A brief survey of the recent advances in Fe-based nanocrystalline soft magnetic alloys has shown that the saturation magnetization (Js) of these alloys is governed by the mass fraction, rather than the atomic fraction, of the nonmagnetic additives. Thus, the ultimate limit of Js in the alloys prepared by nano-crystallization of amorphous precursors is expected in an Fe-B binary system where amorphization by rapid quenching takes place with the lowest mass fraction of glass forming elements in Fe-based systems. We will demonstrate that nano-crystallization is possible in this binary system when the precursor amorphous phase is annealed ultra-rapidly. While the grain size after conventional annealing for amorphous Fe-B alloys is too large for the exchange softening effect, a small grain size well below the exchange length is obtained after annealing with a heating rate of 103 – 104 K/s. This results in magnetically soft nanostructures with Fe content up to 97.2 wt. %, leading to a high Js ≥ 1.9 T with a small coercivity (Hc) between 3.8 and 6.4 A/m. An addition of Co to nc-Fe87B13 results in a higher Js of 2.0 T with a slight increase of Hc to 9.3 A/m. The soft magnetic properties of these ultra-rapidly annealed alloys (named HiB-Nanoperm) is well understood by the random anisotropy model. The formation of nano-meter scale microstructures in a simple binary system unlocks previously unavailable alloy design strategies in nanostructured systems which is not only relevant to magnetic materials but, also to structural materials.

It has been three decades since Finemet, the first example of nanocrystalline soft magnetic alloys, was reported by Yoshizawa et al.1 at the MMM/Intermag meeting in Vancouver in 1988. Unlike conventional crystalline alloys, the magnetic softness in nanocrystalline alloys is due to the exchange-averaging effect2 of the local anisotropy (K1). This has set alloy development free from a traditional prerequisite of reducing intrinsic K1, which usually requires a large amount of nonmagnetic additives. Thus, nanocrystalline soft magnetic alloys stand out with a great potential of realizing both high saturation magnetization (Js) and excellent soft magnetic properties. In spite of this potential, Js in nanocrystalline alloys remains lower than that of Si steels3 due to the use of nonmagnetic additives such as Cu and other early transition metals (e.g. Zr and Nb) for the formation of nanostructures from amorphous precursors. However, these additives may be unnecessary. Recently, we have demonstrated that simple (Fe,Ni)-B4 and Fe-B5 binary amorphous precursors lead to a magnetically soft nanostructure after ultra-rapid annealing. The resultant saturation magnetization of nanocrystalline Fe87B13 is as high as 1.92 T and the coercivity (Hc) is below 8 A/m.

In this report, we will first briefly review the major efforts of alloy development in Fe-based nanocrystalline alloys in recent years with emphasis placed on the saturation magnetization and the concentration of ferromagnetic elements. We will then summarize the effects of ultra-rapid annealing (URA) on both the microstructural and magnetic properties in Fe-B alloys and discuss the origin of the soft magnetic nanostructure in such a simple binary system. Lastly, we will discuss the effects of additives on the enhancement of Js and reduction of Hc in the Fe-B alloys along with the grain size dependence of the coercivity in the Fe-B based nanocrystalline alloys.

There have been excellent review articles on nanocrystalline magnetic materials where the magnetic3 and structural6 properties were surveyed for a range of Fe-based alloy systems. A recent book chapter by Willard and Daniil7 contains a comprehensive literature survey on this topic for a period between 1988 and 2012, covering perhaps the widest range of alloy systems reported in this period. An earlier short review on literature appeared in a period from 1988 to 1998 concluded that the chemical compositions of nanocrystalline soft magnetic alloys prepared from melt-spun amorphous precursors could be expressed by the following formula:8 

(1)

where FM, EM, ML and LM are ferromagnetic metals, early transition metals, metalloids and late transition metals, respectively. Both Finemet (nc-Fe-Si-B-EM-LM alloys9) and Nanoperm (nc-Fe-EM-B alloys10) and their derivational alloys are well described by this formula. Since spontaneous magnetization reflects the concentration of ferromagnetic atoms, new alloys with higher saturation magnetization have been realized by way of reducing the amount of nonmagnetic components while maintaining the grain size well below the exchange length. Thus, we focus our survey here on the efforts of dispensing with nonmagnetic additives in nanocrystalline soft magnetic alloys.

