Pb substituted SrFe12O19 hexaferrites

Pb substituted SrFe12O19 hexaferrites

Journal of Magnetism and Magnetic Materials 387 (2015) 46–52 Contents lists available at ScienceDirect Journal of Magnetism and Magnetic Materials j...

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Journal of Magnetism and Magnetic Materials 387 (2015) 46–52

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Crystal structure refinement, dielectric and magnetic properties of Ca/ Pb substituted SrFe12O19 hexaferrites Ashima Hooda a, Sujata Sanghi b,n, Ashish Agarwal b, Reetu Dahiya c a

Department of Physics, Deenbandhu Chhotu Ram University of Science and Technology, Murthal 131039, Haryana, India Department of Applied Physics, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India c Department of Physics, Hindu Girls College, Sonepat 131001, Haryana, India b

art ic l e i nf o

a b s t r a c t

Article history: Received 22 January 2015 Received in revised form 11 March 2015 Accepted 25 March 2015 Available online 26 March 2015

SrFe12O19 (SFO), Sr0.5Ca0.5Fe12O19 (SCFO) and Sr0.5Pb0.5Fe12O19 (SPFO) hexaferrites have been synthesized by a conventional solid state reaction technique. Powder X-ray diffraction and Rietveld refinement confirm the presence of M-type hexagonal phase in prepared samples. However in SCFO, secondary phase was also present with main phase. Analysis of Nyquist's plots of SFO hexaferrite revealed the contribution of many electrically active regions corresponding to bulk mechanism, distribution of grain boundaries and electrode processes also. Both conductivity and electric modulus formalisms have been employed to study the relaxation dynamics of charge carriers. A perfect overlapping of the normalized plots of modulus isotherms on a single ‘super curve’ for all the studied temperatures reveals a temperature independence of dynamic processes involved in conduction and for relaxation. In SPFO sample coercivity is reduced effectively but accompanied with increase in magnetization, which is requirement for hexaferrites to be used as magnetic recording media. & 2015 Elsevier B.V. All rights reserved.

Keywords: Hexaferrites Dielectric properties Magnetic properties

1. Introduction M-type strontium hexaferrite (SrFe12O19) was discovered in the 1950s by Philips laboratories [1]. The crystal structure of the hexagonal ferrites is derived from a stacking scheme of closepacked oxygen/strontium layers along the hexagonal c-axis with an ordering sequence of spinel (S) two layer building units (Fe6O8)2 þ and three layer (R) blocks (SrFe6O11)2  . Combination of RS gives the building motif of the M-type SrFe12O19ferrite [2]. This structure belongs to the magnetoplumbite-type structure [3]. Strontium hexaferrites are known to be hard ferrites due to high values of electrical resistivity, saturation magnetization, coercivity, Curie temperature, mechanical hardness and chemical inertness [4]. Due to these properties, strontium hexaferrite have recently attracted much attention for high density magnetic recording and magnetic–optical recording media [5–8]. It has been recognized that it can be used as permanent magnet, plasto-ferrite, in dcmotor for automotive industry, in telecommunication, and as components in microwave devices [9–12]. The electrical and magneto-dielectric properties of hexaferrites may effectively vary in wide ranges by doping with cations that define their use in n

Corresponding author. Fax: þ91 1662 276240. E-mail address: [email protected] (S. Sanghi).

http://dx.doi.org/10.1016/j.jmmm.2015.03.078 0304-8853/& 2015 Elsevier B.V. All rights reserved.

