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Influence of Al2O3 addition on microstructure, defects level and magnetic properties of LiTiZn ferrite ceramics
Ceramics International 44 (2018) 20749–20754
Contents lists available at ScienceDirect
Ceramics International journal homepage: www.elsevier.com/locate/ceramint
Influence of Al2O3 addition on microstructure, defects level and magnetic properties of LiTiZn ferrite ceramics
T
⁎
A.V. Malyshev , A.B. Petrova, A.P. Surzhikov Tomsk Polytechnic University, 634050 Tomsk, Russia
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Sintering B. Defects C. Magnetic properties D. Ferrites
In the present work, the results of the influence of diamagnetic additives on the defects level of ferrite ceramics, its microstructure and magnetic properties are presented. A method based on a mathematical analysis of the experimental temperature dependences of the initial permeability was used for estimation of the defects level in the samples. Model samples containing a controlled amount of the diamagnetic additive Al2O3 served to test the possibility of monitoring this method of nonmagnetic phases of ferrite ceramics. It was shown that with an increase in the concentration of the Al2O3 additive in the range of (0–0.5) wt%, a significant increase in the defects level was observed almost 6-fold. The data from SEM micrographs showed that the addition of Al2O3 affects the type of grains of ferrite ceramics, but does not affect their grain size. Grains are highly agglomerated and show large grain size dispersion and also pore. Obtained data were compared to hysteresis loop parameters. It is shown that with an increase in the concentration of the Al2O3 addition, there is a regular decrease in the residual induction and an increase in the coercive force. However, such changes in hysteresis loop parameters are small in comparison to defects level. Investigations of the true physical broadening of the diffraction reflections were performed for the same model samples in order to compare the change in the defects level to the direct X-ray diffraction measurements of micro deformations. The defects level as a characteristic of the elastic stress of a ferrite ceramics is proposed. This assumption follows from a linear relationship between the defects level and the width of the diffraction reflections. The consistency of the obtained results made it possible to evaluate the high efficiency and sensitivity of the method for defects level estimating.
1. Introduction The properties of ferrite materials which used in practice can differ significantly from the properties predicted on the basis of crystallochemical composition. This is mainly due to the presence of various crystal structure defects in the material. As a rule, the defectiveness of materials occurs at the stage of their manufacture, and therefore the development of technological regimes for the production of ferrites should provide the possibility of controlling not only the crystallochemical composition, but also the defects level of the material. In general, defects level of ferrite ceramics includes intragranular crystal lattice defects and interface defects of grain boundaries. It is known that in the production of standard ceramic technology, ferrite ceramics often have side phase inclusions and various defects [1]. Such defects, together with intragranular porosity, cause the deterioration of the electromagnetic properties of ferrites. It is known also that such properties are determined by the dynamics of the magnetization reversal processes and the magnetic state of the material, which in turn depend
⁎
not only on its chemical composition but also on the content and distribution of defects in it. Thus, the accumulation of information regarding the relationship of defects with the basic magnetic properties of ferrites is important in the manufacture of products from this material [2]. The processes of magnetization of ferrites are determined by the dynamics of the domain walls motion, which in turn is determined by the action of the braking forces arising from defects in the material. According to Kersten [3] a decrease in the energy of the domain wall due to a decrease in its area at the intersection of nonmagnetic inclusions serves as a source of inhibitory forces. The decrease in the energy of the domain wall occurs under the condition that the domain wall completely contains a dislocation. In this case, the exchange energy of magnetic crystallographic anisotropy will decrease in the places of violation of atomic ordering, which will lead to a decrease in the energy of the domain wall. Neel [4,5] showed that the decrease in the energy of the domain wall in the region of inclusions occurs mainly due to a decrease in the
Corresponding author. E-mail address: [email protected] (A.V. Malyshev).
https://doi.org/10.1016/j.ceramint.2018.08.073 Received 16 July 2018; Received in revised form 7 August 2018; Accepted 7 August 2018 Available online 08 August 2018 0272-8842/ © 2018 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Ceramics International 44 (2018) 20749–20754
A.V. Malyshev et al.
