Saturation magnetization, Bs, and coercive force, Hc, depending on silicon content,
Nanocrystalline Fe-Si-B-Nb-Cu alloys (Finemets) obtained by crystallization of amorphous ribbons quenched from the melt exhibit high soft magnetic properties: the permeability greater than 105, coercive force of about 0.002 Oe and the saturation magnetization exceeding 10 kGs (Yoshizawa et al., 1988). In addition, their permeability can be purposefully controlled by inducing a magnetic anisotropy during annealing in a magnetic field (Herzer, 1992; Yoshizawa & Yamauchi, 1989) or in the field of tensile stress (Glazer et al., 1991; Herzer, 1994; Hofmann & Kronmüller, 1996). Magnetic anisotropy energy exceeding 5000 J/m3 is attained by annealing under a tensile stress of 400-600 MPa. For the first time the effect of tensile load applied along the ribbon at nanocrystallization annealing was investigated in (Glazer et al., 1991) and it was shown that after such treatment in a sample of the alloy Fe73.5Si13.5B9Nb3Cu1 a state with the magnetic anisotropy of the “easy-plane” type is formed. The plane of the magnetic anisotropy is oriented perpendicularly to the direction of stretching. For the first time it was assumed that the transverse magnetic anisotropy is due to residual elastic strain in the lattice of nanocrystals having a negative constant of the magnetostriction.
It is known that the type of the magnetic anisotropy induced in the Fe87-
If the formation of a state with magnetic anisotropy after annealing and cooling under a tensile load is associated with residual elastic stresses (Glazer et al. 1991; Herzer, 1994), − a result of the so-called Villari effect, then the type of magnetic anisotropy can be explained by the nature of magnetoelastic interactions in the nanoparticles (Serikov et al., 2006; Filippov, 2006) mainly consisting of Fe-Si crystals having a bcc lattice. This argument is supported by the fact that, in bulk crystalline samples of the Fe1-xSix alloy, with increasing concentration of silicon the magnetostriction constant changes its sign from positive to negative at x ~ 0.12 (Bozorth, 1993; Bertotti & Fiorillo, 1994c), and that the silicon concentration in nanoparticles is a few percent higher then the average Si concentration
In the Fe73.5Si15.5B7Nb3Cu1 alloy after TSA, residual deformations of a bcc nanocrystal lattice were detected by X-ray diffraction analysis judging from the shifts of one Bragg reflection (Ohnuma et al., 2003, 2005). In these papers it has been shown that the crystal lattice is stretched in the direction of load application and is compressed in the transverse direction, the strain and the magnetic anisotropy energy being proportional to the load.
Detailed studies of the residual strains have shown that deformations of the bcc lattice of Fe-Si nanocrystals are not isotropic: extension and compression along the <100> directions are maximum, and in the <111> − are minimum (Chernenkov et al., 2010). Therefore, the formation of a state with transverse magnetic anisotropy in the nanocrystals of the Fe73.5Si13.5B9Nb3Cu1 alloy, which is characterized by the orientation of magnetic moments transverse to the direction of stretching, is due to the negative magnetoelastic coupling that is caused by residual anisotropic lattice deformations of the Fe-Si nanocrystals with a large fraction of the Fe3Si phase. The research presented was undertaken to ascertain in detail the atomic structure of nanocrystals of Fe-Si-B-Nb-Cu alloys, depending on the silicon content and the thermal treatment of the samples.
2. Nanocrystalline Fe-Si-B-Nb-Cu alloys and their magnetic properties
The investigations were carried out using Fe87-
As a result of the heat treatments, samples from the alloys in three different states: initial (or immediately after quenching on the wheel), nanocrystalline (after NCA) and subjected to TSA were obtained. The magnetic state of the samples after NCA and TSA was controlled by the shape of hysteresis loops measured by the ballistic method using an F-190 microwebermeter (Serikov et al., 2006). The hysteresis loops of the samples after NCA and TSA treatments measured upon reversal magnetization along the ribbon are compared in Fig. 1. It is seen that with increasing silicon content
For samples after TSA with
3. Nanocrystal structure
3.1. X-ray diffraction analysis
The X-ray diffraction patterns of Fe87-
The samples in the form of a rectangular plate were prepared from ribbon fragments, which were glued to the thin narrow ring-like holder parallel to each other in several overlapping layers of thickness about 40 mcm. During the θ-2θ scanning, when ω angle is equal to θ, the scattering vector q was in the sample plane. The ω angle is equal to zero, when a sample plate is perpendicular to the direction of the incident X-ray beam. By rotating the sample around the horizontal axis by 90 , the transition from the longitudinal scan, when the scattering vector is directed along the axis of the ribbons, to the transverse scan was carried out. In the case of the samples annealed under stress at the longitudinal scan the scattering vector was parallel to the direction of the tensile load application and perpendicular to it in the transverse scan. For each sample, the diffraction patterns were measured for two orientations, i.e. in the form of longitudinal and transverse scans.
