtained for the Fe Zr B Cu (x"0 87~x 7 6 x or 1) alloy in the as-quenched state and after annealing at 725 K for 30 min and at 820 K for 1 h are shown in Figs. 1 and 2. The spectra for both asquenched samples and the sample of Fe Zr B 87 7 6 alloy annealed at 725 K for 30 min consist of very broad and overlapped lines. The hyper"ne "eld distributions observed for these samples are typical for the amorphous alloys (Figs. 1d and e and 2d). However, in the MoK ssbauer spectrum of the Fe Zr B Cu alloy annealed at 725 K for 30 min, 86 7 6 1
(2)
and R C@ Fe " m F% , m R < 505 m
(3)
where C@ is the percentage iron concentration in F% the as-quenched alloys and R is the area of MoK sm sbauer subspectra corresponding to the amorphous matrix. Moreover, the volume fraction of the interface and its composition were estimated. The initial susceptibility was measured for toroidal samples of 2 cm inner diameter in ac magnetizing "eld of the amplitude H "0.32 A/m and m frequency f"2 kHz by means of a completely automated set-up. From those results the isochronal disaccommodation curves were constructed ac-
Fig. 1. MoK ssbauer spectra (a}c) and hyper"ne "eld distributions (d}f) of the Fe Zr B alloy in: as-quenched state (a, d), an87 7 6 nealed at 725 K for 30 min (b, e) and 820 K for 1 h (c, f ).
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
63
Fig. 3. Magnetic susceptibility versus temperature for the Fe Zr B alloy in: as-quenched state (a), annealed at 725 K for 87 7 6 30 min (b) and 820 K for 1 h (c).
Fig. 2. MoK ssbauer spectra (a}c) and hyper"ne "eld distributions (d}f ) of the Fe Zr B Cu alloy in: as-quenched state (a, d), 86 7 6 1 annealed at 725 K for 30 min (b, e) and 820 K for 1 h (c, f ).
the additional narrow lines corresponding to the crystalline phase appear (Fig. 2b) In MoK ssbauer spectra of both the Fe Zr B 87 7 6 and Fe Zr B Cu alloys annealed at 820 K for 86 7 6 1 1 h (Figs. 1c and 2c) the sharp lines are observed. In Figs. 3 and 4 the magnetic susceptibility (s ) 1 versus temperature for the as-quenched and annealed at 725 K for 30 min and 820 K for 1 h samples of the Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys is shown. It can be seen that the magnetic susceptibility for the as-quenched samples slightly increases with temperature up to about 325 K; for higher temperatures s drastically decreases. After 1 annealing the sample of the Fe Zr B alloy at 87 7 6 725 K for 30 min, the magnetic susceptibility at room temperature is about three times as large as that of the as-quenched sample. After the heat treatment of the Fe Zr B alloy at 820 K the 87 7 6 value of the susceptibility decreases to the value almost equal to that for the as-quenched sample. The increase of the magnetic susceptibility is observed for the Fe Zr B Cu after annealing at 86 7 6 1 725 K for 30 min (Fig. 4). However, the magnetic susceptibility for this sample monotonically decreases with temperature. The heat treatment of
Fig. 4. Magnetic susceptibility versus temperature for the Fe Zr B Cu alloy in: as-quenched state (a), annealed at 86 7 6 1 725 K for 30 min (b) and 820 K for 1 h (c).
this alloy at 820 K leads to the further increase of the magnetic susceptibility. The isochronal disaccommodation curves for the Fe Zr B and Fe Zr B Cu alloys in the as87 7 6 86 7 6 1 quenched state and after annealing at 725 K for 30 min and 820 K for 1 h are shown in Figs. 5 and 6. The relaxation spectra for the as-quenched samples of both alloys show one pronounced maximum at about 210}220 K and the next smaller one at 300}320 K. For temperatures higher than 325 K, the amplitude of disaccommodation distinctly increases. After annealing the sample of the Fe Zr B alloy at 725 K for 30 min (Fig. 5), the 87 7 6
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4. Discussion
Fig. 5. Isochronal disaccommodation curves for the Fe Zr B 87 7 6 alloy in: as-quenched state (a), annealed at 725 K for 30 min (b) and 820 K for 1 h (c).
Fig. 6. Isochronal disaccommodation curves for the Fe Zr B Cu alloy in: as-quenched state (a), annealed at 86 7 6 1 725 K for 30 min (b) and 820 K for 1 h (c).
disaccommodation amplitude decreases and in the isochronal disaccommodation curve very low and broad maximum at about 250 K is observed. Moreover, above 325 K the intensity of disaccommodation rapidly increases. The disaccommodation intensity for the sample of the Fe Zr B Cu alloy 86 7 6 1 annealed at 725 K for 30 min is almost temperature independent in the temperature range from 130 to 300 K and then increases with temperature (Fig. 6). After annealing the samples of the Fe Zr B 87 7 6 and Fe Zr B Cu alloys at 820 K for 1 h, only 86 7 6 1 temperature-independent background in the isochronal disaccommodation curves is observed.
