SNOEK'S LIMIT AND THE RELAXATION TIME IN

Bangladesh Journal of Physics, 16, 1-10, 2014

SNOEK’S LIMIT AND THE RELAXATION TIME IN HIGH-FREQUENCY PERMEABILITY OF POLYCRYSTALLINE Al SUBSTITUTED NiCuZn SPINEL FERRITES WITH VARIOUS SINTERING TIME M. BELAL HOSSEN* AND A. K. M. AKTHER HOSSAIN1 Department of Physics, Chittagong University of Engineering and Technology, Bangladesh 1 Department of Physics, Bangladesh University of Engineering and Technology, Bangladesh Received on 21.04.2014, Accepted for Publication on 14.08.2014 ABSTRACT Various nominal compositions of Al substituted NiCuZn polycrystalline spinel ferrites were prepared by the solid state reaction technique. The complex initial permeability spectra of each composition were measured at room temperature. The frequency dependence complex initial permeability decreases with Al content. However, the natural resonance frequency shifted up as the Al content increased. Additionally, it was found that the product of the real part of complex initial permeability and the natural resonance frequency is proportional to the Al content, irrespective of the sintering time of spinel ferrite. These relationships correspond to Snoek’s limitation rule. The variation of complex initial permeability for Al substituted NiCuZn ferrites can be presented as a form of semi-circle and the relaxation phenomena were explained with various shapes of the plots. The results suggest that polycrystalline ferrites having large resonance frequency are suitable for high-frequency applications.

Keywords: NiCuZnAl ferrites, sintering time, complex initial permeability, relaxation time 1.

INTRODUCTION

Ferrites are still the advanced ceramic material in high and very-high-frequency applications. Especially, the polycrystalline form of ferrites has been extensively used in many electronic devices because of its high permeability in the radio frequency region and high electrical resistivity, mechanical hardness, and chemical stability [1, 2]. The complex initial permeability ( i ) spectra of polycrystalline ferrites that exhibit Snoek’s limit can be tailored by substitution *

[2,3] or addition [4] and also by controlling the sintering temperature and time which ultimately changed the physical properties such as density, microstructure related parameter like grain size, grain boundary, porosity, and intra or intergranular pores [3]. Ni-Cu–Zn ferrite is a pertinent magnetic material due to its high electrical resistivity, relatively high initial permeability and low cost [5]. The real part of complex initial permeability (  i ) decreases with frequency and the /

imaginary part of complex initial permeability (  i ) exhibits broad peak, which is related with //

the relaxation phenomena. As the frequency of excitation increases, the substance reaches a point beyond which the spins cannot fully respond to the excitation [6]. The magnetization no longer moves in phase with the excitation and losses occur. The  i decreases with increasing the /

*Corresponding Author: E-mail: [email protected]

2

M. BELAL HOSSEN AND A. K. M. AKTHER HOSSAIN

 i// goes

frequency and

through a broad resonance. The phase difference between the applied

field and magnetization of the ferrite occurs due to damping phenomena. If there is no damping in magnetization process,  i is zero for all frequencies except at the resonance frequency, and then //

 i//

becomes infinitely large [7, 8]. The broadening of the  i curves at higher frequencies due to //

the fact that the alternating measuring field possess a component parallel to the domain walls and perpendicular to the magnetization [7]. Magnetic relaxations appear as a decrease of increasing frequency, while



// i

 i/

with

has a maximum near the resonance frequency (fres). In

characterization of frequency dependence of spinel type ferrimagnetic substances, the dispersion phenomena due to relaxation can be observed at some frequency range, and this is related with the ferrite composition and their initial permeability [9]. Therefore it is important to investigate the variation of complex initial permeability ( i ) with frequency for high frequency applications. In *

this study, polycrystalline spinel ferrites with various compositions and sintering time (T ) have t

been synthesized via the usual solid state reaction technique. The frequency dispersion of

i*

for

various polycrystalline ferrites and Tt are discussed, and the corresponding Snoek’s limit is obtained. The Cole-Cole plots for Al substituted NiCuZn ferrites were presented to describe its relaxation process. The relaxation process is characterized by the magnitude of initial permeability in the semicircle curve of complex permeability. The purpose of the present work is to investigate the frequency dependence of i for various Al substituted NiCuZn ferrites at *

various

 2.