Within the nonmagnetic additives in Eq. (1), the roles played by EM and LM have been studied extensively.6 As a result, it is well known that Cu promotes the nucleation kinetics of bcc-Fe11 while Nb is believed to act as a crystal growth inhibitor12 during the nano-crystallization process. These additives are essential in nc-Fe73.5Si13.5B9Nb3Cu1. However, in 1990 a magnetically soft nanostructure was reported for a LM-free Fe-Zr-B system,10 demonstrating that the nucleation frequency of bcc-Fe in some alloy systems is naturally high enough to realize magnetically soft nanostructures. In 2007, Ohta and Yoshizawa13 reported that soft magnetic nanostructures could be obtained in EM-free Fe-Si-B-Cu alloys. Makino et al.14 also obtained a similar nanostructure in an EM-free Fe-Si-B-P-Cu system. These EM-free nanocrystalline alloys suggest that addition of the heavy early transition metal, believed to act as a growth inhibitor, is not an essential condition for the formation of Fe grains with sizes smaller than the exchange length.

The magnetic properties of these nanocrystalline alloys in the FM-EM-ML-LM, FM-EM-ML and FE-ML-LM systems are listed in Table I along with the properties of commercial amorphous alloys.15 Owing to the small random magnetocrystalline anisotropy (<K1>) brought about by the exchange averaging effect, small Hc values are commonly seen for the nanocrystalline alloys. However, high initial permeability (μi) above 104 are limited to the Finemet and Nanoperm families. The μi value of nc-Fe73.5Si15.5B7Nb3Cu1 is truly comparable to that of Co-based amorphous alloys where the high cost of Co limits their practical applicability. The high permeability of the Fe-Si-B-Nb-Cu alloys is attributable to their low saturation magnetostriction (λs) in the order of 10-6 or less. The Fe-Zr-B based nanocrystalline alloys10,16 also exhibit similar low λs and thus, their permeability is well above 104. However, unlike these two traditional nanocrystalline alloy families, small magnetostriction < 10-6 has not been confirmed for those EM-free Fe-Si-B-Cu13 and Fe-(Si)-B-P-Cu14,17 alloys because these newer nanocrystalline alloys contain relatively large fractions of the residual amorphous phase. Hence, their μi is expected to remain similar to that of Fe-based amorphous alloys (< 104). Naturally, the removal of EM additives is effective in enhancing the saturation magnetization and high Js well above those of Finemet and Nanoperm has been reported for the EM-free alloys.

TABLE I.

Saturation magnetization (Js), coercivity (Hc), initial permeability at 1 kHz (μi) and saturation magnetostriction (λs) of various nanocrystalline soft magnetic materials.

Composition (at. %)Js (T)Hc (A/m)μi at 1kHzλs (ppm)References
Fe73.5Si13.5B9Nb3Cu1 1.24 0.5 100000 2.1 1 and 9  
Fe73.5Si15.5B7Nb3Cu1 1.15 0.5 150000 ∼ 0 9  
Fe81Si2B13Nb3Cu1 1.55 12.8 9000 9  
Fe91Zr7B2 1.7 4.2 31000a - 2 16  
Fe86Zr7B6Cu1 1.52 3.2 48000a - 1 10  
Fe82.7Cu1.3Si2B14 1.85 6.5 14 13  
Fe84.3B6P9Cu0.7 1.72 2.9 15 17  
Fe81.2Co4Si0.5B9.5P4Cu0.8 1.82 - 1.83 3 - 5 19 21  
Fe-based amorphous 1.45 8000 32 15  
Co-based amorphous 0.55 0.3 150000 ∼ 0 15  
Composition (at. %)Js (T)Hc (A/m)μi at 1kHzλs (ppm)References
Fe73.5Si13.5B9Nb3Cu1 1.24 0.5 100000 2.1 1 and 9  
Fe73.5Si15.5B7Nb3Cu1 1.15 0.5 150000 ∼ 0 9  
Fe81Si2B13Nb3Cu1 1.55 12.8 9000 9  
Fe91Zr7B2 1.7 4.2 31000a - 2 16  
Fe86Zr7B6Cu1 1.52 3.2 48000a - 1 10  
Fe82.7Cu1.3Si2B14 1.85 6.5 14 13  
Fe84.3B6P9Cu0.7 1.72 2.9 15 17  
Fe81.2Co4Si0.5B9.5P4Cu0.8 1.82 - 1.83 3 - 5 19 21  
Fe-based amorphous 1.45 8000 32 15  
Co-based amorphous 0.55 0.3 150000 ∼ 0 15  
a

H = 0.4 A/m.