The samples of the Fe Zr B and 87 7 6 Fe Zr B Cu alloys in the as-quenched state and 86 7 6 1 after annealing at 725 K for 30 min (in the case of the Fe Zr B alloy) are fully amorphous which is 87 7 6 con"rmed by X-ray di!ractometry and MoK ssbauer spectroscopy investigations (Figs. 1 and 2). However, annealing the Fe Zr B Cu alloy at 725 K 87 7 6 1 for 30 min leads to its partial crystallization. The crystalline a-Fe phase appears in the samples of both alloys after annealing at 820 K for 1 h (Figs. 1 and 2). The results obtained from the MoK ssbauer spectra analysis for the investigated samples are presented in Table 1. It is seen that the as-quenched samples of both alloys reveal the large component of the magnetization vector perpendicular to the ribbon surface (the ratios of the line intensities in Zeeman sextets are 3 : A : 1"3 : 0.9 : 1 and 2,5 3 : A : 1"3 : 0.8 : 1 for the Fe Zr B and 2,5 87 7 6 Fe Zr B Cu alloys, respectively). The magneti86 7 6 1 zation in the samples annealed at 725 K for 30 min and at 820 K for 1 h is randomly distributed (3 : A : 1+3 : 2 : 1, Table 1). From the MoK s2,5 sbauer spectra analysis we have found that the e!ective hyper"ne "eld of the crystalline phase in the nanocrystalline Fe Zr B Cu alloy depends 86 7 6 1 on the annealing conditions. It indicates that in the a-Fe phase small amount of Zr, Cu and B atoms is also present. It is known that the nucleation of a-Fe grains takes place in the regions rich in iron and during this process the di!usion of Zr, Cu and Nb atoms outside these regions occurs. When the crystallization occurs at low temperature the di!usion of these atoms may be incomplete. In Fig. 7 the hyper"ne "eld distributions of the amorphous matrix for the nanocrystalline Fe Zr B and Fe Zr B Cu alloys are shown. 87 7 6 86 7 6 1 In these distributions one can distinguish the additional component as compared to the as-quenched state (Figs. 1 and 2). That component may be attributed to the interfacial layer that is formed at the grain}matrix boundaries. After extraction of the interfacial component, the hyper"ne "eld distributions of the amorphous matrix consisting of at least two components are similar to those obtained for the amorphous samples (Figs. 1, 2 and 7). It has been found [5] that during annealing of the
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
65
Table 1 The average hyper"ne "eld at 57Fe nuclei (B ), second line intensity in Zeeman sextets (SA T), hyper"ne "eld for the crystalline phase %&& 2,5 (B ), volume fraction of the crystalline phase (< ), interfacial layer (< ) and amorphous matrix (< ), and the iron content in the #3 #3 */5 m crystalline phase (Fe ), interfacial layer (Fe ) and amorphous matrix (Fe ) for the Fe Zr B and Fe Zr B Cu alloys in the #3 */5 m 87 7 6 86 7 6 1 as-quenched state and after annealing at 725 K for 30 min and 820 K for 1 h B (T) %&&
A
< #3
< */5
Fe (at%) m
Fe (at%) */5
B (T) #3
Fe (at%) #3
9.60
0.9
*
*
87
*
*
*
Annealed at 725 K for 30 min
10.60
2.0
*
*
87
*
*
*
Annealed at 820 K/1 h
24.00
2.2
0.44
0.16
80
69
32.70
Fe86 Zr7 B6 Cu1 alloy As-quenched
11.11
0.8
*
*
86
*
*
Annealed at 725 K for 30 min
15.59
2.0
0.09
0.05
85
75
32.37
96
Annealed at 820 K/1 h
24.96
2.0
0.43
0.26
80
70
32.95
100
Sample Fe87 Zr7 B6 alloy As-quenched
2,5
Fig. 7. Magnetic "eld distribution for the nanocrystalline Fe Zr B alloy obtained by annealing at 820 K for 1 h (a, d), 87 7 6 and nanocrystalline Fe Zr B Cu after annealing at 725 K for 86 7 6 1 30 min (b, e) and 820 K for 1 h (c, f ) after extraction of the crystalline components (a}c) and after extraction of the crystalline and interfacial components (d}f ).
samples, the change of the contributions of these components takes place. From the hyper"ne "eld distribution (Fig. 7) it is seen that the interfacial zone is not homogenous.
98
*
The higher "eld component in this distribution is very broad (B about 30 T) and cannot be a super%&& position of discrete hyper"ne "elds of iron atoms in a-Fe phase in which Fe atoms have one nonmagnetic atom as nearest neighbour (nn). Moreover, assuming that the part of Fe atoms have one nonmagnetic atom as nearest neighbour, we can "nd Fe atoms having eight Fe atoms as nn and nonmagnetic atoms in the second coordination zone. These e!ects would lead to the widening of the MoK ssbauer line and decrease of the hyper"ne "eld corresponding to the a-Fe phase. However, these e!ects have not been observed in our samples. It is worth adding that the peak widening of the a-Fe phase in the hyper"ne distributions (Figs. 1f and 2e and f ) are connected with smoothing procedure in Hesse}RuK bartsch method. It is justi"ed to assume that one component of the interfacial zone is connected with Fe atoms which structurally belong to a-Fe grains but constitute the outer surfaces of these grains and the second one is connected with atoms situated in the nanocrystal-to-amorphous interfaces [5]. Assuming that the dependence of the average hyper"ne "eld on iron concentration in the interfacial layer is the same as for the crystalline phase, we have evaluated the volume fraction of that
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W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