/ i

Tt

and

especially

to

discuss

its

relaxation

phenomena

with

respect

to

versus  curves. // i

EXPERIMENTAL

Various Ni0.27Cu0.10Zn0.63AlxFe2-xO4 with nominal chemical compositions x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.12, and 0.16 were prepared by the standard solid-state reaction technique. High purity powders of NiO (99.9%), CuO (99.9%), ZnO (99.9%), Al2O3 (99.9%) and Fe2O3 (99.9%) were used as raw materials. Stoichiometric amounts of required powders were mixed thoroughly in both dry and acetone media. The mixed powders were calcined in air at 900 oC for 5h. The fine calcined powders were mixed with an organic binder (poly vinyl alcohol), and compressed into toroid-shaped samples. All samples were sintered in air for 1 h, 5 h, 9h, 13 h and 16 h at 1200 oC. The temperature ramp for calcination and sintering were 10oC/min for heating, and 5oC/min for cooling. The surface of the samples were polished well to be smooth and parallel as well as to remove any oxides layer formed during the process of sintering, using fine sand paper. The  i and  i of the i were calculated using the following relations: /

//

*

 i//   i/ tan  , where Ls is the self-inductance of the sample core and

 i/  Ls L0 and L0   o N 2 S d is

derived geometrically, where L0 is the inductance of the winding coil without the sample core, N 

is the number of turns of the coil (N = 4), h is the thickness, d is the mean diameter and S is the area of cross section of the toroidal sample. For these measurements an applied voltage of 0.5 V was used with a low inductive coil.

SNOEK’S LIMIT AND THE RELAXATION TIME 3.

3

RESULTS AND DISCUSSION

The Al substituted NiCuZn ferrite compositions in this study were prepared with a common guide lines, and then classified as the following categories [9]: (i) The substitution of Al in NiCuZn ferrites were sintered at optimum temperature, (ii) permeability depends on Al content and Tt, (iii) the substitution of Al is effective to increase the f res as well as depends on Tt and (iv) from the view point of Snoek’s limitation rule, which polycrystalline ferrites are the most suitable for high frequency device applications. For these Al substituted NiCuZn ferrites, the following characterizations are reported here as the experimental results which enables us to describe Snoek’s limits and the relaxation phenomena from frequency dependence of complex initial permeability. Fig. 1(a-d) shows complex initial permeability ( i ) of all the samples as a function of frequency. *

The i is given by i = *

*

 i/

+ i  i , where //

 i/

and

 i//

are the real and imaginary parts of

i*

 i/ describes the stored energy expressing the component of magnetic induction // (B) in phase with the alternating magnetic field (H). The  i describes the dissipation of energy / expressing the component of B 90o out of phase with the H. From Fig. 1, it is seen that the  i respectively. The

remains almost constant until the frequency is raised to a certain value and then drops to very low values at higher frequencies. The  i gradually increases with the frequency and become //

 i/ rapidly decreases. This feature is well known as the // curves for  i of Fig. 1, with increasing Al substitution a

maximum at a certain frequency, where ferrimagnetic resonance [10]. In the

peak is observed at a higher frequency range. This means that the high-frequency loss decreases with increasing Al content. At low frequencies, a ferrite inductor is a low loss constant selfinductor where

 i/

is highest and the core is mostly inductive, rejecting the electromagnetic

interference signal to the source. At high frequencies where the  i parameter becomes more //

significant, the inductors show high impedance and become resistive and dissipate interfering signals rather than reflecting these to the source [11]. The resonance frequency (fres) peaks are the results of the absorption of energy due to matching of the oscillation frequency of the magnetic dipoles and the applied frequency. At the resonance, maximum energy is transferred from the applied field to the lattice resulting in the rapid increase in the magnetic loss (tanδ).

 i/ for all the samples sintered at 1200oC at typical frequencies are shown in Fig. 2. / It is observed from Fig. 2 that  i increases with increasing sintering time (Tt) from 1 h to 9 h and / / for 9 h, 13 h, 16 h of T t, there is no remarkable changed in  i . This increase of  i with increasing The values of

Tt is attributed to the contribution of domain wall motion, which becomes more significant as the sintered density and grain size of the ferrite increases with increasing T t. Generally, a higher initial permeability is achieved through the control of both the composition and microstructure which depends on the sintering conditions.