various devices and instruments. These properties are strongly dependent on the electronic configuration, atomic magnetism and site preference of the substituted ions [13]. Strontium hexaferrite has high saturation magnetization of about 69 emu/g due to its high value of anisotropic constant (K ¼ 3.57  106 erg/cm3 at T¼ 300 K) [14]. However their coercivity is also very high (about 6.7 kOe) and it is difficult to use as magnetic recording media. During the past few years it becomes possible to synthesize some new hexaferrites in which coercivity decrease effectively with cations substitution. The substitutions of transition metals, e.g., Zn2 þ , Co2 þ , Mn2 þ , Ni2 þ , Ti4 þ , and Ir4 þ , has been investigated by several researchers [15–17]. Because the properties of SrFe12O19 strongly depend on the size and shape of the particles [18,19], several routes have been used to prepare strontium hexaferrite, including the sol–gel process, solid state reaction method, ball milling, chemical co-precipitation method, etc. [20–22]. With the help of experiments it was found that coercivity reduced effectively but also with magnetization also decrease, which is limit of the use of hexaferrites for magnetic recording media. Here are very few examples in which saturation magnetization can be increased when coercivity decrease [23,24]. Hence, how to decrease coercivity and simultaneously increase saturation magnetization has attracted much attention. In view of above, the objective of present work is to study the structural, dielectric and magnetic properties of prepared SrFe12O19, Sr0.5Ca0.5Fe12O19 and Sr0.5Pb0.5Fe12O19 hexaferrites.

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2. Experimental details Samples SrFe12O19 (SFO), Sr0.5Ca0.5Fe12O19 (SCFO) and Sr0.5Pb0.5Fe12O19 (SPFO) were synthesized by a solid state reaction technique. The starting raw materials used were analytical grade SrCO3, PbCO3, CaCO3, and Fe2O3 of high purity ( Z99.0%). The reagents were mixed in an appropriate stoichiometric ratio. First the mixed oxides were ground using an agate mortar and pestle. Then a presintering process was carried out in an air-furnace at 873 K for 4 h at a ramp of 5 K/min for all the powders. The powders were slowly cooled to room temperature. The grinding process was repeated again for 20 min; afterwards the powders were finally sintered in the air-furnace at 1473 K for 4 h and left to be slowly cooled to room temperature. The sintered ceramics were structurally characterized by using a Rigaku Miniflex-II X-ray diffractometer. The X-ray diffraction patterns were obtained at room temperature. The structural parameters were refined by GSAS and EXPGUI programs. The dielectric properties were measured using an impedance/gain-phase analyzer (Newton's 4th Ltd.). The samples were used in the form of pellets of about 13 mm diameter. The pellets were made at a pressure of 10 t at room temperature. The two surfaces of sample pellets were coated with silver paste as a contact material. The dielectric measurements were carried out in the frequency range 1 kHz to 5 MHz and temperature range 323– 573 K. The magnetic properties were measured by using a vibrating sample magnetometer (Lakeshore VSM 7410) at room temperature with a maximum applied field of 20 kOe.

3. Results and discussion 3.1. XRD analysis X-ray diffraction patterns of all prepared hexaferrites are shown in Fig. 1. The X-ray diffraction corresponding to SFO and SPFO samples showed that only one phase is present; however for the SCFO sample a secondary phase (α-Fe2O3) can be seen at 33.70° (2θ). The diffractions peaks corresponding to main phase presented by samples were identified by JCPDS file number 00043-0002 [25]. The diffraction line corresponding to α-Fe2O3 secondary phase is identified by JCPDS file number 00-072-6227. However, others authors [26,27] utilizing other techniques observed a peak at 33.11° or at 38.74°. 3.2. Rietveld analysis Rietveld refinement data of all prepared hexaferrites are given in Fig. 2(a)–(c), respectively. The refinements were carried out by using GSAS þ EXPGUI software [28,29]. Rietveld refinement requires a structural model that has an approximation for the actual structure. Rietveld refinement of XRD patterns of all the samples was performed by using the space group P63/mmc for hexagonal structure or for main phase while for SCFO sample space group R3c also used for secondary phase. Hence a structural model allows us to reproduce the entire observed peak. The initial Rietveld refinement was performed considering systemic errors in to account as zero-point shift, then unit cell and background parameters were refined. To further improve the fitting, the peak profile parameters, thermal parameters, lattice parameters, scale factors, occupancy and atomic functional positions were refined. The background was corrected using a Chebyschev polynomial of first kind and the diffraction peak profiles were fitted by pseudoVoigt function. A good agreement was obtained between experimental and calculated data. The parameters Rp (profile fitting RValue), Rwp (weighted profile R-Value), and χ2 (goodness-of-fit quality factor) obtained after refinement (Fig. 2) for all the samples