energy of the demagnetizing fields surrounding the defects. The decrease in the energy of the demagnetizing field during the passage of the 100-degree domain wall through the inclusions is due to a change in the polarity of the magnetic charges in the part of the volume surrounding the inclusion. In Globus theory [6–8], the parameters determining the motion of domain walls depend on the dimensions of these walls. In turn, the dimensions of the walls depend on the grain sizes (provided that it does not contain defects). At present, in the area of ferrite ceramics, most of the research is devoted to the temperature and composition dependence of magnetic properties [9–16]. At the same time, there is practically no research about the relationship between the nominal electromagnetic and dielectric parameters of ferrite materials to their defective structure. The ferrite ceramics manufactured in production is tested for a number of the basic parameters that are compared to the reference parameters of ferrite materials from the product catalogue. From their comparison, a conclusion is made about the quality of the products. The defects level of ferrite ceramics caused by intragranular porosity, non-magnetic phases, and defects in the crystal structure is practically not investigated. In our work [17], we proposed a structurally sensitive method for estimating the defects level of ferrite ceramics on the basis of an analysis of the temperature dependences of the initial permeability in a wide temperature range, including the Curie point. For the experimental approbation of the developed ideas regarding the relationship between the parameters of the temperature variation of μi(Т) and the defects level of ferrite ceramics, we studied the results of the investigation of the μi(Т) dependences of model samples containing a controlled amount of intergranular phase inclusions of alumina. The choice of the additive type is due to its diamagnetism, which makes it possible to verify the possibility of monitoring by the indicated method of secondary non-magnetic phases of ferrite ceramics. In addition, a doping of the samples with aluminium oxide provided a predetermined defects level with respect to samples not containing non-magnetic additives. The data of magnetic hysteresis loops are given for comparison of the proposed method with traditional magnetic methods of quality control of ferrites. The data of the true physical broadening of the reflexes served to compare the defects level change in model samples with direct X-ray diffraction measurements of microdeformations, as well as to assess the sensitivity of the method. We also showed that defects level correlates with the elastic stress of a ferrite ceramics. Therefore, this parameter can serve as a characteristic of the elastic stress of a soft ferrite ceramics. 2. Experimental The samples for research were rectangular-shaped toroids sintered in laboratory conditions [17]. Sintering of the samples was carried out at a temperature of 1010 °C for 2 h. In addition to samples without additives, 3 batches of samples with different concentrations of Al2O3 additives – 0.1, 0.25 and 0.5 wt% were produced. In each of the batches, 5–7 samples were made. The X-ray diffraction patterns of these compositions confirmed the formation of the single phase spinel structure. The XRD patterns were measured by ARLX’TRAX-ray diffractometer (Switzerland) with a Peltier Si(Li) semiconductor detector and Cukα radiation for 2θ = (10–80)° with a scan rate of 0.01°/s. The processing of the diffractograms was carried out using the Powder Cell 2.5 program. The measurements and mathematical processing of the temperature dependences of the initial permeability were carried out according to the method proposed in [17]. As a result, the calculated values of the main parameters of the phenomenological expression, including the Curie point (Тс), were obtained. Also, Curie point was obtained graphically from temperature
dependencies of initial permeability μi. The hydraulic press PGr-10 with press mold was used for compaction of ferrite samples. Samples dimensions, toroidal form: 18.4 × 14.1 × 2 mm. We utilized SEM micrographs of polished and chemically etched cross-sections for microstructure and grain size evaluation. The average grain size (D) was calculated by using the intercept method. The defects level (β/α) was determined from mathematical analysis of temperature dependences of initial permeability μi by the phenomenological expression (1) obtained in [17].