4


(a)

400

1600 1200

x=0.00 x=0.02 x=0.04 x=0.06 x=0.08 x=0.12 x=0.16

1h

800

200

i



Real part of complex initial permeability,  

5

6

10

10

7

8

10 104

10

5

10

6

10

7

10

8

10

0



0 4 10 1600

(b)

400

9h 1200

200

800 400 0 4 10

(c)

5

10

6

10

7

8

10 104

10

5

10

6

10

7

10

8

Imaginary part of complex initial permeability,   i

400

0

10

400

1600

13 h 1200 800

200

400 0 4 10 1600

(d)

5

10

6

10

7

8

10

10 104

5

10

6

10

7

10

8

10

0 400

16 h 1200 800

200

400 0 4 10

Fig. 1.

5

10

6

7

8

10 104

10 10 Frequency (Hz)

5

10

6

7

10 10 Frequency (Hz)

8

0

10

Real (  i ) and imaginary (  i ) part of complex initial permeability ( i ) for /

//

*

Ni0.27Cu0.10Zn0.63AlxFe2-xO4 sintered at 1200oC for (a) 1 h, (b) 9 h, (c) 13 h and (d) 16 h respectively.

SNOEK’S LIMIT AND THE RELAXATION TIME

5



900 1h 5h 9h 13 h 16 h



at 1 MHz

600

300 (a)

0

Real part of complex initial permeability,   i



Real part of complex initial permeability,   i

Although pores and grain boundary would obstruct the movement of domain wall, the fewer amounts of pores and grain boundary could be obtained at higher sintering temperature and leads to easy movement of domain walls and high initial permeability. We believe that the reason behind this phenomenon may be due to the formation of trapped pores within the grains and/or grain boundaries. If these pores act as domain wall pinning factor, the domain wall movement would be obstructed. It is clear that, if pores can be suppressed or located at the grain boundaries, the permeability may increase with grain size [3].

0.00

0.04

0.08 0.12 Al content (x)

0.16

400



300

at 10 MHz

200 (b)

100

0.00

0.04 0.08 0.12 Al content (x)

0.16

Fig. 2. Variation of the real part of complex initial permeability (  i ) with Al content (x) for the /

Ni

0.27

Cu

0.10

Zn

0.63

Al Fe O ferrites at different sintering time (T ), at two selected frequencies (a) x

2-x

4

t

1 MHz and (b) 10 MHz.

Resonance frequency, fres (Hz)

24.0M

1h 5h 9h 13 h 16 h

16.0M

8.0M

0.0

0.00

0.04 0.08 0.12 Al content (x)

0.16

Fig. 3. The variation of resonance frequency (f ) with Al content for Ni res

ferrites at various sintering time (T ). t

0.27

Cu

0.10

Zn

0.63

Al Fe O x

2-x

4

6


Fig. 3 shows the variation of resonance frequency (fres) for Ni0.27Cu0.10Zn0.63AlxFe2-xO4 ferrites

with various sintering time (Tt). The fres were determined from the maximum of  i . It is //

observed from Fig. 3 that fres increases with increasing Al and with increasing Tt, fres decreases up to x = 0.08 and above x = 0.08 it increases. The effect of Tt on fres tuned little bit among 9 h, 13 h and 16 h. It is also observed from Fig. 2 and Fig. 3 that the higher the permeability of the samples, the lower the frequency of the onset of ferrimagnetic resonance. Similar results were observed for the samples Ni-Zn, Mg-Zn, Ni-Cu-Zn by Nakamura [2], Mg-Cu-Zn by Haque et al. [3], WO3 substituted NiCuZn by Zhong et al. [12] and Li-Ni-Mg by Hossain et al. [13].

