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Microstructure and permeability studies of mixed Li-Cd ferrites
Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
Microstructure and permeability studies of mixed Li-Cd ferrites S.S. Bellad*, S.C. Watawe, B.K. Chougule Materials science lab, Department of Physics, Shivaji University, Kolhapur 416 004, India Received 4 August 1998; received in revised form 9 November 1998
Abstract Some microstructure-related properties of Li Cd Fe O ferrites have been reported. SEM micrographs \V V \V show an interesting grain growth mechanism. Grain size increases up to x"0.3 and then decreases very slowly beyond it. Saturation magnetisation also follows the same trend. But initial permeability shows continuous increase up to x"0.6 and is explained on the basis of non-magnetic grain-boundary model. The variation of initial permeability and AC susceptibility with temperature shows normal ferrimagnetic behaviour. The Curie temperature decreases continuously with x, which is attributed to the decrease in the strength of the A—B interaction. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microstructure; Scanning Electron Microscopy; Grain boundary; Initial permeability; Magnetic materials
1. Introduction Lithium ferrite and mixed-lithium-based ferrites are equally important materials as compared to Mn—Zn and Mg—Zn ferrites in the field of microwave technology. Squareness of the hysteresis loop along with superior high-temperature performance due to their high Curie temperature have made them very promising candidates for microwave devices than the latter ones [1]. Several investigations on properties of mixed Li—Cd ferrites such as structural, electrical conductivity, thermoelectric power, elastic properties and dielectric behaviour have been reported in literature [1—5]. However, no such reports have been found which relates the microstructure, effect of grain boundary on permeability
* Corresponding author. Fax: 0091 231 656133.
and suitability of models such as the domain wall bulging model, and the non-magnetic grain boundary model to explain the variation of permeability with composition in substituted lithium ferrites. As such an attempt has been made to discuss the above facts in this communication.
2. Experimental The ferrites of the composition Li Cd Fe O (with x"0, 0.1, 0.2, 0.3, \V V \V 0.4, 0.5, 0.6 and 0.7) were prepared by the standard double-sintering ceramic method using analytical reagent (AR) grade oxides as starting materials. The pellets (1 cm. diameter and 0.5 cm thick) and torroids (1.5 cm OD, 1 cm ID and 0.35 cm thick) were prepared by dry pressing under pressure of 6 t/cm using powder presintered at 750°C for 10 h.
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 1 0 7 3 - 7
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S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
The final sintering of the samples was carried out at 1000°C for 24 h. and then allowed to furnace cool at the rate +80°C/h. The completion of the solid state reaction was confirmed by X-ray diffraction patterns taken on powder samples using a PHILIPS PW 1710 X-ray diffractometer with Cu-K ? radiation (j"1.5418 As ). All the samples show single phase formation of the spinel structure. The scanning electron micrographs were taken using a Cambridge Stereoscan — 250 MK — III machine. Magnetisation measurement was done by using a high field hysteresis loop tracer at a constant magnetic field of 3 kOe whereas, initial permeability was measured using an LCR-Q meter (APLAB - 4912) at a fixed frequency of 1 kHz. The low-field AC susceptibility measurement was done by using a double coil apparatus operating at 263 Hz in an rms field of 7 Oe.
3. Results and discussion Fig. 1 shows the variation of lattice parameter ‘a’ obtained from X-ray data with the content of cad-
mium. A linear increase in lattice parameter with content of cadmium indicates that the present system obeys the Vegard’s law. An increase in lattice parameter with an increase in the content of cadmium can be attributed to the ionic size differences since the unit cell has to expand when substituted by ions with large ionic size [4]. Fig. 2 shows the microstructure of finally sintered samples at different compositions. The SEM micrographs were taken on smooth surfaces of the samples obtained on polishing by soft polish paper. The upper surfaces of the grains seem to be just like the etched surface in the samples with x"0.1, 0.3 and 0.5, but it is not observed in the lithium ferrite sample (x"0). The samples with x"0 shows the solid grains whereas, in other samples small particles are packed in grains as it can be seen at the grain boundary around the particles. The particle size found to increase continuously with increasing cadmium content. Small pores were also seen at the corners of the grains for the samples with x"0, 0.1, 0.3, whereas they were found to decrease for x'0.3 as it can be observed in the SEM micrograph of the sample with x"0.5. The variation of grain size
Fig. 1. Variation of lattice parameter ‘a’ with cadmium content.