component which is equal to about 0.16 for the nanocrystalline Fe Zr B alloy (annealed at 87 7 6 820 K for 1 h) and 0.05 and 0.26 for the Fe Zr B Cu alloy annealed at 725 K for 30 min 86 7 6 1 and 820 K for 1 h, respectively. Under an assumption that the a-Fe grains have the spherical shape, we have estimated the ratio of the average radius r (a-Fe grain#interfacial layer) to the 1 average radius of a-Fe grain (r). From these calculations we have found that r /r is equal to 1 1.11 and 1.17 for the Fe Zr B and 87 7 6 Fe Zr B Cu alloys (annealed at 820 K for 86 7 6 1 1 h), respectively. For the grain size of about 10}20 nm the thickness of the interfacial layer is about 2}4 atomic distance. It is worth noting that the contribution of the interfacial zone decreases with the increase of the grain size. From results presented in Table 1 one may conclude that the replacement of 1% Fe atoms by Cu atoms in Fe Zr B alloy involves the creation of smaller 87 7 6 a-Fe grains. Additionally, this was con"rmed by the magnetic susceptibility measurements (Figs. 3c and 4c). The nanocrystalline Fe Zr B Cu alloy 86 7 6 1 exhibits the higher magnetic susceptibility than the Fe Zr B one. This e!ect can be explained by the 87 7 6 random anisotropy model [4]. The structural changes occurring during annealing the amorphous ribbons in#uence their magnetic properties. The alloys in the as-quenched state exhibit poor soft magnetic properties i.e. the low magnetic susceptibility (Figs. 3 and 4). The annealing of the amorphous ribbons at 725 K for 30 min leads to the increase of the magnetic susceptibility. It is connected with the stress relief of the samples which is con"rmed by the results obtained from MoK ssbauer spectroscopy investigations (the increase of the intensity of the second line in Zeeman sextets, Table 1). One can note that the partial crystallization of the Fe Zr B alloy (after an87 7 6 nealing at 820 K for 1 h) leads to the decrease of the susceptibility in comparison with that value for the sample annealed at 725 K for 30 min. However, the increase of the magnetic susceptibility is observed for the nanocrystalline Fe Zr B Cu alloy 86 7 6 1 (after annealing at 820 K for 1 h). It seems to be connected with the smaller grain sizes in the nanocrystalline Fe Zr B Cu alloy than those in the 86 7 6 1 Fe Zr B alloy. This leads to the diminishing of 87 7 6
the magnetocrystalline anisotropy in the nanocrystalline Fe Zr B Cu alloy [4]. 86 7 6 1 As for the magnetic susceptibility disaccommodation, its intensity decreases after annealing the samples. It is known that magnetic after-e!ect phenomena in the amorphous alloys is connected with the reorientation of atom pairs in the vicinity of free volumes [9,10] which play the similar role as vacancies in the crystalline materials. The decrease of the disaccommodation intensity of the amorphous alloys after annealing is connected with the annealing out of some free volumes in the investigated samples. This e!ect leads to the increase of the packing density of atoms which is con"rmed by the results obtained from MoK ssbauer spectroscopy investigations (i.e. the increase of the average hyper"ne "eld at 57Fe nuclei after annealing the samples) (Table 1). The investigated alloys in the amorphous state exhibit very broad relaxation spectrum (Figs. 5 and 6) so, for the analysis of this spectrum, the continuous distribution of relaxation times should be assumed. Until now, the box distribution of relaxation times was applied [9,10]. In this paper we assumed a Gaussian distribution of relaxation times [11] which seems to be more realistic for the description of relaxation processes occurring in the amorphous materials. The Gaussian distribution function has a form:
C A
BD
1 ln q/q 2 m u(ln q)" exp ! , b Jpb
(5)
where b is the distribution parameter and q is an m average value of relaxation times which ful"ls the Arrhenius law:
C D
E q "q exp m , m om k¹
(6)
where q is the pre-exponential factor, E the averom m age activation energy, and k the Boltzmann constant. Under this assumption the isochronal disaccommodation curve can be ascribed by the following expression:
AB
*
P
G C A BD C A BDH C A B D
`3bi ¹ 1 t n 1 "+ I pi exp ! 1 pi q ez ¹ s mi i/1 Jpbi ~3bi t z 2 !exp ! 2 exp ! dz, q ez b mi i (7)
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
67
where I ¹ /¹"I denotes the disaccommodapi pi i tion intensity of ith process at temperature ¹, I is pi the disaccommodation intensity at the peak temperature (¹ ) and z"ln(q/q ). We assume the limit pi m value for z of $3b which approximately corresponds to $R. Under the assumption that the Gaussian distribution of ln q corresponds to the distribution of the activation energies E, we obtain E !b k¹ )E )E #b k¹ . (8) mi i pi i mi i pi The isochronal disaccommodation curves for the as-quenched Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys and Fe Zr B alloy annealed at 725 K for 87 7 6 30 min were decomposed into three elementary processes. The results obtained from this decomposition are presented in Table 2. The experimental points and theoretical disaccommodation curves are shown in Fig. 8. The values of the pre-exponential factor (q ) obtained from the analysis of the om isochronal disaccommodation curves are of the order of 10~15 s (Table 2). This indicates that disaccommodation phenomenon in the amorphous Fe Zr B and Fe Zr B Cu alloys is connected 87 7 6 86 7 6 1 with directional ordering of atom pairs in the vicinity of the `free volumesa [10]. As for the nanocrystalline samples of both alloys (Figs. 5 and 6), the contribution of the crystalline
Table 2 The intensity of individual processes (I ) at the peak temperature p (¹ ), activation energy (E) and pre-exponential factor of Arrhenius p law (q ) obtained for the Fe Zr B and Fe Zr B Cu alloys in om 87 7 6 86 7 6 1 the as-quenched state and after annealing at 725 K for 30 min Process ¹ (K) p
105 I p
1015 q (s) E (eV) om
I II III
193 214 294
4 7 7
9.4 7.1 4.3
0.50}0.69 0.62}0.71 0.85}1.00
I II III
213 247 279
0.3 0.7 0.3
6.5 2.7 1.0
0.61}0.71 0.75}0.82 0.87}0.92
Fe86 Zr7 B6 Cu1 alloy As-quenched I II III
188 211 319
3 6 6
1.4 8.8 5.8
0.58}0.64 0.62}0.68 0.88}1.10
Sample Fe87 Zr7 B6 alloy As-quenched
Annealed at 725 K/30 min
Fig. 8. The experimental points and theoretical isochronal disaccommodation curves obtained for the Fe Zr B alloy in the 87 7 6 as-quenched state (third run) (a) and after annealing at 725 K for 30 min (b), and for the Fe Zr B Cu alloy in the as-quenched 86 7 6 1 state (third run) (c).