Higher Js values in Fe-based alloys can also be obtained by Co addition. However, Co addition results in a large annealing-induced anisotropy (Ku) due to the well-known pair ordering effect where Ku becomes proportional to the square of Co content.18 The magnetostriction is also increased dramatically by Co addition. For example, λs of nc-Fe43Co43Zr7B6Cu1 reported by Müller et al.19 is as large as 30 x 10-6. Johnson et al.20 reported that the permeability at 1 kHz and 0.4 A/m for nc-Fe44.5Co44.5Zr7B4 was 650, two orders of magnitude lower than that of the Co-free Fe-Zr-B alloys.16 Hence, this approach is accompanied by severe deterioration of the softness, although minor additions of Co are often effective in enhancing Js slightly while maintaining the softness.21 Still, Co addition can be beneficial to prevent grains from decoupling magnetically at elevated temperatures by which the exchange softening effect is lost. Škorvánek et al.22 demonstrated that Hc of nc-Fe44.5Co44.5Zr7B4 remained around 30 A/m even at elevated temperatures up to 675 K. This temperature stability was identified earlier by McHenry et al.23 and the Fe50Co50-based nanocrystalline alloys were proposed for applications at high operation temperatures.

Hence, for a further enhancement of Js in Fe-based nanocrystalline soft magnetic alloys, Fe-ML-based systems are the most promising. In Fig. 1 we show the relationship between the saturation magnetization and the amount of nonmagnetic additives both in atomic and mass fractions for Fe-ML-based nanocrystalline alloys.13–15,17,24–26 Alloys containing limited amounts of ML elements have been excluded from these plots. Although Js in both the plots shows a tendency to decrease with increasing the amount of nonmagnetic additives, a better correlation is seen with the mass fraction presumably because the magnetization reflects the volume density of magnetic moment and heavy atoms take up space. This empirical correlation in Fig. 1 predicts that the total amount of nonmagnetic additives must be below about 4 wt. % in order to realize Js well above 1.9 T. In addition, the precursor melt-spun ribbons need to be fully amorphized for a homogeneous nanostructure after crystallization. These conditions are feasible in the Fe-B binary system27 since the minimum B content for the formation of an amorphous single phase is about 13 at. % (2.81 wt. %). Because B is the lightest ML element, the highest possible Js value in Fe-based alloys must be obtained in the Fe-B binary system free of other heavier elements such as Si and P. Consequently, we have focused our attention to the crystallization behavior of amorphous Fe87B13.

FIG. 1.

Saturation magnetization of Fe-based nanocrystalline soft magnetic alloys.13–15,17,24–26

FIG. 1.

Saturation magnetization of Fe-based nanocrystalline soft magnetic alloys.13–15,17,24–26

Close modal

The crystallization behaviours of Fe-B amorphous alloys27 are one of the most extensively investigated topics in amorphous alloys. Although primary crystallization of bcc-Fe, the crystallization reaction seen in Finemet and Nanoperm, takes place in the hypo-eutectic composition range (e.g. Fe86B14), the grain size of bcc-Fe after primary crystallization in the Fe-B binary alloys is typically around 30 to 50 nm, above the natural exchange length (Lex0 ∼ 30 – 40 nm for bcc-Fe).2 Hence, amorphous Fe-B binary precursors fail to produce magnetically soft nanostructures when annealed conventionally. One of the potential approaches to refining the crystallization-induced microstructure is flash annealing. We have shown in our earlier study29 on Nanoperm that the mean grain size in nc-Fe90Zr7B3 is reduced by 30 % through an increase of heating rate during annealing from 0.042 to 3.3 K/s. It was also found in a time-temperature-transformation study16 of nc-Fe91Zr7B2 that the highest initial permeability (3.1 x 104) was obtained after 60 s annealing at 923 K, rather than the commonly used condition of 3.6 ks annealing. These preliminary investigations suggest that a short annealing time combined with a high heating rate is preferred for magnetic softness in Cu-free alloys where the nucleation frequency is relatively limited.