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
59
Fig. 2. SEM micrographs of the samples with x"0, 0.1, 0.3, 0.5.
with content of cadmium (x) is shown in Fig. 3. The average grain diameter was carefully measured by the line intercept method using SEM data. The grain size increases up to x"0.3 and then decreases very slowly with further increase in the Cd content. The grain growth behaviour is compromised between the driving force for grain-boundary movement and retarding force by pores [6]. During the sintering process, a force is generated due to thermal energy, which drives the grain boundaries to grow over pores thereby decreasing the pore volume and making the material dense. When the driving force of the grain-boundary for each grain is homogeneous, the sintered body attains uniform grain size distribution and unless homogeneous, abnormal grain growth occurs. Further, the strength of the driving force depends upon diffusivity of individual grains, sintering temperature and porosity. Therefore, the smaller values of grain size
for x(0.3 could be due to more porosity since the pores neutralize the driving force. It is also confirmed by Visser et al. [7] that the non-magnetic particles and trace amounts of impurities like calcium mostly segregate at grain boundaries forming a non-magnetic grain boundary. They have developed a non-magnetic grain boundary model to explain the initial permeability [8,9]. In the present samples also, it can be seen from the SEM micrographs that the thickness of the grain boundary seems to be large as compared to the small sized magnetic particles for x"0, 0.1 samples. Then for x'0.1, the thickness of the non-magnetic grain boundary is found to decrease with an increase in grain size. Therefore, we conclude that for x(0.3, the effective grain size could be less than the apparent one which we have plotted in Fig. 3 as a function of Cd content. Further, the effect of this non-magnetic grain-boundary on magnetic properties of samples with x'0.3 could be small because
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Fig. 4. Variation of Saturation magnetisation M with cadmium content. Fig. 3. Variation of grain size with cadmium content.
of large grain size. As such it is assumed that magnetic ordering can be broken up easily at nonmagnetic grain boundaries and then there exists only a short range magnetic exchange interaction. Then we will correlate all the above effects to the variation of permeability with composition and temperature. Fig. 4 shows the variation of saturation magnetisation M with Cadmium content. The increase in magnetisation with cadmium content up to x"0.3 is due to dilution of magnetisation of the A-sublattice by non-magnetic Cd> ions, which can be explained on the basis of Neel’s two sublattice model [4]. The reason for the decrease of magnetisation beyond x"0.3 is that beyond this limit, the magnetisation of A-sublattice is so dilute that the A—B lattice interaction remains no longer stronger and thereby B—B sublattice interaction becomes strong, which in turn disturbs the parallel arrangement of spin magnetic moments on the B-site and hence canting of spin occurs. Almost all Zn> and Cd> substituted ferrites have shown a similar type of canting behaviour above certain limit of their contents [4,5]. The variation in the initial permeability with cadmium content in Fig. 5 shows that it increases continuously up to x"0.6 and above this the samples showed paramagnetic nature.
Fig. 5. Variation of initial permeability with cadmium content.