phase to the disaccommodation is not evident. The presence of the temperature-independent background with a very low intensity (in the temperature range from 130 to 300 K) indicate that most of the free volumes in the amorphous matrix was annealed out during the partial crystallization of the samples. The increase of the disaccommodation intensity near the temperature of 325 K is connected with the magnetic phase transition of the amorphous matrix from the ferro- to paramagnetic state.
5. Conclusions (a) In the as-quenched samples the perpendicular component of the magnetization is relevant. (b) In the nanocrystalline samples one may distinguish three components: the crystalline a-Fe phase, amorphous matrix and interfacial layer. (c) The substitution of 1% Fe atoms by Cu atoms in the Fe Zr B alloy leads to the increase of 87 7 6 the magnetic susceptibility of the nanocrystalline samples. (d) The Fe Zr B and Fe Zr B Cu alloys in 87 7 6 86 7 6 1 the amorphous state exhibit the broad magnetic relaxation spectrum in the temperature range from 130 to 300 K.
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(e) The relaxation processes occurring in the amorphous matrix are the main sources of the relaxation processes in the nanocrystalline Fe Zr B and Fe Zr B Cu alloys. 87 7 6 86 7 6 1 (f ) The Gaussian distribution of the relaxation times enables the calculation of the activation energy of relaxation processes responsible for the magnetic susceptibility disaccommodation.
References [1] A. Makino, K. Suzuki, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 551.
[2] G. Rixecker, P. Schaaf, U. Gonser, J. Phys.: Condens. Matter 4 (1992) 10295. [3] M. Miglierini, J. Phys.: Condens. Matter 6 (1994) 1431. [4] G. Herzer, IEEE Trans. Magn. 26 (1990) 1397. [5] M. Miglierini, J.M. Greneche, J. Phys.: Condens. Matter 9 (1997) 2303. [6] A. SD lawska-Waniewska, J.M. Greneche, Phys. Rev. B 56 (1997) R8491. [7] J. Zbroszczyk, W.H. CiurzynH ska, J. Phys.: Condens. Matter 9 (1997) 4303. [8] J. Hesse, A. RuK bartsch, J. Phys. E: Sci. Instrum. 7 (1974) 526. [9] H. KronmuK ller, Phil. Mag. 48 (1983) 127. [10] H. KronmuK ller, J. Magn. Magn. Mater. 41 (1984) 366. [11] W.H. CiurzynH ska, G. Haneczok, J. Zbroszczyk, J. Magn. Magn. Mater. 189 (1998) 384.
MoK ssbauer studies and some magnetic properties of amorphous and nanocrystalline Fe Zr B Cu alloys 87~x 7 6 x W.H. CiurzynH ska!,*, L.K. Varga", J. Olszewski!, J. Zbroszczyk!, M. Hasiak! !Institute of Physics, Technical University of Cze9 stochowa, Al. Armii Krajowej 19, 42-200 Cze9 stochowa, Poland "Research Institute for Solid State Physics, Budapest, Hungary Received 1 April 1999; received in revised form 11 August 1999
Abstract The structure and low-"eld magnetic properties (i.e. the magnetic susceptibility and its disaccommodation) for the Fe Zr B and Fe Zr B Cu alloys in the amorphous and nanocrystalline states are investigated. It was stated that 87 7 6 86 7 6 1 the replacement of 1 at% iron atoms by Cu atoms in Fe Zr B leads to the decrease of the crystallization temperature. 87 7 6 Moreover, the results obtained indicate that in the nanocrystalline alloys, besides the amorphous matrix and a-Fe grains, the interfacial zone consisting of two components may be distinguished. The volume fraction of the interfacial zone is higher for the nanocrystalline Fe Zr B Cu alloy. From studies on the magnetic susceptibility disaccommodation in 86 7 6 1 investigated alloys, it is evident that the relaxation processes occurring in the amorphous phase are the main source of this phenomenon. From the analysis of the isochronal disaccommodation curves (applying a Gaussian distribution of relaxation times) the values of activation energy of the individual processes are found. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 7680; 7560L Keywords: Alloys } amorphous; Alloys } nanocrystalline; MoK ssbauer e!ect; Magnetic permeability disaccommodation
1. Introduction Fe-Zr-based nanocrystalline materials are obtained by a controlled crystallization of melt-spun amorphous ribbons. These nanocrystalline alloys consist of a-Fe grains of about 10}20 nm in size surrounded by an intergranual amorphous layer [1] with highly disordered structure [2,3]. The magnetic properties of the nanocrystalline materials were usually described taking into account
* Corresponding author. Fax: #48-34-3250791. E-mail address: [email protected] (W.H. CiurzynH ska)
these two phases [4]. However, the additional structural component consisting of iron atoms at the grain surfaces is also considered [5,6]. The structure of the amorphous matrix and phase composition of the nanocrystalline alloys in#uence their magnetic properties. The magnetic susceptibility disaccommodation, one of the magnetic after-e!ect phenomena, is very sensitive to the structural changes in these materials [7]. In this paper we study the structure, magnetic susceptibility and its disaccommodation for the asquenched, stress relieved and nanocrystalline Fe Zr B Cu (x"0 or 1) alloys. 87~x 7 6 x
0304-8853/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 5 6 9 - 7
62
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
2. Experimental procedure
cording to the expression:
The amorphous ribbons of Fe Zr B and 87 7 6 Fe Zr B Cu alloys were obtained by the rapid 86 7 6 1 quenching method. The ribbons were 1 mm wide and 0.022 mm thick. The microstructure of the samples was studied by MoK ssbauer spectroscopy and X-ray di!ractometry. From MoK ssbauer spectroscopy investigations the average hyper"ne "eld, distribution of the magnetization and phase composition were determined. The average hyper"ne "eld was obtained from hyper"ne "eld distributions which were evaluated according to the Hesse}RuK barsch method [8]. Assuming that the crystalline grains consist of a-Fe phase, the volume fraction of that phase was estimated from the expression:
*
C R < " F% #3 , #3 R 505
(1)
where C is the fractional iron concentration in F% the as-quenched alloys, R and R are relative #3 505 areas of MoK ssbauer subspectra corresponding to the crystalline phase and total area of the spectrum, respectively. The volume fraction of the amorphous matrix (< ) and the iron content in it (Fe ) were calculated m m from < "1!< m #3
AB
1 1 1 " ! "f (¹), s s s 2 1
(4)
where s and s are susceptibilities at times 1 2 t "2 s and t "120 s after demagnetization, re1 2 spectively. All investigations were carried out for the samples of the Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys in the as-quenched state and after annealing at 725 K for 30 min and 820 K for 1 h.
3. Results The MoK ssbauer spectra obtained at room temperature and corresponding hyper"ne "eld distributions obtained for the Fe Zr B Cu (x"0 87~x 7 6 x or 1) alloy in the as-quenched state and after annealing at 725 K for 30 min and at 820 K for 1 h are shown in Figs. 1 and 2. The spectra for both asquenched samples and the sample of Fe Zr B 87 7 6 alloy annealed at 725 K for 30 min consist of very broad and overlapped lines. The hyper"ne "eld distributions observed for these samples are typical for the amorphous alloys (Figs. 1d and e and 2d). However, in the MoK ssbauer spectrum of the Fe Zr B Cu alloy annealed at 725 K for 30 min, 86 7 6 1
(2)
and R C@ Fe " m F% , m R < 505 m
(3)
where C@ is the percentage iron concentration in F% the as-quenched alloys and R is the area of MoK sm sbauer subspectra corresponding to the amorphous matrix. Moreover, the volume fraction of the interface and its composition were estimated. The initial susceptibility was measured for toroidal samples of 2 cm inner diameter in ac magnetizing "eld of the amplitude H "0.32 A/m and m frequency f"2 kHz by means of a completely automated set-up. From those results the isochronal disaccommodation curves were constructed ac-
Fig. 1. MoK ssbauer spectra (a}c) and hyper"ne "eld distributions (d}f) of the Fe Zr B alloy in: as-quenched state (a, d), an87 7 6 nealed at 725 K for 30 min (b, e) and 820 K for 1 h (c, f ).
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
63
Fig. 3. Magnetic susceptibility versus temperature for the Fe Zr B alloy in: as-quenched state (a), annealed at 725 K for 87 7 6 30 min (b) and 820 K for 1 h (c).
Fig. 2. MoK ssbauer spectra (a}c) and hyper"ne "eld distributions (d}f ) of the Fe Zr B Cu alloy in: as-quenched state (a, d), 86 7 6 1 annealed at 725 K for 30 min (b, e) and 820 K for 1 h (c, f ).
the additional narrow lines corresponding to the crystalline phase appear (Fig. 2b) In MoK ssbauer spectra of both the Fe Zr B 87 7 6 and Fe Zr B Cu alloys annealed at 820 K for 86 7 6 1 1 h (Figs. 1c and 2c) the sharp lines are observed. In Figs. 3 and 4 the magnetic susceptibility (s ) 1 versus temperature for the as-quenched and annealed at 725 K for 30 min and 820 K for 1 h samples of the Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys is shown. It can be seen that the magnetic susceptibility for the as-quenched samples slightly increases with temperature up to about 325 K; for higher temperatures s drastically decreases. After 1 annealing the sample of the Fe Zr B alloy at 87 7 6 725 K for 30 min, the magnetic susceptibility at room temperature is about three times as large as that of the as-quenched sample. After the heat treatment of the Fe Zr B alloy at 820 K the 87 7 6 value of the susceptibility decreases to the value almost equal to that for the as-quenched sample. The increase of the magnetic susceptibility is observed for the Fe Zr B Cu after annealing at 86 7 6 1 725 K for 30 min (Fig. 4). However, the magnetic susceptibility for this sample monotonically decreases with temperature. The heat treatment of
Fig. 4. Magnetic susceptibility versus temperature for the Fe Zr B Cu alloy in: as-quenched state (a), annealed at 86 7 6 1 725 K for 30 min (b) and 820 K for 1 h (c).
this alloy at 820 K leads to the further increase of the magnetic susceptibility. The isochronal disaccommodation curves for the Fe Zr B and Fe Zr B Cu alloys in the as87 7 6 86 7 6 1 quenched state and after annealing at 725 K for 30 min and 820 K for 1 h are shown in Figs. 5 and 6. The relaxation spectra for the as-quenched samples of both alloys show one pronounced maximum at about 210}220 K and the next smaller one at 300}320 K. For temperatures higher than 325 K, the amplitude of disaccommodation distinctly increases. After annealing the sample of the Fe Zr B alloy at 725 K for 30 min (Fig. 5), the 87 7 6
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4. Discussion
Fig. 5. Isochronal disaccommodation curves for the Fe Zr B 87 7 6 alloy in: as-quenched state (a), annealed at 725 K for 30 min (b) and 820 K for 1 h (c).
