Effect of Annealing Temperature on the Complex Permeability of (Fe0.95Co0.05)73.5Cu1Nb3Si13.5B9 Nanocrystalline Amorphous Ribbon

Over the past several decades, amorphous and most recently, research interest in nanocrystalline soft magnetic alloys has dramatically increased. Soft magnetic materials face demanding requirements for high performance electronic and power distribution systems. With the reduction of size into nanometer range, the materials exhibit interesting properties including physical, chemical, magnetic and electrical properties compare to conventional coarse grained counterparts. Soft magnetic nanostructured materials have a number of potential technological applications [1-11]. Nanocrystalline soft magnetic materials were first reported in 1988 by Yoshizawa et al. [12] through controlled crystallization of Fe-Si-B amorphous alloys with the addition of copper (Cu) and niobium (Nb). The development of nanocrystalline Fe-Si-B-Nb-Cu alloys, commercially known as FINEMET, established a new approach to develop soft magnetic materials. The nanocrystalline state is achieved by subsequent heat treatment from their as cast amorphous precursor above the primary crystallization temperature. Excellent soft magnetic properties can be found in nanocrystalline materials of Fe-Si-B amorphous ribbons containing Cu and Nb. The addition of Cu and Nb results in the formation of an ultra-fine grain structure. The main purpose of this research is to determine empirically the optimum annealing temperature, corresponding to maximum permeability, constancy of permeability and maximum frequency range over which the sample can be used as a soft magnetic material.


INTRODUCTION
Over the past several decades, amorphous and most recently, research interest in nanocrystalline soft magnetic alloys has dramatically increased. Soft magnetic materials face demanding requirements for high performance electronic and power distribution systems. With the reduction of size into nanometer range, the materials exhibit interesting properties including physical, chemical, magnetic and electrical properties compare to conventional coarse grained counterparts. Soft magnetic nanostructured materials have a number of potential technological applications [1][2][3][4][5][6][7][8][9][10][11] . Nanocrystalline soft magnetic materials were first reported in 1988 by Yoshizawa et al. [12] through controlled crystallization of Fe-Si-B amorphous alloys with the addition of copper (Cu) and niobium (Nb). The development of nanocrystalline Fe-Si-B-Nb-Cu alloys, commercially known as FINEMET, established a new approach to develop soft magnetic materials. The nanocrystalline state is achieved by subsequent heat treatment from their as cast amorphous precursor above the primary crystallization temperature. Excellent soft magnetic properties can be found in nanocrystalline materials of Fe-Si-B amorphous ribbons containing Cu and Nb. The addition of Cu and Nb results in the formation of an ultra-fine grain structure. The main purpose of this research is to determine empirically the optimum annealing temperature, corresponding to maximum permeability, constancy of permeability and maximum frequency range over which the sample can be used as a soft magnetic material.

MATERIALS AND METHODS
The amorphous ribbon with a composition (Fe 0.95 Co 0.05 ) 73.5 Cu 1 Nb 3 Si 13.5 B 9 was prepared from high purity Fe (99.9%), Co (99.9%), Nb (99.9%), Si (99.9%), Cu (99.9%) and B (99.9%). The ribbons were produced in an arc furnace on a water-cooled copper hearth by a single roller melt-spinning technique under an atmosphere of pure Ar at the Centre of Materials Science, National University of Hanoi, Vietnam. The wheel velocity was about 34 m/s. The ribbons were annealed in a vacuum heat treatment furnace at 550, 600, 625, 650, 675, 700, 725 and 750°C respectively for constant time 30 minutes and then cooled down to the room temperature. Amorphousity of the ribbon and nanocrystalline structure has been observed by XRD (Philips (PW 3040) X 'Pert PRO XRD) with Cu-Kα radiation. Lattice parameter (a 0 ) were calculated using equations λ θ = sin 2d radiation. Grain size (D g ) of all annealed samples of the alloy composition has been determined using Debye-Scherrer method [13] . Si contents were calculated using the equation: where X is at.% Si in the nanograins. The

ABSTRACT
FINEMET-like amorphous ribbon of composition (Fe 0.95 Co 0.05 ) 73.5 Cu 1 N b 3 Si 13.5 B 9 was prepared by rapid quenching method in an Argon (Ar) atmosphere. The alloy has been annealed in a controlled way in the temperature range of 550 to 750°C for 30 minutes. Nanocrystalline state was evaluated by X-ray diffraction (XRD). In the range of annealing temperature (Ta), the grain size has been found in the range of 9-26 nm. Frequency dependence of permeability of amorphous and nanocrystalline toroid shaped samples have been measured. The low frequency initial permeability for the optimum annealed samples has been found to 5.8 × 10 3 and the highest value of quality factor is found for the sample annealed at 550°C; which also indicates the best heat treatment temperature. , where m is the weight of the ribbon, d and ρ are the mean diameter and density of the sample. The imaginary part of complex permeability (µ'') was determined using the formula µ''=µ' × D.