The contribution to initial permeability comes from spin rotations and domain wall motion and the contribution of the latter is considered as dominant. The initial permeability of ferrite polycrystals is known to depend more or less linearly on the grain size, for which an explanation has been given by Globus and co-workers using their wall bulging model [10]. However, Smith [11] pointed out that the spherical wall bulging model will again give wall permeability only. In a technologically
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
important class of Mn—Zn ferrites, it is shown that they possess a large contribution of rotational permeability [12]. This is especially found to be true in case of Mn—Zn ferrites with grain size under 4 lm for which a neutron depolarisation study revealed that these grains contain no domain walls [13]. Although, in the high permeability ferrites even with multidomain structure and grain size above 5 lm, the large contribution to such high values is found mainly to come from domain wall moment. Therefore, in the present samples the grain size is above 5 lm and thus we assume that the dominant contribution to permeability is from domain wall motion only. The contribution from domain wall motion is given by 3pMd , (k !1) " U c
(1)
where M is the saturation magnetisation, d is the
mean grain diameter and c is the magnetic domain wall energy proportional to the global anisotropy constant. In the present case, the initial permeability further increases beyond x"0.3 instead of decreasing since both M and d decrease beyond this
limit (Fig. 4). Then the remaining term in the above relation is ‘c’ only and this indicates that the domain wall energy plays an important role above x"0.3. The higher the grain boundary, higher will be the domain wall energy which in turn leads to higher values of anisotropy constant. It is reported that the thickness of the non-magnetic grain boundary affects the value of k [7]. The samples of the same composition with nearly the same grain sizes are found to possess different values of initial permeability because of the difference in non-magnetic grain boundary thickness. As observed in SEM micrographs and described above, it seems that the thickness of the non-magnetic grain boundary definitely has decreased above x"0.3. In order to see the effect of non-magnetic grain boundary on initial permeability in the samples for x'0.3, the thickness of the non-magnetic grain boundaries are estimated by combining the theory of Globus and the non-magnetic grain boundary model as reported in [7]. Visser et al. correlated the permeability and grain boundary by
61
the relation D D " #d, k k
(2)
where D is the mean grain diameter, k is the effective permeability, k is the intrinsic permeabil ity of the grains and d is the thickness of the non-magnetic grain boundary. From the variation of initial permeability with temperature (Fig. 7), the (D/k ) values were esti mated for the samples with x"0.4, 0.5 and 0.6 at different temperatures, up to the point where k drops off. Here D is the mean grain diameter of the corresponding samples. Then the (D/k ) values are plotted against the corresponding temperatures as shown in Fig. 6. It is seen that the (D/k ) values decrease with the increase in temper ature and are in a decreasing order for samples with x"0.4, 0.5 and 0.6. The asymptotic limits of each curve i.e. the lowest value of (D/k ) is considered as the thickness of the non-magnetic grain boundary ‘d’ [7]. The x"0.6 sample possesses lowest values of d. The thickness of the grain boundary also depends on the lattice misfit which involves adjacent grains growing along different crystalline lattice orientations, thus generating large plastic strains at
Fig. 6. Variation of non-magnetic grain boundary with composition for the samples with x"0.4, 0.5 and 0.6.
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the grain boundaries, disrupting there the magnetic ordering and creating non-magnetic regions. Argentina et al. [14] have also considered the role of Fe> ions on k , which can form at elevated firing temperature. Because, even though most of the magnetic ions contribute to the negative values of crystal anisotropy, Fe> and Co> found to contribute to positive crystalline anisotropy and thus enhance permeability. Therefore, if we assume that the increase in initial permeability above x"0.3 is due to the excess formation of Fe> ions, the k —T curves (Fig. 7) do not show any secondary
maximas which could be observed on excess formation of these ions. Further, the electrical resistivity measurements have confirmed that the resistivity values of these samples are in increasing order from x"0.3 which are not presented here. Hence the possibility of excess formation of Fe> ions and their dominant contribution to the permeability is ruled out. Therefore, it can be concluded that, the increase in k above x"0.3 can be attributed to the decrease in thickness of the non-magnetic grain boundary which in turn decreases the domain wall energy and allows the easy moment of the domain walls.
Fig. 7. Variation of initial permeability with temperature.
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
The variation of initial permeability with temperature is shown in Fig. 7. The trend exhibited by all the samples is similar. With increase in temperature, k initially increases gradually and afterwards rapidly. Near T , the Curie temperature of the sam ples, k drops off sharply. The sharp decrease sug gests the single-phase formation of the ferrites. This observation is supported by XRD patterns which do not show any impurity peaks. The increase of k with temperature can be ex plained as follows. The anisotropy constant and saturation magnetisation usually decrease with the increase in temperature, due to thermal agitation which disturbs the alignment of magnetic moments [5]. But, the decrease of anisotropy constant with temperature is much faster than the decrease of M . When the anisotropy constant reaches zero, k at tains its maximum value and then drops off to zero above T . The k —T curves do not show any second
63
ary maximas which occur due to excess formation of Fe> ions thereby indicating the single-phase formation of the samples. The variation of normalised AC-susceptibility with temperature is shown in Fig. 8. It is seen that for the samples with x"0 to 0.3, s remains ! temperature invariant suggesting the presence of multidomain (MD) particles. Thus H and M must be small for these samples. H is also inversely proportional to grain diameter. Whereas for samples with x"0.5 to 0.6, s decreases with increase ! in temperature indicating the presence of superparamagnetic (SP) type of particles. From both the Figs. 5 and 6, it is observed that the Curie temperature at which permeability as well as normalised susceptibility drops off sharply, decreases with increase in the cadmium content. The Curie temperature mainly depends upon the strength of the A—B interaction. The non-magnetic
Fig. 8. Variation of normalised AC susceptibility with temperature.