Fig. 6. Isochronal disaccommodation curves for the Fe Zr B Cu alloy in: as-quenched state (a), annealed at 86 7 6 1 725 K for 30 min (b) and 820 K for 1 h (c).
disaccommodation amplitude decreases and in the isochronal disaccommodation curve very low and broad maximum at about 250 K is observed. Moreover, above 325 K the intensity of disaccommodation rapidly increases. The disaccommodation intensity for the sample of the Fe Zr B Cu alloy 86 7 6 1 annealed at 725 K for 30 min is almost temperature independent in the temperature range from 130 to 300 K and then increases with temperature (Fig. 6). After annealing the samples of the Fe Zr B 87 7 6 and Fe Zr B Cu alloys at 820 K for 1 h, only 86 7 6 1 temperature-independent background in the isochronal disaccommodation curves is observed.
The samples of the Fe Zr B and 87 7 6 Fe Zr B Cu alloys in the as-quenched state and 86 7 6 1 after annealing at 725 K for 30 min (in the case of the Fe Zr B alloy) are fully amorphous which is 87 7 6 con"rmed by X-ray di!ractometry and MoK ssbauer spectroscopy investigations (Figs. 1 and 2). However, annealing the Fe Zr B Cu alloy at 725 K 87 7 6 1 for 30 min leads to its partial crystallization. The crystalline a-Fe phase appears in the samples of both alloys after annealing at 820 K for 1 h (Figs. 1 and 2). The results obtained from the MoK ssbauer spectra analysis for the investigated samples are presented in Table 1. It is seen that the as-quenched samples of both alloys reveal the large component of the magnetization vector perpendicular to the ribbon surface (the ratios of the line intensities in Zeeman sextets are 3 : A : 1"3 : 0.9 : 1 and 2,5 3 : A : 1"3 : 0.8 : 1 for the Fe Zr B and 2,5 87 7 6 Fe Zr B Cu alloys, respectively). The magneti86 7 6 1 zation in the samples annealed at 725 K for 30 min and at 820 K for 1 h is randomly distributed (3 : A : 1+3 : 2 : 1, Table 1). From the MoK s2,5 sbauer spectra analysis we have found that the e!ective hyper"ne "eld of the crystalline phase in the nanocrystalline Fe Zr B Cu alloy depends 86 7 6 1 on the annealing conditions. It indicates that in the a-Fe phase small amount of Zr, Cu and B atoms is also present. It is known that the nucleation of a-Fe grains takes place in the regions rich in iron and during this process the di!usion of Zr, Cu and Nb atoms outside these regions occurs. When the crystallization occurs at low temperature the di!usion of these atoms may be incomplete. In Fig. 7 the hyper"ne "eld distributions of the amorphous matrix for the nanocrystalline Fe Zr B and Fe Zr B Cu alloys are shown. 87 7 6 86 7 6 1 In these distributions one can distinguish the additional component as compared to the as-quenched state (Figs. 1 and 2). That component may be attributed to the interfacial layer that is formed at the grain}matrix boundaries. After extraction of the interfacial component, the hyper"ne "eld distributions of the amorphous matrix consisting of at least two components are similar to those obtained for the amorphous samples (Figs. 1, 2 and 7). It has been found [5] that during annealing of the
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65
Table 1 The average hyper"ne "eld at 57Fe nuclei (B ), second line intensity in Zeeman sextets (SA T), hyper"ne "eld for the crystalline phase %&& 2,5 (B ), volume fraction of the crystalline phase (< ), interfacial layer (< ) and amorphous matrix (< ), and the iron content in the #3 #3 */5 m crystalline phase (Fe ), interfacial layer (Fe ) and amorphous matrix (Fe ) for the Fe Zr B and Fe Zr B Cu alloys in the #3 */5 m 87 7 6 86 7 6 1 as-quenched state and after annealing at 725 K for 30 min and 820 K for 1 h B (T) %&&
A
< #3
< */5
Fe (at%) m
Fe (at%) */5
B (T) #3
Fe (at%) #3
9.60
0.9
*
*
87
*
*
*
Annealed at 725 K for 30 min
10.60
2.0
*
*
87
*
*
*
Annealed at 820 K/1 h
24.00
2.2
0.44
0.16
80
69
32.70
Fe86 Zr7 B6 Cu1 alloy As-quenched
11.11
0.8
*
*
86
*
*
Annealed at 725 K for 30 min
15.59
2.0
0.09
0.05
85
75
32.37
96
Annealed at 820 K/1 h
24.96
2.0
0.43
0.26
80
70
32.95
100
Sample Fe87 Zr7 B6 alloy As-quenched
2,5
Fig. 7. Magnetic "eld distribution for the nanocrystalline Fe Zr B alloy obtained by annealing at 820 K for 1 h (a, d), 87 7 6 and nanocrystalline Fe Zr B Cu after annealing at 725 K for 86 7 6 1 30 min (b, e) and 820 K for 1 h (c, f ) after extraction of the crystalline components (a}c) and after extraction of the crystalline and interfacial components (d}f ).
samples, the change of the contributions of these components takes place. From the hyper"ne "eld distribution (Fig. 7) it is seen that the interfacial zone is not homogenous.