RESULTS AND DISCUSSION
XRD XRD spectra of as-cast and annealed at 550 to 750°C for 30 minutes have been presented in Figure 1. One broad peak at 2θ=45° for the as-cast sample confirms the amorphous state. XRD pattern clearly indicates the formation of bcc α-FeCo(Si) phase at T a =550°C or above with the appearance of (110), (200) and (211) fundamental diffraction peaks. With the increase of T a , (110) peak becomes sharper which means the grains are growing bigger. From the Figure 1 it is also observed that just before (110) peak, another diffraction line with small peak at 2θ≈44° appeared for the samples annealed at 700 to 750°C. This diffraction peak has been matched with Fe 23 B 6 phase (boride phase). This is because, with increasing T a the diffusion of Si into α-FeCo space lattice increases and hence increases the formation of α-FeCo(Si) nanograin. At higher T a , Si diffuses out of nanograins due to recrystallization corresponding to formation of boride phase which is consistent with the result of other FINEMET's [14] . Absence of boride phase in the XRD spectra is possibly due to very small volume fraction of Fe 23 B 6 . Figure 2 shows the variation of D g of α-FeCo(Si) phase with T a . Enhancement of D g with T a complies with the reported result [15] . All the results of θ, d-values, FWHM, a 0 , D g and Si-content from XRD analysis are listed in Table 1.  Annealing temperature (°C) Figure 2. Variation of grain size with annealing temperature of (Fe0.95Co0.05)73.5Cu1Nb3Si13.5B9 alloy. Complex Permeability Figure 3 shows the frequency dependence of the μ / for as-cast and the samples annealed at temperature 550 to 700°C for a constant annealing time of 30 minutes. From the figure it is observed that the low frequency value of μ / increases with the increase of T a and attains the maximum value at 550°C. A sharp increase of μ / is found due to crystallization of α-FeCo(Si) phase. When the T a is higher than 550°C, μ / decreases rapidly. At higher T a , the decrease of μ / may be attributed to the stress developed in the amorphous matrix by growing crystallites. The newly grown crystallites serve as pinning centers at which domain walls are pinned and creates obstructions for their mobility resulting in a decrease in μ / .The evolution of boride phases and the nonmagnetic fcc phases including Cu clusters leads to the increase of magnetocrystalline anisotropy to a high value, as a result of which magnetic hardening takes place [16] . The general characteristic of the curve is that μ / remains fairly constant up to some critical frequency characterized by the onset of resonance connected with the loss component. At critical frequencies, μ/ drops rapidly. The frequency dependent imaginary part of the complex initial permeability (μ // ) annealed at different temperatures at constant annealing time 30 minutes are shown in Figure 4. These results are quite complimentary to the results of the real part of the complex permeability of samples. After critical frequencies the μ // increases with increasing frequency. The high value of μ // for the samples corresponds to high loss factor as shown in Figure 3. The origin of the loss factor can be attributed to various domain effects [17] , which include non-uniform and non-repetitive domain wall motion, domain wall bowing, localized variation of flux densities and nucleation and annihilation of domain walls.

Relative Quality Factor
The frequency dependence of relative quality factor (μ / Q) of the sample annealed at different temperatures is shown in Figure 5. From the figure it is observed that the μ / Q initially rises with increasing frequency and reaches a peak value. Beyond the peak value, the μ / Q is found to decrease. It is also found that the μ / Q increases with the increase of T a up to 550°C and with further increase of T a the μ / Q decreases. At high frequency, the flux penetration becomes low, as a result the loss is mainly controlled by interaction between the grains of the alloy but at very low frequency the loss is controlled by hysteresis losses. The decrease of μ / Q with increasing T a after 550°C is due to increase of D g for the precipitation of Fe borides [16] . The precipitation of very small percent of particles increases the high frequency losses. The highest value of μ / Q is found for the sample annealed at 550°C, which also indicates the best heat treatment temperature. From all curves, it is noted that the higher values of the μ / Q in general lie within the frequency range of 10 kHz to 100 kHz. Thus the frequency range for application area might be chosen.