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Cd> ions continuously decreases the magnetisation of the A-sublattice and for x'0.3, it is so diluted that the A—B interaction remains no longer stronger and B—B interaction becomes stronger and creates canting of spins. The overall effect is that the A—B interaction decreases continuously and hence Curie temperature decreases. 4. Conclusions The decrease of magnetisation above x"0.3 is due to the canting of spin magnetic moments on an octahedral (B) site. The increase in initial permeability above x"0.3 is due to the decrease in non-magnetic grain boundary thickness. The continuous decrease in Curie temperature is due to the dilution of strength of the A—B interaction. Acknowledgements The authors are very thankful to the UGC, New Delhi for providing financial assistance to the research project - F. 10-8/94 (SR - I), dt. 6-6-1995.
References [1] D. Ravinder, J. Appl. Phys. 75 (10) (1994). [2] D. Ravinder, T. Seshagiri Rao, Crystal Res. Technol. 25 (8) (1990) 963. [3] K. Radha, D. Ravinder, Ind. J. Pure Appl. Phys. 33 (1995) 74. [4] S.S. Bellad, R.B. Pujar, B.K. Chougule, Mater. Chem. Phys. 52 (1998) 166. [5] S.S. Bellad, B.K. Chougule, Mater. Res. Bull. 33 (8) (1998) 1165. [6] D.S. Kand, H.S. Kim, B.D. You, J.G. Paik, S.J. Kim, Ferrites: Proc. ICF-6, Japan, 1992, p. 1302. [7] E.G. Visser, M. T. Johnson, P.J. Van Der Zaag, Ferrites: Proc. ICF-6, Japan, 1992, p. 807. [8] M.T. Johnson, E.G. Visser, IEEE Trans. Magn. MAG - 26 (5) (1990) 1987. [9] E.G. Visser, M.T. Johnson, J. Magn. Magn. Mater. 101 (1991) 143. [10] A. Globus, J. Phys. (Suppl.) C1 (1977) 1. [11] J. Smit, Proc. ICF-4, Adv. Ceram. 1 (1986) 16. [12] E.G Visser, J.J. Roelofsma, G.J. M. Aaftnik, Advances in Ferrite Materials, Proc. ICF-5, Bombay, 1989, p. 605. [13] P.J. Van Der Zaag, M.T. Johnson, A. Noordermeer, P.T. Por, M.Th. Rekveldt, J. Magn. Magn. Mater. L1 (1991) 99. [14] G.M. Argentina, P.D. Baba, IEEE Trans. Microwave Theory Technol 22 (1974) 652.
Microstructure and permeability studies of mixed Li-Cd ferrites S.S. Bellad*, S.C. Watawe, B.K. Chougule Materials science lab, Department of Physics, Shivaji University, Kolhapur 416 004, India Received 4 August 1998; received in revised form 9 November 1998
Abstract Some microstructure-related properties of Li Cd Fe O ferrites have been reported. SEM micrographs \V V \V show an interesting grain growth mechanism. Grain size increases up to x"0.3 and then decreases very slowly beyond it. Saturation magnetisation also follows the same trend. But initial permeability shows continuous increase up to x"0.6 and is explained on the basis of non-magnetic grain-boundary model. The variation of initial permeability and AC susceptibility with temperature shows normal ferrimagnetic behaviour. The Curie temperature decreases continuously with x, which is attributed to the decrease in the strength of the A—B interaction. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microstructure; Scanning Electron Microscopy; Grain boundary; Initial permeability; Magnetic materials
1. Introduction Lithium ferrite and mixed-lithium-based ferrites are equally important materials as compared to Mn—Zn and Mg—Zn ferrites in the field of microwave technology. Squareness of the hysteresis loop along with superior high-temperature performance due to their high Curie temperature have made them very promising candidates for microwave devices than the latter ones [1]. Several investigations on properties of mixed Li—Cd ferrites such as structural, electrical conductivity, thermoelectric power, elastic properties and dielectric behaviour have been reported in literature [1—5]. However, no such reports have been found which relates the microstructure, effect of grain boundary on permeability
* Corresponding author. Fax: 0091 231 656133.
and suitability of models such as the domain wall bulging model, and the non-magnetic grain boundary model to explain the variation of permeability with composition in substituted lithium ferrites. As such an attempt has been made to discuss the above facts in this communication.