98
*
The higher "eld component in this distribution is very broad (B about 30 T) and cannot be a super%&& position of discrete hyper"ne "elds of iron atoms in a-Fe phase in which Fe atoms have one nonmagnetic atom as nearest neighbour (nn). Moreover, assuming that the part of Fe atoms have one nonmagnetic atom as nearest neighbour, we can "nd Fe atoms having eight Fe atoms as nn and nonmagnetic atoms in the second coordination zone. These e!ects would lead to the widening of the MoK ssbauer line and decrease of the hyper"ne "eld corresponding to the a-Fe phase. However, these e!ects have not been observed in our samples. It is worth adding that the peak widening of the a-Fe phase in the hyper"ne distributions (Figs. 1f and 2e and f ) are connected with smoothing procedure in Hesse}RuK bartsch method. It is justi"ed to assume that one component of the interfacial zone is connected with Fe atoms which structurally belong to a-Fe grains but constitute the outer surfaces of these grains and the second one is connected with atoms situated in the nanocrystal-to-amorphous interfaces [5]. Assuming that the dependence of the average hyper"ne "eld on iron concentration in the interfacial layer is the same as for the crystalline phase, we have evaluated the volume fraction of that
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component which is equal to about 0.16 for the nanocrystalline Fe Zr B alloy (annealed at 87 7 6 820 K for 1 h) and 0.05 and 0.26 for the Fe Zr B Cu alloy annealed at 725 K for 30 min 86 7 6 1 and 820 K for 1 h, respectively. Under an assumption that the a-Fe grains have the spherical shape, we have estimated the ratio of the average radius r (a-Fe grain#interfacial layer) to the 1 average radius of a-Fe grain (r). From these calculations we have found that r /r is equal to 1 1.11 and 1.17 for the Fe Zr B and 87 7 6 Fe Zr B Cu alloys (annealed at 820 K for 86 7 6 1 1 h), respectively. For the grain size of about 10}20 nm the thickness of the interfacial layer is about 2}4 atomic distance. It is worth noting that the contribution of the interfacial zone decreases with the increase of the grain size. From results presented in Table 1 one may conclude that the replacement of 1% Fe atoms by Cu atoms in Fe Zr B alloy involves the creation of smaller 87 7 6 a-Fe grains. Additionally, this was con"rmed by the magnetic susceptibility measurements (Figs. 3c and 4c). The nanocrystalline Fe Zr B Cu alloy 86 7 6 1 exhibits the higher magnetic susceptibility than the Fe Zr B one. This e!ect can be explained by the 87 7 6 random anisotropy model [4]. The structural changes occurring during annealing the amorphous ribbons in#uence their magnetic properties. The alloys in the as-quenched state exhibit poor soft magnetic properties i.e. the low magnetic susceptibility (Figs. 3 and 4). The annealing of the amorphous ribbons at 725 K for 30 min leads to the increase of the magnetic susceptibility. It is connected with the stress relief of the samples which is con"rmed by the results obtained from MoK ssbauer spectroscopy investigations (the increase of the intensity of the second line in Zeeman sextets, Table 1). One can note that the partial crystallization of the Fe Zr B alloy (after an87 7 6 nealing at 820 K for 1 h) leads to the decrease of the susceptibility in comparison with that value for the sample annealed at 725 K for 30 min. However, the increase of the magnetic susceptibility is observed for the nanocrystalline Fe Zr B Cu alloy 86 7 6 1 (after annealing at 820 K for 1 h). It seems to be connected with the smaller grain sizes in the nanocrystalline Fe Zr B Cu alloy than those in the 86 7 6 1 Fe Zr B alloy. This leads to the diminishing of 87 7 6
the magnetocrystalline anisotropy in the nanocrystalline Fe Zr B Cu alloy [4]. 86 7 6 1 As for the magnetic susceptibility disaccommodation, its intensity decreases after annealing the samples. It is known that magnetic after-e!ect phenomena in the amorphous alloys is connected with the reorientation of atom pairs in the vicinity of free volumes [9,10] which play the similar role as vacancies in the crystalline materials. The decrease of the disaccommodation intensity of the amorphous alloys after annealing is connected with the annealing out of some free volumes in the investigated samples. This e!ect leads to the increase of the packing density of atoms which is con"rmed by the results obtained from MoK ssbauer spectroscopy investigations (i.e. the increase of the average hyper"ne "eld at 57Fe nuclei after annealing the samples) (Table 1). The investigated alloys in the amorphous state exhibit very broad relaxation spectrum (Figs. 5 and 6) so, for the analysis of this spectrum, the continuous distribution of relaxation times should be assumed. Until now, the box distribution of relaxation times was applied [9,10]. In this paper we assumed a Gaussian distribution of relaxation times [11] which seems to be more realistic for the description of relaxation processes occurring in the amorphous materials. The Gaussian distribution function has a form:
C A