(
)
g
δ
T ⎡ ⎤ 1− T c ⎢ ⎥ x= γ ⎢ ⎥ T α 1 β − + ⎢ ⎥ Tc ⎣ ⎦
1+x , μi = 1 + N ⋅x
(
)
(1)
The coefficientsα , β , γ and δ are determined by the relations (2), (3), (4):
α=
K1 (0) λ (0) , β = sr ⋅σ , δ = (r − n) f , γ = (m − n) f Msr (0) Ms (0) m
K1 (T ) M (T ) ⎤ λ (T ) M (T ) ⎤ =⎡ s =⎡ s , s ⎢ ⎥ ⎢ K1 (0) M (0) λ (0) s ⎣ s ⎦ ⎣ Ms (0) ⎥ ⎦
T Ms (T ) = Ms (0) ⎡1 − ⎤ ⎢ Tc ⎥ ⎣ ⎦
(2)
n
(3)
f
(4)
Where g= 2 and r = 2 – exponent of power in (1), (2) for model of initial permeability by Smith and Wijn; m, n, f – exponent of power in (3), (4); К1 – crystallographic magnetic anisotropy; λs – magnetostriction constant; σ – average level of elastic stresses; N – the magnitude of the demagnetizing factor; Ms – saturation magnetization; Tc – Curie temperature. Mathematical processing of experimental temperature dependences μi was carried out using the least squares method (LevenbergMarquardt algorithm) of Origin 9.0 software package [17]. The measurement of the magnetic hysteresis loops was carried out using a classical oscilloscope measurement circuit using an oscilloscope Tektronix-2012B. 3. Results and discussion Fig. 1 shows the diffractograms of LiTiZn model samples of ferrite ceramics. The scale of the mapping is the same as for the axis of 2θ and the axis of intensity. It turned out that the addition of even 0.5 wt% Al2O3 to the LiTiZn ferrite mixture was not detected by the XRD method. The concentrations of the Al2O3 additive of more than 0.5% significantly influenced onthe chemical composition of the ferrite, which resulted in a significant increase in the Curie point (by 10 degrees for 1% Al2O3). Therefore, the data with the results of the addition of Al2O3 above 0.5% are not included in this work. Fig. 1 shows that the addition of Al2O3 affects the intensity of the main reflections of the diffractograms. At the same time, the lattice parameter a does not depend on the concentration of the additive. However, crystallite size and microstrain increased significantly with an increase in the concentration of the additive (Table 1). Fig. 2 shows the microstructure of the model samples. As it can be seen from Fig. 2, the shape of grains in LiTiZn samples of ferrite ceramics with additives differs markedly from samples without additives, but the grain size calculated by the method of secants differs insignificantly D = (2.5 ± 0.4) μm. A polycrystalline structure with well-formed grain boundaries is observed for all samples. In addition, grains are highly agglomerated and show large grain size dispersion and also pore. In the next stage of the experimental study, the temperature dependences of the initial permeability were measured for each of the
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Fig. 1. The XRD patterns of model samples: no additives (a); additive Al2O3 0.1% (b); additive Al2O3 0.25% (c); additive Al2O3 0.5% (d). Table 1 Effect of Al2O3 additives on the X-ray structural data of model samples. Samples type
a (nm)
Micro-strain·104
Crystallite size (nm)
No additive Add. 0.1% Add. 0.25% Add. 0.5%
0.83626 0.83638 0.83617 0.83627
3.2 5.8 17 18.4
280 360 445 603
model samples. Fig. 3 shows that the addition of Al2O3 significantly affects both the shape of the curves μi(T) and their maximum, but the Curie points are close (about 270 °C). Each of the temperature curves was mathematically processed by the phenomenological expression (1); the values of the parameters included in this expression were obtained (Table 2). From the data in Table 2, it follows that the Curie point does not depend on the concentration of the Al2O3 additive in the range of (0–0.5) wt%. The demagnetizing factor N increased by almost 50%, and the parameter β increased by 5.3 times. The maximum value of the initial permeability on the temperature dependence (μmax) (Table 2) was determined from the dependence graphs on (Fig. 3). With an increase in the concentration of the additive, the μmax falls by almost 70%, hence this parameter characterizes the defects level of ferrite ceramics. A similar result was obtained in [18] for NiCuZn ferrites. In this paper, it was shown that the decrease in the temperature dependence of the initial magnetic permeability is due to the effect of the Al2O3 additives on the domain wall motion. Then, the decrease in μmax is probably due to the effect of additives on domain wall motionin our material. As the concentration of the Al2O3 additive increases, the level of β/ α defects increases almost 6-fold. From the analysis of the data in
Table 1, it follows that the most sensitive parameter of the phenomenological expression with respect to diamagnetic additives is the ratio β/α. Consequently, as a result of mathematical processing of the experimental curves, it was confirmed that the ratio β/α is the most sensitive characteristic of defects level [17]. The appearance of elastic stress fields at the introduction of Al2O3 additives into ferrite is explained by the baking of the oxide particles with the ferrite matrix grains and the difference in the coefficients of thermal expansion, the structure of the lattices of both phases. In this case, the value of the residual stresses can be estimated according to the scheme proposed in [19]. At sufficiently moderate inclusions concentrations, the overlapping of the elastic stress fields can be neglected, and in this case, the total volume of the sample that underwent deformation effects will be proportional to the amount of introduced additive. Such exact behavior is observed in the model samples of ferrite ceramics studied in this work (Fig. 4).