2. Experimental The ferrites of the composition Li Cd Fe O (with x"0, 0.1, 0.2, 0.3, \V V \V 0.4, 0.5, 0.6 and 0.7) were prepared by the standard double-sintering ceramic method using analytical reagent (AR) grade oxides as starting materials. The pellets (1 cm. diameter and 0.5 cm thick) and torroids (1.5 cm OD, 1 cm ID and 0.35 cm thick) were prepared by dry pressing under pressure of 6 t/cm using powder presintered at 750°C for 10 h.
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 1 0 7 3 - 7
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S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
The final sintering of the samples was carried out at 1000°C for 24 h. and then allowed to furnace cool at the rate +80°C/h. The completion of the solid state reaction was confirmed by X-ray diffraction patterns taken on powder samples using a PHILIPS PW 1710 X-ray diffractometer with Cu-K ? radiation (j"1.5418 As ). All the samples show single phase formation of the spinel structure. The scanning electron micrographs were taken using a Cambridge Stereoscan — 250 MK — III machine. Magnetisation measurement was done by using a high field hysteresis loop tracer at a constant magnetic field of 3 kOe whereas, initial permeability was measured using an LCR-Q meter (APLAB - 4912) at a fixed frequency of 1 kHz. The low-field AC susceptibility measurement was done by using a double coil apparatus operating at 263 Hz in an rms field of 7 Oe.
3. Results and discussion Fig. 1 shows the variation of lattice parameter ‘a’ obtained from X-ray data with the content of cad-
mium. A linear increase in lattice parameter with content of cadmium indicates that the present system obeys the Vegard’s law. An increase in lattice parameter with an increase in the content of cadmium can be attributed to the ionic size differences since the unit cell has to expand when substituted by ions with large ionic size [4]. Fig. 2 shows the microstructure of finally sintered samples at different compositions. The SEM micrographs were taken on smooth surfaces of the samples obtained on polishing by soft polish paper. The upper surfaces of the grains seem to be just like the etched surface in the samples with x"0.1, 0.3 and 0.5, but it is not observed in the lithium ferrite sample (x"0). The samples with x"0 shows the solid grains whereas, in other samples small particles are packed in grains as it can be seen at the grain boundary around the particles. The particle size found to increase continuously with increasing cadmium content. Small pores were also seen at the corners of the grains for the samples with x"0, 0.1, 0.3, whereas they were found to decrease for x'0.3 as it can be observed in the SEM micrograph of the sample with x"0.5. The variation of grain size
Fig. 1. Variation of lattice parameter ‘a’ with cadmium content.
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
59
Fig. 2. SEM micrographs of the samples with x"0, 0.1, 0.3, 0.5.
with content of cadmium (x) is shown in Fig. 3. The average grain diameter was carefully measured by the line intercept method using SEM data. The grain size increases up to x"0.3 and then decreases very slowly with further increase in the Cd content. The grain growth behaviour is compromised between the driving force for grain-boundary movement and retarding force by pores [6]. During the sintering process, a force is generated due to thermal energy, which drives the grain boundaries to grow over pores thereby decreasing the pore volume and making the material dense. When the driving force of the grain-boundary for each grain is homogeneous, the sintered body attains uniform grain size distribution and unless homogeneous, abnormal grain growth occurs. Further, the strength of the driving force depends upon diffusivity of individual grains, sintering temperature and porosity. Therefore, the smaller values of grain size
for x(0.3 could be due to more porosity since the pores neutralize the driving force. It is also confirmed by Visser et al. [7] that the non-magnetic particles and trace amounts of impurities like calcium mostly segregate at grain boundaries forming a non-magnetic grain boundary. They have developed a non-magnetic grain boundary model to explain the initial permeability [8,9]. In the present samples also, it can be seen from the SEM micrographs that the thickness of the grain boundary seems to be large as compared to the small sized magnetic particles for x"0, 0.1 samples. Then for x'0.1, the thickness of the non-magnetic grain boundary is found to decrease with an increase in grain size. Therefore, we conclude that for x(0.3, the effective grain size could be less than the apparent one which we have plotted in Fig. 3 as a function of Cd content. Further, the effect of this non-magnetic grain-boundary on magnetic properties of samples with x'0.3 could be small because
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Fig. 4. Variation of Saturation magnetisation M with cadmium content. Fig. 3. Variation of grain size with cadmium content.