BD
1 ln q/q 2 m u(ln q)" exp ! , b Jpb
(5)
where b is the distribution parameter and q is an m average value of relaxation times which ful"ls the Arrhenius law:
C D
E q "q exp m , m om k¹
(6)
where q is the pre-exponential factor, E the averom m age activation energy, and k the Boltzmann constant. Under this assumption the isochronal disaccommodation curve can be ascribed by the following expression:
AB
*
P
G C A BD C A BDH C A B D
`3bi ¹ 1 t n 1 "+ I pi exp ! 1 pi q ez ¹ s mi i/1 Jpbi ~3bi t z 2 !exp ! 2 exp ! dz, q ez b mi i (7)
W.H. Ciurzyn& ska et al. / Journal of Magnetism and Magnetic Materials 208 (2000) 61}68
67
where I ¹ /¹"I denotes the disaccommodapi pi i tion intensity of ith process at temperature ¹, I is pi the disaccommodation intensity at the peak temperature (¹ ) and z"ln(q/q ). We assume the limit pi m value for z of $3b which approximately corresponds to $R. Under the assumption that the Gaussian distribution of ln q corresponds to the distribution of the activation energies E, we obtain E !b k¹ )E )E #b k¹ . (8) mi i pi i mi i pi The isochronal disaccommodation curves for the as-quenched Fe Zr B and Fe Zr B Cu 87 7 6 86 7 6 1 alloys and Fe Zr B alloy annealed at 725 K for 87 7 6 30 min were decomposed into three elementary processes. The results obtained from this decomposition are presented in Table 2. The experimental points and theoretical disaccommodation curves are shown in Fig. 8. The values of the pre-exponential factor (q ) obtained from the analysis of the om isochronal disaccommodation curves are of the order of 10~15 s (Table 2). This indicates that disaccommodation phenomenon in the amorphous Fe Zr B and Fe Zr B Cu alloys is connected 87 7 6 86 7 6 1 with directional ordering of atom pairs in the vicinity of the `free volumesa [10]. As for the nanocrystalline samples of both alloys (Figs. 5 and 6), the contribution of the crystalline
Table 2 The intensity of individual processes (I ) at the peak temperature p (¹ ), activation energy (E) and pre-exponential factor of Arrhenius p law (q ) obtained for the Fe Zr B and Fe Zr B Cu alloys in om 87 7 6 86 7 6 1 the as-quenched state and after annealing at 725 K for 30 min Process ¹ (K) p
105 I p
1015 q (s) E (eV) om
I II III
193 214 294
4 7 7
9.4 7.1 4.3
0.50}0.69 0.62}0.71 0.85}1.00
I II III
213 247 279
0.3 0.7 0.3
6.5 2.7 1.0
0.61}0.71 0.75}0.82 0.87}0.92
Fe86 Zr7 B6 Cu1 alloy As-quenched I II III
188 211 319
3 6 6
1.4 8.8 5.8
0.58}0.64 0.62}0.68 0.88}1.10
Sample Fe87 Zr7 B6 alloy As-quenched
Annealed at 725 K/30 min
Fig. 8. The experimental points and theoretical isochronal disaccommodation curves obtained for the Fe Zr B alloy in the 87 7 6 as-quenched state (third run) (a) and after annealing at 725 K for 30 min (b), and for the Fe Zr B Cu alloy in the as-quenched 86 7 6 1 state (third run) (c).
phase to the disaccommodation is not evident. The presence of the temperature-independent background with a very low intensity (in the temperature range from 130 to 300 K) indicate that most of the free volumes in the amorphous matrix was annealed out during the partial crystallization of the samples. The increase of the disaccommodation intensity near the temperature of 325 K is connected with the magnetic phase transition of the amorphous matrix from the ferro- to paramagnetic state.
5. Conclusions (a) In the as-quenched samples the perpendicular component of the magnetization is relevant. (b) In the nanocrystalline samples one may distinguish three components: the crystalline a-Fe phase, amorphous matrix and interfacial layer. (c) The substitution of 1% Fe atoms by Cu atoms in the Fe Zr B alloy leads to the increase of 87 7 6 the magnetic susceptibility of the nanocrystalline samples. (d) The Fe Zr B and Fe Zr B Cu alloys in 87 7 6 86 7 6 1 the amorphous state exhibit the broad magnetic relaxation spectrum in the temperature range from 130 to 300 K.
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(e) The relaxation processes occurring in the amorphous matrix are the main sources of the relaxation processes in the nanocrystalline Fe Zr B and Fe Zr B Cu alloys. 87 7 6 86 7 6 1 (f ) The Gaussian distribution of the relaxation times enables the calculation of the activation energy of relaxation processes responsible for the magnetic susceptibility disaccommodation.
References [1] A. Makino, K. Suzuki, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 551.
[2] G. Rixecker, P. Schaaf, U. Gonser, J. Phys.: Condens. Matter 4 (1992) 10295. [3] M. Miglierini, J. Phys.: Condens. Matter 6 (1994) 1431. [4] G. Herzer, IEEE Trans. Magn. 26 (1990) 1397. [5] M. Miglierini, J.M. Greneche, J. Phys.: Condens. Matter 9 (1997) 2303. [6] A. SD lawska-Waniewska, J.M. Greneche, Phys. Rev. B 56 (1997) R8491. [7] J. Zbroszczyk, W.H. CiurzynH ska, J. Phys.: Condens. Matter 9 (1997) 4303. [8] J. Hesse, A. RuK bartsch, J. Phys. E: Sci. Instrum. 7 (1974) 526. [9] H. KronmuK ller, Phil. Mag. 48 (1983) 127. [10] H. KronmuK ller, J. Magn. Magn. Mater. 41 (1984) 366. [11] W.H. CiurzynH ska, G. Haneczok, J. Zbroszczyk, J. Magn. Magn. Mater. 189 (1998) 384.