Fig. 1. X-ray diffraction patterns of prepared hexaferrites. þ corresponds to αFe2O3 phase.

are presented in Table 1. The low values of χ2 and profile parameters (Rp, Rwp) suggest that the derived samples are of better quality and refinements of samples are effective. The structural parameters: lattice constants (‘a’, ‘c’) and volume (V) are also given in Table 1. The atomic positions and bond length, bond angles obtained from Rietveld refinement for SFO sample are listed in Tables 2 and 3, respectively. Similar refined atomic positions with small variations were observed for SCFO and SPFO samples. With substitutions, the value of ‘a’ almost remains same but the value of ‘c’ decreases due to difference in ionic radii of Sr2 þ (1.32 Å), Ca2 þ (0.99 Å), and Pb2 þ (1.19 Å). This suggests that the crystal structure becomes more compact with substitution. 3.3. Impedance spectroscopy Fig. 3 shows the impedance Nyquist plots of SFO sample at different temperatures. Nyquist plots commonly represent the experimental data, that is, plots between Im (Z) and Re (Z). These plots are usually semicircles or semicircles arcs as shown in Fig. 3. The analysis of these diagrams provides the important parameters which characterize non-Debye relaxation behavior [30]. Their center of axis depressed below the real axis and intercept on real axis shifts towards origin with increase in temperature. These reveal a non-Debye relaxation behavior with distributed relaxation time. We have known that the ferrites consist of non-homogeneous layered structures. Therefore, the semicircles obtained in this sample may be due to many electric active regions

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Table 2 Atomic positions obtained from Rietveld refinement for SFO sample. Atom

Site

x

y

z

Sr Fe1 Fe2 Fe3 Fe4 Fe5 O1 O2 O3 O4 O5

2d 2a 2b 4f1 4f2 12k 4e 4f 6h 12k 12k

0.6667 0.0000 0.0000 0.3333 0.3333 0.1572 0.0000 0.3333 0.2343 0.1745 0.5181

0.3333 0.0000 0.0000 0.6667 0.6667 0.3145 0.0000 0.6667 0.4687 0.3490 0.0363

0.2500 0.0000 0.2531 0.0271 0.1928  0.1097 0.1515  0.0732 0.2500 0.0615 0.1556

Table 3 Bond lengths, bond angles from Rietveld refinement for SFO sample. Type

Bond length (Å)

Type

Bond length (Å)

Type

Bond angle (deg)

Sr–O Sr–Fe2 Sr–Fe5 Fe1–O4 Fe2–O1 Fe2–O3 Fe3–O2 Fe3–O4

3.0270 3.4020 3.7130 2.2822 2.2824 2.3923 2.2830 1.8260

Fe4–O3 Fe4–O5 Fe5–O1 Fe5–O2 Fe5–O4 Fe5–O5 Fe4–Fe4 Fe5–Fe5

1.6599 2.0730 1.8738 1.9871 2.0345 1.9834 2.7742 2.8662

Fe5–O1–Fe5 Fe3–O2–Fe5 Fe4–O3–Fe4 Fe5–O4–Fe5

95.784 127.163 105.335 86.209

Fig. 2. Rietveld refinement data of prepared hexaferrites.

Table 1 Refined structural parameters of all prepared samples. Sample SFO SCFO SPFO

1 Phase 2 Phase

Fig. 3. The Nyquist plots for SFO hexaferrite at different temperatures.