of large grain size. As such it is assumed that magnetic ordering can be broken up easily at nonmagnetic grain boundaries and then there exists only a short range magnetic exchange interaction. Then we will correlate all the above effects to the variation of permeability with composition and temperature. Fig. 4 shows the variation of saturation magnetisation M with Cadmium content. The increase in magnetisation with cadmium content up to x"0.3 is due to dilution of magnetisation of the A-sublattice by non-magnetic Cd> ions, which can be explained on the basis of Neel’s two sublattice model [4]. The reason for the decrease of magnetisation beyond x"0.3 is that beyond this limit, the magnetisation of A-sublattice is so dilute that the A—B lattice interaction remains no longer stronger and thereby B—B sublattice interaction becomes strong, which in turn disturbs the parallel arrangement of spin magnetic moments on the B-site and hence canting of spin occurs. Almost all Zn> and Cd> substituted ferrites have shown a similar type of canting behaviour above certain limit of their contents [4,5]. The variation in the initial permeability with cadmium content in Fig. 5 shows that it increases continuously up to x"0.6 and above this the samples showed paramagnetic nature.
Fig. 5. Variation of initial permeability with cadmium content.
The contribution to initial permeability comes from spin rotations and domain wall motion and the contribution of the latter is considered as dominant. The initial permeability of ferrite polycrystals is known to depend more or less linearly on the grain size, for which an explanation has been given by Globus and co-workers using their wall bulging model [10]. However, Smith [11] pointed out that the spherical wall bulging model will again give wall permeability only. In a technologically
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
important class of Mn—Zn ferrites, it is shown that they possess a large contribution of rotational permeability [12]. This is especially found to be true in case of Mn—Zn ferrites with grain size under 4 lm for which a neutron depolarisation study revealed that these grains contain no domain walls [13]. Although, in the high permeability ferrites even with multidomain structure and grain size above 5 lm, the large contribution to such high values is found mainly to come from domain wall moment. Therefore, in the present samples the grain size is above 5 lm and thus we assume that the dominant contribution to permeability is from domain wall motion only. The contribution from domain wall motion is given by 3pMd , (k !1) " U c
(1)
where M is the saturation magnetisation, d is the
mean grain diameter and c is the magnetic domain wall energy proportional to the global anisotropy constant. In the present case, the initial permeability further increases beyond x"0.3 instead of decreasing since both M and d decrease beyond this
limit (Fig. 4). Then the remaining term in the above relation is ‘c’ only and this indicates that the domain wall energy plays an important role above x"0.3. The higher the grain boundary, higher will be the domain wall energy which in turn leads to higher values of anisotropy constant. It is reported that the thickness of the non-magnetic grain boundary affects the value of k [7]. The samples of the same composition with nearly the same grain sizes are found to possess different values of initial permeability because of the difference in non-magnetic grain boundary thickness. As observed in SEM micrographs and described above, it seems that the thickness of the non-magnetic grain boundary definitely has decreased above x"0.3. In order to see the effect of non-magnetic grain boundary on initial permeability in the samples for x'0.3, the thickness of the non-magnetic grain boundaries are estimated by combining the theory of Globus and the non-magnetic grain boundary model as reported in [7]. Visser et al. correlated the permeability and grain boundary by
61
the relation D D " #d, k k
(2)
where D is the mean grain diameter, k is the effective permeability, k is the intrinsic permeabil ity of the grains and d is the thickness of the non-magnetic grain boundary. From the variation of initial permeability with temperature (Fig. 7), the (D/k ) values were esti mated for the samples with x"0.4, 0.5 and 0.6 at different temperatures, up to the point where k drops off. Here D is the mean grain diameter of the corresponding samples. Then the (D/k ) values are plotted against the corresponding temperatures as shown in Fig. 6. It is seen that the (D/k ) values decrease with the increase in temper ature and are in a decreasing order for samples with x"0.4, 0.5 and 0.6. The asymptotic limits of each curve i.e. the lowest value of (D/k ) is considered as the thickness of the non-magnetic grain boundary ‘d’ [7]. The x"0.6 sample possesses lowest values of d. The thickness of the grain boundary also depends on the lattice misfit which involves adjacent grains growing along different crystalline lattice orientations, thus generating large plastic strains at
Fig. 6. Variation of non-magnetic grain boundary with composition for the samples with x"0.4, 0.5 and 0.6.