Rapid thermal processing techniques and their application in magnetic materials have been reviewed by Jin and Liu.30 According to this review the upper limit of heating rate in lamp or joule heating techniques is about 300 K/s. However, the practical upper limit for applying these conventional techniques to nano-crystallization is well below this heating rate because of the significant overheating effect due to the latent heat of crystallization.31 Thus, the challenge is not to realize ultra-high heating conditions but, rather to prevent this detrimental overheating from happening during annealing. To solve this problem, utilising preheated Cu blocks for annealing32 is effective. We have designed and implemented a semi-automated furnace with two pneumatically-driven Cu blocks with embedded heating elements28 where annealing time can be controlled with a precision of 0.1 s. The maximum heating rate measured by a 25 μm thick thermocouple was 2 x 104 K/s and the heating process was virtually free of the overheating effect. It is to be noticed that the heating rates quoted in some of our previous reports4,5 were measured with a thicker thermocouple and the rates quoted were lower than this value. In the present report, all the heating rates were determined by a 25 μm thick thermocouple for consistency.

Examples of the effects of ultra-rapid annealing (URA) on the structural and magnetic properties of the Fe-B based alloys are shown in Fig. 2. In this figure the changes in mean grain size (D) estimated from X-ray diffraction patterns (XRD) and the coercivity (Hc) after primary crystallization are shown as a function of heating rate for Fe87B135 and Fe85B13Ni24 alloys. The heating rate (α) was lowered by adding thermally insulating sheets between the sample and the Cu block. The grain size of the samples annealed at α = 1.7 K/s is 30 to 40 nm, right in the range of Lex0. Thus, the coercivity is as large as 80 to 160 A/m. The grain size shows a marked decrease with increasing heating rate and a small size around 20 nm is obtained at α > 103 K/s. As a result of this grain refinement, a small Hc < 8 A/m is confirmed for these two alloys after ultra-rapid annealing. Figure 3 shows the cross-sectional transmission electron micrographs acquired from both the free surface and roll-chilled sides of the Fe85B13Ni2 ribbon after URA. A homogeneous nanostructure is confirmed across the ribbon, consistent with the mean grain size estimated by XRD. Similar cross-sectional microstructures have also been confirmed for Fe87B13 after URA.28 The volume fraction of the bcc-Fe in these alloys estimated by 57Fe Mössbauer spectroscopy is around 50 %.

FIG. 2.

Changes in mean grain size and coercivity as a function of heating rate for Fe87B135 and Fe85B13Ni24.

FIG. 2.

Changes in mean grain size and coercivity as a function of heating rate for Fe87B135 and Fe85B13Ni24.

Close modal
FIG. 3.

Cross-sectional transmission electron micrographs taken from (a and b) free surface side and (c and d) roll-chilled side for nanocrystalline Fe85B13Ni2.

FIG. 3.

Cross-sectional transmission electron micrographs taken from (a and b) free surface side and (c and d) roll-chilled side for nanocrystalline Fe85B13Ni2.

Close modal

An obvious question here is the origin of the nano-meter scale microstructure in a simple binary alloy system. One of the significant consequences of rapid heating is that the onset of crystallization is delayed and the reaction takes place at a higher temperature where the nucleation and growth kinetics may differ significantly from that under the conventional annealing. Although the nucleation and crystal growth rates both exhibit positive temperature dependence in the amorphous precursors, the refined microstructures after rapid annealing suggest that the former effect is dominant in the rapid annealing process. The significance of annealing temperature on the nucleation kinetics has been discussed by Köster and Meinhardt.33 They investigated experimentally the number density of crystallites at a wide range of annealing temperatures for amorphous Fe-Ni-B alloys including compositions where primary crystallization is seen. It was found that the volume density of crystallites is increased by 2 to 7 orders of magnitude when the annealing temperature is raised to above the glass transition temperature (Tg). This dramatic effect has been attributed to the contribution of viscous flow to the atomic transport term of the homogeneous nucleation kinetics. The reduction of the mean grain size observed for the Fe87B13 alloy by rapid annealing (Fig. 2) corresponds to approximately an order of magnitude increase in the number density, well within the effect confirmed by Köster and Meinhardt. Thus, the nanostructural formation in the Fe-B alloys is attributable to the potential viscous flow contribution. Most recently, we have investigated the crystallization kinetics of amorphous Fe86B14 by tracing the electrical resistivity during ultra-rapid annealing.28 It has been found that the crystallization temperature is raised by at least 100 K when the ultra-rapid annealing is employed. This brings the crystallization reaction near the predicted Tg (750 – 800 K at a heating rate ∼ 102 K/s) for this alloy. Hence, the effect proposed by Köster and Meinhardt may well be responsible to the nanostructural formation in the rapidly annealed Fe-B alloys.