Space group

Rp

Rwp

χ2

a (Å)

c (Å)

V (Å3)

P63/mmc P63/mmc R3c P63/mmc

2.27 2.37

3.02 3.64

6.57 2.55

2.48

3.56

2.49

5.89 5.89 5.39 5.89

23.17 23.15 11.96 23.16

696.96 696.10 302.10 696.38

corresponding to bulk grains, grain boundaries and also electrode process, etc. The contribution of these regions can be obtained by stimulating the experimental data using equivalent circuit. The fitted Nyquist plots of SFO sample are shown in Fig. 4. The modeled circuit (Fig. 4(a) inset) for the studied sample consists of a

series array of three subcircuits: one represent grain effect while others correspond to the distribution of grain boundaries and electrode processes. Each subcircuit consists of a parallel combination of a resistor and a capacitor, i.e. (Rg, Rgb, Re) and (Cg, Cgb, Ce) be the resistances and capacitances of grains, grain boundaries and electrodes, respectively. The capacitance values can be estimated using the relation ωmaxRC ¼1, where ωmax is the frequency corresponding to maximum value of Z′′ on the semicircle. The resistances are representative of the bulk conductivity of the system; and capacitances are generally associated with the space charge

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Fig. 5. Frequency dependence of real (M′) and imaginary (M′′) parts of electric modulus for SCFO hexaferrite at different temperatures.

appropriately represented by the electric modulus as [31]

M *(ω) = M′(ω) + iM″(ω) =

1⎡ ⎢1 − ε∞ ⎣

∫0



⎛ dφ ⎞ ⎤ ⎟dt ⎥ e−jωt ⎜ − ⎝ dt ⎠ ⎦

(1)

where ε1 is the high-frequency asymptotic value of the real part of the dielectric constant and φ(t) is the stretched exponential function of a material called Kohlrausch–Williams–Watts (KWW) function [32,33] given by

⎡ ⎛ t ⎞ β⎤ φ(t) = φ(0)exp⎢ − ⎜ ⎟ ⎥ ⎣ ⎝τ ⎠ ⎦

Fig. 4. Fitted Nyquist plots with equivalent circuit elements for SFO at (a) 513 K and (b) 573 K.

polarizations and specific processes at ceramic–electrode interfaces. The observed decrease in resistance offered by grains, grain boundaries and electrode processes (Fig. 4 and Table 4) with increase in temperature reveals the reduction of barrier posed to the charge carriers, and hence contributing to an increase in conduction at higher temperatures. 3.4. Electric modulus analysis In the modulus formalism, the electrical relaxation is

(2)

The exponent ‘β’ is a fractional number, giving the extent of non-exponentiality which measures the degree of correlation between ions in ionic transport. A completely uncorrelated motion of mobile ions occurs for β ¼1. Fig. 5 shows the frequency dependence of real (M′) and imaginary (M′′) parts of electric modulus at different temperatures for SCFO sample. It is observed that the real part of electric modulus, M′(ω) shows a dispersion tending to M1 as frequency increased and the imaginary part of electric modulus, M′′(ω) show an asymmetric maximum at frequency fm centered at the dispersion region of M′(ω). It is also evident from Fig. 5 that within the measured frequency window, two relaxation regions appeared about this maximum. The low frequency side of the M′′max represents the range of frequencies in which charge carriers can perform successful hopping from one site to the neighboring site.

Table 4 Equivalent circuit elements (R and C) for the SFO sample at 513 K and 573 K temperature. Temperature (K) 513 573

Rg (kΩ) 23.52 6.40

Cg (mF)

Rgb (kΩ) 4

5.7  10 4.4  10  4

18.67 7.00

Cgb (mF) 3

10  10 9  10  3

Re (kΩ)

Ce (mF)

18.50 6.00

3.1  10  3 8.0  10  4

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Fig. 6. Normalized plot of M′/M1 and M′′/M′′max vs log(f/fmax) at different temperatures for SCFO hexaferrite.