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S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
the grain boundaries, disrupting there the magnetic ordering and creating non-magnetic regions. Argentina et al. [14] have also considered the role of Fe> ions on k , which can form at elevated firing temperature. Because, even though most of the magnetic ions contribute to the negative values of crystal anisotropy, Fe> and Co> found to contribute to positive crystalline anisotropy and thus enhance permeability. Therefore, if we assume that the increase in initial permeability above x"0.3 is due to the excess formation of Fe> ions, the k —T curves (Fig. 7) do not show any secondary
maximas which could be observed on excess formation of these ions. Further, the electrical resistivity measurements have confirmed that the resistivity values of these samples are in increasing order from x"0.3 which are not presented here. Hence the possibility of excess formation of Fe> ions and their dominant contribution to the permeability is ruled out. Therefore, it can be concluded that, the increase in k above x"0.3 can be attributed to the decrease in thickness of the non-magnetic grain boundary which in turn decreases the domain wall energy and allows the easy moment of the domain walls.
Fig. 7. Variation of initial permeability with temperature.
S.S. Bellad et al. / Journal of Magnetism and Magnetic Materials 195 (1999) 57—64
The variation of initial permeability with temperature is shown in Fig. 7. The trend exhibited by all the samples is similar. With increase in temperature, k initially increases gradually and afterwards rapidly. Near T , the Curie temperature of the sam ples, k drops off sharply. The sharp decrease sug gests the single-phase formation of the ferrites. This observation is supported by XRD patterns which do not show any impurity peaks. The increase of k with temperature can be ex plained as follows. The anisotropy constant and saturation magnetisation usually decrease with the increase in temperature, due to thermal agitation which disturbs the alignment of magnetic moments [5]. But, the decrease of anisotropy constant with temperature is much faster than the decrease of M . When the anisotropy constant reaches zero, k at tains its maximum value and then drops off to zero above T . The k —T curves do not show any second
63
ary maximas which occur due to excess formation of Fe> ions thereby indicating the single-phase formation of the samples. The variation of normalised AC-susceptibility with temperature is shown in Fig. 8. It is seen that for the samples with x"0 to 0.3, s remains ! temperature invariant suggesting the presence of multidomain (MD) particles. Thus H and M must be small for these samples. H is also inversely proportional to grain diameter. Whereas for samples with x"0.5 to 0.6, s decreases with increase ! in temperature indicating the presence of superparamagnetic (SP) type of particles. From both the Figs. 5 and 6, it is observed that the Curie temperature at which permeability as well as normalised susceptibility drops off sharply, decreases with increase in the cadmium content. The Curie temperature mainly depends upon the strength of the A—B interaction. The non-magnetic
Fig. 8. Variation of normalised AC susceptibility with temperature.
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Cd> ions continuously decreases the magnetisation of the A-sublattice and for x'0.3, it is so diluted that the A—B interaction remains no longer stronger and B—B interaction becomes stronger and creates canting of spins. The overall effect is that the A—B interaction decreases continuously and hence Curie temperature decreases. 4. Conclusions The decrease of magnetisation above x"0.3 is due to the canting of spin magnetic moments on an octahedral (B) site. The increase in initial permeability above x"0.3 is due to the decrease in non-magnetic grain boundary thickness. The continuous decrease in Curie temperature is due to the dilution of strength of the A—B interaction. Acknowledgements The authors are very thankful to the UGC, New Delhi for providing financial assistance to the research project - F. 10-8/94 (SR - I), dt. 6-6-1995.
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