7.50G

2.50G

0.04 0.08 0.12 Al content (x)

2.50G

5.00G 2.50G

0.00

0.04 0.08 0.12 Al content (x)

10.00G

Snoek's product (Hz)

2.50G

0.08 0.12 Al content (x)

5.00G 2.50G

0.00

0.04 0.08 0.12 Al content (x) 1h 9h 16 h



5.00G

0.16

0.16

(d) Tt=13 h

10.00G

7.50G

0.04

0.04 0.08 0.12 Al content (x)

7.50G

0.00

0.16

(e) Tt=16 h

0.00

0.00

10.00G

7.50G

0.00

5.00G

0.16

(c) Tt=9 h

0.00

(b) Tt=5 h

7.50G

0.00

0.00

10.00G Snoek's product (Hz)

1 kHz 100kHz 10 MHz

5.00G

0.00


100 Hz 10kHz 1 MHz


10.00G (a) Tt=1 h



10.00G

(f) at 1 MHz

7.50G

0.16 5h 13 h

5.00G 2.50G 0.00

0.00

0.04 0.08 0.12 Al content (x)

Fig. 4. The variation of Snoek’s product with Al content for Ni

0.27

Cu

0.10

Zn

0.63

0.16

Al Fe O ferrites at x

2-x

4

various sintering time (T ): (a) 1 h, (b) 5 h, (c) 9 h, (d) 13 h, (e) 16 h and (f) 1 MHz, respectively. t


7

The permeability values and hence the resonance frequency depend on the amount and type of dopant ions and the sintering conditions, which is in agreement with the reported results [14,15]. The onset of the resonance frequency determines the upper limit of the operational frequency of any device. This is in conformity with Snoek’s relation in which Snoek found a relation between fres (where maximum losses take place) and

 i/

as:

 i/ fres

= constant [16]. Fig. 4 shows the

Snoek’s product for various T t at different selected frequencies. It is observed that at all T t and selected the Snoek’s product increases with increasing Al content. The product of frequency and permeability remains almost constant. This indicates that lower the permeability values, the higher the frequencies at which resonance phenomenon occurs. Thus, an effective limit of product of frequency and permeability is established. So that high frequency and high permeability are mutually incompatible. Thus Snoek’s product provides a limitation on the permeability spectrum in spinel ferrite [7, 16]. Fig. 5 is the Cole-Cole plot for the curves of

i*

in Fig. 1. The Cole-Cole plots of

 i// versus  i/

show some semicircle (its tendency) shaped curves which means the relaxation dispersion. But there are some differences in the shape of curves comparing to the normalized curve of i [7]. *

The NiCuZn ferrites and other spinel ferrites in various applications show relaxation phenomena as increasing the frequency owing to the damping in magnetization process. Fig. 5 describes the relation between the magnitude of i and relaxation of Ni0.27Cu0.10Zn0.63AlxFe2-xO4 by introducing *

the Cole-Cole plot of the

i* .

The Cole-Cole plot with increasing Al substitution shows a

decrease in size of ellipsoidal curve as shown Fig. 5, which gives the narrower peak of

i* with

increasing Al contents. This provides another method of representation to identify the relaxation phenomena for various ferrites. From Fig. 5(a) for T t = 1 h the curves for smaller semi-circles than the higher Tt due to the comparatively smaller i . Fig. 5(b) shows the variation of *

 i// of Ni0.27Cu0.10Zn0.63AlxFe2-xO4 ferrites sintered at 1200oC for 5 h. The i*

 i/ with

increases for all the

o

compositions with increasing T t. For ferrite sintered at 1200 C, the real part of complex initial permeability (  i ), which is about 1400 in the low-frequency region, begins to decrease at about /

1 MHz. The imaginary part of complex initial permeability (  i ) has a maximum of about 800 at //

around 2 MHz. This feature is attributed to the natural resonance of spin rotation and the vibrational resonance of magnetic domain walls. The difference in magnitude of  i indicates the /

variation of Tt as shown in the various Cole-Cole plots of Fig. 5. It is shown that the fres of Tt = 5 h becomes lower than that of T t = 1 h. Due to the increase in

i*

for Tt = 5 h semi-circles so

formed becomes larger than that of T t = 1 h. For higher Tt i.e. in Fig. 5(c), Fig. 5(d) and Fig. 5(e), there is no remarkable changed in i . As Al content increases, the peak width of *

 i// versus

 i/ curves become narrower and a sharp changed of the maximum of  i// at higher frequencies is observed. The resonance frequency (fres) of Al substituted NiCuZn ferrites becomes higher than that of pure NiCuZn ferrites as shown in Fig. 5. This improvement is attributed to domain wall stabilization and reduces the high frequency losses [9].