Fig. 8. Frequency dependence of (a) dielectric constant (ε′) and (b) dielectric loss (tan δ) of all the samples at 573 K.

Fig. 7. The complex plot of normalized electric modulus at various temperatures for SCFO hexaferrite.

The high frequency side of the M′′max represents the range of frequencies in which the charge carriers are spatially confined to their potential wells and thus could make localized motion within the well. The region where peak occurs is an indicative of the transition from long range order to short range mobility with increase in frequency. Further, the appearance of peak provides a clear indication of conductivity relaxation [34]. For all prepared hexaferrites, similar types of variation of M′ and M′′ vs frequency

are observed. The normalized plots of modulus isotherm where the frequency axis is scaled by peak frequency fM′′, M′ axis is scaled by M1 and M′′ axis is scaled by M′′max are shown in Fig. 6. A perfect overlapping of all the curves on a single ‘super curve’ for all temperatures reveals a temperature independence of dynamic process involve in conduction and for relaxation. It also supports the temperature independence of the stretched exponential parameter ‘β’. The calculated value of ‘β’ is 0.69 for SCFO sample and it is temperature independent. The complex plots of normalized electric modulus at various temperatures are shown in Fig. 7. On this plot points below the M′′max lie on the arc of semicircle indicates that dc conductivity dominates in this region. The points above M′′max lie on the straight line and follow Jonscher power law (s(ω)¼Aωs, where ‘s’ is an exponent and 0 rs r1) which

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indicates ac conductivity is dominating in this region [35]. 3.5. Dielectric analysis Fig. 8 depicts the frequency dependence of the dielectric constant and tan δ which decreases with increasing frequency for all the prepared hexaferrites. At lower frequency the dielectric dispersion is large and it becomes independent at higher frequency. The variations of tan δ with frequency are qualitatively similar with that of ε0 vs frequency curves. This behaviour is well explained by the Maxwell–Wagner type relaxation [36,37], often occurring in the heterogeneous systems. According to this model, ferrite consists of perfectly conducting grains separated by insulating grain boundaries. Under the influence of an applied field, displacements of charge carriers take place. If the resistances of grain boundaries are large, the charge carriers align themselves at grain boundaries. Thus the surface charges piles up at the interfaces giving rise to interfacial polarization at grain boundaries. This leads to large dielectric constant. According to Koops [38], at low frequency grain boundaries are effective and at high frequency grains are effective. Thus low value of polarization builds up at higher frequency in the material which leads to decrease in the dielectric constant. On the other hand, at low frequencies as high resistance is offered by grains boundaries more energy is required for the motion of charge carriers hence energy loss (tan δ) is also high in this region. But at higher frequencies as low resistance is offered by grains less energy is required by the charge carriers for motion so the energy loss (tan δ) is also low. Fig. 9 shows the frequency dependence of ac conductivity for all the hexaferrites at

Fig. 10. Room-temperature M–H hysteresis loops of prepared samples.

573 K. The frequency dependence of sac can also again be explained with the help of Maxwell–Wagner bi-layer model and Koop's theory [36–38]. The SCFO hexaferrite has highest conductivity among all prepared hexaferrites. The presence of secondary phase in SCFO sample create the internal space charges at phase boundaries that may lead to a significant increase in the concentration of mobile defects and hence corresponds to the high value of sac, and also of ε′ and tan δ. The SPFO hexaferrite has low conductivity than SFO hexaferrite or we can say highly resistive hexaferrite among all prepared hexaferrites. It may be due to the high resistivity of Pb (25  10  8 Ω m at 300 K) as compared to Sr (13  10  8 Ω m at 300 K). A comparison of the structure and dielectric properties of prepared hexaferrites suggests that SPFO hexaferrite has worth attracting results with potential applications useful in microwave devices. 3.6. Magnetic properties

Fig. 9. Frequency dependence of ac conductivity of all the samples at 573 K.