The effect of both nonmagnetic and ferromagnetic additives on the magnetic properties after ultra-rapid annealing was investigated for Fe87B13. In Fig. 4 we show the change in Js as a function of M content (x) for nc-Fe87-xB13Mx (M = Ni, Co, Cu and Nb) alloys prepared by URA. It is clear that Nb has the most detrimental effect on Js followed by Cu whereas Co addition is effective in enhancing the already high Js to above 2 T. Although the Js values is slightly lowered by a minor addition of Ni, Js ≥ 1.9 T is maintained up to 2 at% Ni. In Table II we list the magnetic core properties of typical nc-Fe-B binary and nc-Fe87-xB13Mx (M = Ni, Co and Cu) alloys prepared by URA. The properties of commercial Si steels34 are also included for comparison. The coercivity values of the binary alloys are 6 to 8 A/m while their Js is around 1.9 T. The coercivity of the binary Fe87B13 alloy is suppressed to 3.5 – 3.8 A/m by additions of the late transition metals with a slight loss of Js. Both Cu and Ni have been found to widen the temperature interval between the primary and secondary crystallization reactions (ΔTx)4 in amorphous Fe87B13. A large ΔTx is a natural requirement for attaining the full metastable equilibrium between the primary bcc-Fe and the residual amorphous phases where the softest nanostructure is usually obtained. Thus, this effect can be one of the reasons for the additional magnetic softening induced by these additives. Although the magnetic softness is affected by an addition of 17.4 at% Co, the Hc value remains as low as 9.3 A/m. In our earlier study on nc-(Fe0.8Co0.2)90Zr7B3, it has been demonstrated that the coercivity is reduced from 23.3 A/m to 9.1 A/m by suppressing Ku through a rotating magnetic field during annealing.18 The Hc value of nc-Fe69.6B13Co17.4 is comparable to this Ku suppressed nc-(Fe0.8Co0.2)90Zr7B3 alloy even though no field was applied externally during URA. This suggests that URA could be effective in lowering the influence of annealing-induced Ku, while the mechanism of this remains open. The combination of high Js between 1.9 to 2 T and low Hc between 4 and 10 A/m is truly unique. Moreover, the core losses of our Fe-B based nanocrystalline alloys are an order of magnitude smaller than those of Fe-3wt%Si, demonstrating the effectiveness of the ultra-rapid annealing in our recent work.

FIG. 4.

Saturation magnetic polarization of nanocrystalline Fe87-xB13Mx (M = Ni, Co, Cu and Nb) alloys prepared by ultra-rapid annealing.

FIG. 4.

Saturation magnetic polarization of nanocrystalline Fe87-xB13Mx (M = Ni, Co, Cu and Nb) alloys prepared by ultra-rapid annealing.

Close modal
TABLE II.

Magnetic properties of newly developed Fe-B and Fe-B based nanocrystalline alloys.

JsσsHcλsDensityThicknessW15/50W10/400
Alloy(T)(emu/g)(A/m)(ppm)(g/cc)(µm)(W/kg)(W/kg)
Fe87B13 1.92 200.5 6.4 13 ± 2 7.62 13 0.25 1.27 
Fe86B14 1.89 198.2 7.5 7.59 12 0.38 1.87 
Fe85B13Ni2 1.90 198.4 3.8 16 ± 2 7.62 13 0.23 1.30 
Fe69.6B13Co17.4 2.02 208.8 9.3 7.68 11 0.51 2.62 
Fe86B13Cu1 1.89 197.1 3.5 14 ± 2 7.63 12 0.19 1.06 
Fe-3wt%Si 2.00 208.1 46 7.8a,b 7.65a 350 2.99 20.6 
Fe-6.5wt%Si 1.80a 0.1a,b 7.49a 100a 5.7a 
JsσsHcλsDensityThicknessW15/50W10/400
Alloy(T)(emu/g)(A/m)(ppm)(g/cc)(µm)(W/kg)(W/kg)
Fe87B13 1.92 200.5 6.4 13 ± 2 7.62 13 0.25 1.27 
Fe86B14 1.89 198.2 7.5 7.59 12 0.38 1.87 
Fe85B13Ni2 1.90 198.4 3.8 16 ± 2 7.62 13 0.23 1.30 
Fe69.6B13Co17.4 2.02 208.8 9.3 7.68 11 0.51 2.62 
Fe86B13Cu1 1.89 197.1 3.5 14 ± 2 7.63 12 0.19 1.06 
Fe-3wt%Si 2.00 208.1 46 7.8a,b 7.65a 350 2.99 20.6 
Fe-6.5wt%Si 1.80a 0.1a,b 7.49a 100a 5.7a 
a

From Ref. 34.

b

Magnetostriction at 400 Hz and 1 T.