The X-ray diffraction patterns of Fe87-
Here and below, to describe the shape of reflections, the pseudo-Voigt function defined as a linear combination of Lorentzian and Gaussian with the same halfwidth (FWHM) was selected. After correction for instrumental resolution, integral width of the reflexion was computed, and the average diameter of the bcc grains was calculated by Scherrer formula (Warren, 1969). The dependence of the average sizes of the regions with the bcc order in the atomic arrangement on the silicon concentration is shown in the inset in Fig. 3. Therefore, the structure of the alloy in the initial state can be defined as a fine grained, highly defective bcc structure with the grain sizes about 2 nm. This statement is supported by the fact that the broad diffuse maxima are located close to the calculated positions for the bcc reflections, which are shown in Fig. 3 by triangles. The average size of the ordered regions that contribute to the main peak in the diffraction patterns slightly depends on the concentration of silicon
In the diffraction patterns of the Fe87-
After annealing at temperature 520°C (NCA treatment), the nanocrystals of α-Fe(FeSi) have appeared in all the alloys, independently of the silicon concentration. The average size of the nanocrystals is 10-12 nm.
The intensity of Bragg reflections at higher angles is rather weak. With increasing silicon content (
A large value of
The appearance of the Fe3Si phase in the Fe87-
The diffraction patterns measured in the longitudinal and transverse scans coincide (Fig. 4). The non-linear background is most probably due to the amorphous matrix surrounding the nanocrystallites in the Fe87-
In contrast to the alloys in the initial state and alloys subjected to the nanocrystallization annealing, a shift of peaks is observed in the diffraction patterns from alloys subjected to the tensile stress annealing (Fig. 5).
The diffraction peak profiles measured in the longitudinal and transverse scans for the Fe87-
The relative shifts of the peaks (Fig. 6 and 7) are different, and correspond to the anisotropic residual deformation of the nanocrystals. The largest shifts are observed for reflections (200) and (310), whereas no shifts are seen for the reflections (222) within the limits of the experimental resolution. The character of shifting the reflections in the diffraction patterns of the Fe87-
The anisotropy of the distortion of the nanocrystals can be characterized by the relative change (Δd/d) of the interplanar spacing d in their lattice. The positions of all the peaks (
The distortions of the nanocrystal structure in the Fe87-
The ends of the <100> crystallographic axes of the set of such nanocrystals on the sphere of a unit radius will circumscribe circles, belonging to the planes normal to the scattering vector
|along the ribbon - stretching|
|across the ribbon – compressing|
The specific case of the orientation of the nanocrystalline axes for the (222) reflection is shown in Fig. 10c. The <100> axes of the nanocrystals that contribute to the (222) reflection are on the cone surface with the apex angle ~55 × 2 = 110 , and the angle Φ is zero. It can be assumed that the absence of the deformation or its minimum value in the  direction is provided by a strong interaction of the nearest neighboring atoms arranged along the cube diagonals in the bcc lattice. The interaction hinders an increase in the distances between nearest neighboring atoms during extension. In the case of the tetragonal distortions, the distance between the nearest neighboring atoms is unchanged and only the directions of the bonds between the nearest neighboring atoms are slightly changed.
The residual structure distortions should be discussed using the elastic deformation tensor. However, it is hardly possible to do this, since the available structural information is very limited and the chemical composition of the nanocrystals is likely inhomogeneous: along with Fe and Si, the composition can also include other atoms. Moreover, the deformed nanocrystals are in the rigid amorphous matrix, in which, after the TSA treatment, residual stresses are likely exist as well.
The local atomic structure, phase composition and orientation of magnetization as a function of silicon content −
Mössbauer spectra of the alloys with different silicon content after the nanocrystallizing annealing and after the annealing under tensile load are shown in Fig. 11. Whereas, the distribution function P (H), in Fig. 12. The intensity of contributions at fields below 100 kOe is quite small; therefore, this range is not shown here. When analyzing distributions of HFFs, the Mössbauer data on the structure of FeSi alloys (Litvinov et al., 1982; Randrianantoandro et al., 1999; Stearns, 1963) were used.
Based on the Mössbauer spectra, the coefficients that characterize the deviation of the magnetic moments from the sample plane (Wertheim, 1964) were determined as a ratio of intensities of the second (fifth) and first (sixth) lines of the Mössbauer sextet. If the magnetic moment is perpendicular to the sample plane, i.e., lies along the direction of incidence of γ quanta, then А2/А1 = 0; in the case of an isotropic distribution of the magnetic moment, А2/А1 = 0.67; if the magnetic moments are located in the sample plane, А2/А1 = 1.33.