Fig. 10 depicts the room temperature M–H hysteresis loops for all the prepared hexaferrites samples. As given in Table 5 the value of saturation magnetization (Ms) for SFO sample is about 69.25 emu/g at room temperature, which is comparable to theoretically predicted value [14]. Due to non-magnetic α-Fe2O3 pining, the resistance of particles increases in the domain rotation process. Therefore, In BCFO, low value of magnetization is due to presence of a small amount of weak ferromagnetic secondary phase (α-Fe2O3). Hence value of Ms decreased from 69.25 emu/g to

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(DST), Government of India, New Delhi for providing XRD facilities through FIST scheme.

Table 5 Magnetic parameters of prepared samples. Samples

Ms (emu/g)

Hc (kOe)

SFO SCFO SPFO

69.25 50.60 78.36

5.08 4.35 4.94

References

50.60 emu/g. The coercivity (Hc) of both SCFO and SPFO samples is also decreased to 4.35 kOe and 4.95 kOe, respectively, in comparison to SFO sample (5.08 kOe). It may due to the difference of the magnetocrystalline anisotropy for the radii of Sr2 þ , Ca2 þ and Pb2 þ . According to ferromagnetic theory [39], coercivity Hc, for a uniaxial, single domain and non-interaction particle system is related to the magnetocrystalline anisotropy constant (к) as

Hc =

ακ μ 0 Ms

(3)

where α is the orientation coefficient, which denotes the extent of coherent rotation for a non-interaction particle assembly and m0 is permittivity of the free space. According to Eq. (3), the value of Ms in SPFO sample increased due to decrement in value of coercivity. With substitution of Pb in place of Sr, it was found that coercivity reduced effectively but also with magnetization also increase, which is requirement of hexaferrites to use for magnetic recording media. Hence SPFO sample is beneficial for magnetic recording media.

4. Conclusions All samples were successfully prepared and Rietveld refinement revealed a single hexagonal phase with space group P63/ mmc in all the samples, whereas SCFO sample also contains hematite (α-Fe2O3) phase with space group R3c. Nyquist plots of SFO revealed a non-Debye relaxation behavior with distributed relaxation time. The frequency-dependent dielectric data were analyzed in the framework of the conductivity and modulus formalisms. The modulus spectra have been analyzed in terms of non-exponential decay function for SCFO, giving a value of β 0.69 for all the temperatures. The SPFO hexaferrite has low conductivity (sac), low ε′ and low tan δ among all prepared hexaferrites which shows that this hexaferrite may be used in microwave devices. SPFO hexaferrite is also beneficial for magnetic recording media due to its high saturation magnetization and low coercivity.