In Fig. 5 we show the elemental maps of Fe, B, Ni and Cu for nanocrystalline Fe83.5B13Ni3Cu0.5 prepared by ultra-rapid annealing at 758 K for 3 s. The elemental maps were obtained by atom probe tomography on an Ametec LEAP4000XSi. The maps show Fe enriched regions with a size of about 10 to 20 nm where B is depleted, reflecting the typical partitioning behaviour of solute atoms between the crystalline and the residual amorphous phases during primary crystallization.27 The B atoms rejected from the Fe grains are confirmed to be enriched in the intergranular region where the residual amorphous phase resides. The distribution of Ni atoms basically follows that of Fe atoms since the solubility of Ni in bcc-Fe is above the nominal Ni content. The distribution of Cu atoms also follows this trend and the well-known Cu clusters6 seem to be absent. Ohnuma et al.12 investigated the Cu clustering behaviour in Fe78.8-xCoxNb2.6Si9B9Cu0.6 (x = 5 to 60) alloys and have found that the onset of Cu clustering shifts to a higher temperature when Co content is increased and it eventually exceeds the crystallization onset for x > 20. They discussed this behaviour based on thermodynamics and the delayed clustering reaction was attributed to the reduced chemical driving force for the cluster formation. The absence of Cu clusters in nc-Fe83.5B13Ni3Cu0.5 suggests that the thermodynamic driving force for the Cu cluster formation is rather small presumably because of the relatively low nominal content of Cu in the sample.

FIG. 5.

Elemental maps of Fe, B, Ni and Cu for nanocrystalline Fe83.5B13Ni3Cu0.5 obtained by atom probe tomography.

FIG. 5.

Elemental maps of Fe, B, Ni and Cu for nanocrystalline Fe83.5B13Ni3Cu0.5 obtained by atom probe tomography.

Close modal

In Fig. 6 we show the relationship between the mean grain size (D) and the coercivity (Hc) for Fe-B binary and Fe87-xB13Mx (M = Co, Ni and Cu) nanocrystalline alloys prepared by annealing at a range of heating rates (from 1.7 to 9.2 x 103 K/s). Over-annealed samples containing magnetically hard compounds were carefully excluded from the plots. The D dependence of the coercivity is well understood under the framework of Herzer’s random anisotropy model (RAM)3,15 where D6 and D3 scaling behaviours have been predicted for the coercivity governed by the domain wall displacement. Needless to say, the D6 dependence from Herzer’s original RAM should be applicable strictly for the case where the total anisotropy energy (<K>) is approximated by the random magnetocrystalline anisotropy (<K1>), i.e. <K> ≈ β<K1> where β is a factor to convert K1 to the fluctuation amplitude of the anisotropy energy which also includes a statistical correction for the random averaging process; Herzer’s numerical calculation has shown β ≈ 0.4 for a cubic case.35 Contrarily, when <K> is governed by extrinsic effects (Ku), the random averaging process of K1 is affected because the exchange length (Lex) is capped by Ku and the number of grains involved in the averaging process is limited. The alternative D3 dependence is due to this capping effect on Lex by a large coherent Ku. The analytical solution of the total anisotropy energy in such a case has been shown elsewhere36 and <K> under the limiting condition Ku >> β<K1> is approximated by3,15

(2)

where vcr is the volume fraction of the crystalline phase. If Ku is coherent over the length scale well above the wall width, the wall coercivity becomes unaffected by Ku. Thus, Hc is governed by the 2ndD3 term of this equation which determines the fluctuation amplitude of the wall potential energy. It has been shown that the changeover from the D6 to D3 dependence occurs when β<K1> is reduced to approximately a half of Ku in the sample.37 In the Fe-B based nanocrystalline alloys in Fig. 6, this occurs at Hc ≈ 20 A/m. This coercivity value corresponds to a β<K1> value of 40 to 80 J/m3 if a coherent rotation mode in an assembly of randomly-oriented easy axes is adopted. Thus, the changeover point suggests that a coherent Ku in the order of 100 J/m3 is inherent in the nanocrystalline Fe-B based alloys. This is consistent with the typical Ku value24 induced by field annealing in Si-free bcc-Fe based nanocrystalline alloys. Consequently, the magnetic softening effect induced by the grain refinement upon ultra-rapid annealing is well understood by the exchange averaging effect of K1.