8


400

0

0

300

i

(a) 1 h

200

200

600





0

900

i

400

(b) 5 h



x=0.00 x=0.02 x=0.04 x=0.06 x=0.08 x=0.12 x=0.16

i





400

0

300



i

400

600

900

600

900

(d) 13 h

i

i





(c) 9 h 200

200

0

0

0

300

600





i

900

0

300





i

400

i



(e) 16 h 200

0

0

300

600





900

i

o

Fig. 5. Cole-Cole plots of Ni

0.27

Cu

0.10

Zn

0.63

Al Fe O ferrites sintered at 1200 C for (a) 1 h, (b) 5

h, (c) 9 h, (d) 13 h and (e) 16 h, respectively.

x

2-x

4


9

Relaxation time (s)

48.00n 1h 5h 9h 13 h 16 h

32.00n

16.00n

0.00

400

800 



1200

1600

Fig. 6. Real part of complex initial permeability (  i ) versus relaxation time (τ) plots for /

o

Ni

0.27

Cu

0.10

Zn

0.63

Al Fe O ferrites sintered at 1200 C at different sintering time. x

2-x

4

Fig. 6 shows the relation between

 i/

and relaxation time (τ) which is calculated from the relation

τ = (1/2πfres) for the Al substituted NiCuZn ferrites at various Tt. It is found that τ is nearly proportional to the  i . This means that the magnitude of  i is crucial to classify the relaxation /

/

process in application of Al substituted NiCuZn at high frequencies. 4.

CONCLUSIONS

The complex initial permeability spectra of Ni0.27Cu0.10Zn0.63AlxFe2-xO4 polycrystalline spinel ferrites were measured at various sintering time. The natural resonance frequency fres shifts toward higher frequency as the Al content x increases. The product of

 i/

and fres corresponds to

Snoek’s limitation value, and it increases with Al content. The ferrimagnetic resonance frequency shifted to 9.81 GHz range (x = 0.02) from 9.17 GHz (x = 0.00), but the real part of permeability decreases from 1329 to 1092 with increasing Al content. Therefore, in high-frequency devices, the polycrystalline ferrites having large resonance frequency (fres) show good performance stability, since they have low permeability in the low-frequency region, but high permeability in the high-frequency region. ACKNOWLEDGEMENTS The present study was supported by CASR, Bangladesh University of Engineering and Technology (BUET). REFERENCES [1] [2] [3] [4]

J. Lee, Y. K. Hong, W. Lee, G. S. Abo, J. Park, R. Syslo, W. M. Seong, S. H. Park and W. K. Ahn, J. Appl. Phys. 111, pp 07A516 (2012). T. Nakamura, J. Appl. Phys. 81, pp 348 (2000). M. M. Haque, M. Huq and M. A. Hakim, J. Magn. Magn. Mater. 320, pp 2792 (2008). M. Yan, J. Hu, W. Luo and W. Y. Zhang, J. Magn. Magn. Mater. 303, pp 249 (2006).

10


[5]

M. P. Reddy, G. Balakrishnaiah, W. Madhuri, M. V. Ramana, N. R. Reddy, K. V. S. Kumar, V. R. K. Murthy and R. R. Reddy, J. Phys. Chem. Sol. 71, pp 1373 (2010). G. G. Bush, J. Appl. Phys. 63, pp 3765 (1988). J. Smit and H. M. J. Wijn, Ferrites (Netherlands: Eindhoven) pp 78 (1959). S. Chikazumi, Physics of Magnetism (New York: John Wiley & Sons) pp 321 (1964). J. H. Nam and J. H. Oh, J. Magnetics, 1, pp 37 (1996). F. G. Brockman, P. H. Dowling and W. G. Steneck, Phys. Rev. 77, pp 85 (1950). E. C. Snelling, Soft Ferrites, Properties and Application (London: Butterworth) (1988). H. Zhong, H. W. Zhang, H. Zhou and L. J. Jia, J. Magn. Magn. Mater. 300, pp 445 (2006). A. K. M Aktther Hossain, M. M. A. Chowdhury, B. Vilquin and H. Tanaka, Mater. Chem. Phys. 133, pp 141 (2012). T. Nakamura, J. Magn. Magn. Mater. 168, pp 285 (1996). O. F. Caltun, L. Spinu, A. I. Stancu, D. Thung and W. Zhou, J. Magn. Magn. Mater. 242– 245, pp 160 (2002). J. L. Snoek, Physica 4, pp 207 (1948).

[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]