Fig. 13 displays the concentration dependence of the coefficient А2/А1 for the alloys studied, which is compared with the magnitudes of the constant of induced anisotropy, KTSA, found from the hysteresis loops measured on the samples subjected to TSA (Serikov et al., 2006). It is seen that in all the curves there is a feature near the Si content
The qualitative analysis of the concentration dependence of the distributions P(H) shown in Fig. 12 gives the following results. For
An observed fact that after TSA the peaks of 8:0 and 7:1 coordinations are broader than those after the heat treatment without stresses can be explained by the effect of residual strains (
4. Residual distortions and magnetic anisotropy
Thus, it is shown that in the samples subjected to TSA, there is a significant residual distortion of the nanocrystal lattice, the anisotropic character of which does not change when the concentration of silicon
The formation of the magnetic anisotropy after annealing and cooling under tensile load (TSA treatment) can be attributed to the residual elastic stresses in the alloy nanoparticles (Glaser et al., 1991; Herzer, 1994). Then, the change of the magnetic-anisotropy type from longitudinal to transverse is explained, respectively, by changing the sign of the magnetoelastic coupling in the nanocrystals from positive to negative with increasing the silicon content. The magnetoelastic Villari effect consisting in the change of magnetization in magnetic materials under the influence of mechanical stretching is the inverse phenomenon of the magnetostriction. If at the positive Villari effect, the magnetization along the direction of elongation increases, then at the negative magnetoelastic effects, on the contrary, an elastic elongation leads to a decrease of magnetization. In the bulk α-Fe(Si) crystals with the positive magnetostriction (and the positive Villari effect), the magnetization is predominantly oriented along one of the easy axes <100> forming the smallest angle with the direction of elongation. Upon saturation of the effect, which corresponds to the strain ~ 20-25 × 10-6, almost 100% of the magnetic moments are directed along this axis. If the magnetoelastic coupling takes up a negative value, as in the ordered Fe3Si alloy, the elongation would result in a deviation of the magnetic moments of individual Fe atoms from the longitudinal direction toward the transverse direction. They will be mainly oriented along one of the easy axes <100> that is perpendicular to the direction of the elongation or has the smallest angle with the plane transverse to it. The critical point of silicon concentration CSi, in which the magnetostriction constant changes its sign (see, for example, λ100 in Fig. 15), is the value of CSi ≈ 0.12 (Bertotti & Fiorillo, 1994c).
The dependence of the magnetostriction constant λ100 on the CSi largely reflects an increase in the volume fraction of the ordered Fe3Si phase with increasing concentration of silicon (Hilfrich et al., 1994), which, as known (Bertotti & Fiorillo, 1994c), has a negative value of the magnetostriction constant (λ100 ≈ -20 × 10-6, λ111 = -5 × 10-6). With the negative magnetoelastic coupling, which is typical of the ordered Fe3Si phase, the relative compression of the lattice should cause an increase in the magnetization along the direction of reduction.
The microstructure of the nanocrystalline FeSiBNbCu alloy can be represented as a huge number of the isotropically oriented α-Fe (Si) nanocrystals of about 10 nm in average grain diameter with the bcc lattice, and the clusters of nonmagnetic fcc Cu(Fe) grains about 5 nm placed in the residual amorphous matrix phase Fe(Nb)-B (Yoshizawa, 2006). The concentration of silicon in the nanoparticles is a few percent higher than its average concentration in the alloy (Serikov et al., 2006). For example, at an average value of
At this point it should be noted the role of Fe3Si phase in the formation of the transverse magnetic anisotropy. The iron-silicon alloy in the ordered Fe3Si state (D03 structure) is characterized by a negative constant of the magnetoelastic coupling. The transverse orientation of the magnetization with respect to the extension direction is characteristic of it, the so-called the transverse Villari effect; and negative magnetostriction − in the magnetic field, the length of the sample in the direction of the field application decreases. Therefore, the transverse magnetic anisotropy induced in the nanocrystalline alloy ribbons after the SA treatment should be attributed to the presence of a substantial fraction of Fe3Si phase in the nanocrystals. The presence of Fe3Si phase in the nanocrystals grown during NCA or TSA was supported by the following experimental observations. Firstly, as well as in the crystalline α-FeSi alloys the line
Fig. 16a represents schematically one of the 48 equivalent spherical triangles. The direction of tensile stress application relative to the nanocrystalline axes is shown by the radius–vector for three most interesting cases, namely, along , , and . We remind that the nanocrystals have random orientation in the Fe–Si–Nb–Cu–B alloy and, hence, a random one relative to the ribbon axis. The distortions of the nanocrystal lattice are different for the radius–vectors within this spherical triangle. The nearly tetragonal distortions correspond to the case where the radius–vector is directed along an easy-magnetization <100> axis of a nanocrystal, for example,  in Fig. 16a. After TSA in the nanocrystals of the Fe87-
Summing up the results of X-ray diffraction and NGR-spectroscopy studies on the structure of the nanocrystals in soft magnetic alloys Fe87-
For nanocrystalline alloy Fe87-XSiXB9Nb3Cu1, a phenomenological model of the mechanism of inducing the longitudinal magnetic anisotropy at X < 9 and the transverse magnetic anisotropy at X > 9 due to the anisotropic distortions of nanocrystals was proposed.
This study was supported by the Russian Foundation for Basic Research (project no. 10-02-00435) and by the Presidium of Russian Academy of Sciences (project no. 09-Π-2-1035).