FIG. 6.

Grain size dependence of the coercivity for nanocrystalline Fe-B and Fe-B-M (M = Ni, Cu) alloys prepared by ultra-rapid annealing.

FIG. 6.

Grain size dependence of the coercivity for nanocrystalline Fe-B and Fe-B-M (M = Ni, Cu) alloys prepared by ultra-rapid annealing.

Close modal

In summary, we have found that small grain sizes well below the natural exchange length can be obtained in simple Fe-B based systems including Fe87B13 and Fe86B14 binary alloys with an exceptionally high mass fraction (up to 97.2 wt. %) of Fe when ultra-rapid annealing is employed. This results in magnetically soft nanostructures with a high Js above 1.9 T and a small coercivity (Hc) between 3.8 and 6.4 A/m. A higher Js of 2.0 T with Hc = 9.3 A/m is also obtained by Co addition to nc-Fe87B13. These saturation magnetization values are truly comparable to that of Si steels while the core losses are an order of magnitude smaller than those of the Fe-3wt%Si steel. Ultra-rapid annealing is effective in suppressing the amount of nonmagnetic additives in nanocrystalline soft magnetic alloys and thereby enhancing the saturation magnetization while maintaining the magnetic softness.

We are grateful to the Program Committee of the 2019 MMM-Intermag Conference for giving us the opportunity to present this invited paper. We are also thankful to the Australian Research Council for its financial support.