Acknowledgment Authors are thankful to Department of Science and Technology

[1] J.J. Went, G.W. Ratheneau, E.W. Gorter, G.W. VanDosterhout, Philips Tech. Rev. 13 (1951) 194. [2] H. Kojima, in: E.P. Wohlfarth (Ed.), Ferromagnetic Material, Vol. 3, NorthHolland Publishing Company, Amsterdam, 1982, pp. 305–391. [3] A. Goldman, Modern Ferrite Technology, Springer Science, Inc., USA (2006) 63. [4] D.E. Speliotis, IEEE Trans. Magn. 25 (1989) 4048. [5] Q.Q. Fang, W. Zhong, Y.W. Du, J. Appl. Phys. 85 (1999) 1667. [6] X.X. Liu, J.M. Bai, F.L. Wei, H. Xu, Z. Yang, J. Appl. Phys. 87 (2000) 2503. [7] A. Ishikawa, K. Tanahashi, M. Futamoto, J. Appl. Phys. 87 (2000) 5588. [8] C. Surrig, K.A. Hempet, D. Bonnenberg, Appl. Phys. Lett. 74 (1999) 2513. [9] J.M.D. Coey, J. Alloy. Compd. 326 (2001) 2. [10] A. Morisako, T. Naka, K. Ito, A. Takizawa, M. Matsumoto, K.Y. Hong, J. Magn. Magn. Mater. 242 (2002) 304. [11] M.J. Iqbal, M.N. Ashiq, P.H. Gomez, J.M. Munoz, J. Magn. Magn. Mater. 320 (2008) 881. [12] Z. Jin, W. Tang, J. Zhang, H. Lin, Y. Du, J. Magn. Magn. Mater. 182 (1998) 231. [13] R.G. Simmons, IEEE Trans. Magn. 25 (1989) 405. [14] B.T. Shirk, W.R. Buessem, J. Appl. Phys. 40 (1969) 1294. [15] S.Y. An, I.B. Shim, C.S. Kim, J. Appl. Phys. 91 (2002) 8465. [16] Q.Q. Fang, Y.M. Liu, P. Yin, X.G. Li, J. Magn. Magn. Mater. 234 (2001) 366. [17] J.M. Bai, X.X. Liu, H. Xu, F.L. Wei, Z. Yang, Acta Phys. Sin. 49 (2000) 1595. [18] A. Ataie, S.H. Manesh, J. Eur. Ceram. Soc. 21 (2001) 1951. [19] D.H. Chen, Y.Y. Chen, Mater. Res. Bull. 37 (2002) 801. [20] A. Morisako Ali Ghasemi, J. Magn. Magn. Mater. 320 (2008) 1167. [21] S.V. Ketov, Yu. D. Yagodkin, A.L. Lebed, Y.V. Chernopyatova, K. Khlopkov, J. Magn. Magn. Mater. 300 (2006) 479. [22] V.V. Pankov, M. Pernet, P. Germi, P. Mollard, J. Magn. Magn. Mater. 120 (1993) 69. [23] Q.Q. Fang, H.W. Bao, D.M. Fang, J.Z. Wang, J. Magn. Magn. Mater. 278 (2004) 122. [24] Q.Q. Fang, H. Cheng, K. Huang, J. Wang, R. Li, Y. Jiao, J. Magn. Magn. Mater. 294 (2005) 281. [25] Joint Committee On Powder Diffraction Standard (JCPDS), International Center for Diffraction Data, (JCPDS 00-043-0002). [26] R. Martinez-Garcia, E.R. Ruiz, E.E. Rams, Mater. Lett. 50 (2001) 183. [27] M. Sivakumar, A. Gedanken, W. Zhong, Y.W. Du, D. Bhattacharya, Y. Yeshurun, I. Felner, J. Magn. Magn. Mater. 286 (2004) 95. [28] A.C. Larson, R.B. Von Dreele, LANL Report LAUR 86, 2000 [29] B.H. Toby, J. Appl. Crystallogr. 34 (2001) 210. [30] J.R. Macdonald, E. Barsoukov, Impedance Spectroscopy: Theory, Experiment and Applications, Second edition,. Wiley-Interscience, New York, 2005. [31] G.G. Belmonte, F. Henn, J. Bisquert, Chem. Phys. 330 (2006) 113. [32] R. Kohlrausch, Pogg. Ann. Phys. Chem. 91 (1854) 179. [33] G. Williams, D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. [34] B.V.R. Chowdari, R. Goppalkrishnnan, Solid State Ion. 23 (1987) 225. [35] L.F. Maia, A.C.M. Rodgrigues, Solid State Ion. 168 (2004) 87. [36] J.C. Maxwell, Electricity and Magnetism, Vol. 1, Oxford University Press, Oxford, 1929, Section 328. [37] K.W. Wagner, Ann. Phys. 40 (1913) 817. [38] C.G. Koops, Phys. Rev. 83 (1951) 121. [39] R.J. Parker, Ferrites: Proceedings of ICF-3, 1980