1.
Y.
Yoshizawa
,
S.
Oguma
, and
K.
Yamauchi
,
J. Appl. Phys.
64
,
6044
(
1988
).
2.
G.
Herzer
,
IEEE Trans. Magn.
26
,
1397
(
1990
).
3.
G.
Herzer
,
Acta Mater.
67
,
718
(
2013
).
4.
K.
Suzuki
,
R.
Parsons
,
B.
Zang
,
K.
Onodera
,
H.
Kishimoto
, and
A.
Kato
,
Appl. Phys. Lett.
110
,
012407
(
2017
).
5.
B.
Zang
,
R.
Parsons
,
K.
Onodera
,
H.
Kishimoto
,
A.
Kato
,
A.
Liu
, and
K.
Suzuki
,
Scrpta Mater.
132
,
68
(
2017
).
6.
K.
Hono
and
M.
Ohnuma
,
Magnetic Nanostructures
(
American Sci. Pub.
,
2002
), p.
327
.
7.
M. A.
Willard
and
M.
Daniil
,
Handbook of Magnetic Materials
, Vol. 21 (
Elsevier
,
2013
), p.
173
.
9.
Y.
Yoshizawa
and
K.
Yamauchi
,
J. Magn. Soc. Jpn.
,
13
,
231
(
1989
);
Y.
Yoshizawa
and
K.
Yamauchi
,
Mater. Trans. JIM
31
,
307
(
1990
).
10.
K.
Suzuki
,
A.
Makino
,
A.
Inoue
, and
T.
Masumoto
,
J. Appl. Phys.
70
,
6232
(
1991
).
11.
M.
Ohnuma
,
D. H.
Ping
,
T.
Abe
,
H.
Onodera
,
K.
Hono
, and
Y.
Yoshizawa
,
J. Appl. Phys.
93
,
9186
(
2003
).
12.
U.
Köster
,
U.
Schünemann
,
M.
Biank-Bewersdorff
,
S.
Brauer
,
M.
Sutton
, and
G. B.
Stephenson
,
Mater. Sci. Eng. A
133
,
611
(
1991
).
13.
M.
Ohta
and
Y.
Yoshizawa
,
Jpn. J. Appl. Phys.
46
,
L477
(
2007
);
M.
Ohta
and
Y.
Yoshizawa
,
Appl. Phys. Lett.
91
,
062517
(
2007
).
14.
A.
Makino
,
H.
Men
,
T.
Kubota
,
K.
Yubuta
, and
A.
Inoue
,
IEEE Trans. Magn.
45
,
4302
(
2009
).
15.
G.
Herzer
,
Handbook of Magnetism and Advanced Magnetic Materials
, Volume 4: Novel Materials (
John Wiley & Sons
,
2007
), p.
1882
.
16.
K.
Suzuki
,
J. M.
Cadogan
,
V.
Sahajwalla
,
A.
Inoue
, and
T.
Masumoto
,
J. Appl. Phys.
79
,
5149
(
1996
).
17.
A.
Urata
,
M.
Yamaki
,
K.
Satake
,
H.
Matsumoto
, and
A.
Makino
,
J. Appl. Phys.
113
,
17A311
(
2013
).
18.
K.
Suzuki
,
N.
Ito
,
J. S.
Garitaonandia
, and
J. D.
Cashion
,
J. Appl. Phys.
99
,
08F114
(
2006
).
19.
M.
Müller
,
H.
Grahl
,
N.
Mattern
,
U.
Kühn
, and
B.
Schnell
,
J. Magn. Magn. Mater.
160
,
284
(
1996
).
20.
F.
Johnson
,
H.
Garmestani
,
S. Y.
Chu
,
M. E.
McHenry
, and
D. E.
Laughlin
,
IEEE Trans. Magn.
40
,
2697
(
2004
).
21.
M.
Kuhnt
,
M.
Marsilius
,
T.
Strache
,
C.
Polak
, and
G.
Herzer
,
Scrpta Mater.
130
,
46
(
2017
).
22.
I.
Škorvánek
,
P.
Švec
,
J.
Marcin
,
J.
Kováč
,
T.
Krenický
, and
M.
Deanko
,
Phys. Stat. Sol. (a)
196
,
217
(
2003
).
23.
M. E.
McHenry
,
M. A.
Willard
, and
D. E.
Laughlin
,
Prog. in Mater. Sci.
44
,
291
(
1999
).
24.
N.
Ito
,
K.
Suzuki
,
J. S.
Garitaonandia
, and
J. D.
Cashion
,
J. Appl. Phys.
105
,
07A321
(
2009
).
25.
R.
Parsons
,
J. S.
Garitaonandia
,
T.
Yanai
,
K.
Onodera
,
H.
Kishimoto
,
A.
Kato
, and
K.
Suzuki
,
J. Alloys Compd.
695
,
3156
(
2017
).
26.
S.
Jafari
,
A.
Beitollahi
,
B. E.
Yekta
,
T.
Ohkubo
,
V.
Budinsky
,
M.
Marsilius
,
G.
Herzer
, and
K.
Hono
,
J. Alloys Compd.
674
,
136
(
2016
).
27.
U.
Köster
and
U.
Herold
, in
Glassy Metals I. Topics in Applied Physics
, Eds. by
H. J.
Guntherodt
and
H.
Beck
(
Springer Verlag
,
Berlin
1981
), p.
225
.
28.
R.
Parsons
,
B.
Zang
,
K.
Onodera
,
H.
Kishimoto
,
T.
Shoji
,
A.
Kato
, and
K.
Suzuki
,
J. Phys. D: Appl. Phys.
51
,
415001
(
2018
).
29.
K.
Suzuki
,
A.
Makino
,
A.
Inoue
, and
T.
Masumoto
,
Sci. Rep. RITU. A
39
,
133
(
1994
).
30.
Z. Q.
Jin
and
J. P.
Liu
,
J. Phys. D: Appl. Phys.
39
,
R227
(
2006
).
31.

Given the typical enthalpy change associated with crystallization (∼ 10 kJ/mol) in Fe-based amorphous alloys, the precursor ribbons can be overheated by few 100 K when the crystallization reaction takes place instantaneously. This overheating triggers the secondary crystallization reaction where magnetically-hard compounds form.

32.
K.
Pradeep
,
G.
Herzer
,
P.
Choi
, and
D.
Raabe
,
Acta Mater.
68
,
295
(
2014
).
33.
U.
Köster
and
J.
Meinhardt
,
Mater. Sci. Eng. A
178
,
271
(
1994
).
34.
JEF Steel Cat. No. F1E-002-02: Electrical Steel Sheets for High-frequency Application (
JEF Steel
,
Tokyo
,
2014
).
35.
G.
Herzer
,
Properties and Applications of Nanocrystalline Alloys from Amorphous Precursors
(
Springer
,
2005
), p.
15
.
36.
K.
Suzuki
,
N.
Ito
,
S.
Saranu
,
U.
Herr
,
A.
Michels
, and
J. S.
Garitaonandia
,
J. Appl. Phys.
103
,
07E730
(
2008
).
37.
K.
Suzuki
,
N.
Ito
,
J. S.
Garitaonandia
,
J. D.
Cashion
, and
G.
Herzer
,
J. Non-Cryst. Solids
354
,
5089
(
2008
).