4. Magnetic characterization For comparing the effectiveness of the proposed method with traditional magnetic methods of the ferrites quality control for the same model samples, the measurements of the parameters of the magnetic hysteresis loop were made. Fig. 5 shows the effect of diamagnetic inclusions on the shape and parameters of the magnetic hysteresis loop (Table 3). The amplitude of the magnetizing field is chosen on the basis of saturation of the dependence of the maximum induction on the magnetic field strength Bm(H). The introduction of Al2O3 additives affects the values of the residual induction Br, the maximum induction Bm and the coercive force Hc. It can be seen from Table 3 while the concentration of Al2O3
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Fig. 2. SEM micrographs of model samples: no additives (a); additive Al2O3 0.1% (b); additive Al2O3 0.25% (c); additive Al2O3 0.5% (d).
proportional to the fraction of the sample volume to which the internal stresses propagate [2]. Obviously, this volume will be proportional to the concentration of the introduced inclusions. It should be noted that according to the model of Kersten inclusions, Hc is also proportional to the relative volume of inclusions. Thus, a change in the parameters of the hysteresis loop makes it possible to control the presence of nonmagnetic inclusions in the sample of ferrite ceramics. However, in comparison to the defects level β/α given above, such changes are much weaker.
5. X-ray diffraction reflections broadening
Fig. 3. The temperature dependences of the initial permeability of LiTiZn model samples of ferrite ceramics: no additives (a); with additive Al2O3 0.1% (b); with additive Al2O3 0.25% (c); with additive Al2O3 0.5% (d). Symbols – experimental data, solid lines – calculated curves.
additives increases the values of the Bs parameters decrease monotonically, and Hc increase. This behavior is due to the occurrence of demagnetizing fields, as well as an increase in the fraction of the ferrite volume subjected to the action of elastic stress fields. The latter follows from the near-linear form of the concentration dependence for the coercive force Hc, which, according to the Neel formula, is directly
In order to compare the changes in the defects level β/α in model samples with direct X-ray diffraction measurements of microdeformations, the investigations of the physical broadening of diffraction reflections from planes (400) (800) were performed. The method of X-ray measurements and calculation of the true width of the reflections W and the physical broadening δ with respect to the standard sample is described in [17]. The widths of the reflections were determined by taking into account the doublet reflections on the spectral line with the method of decomposition into Gaussian components. According to XRF data, an increase in the concentration of the Al2O3 additive up to 0.5% shows an increase in the true physical broadening of the reflex δ (400) by 38% (Table 4). A similar behavior was observed in other reflexes, for example, (800). From the data comparison in terms of the increase in the defects
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Table 2 Fitting results. Effect of Al2O3 additives on the parameters of the temperature dependence of the initial permeability. Samples type
α
No additive Add. 0.1% Add. 0.25% Add. 0.5%
0.13315 0.12768 0.13378 0.11941
± ± ± ±
0.0003 0.0002 0.0003 0.0004
β·104
N·103
6.5 ± 0.2 11.3 ± 0.4 25.2 ± 0.5 34.5 ± 0.6
1.79 1.96 2.28 2.65
± ± ± ±
Tc(°C) 0.03 0.04 0.06 0.05
269.2 271.8 269.8 267.3
± ± ± ±
0.3 0.3 0.3 0.2
µmax
β/α·103
430.7 400.3 325 299.6
4.9 8.9 18.8 28.9
Table 3 Hysteresis loop parameters of model ferrite ceramic samples. Samples type
Bs (mT)
Br (mT)
Hc (A/m)
No additives Add. 0.1% Add. 0.25% Add. 0.5%
170 154 143 160
127 129 114 108
77.8 80 81.8 82.7
Table 4 Effect of Al2O3 additives on the true physical broadening δ for diffraction reflection (400).
Fig. 4. Concentration dependence of defects level β/α for model samples. The solid line is an approximation straight line.
Samples type
W (degree)
δ (degree)
Standard No additives Add 0.1% Add 0.25% Add 0.5%
0.083 0.150 0.169 0.171 0.191
– 0.125 0.147 0.150 0.172
Fig. 5. The ac hysteresis loops for model samples: no additives (a); with additive Al2O3 0.1% (b); with additive Al2O3 0.25% (c); with additive Al2O3 0.5% (d). 20753
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broadening of the reflex by the X-ray diffraction method, have confirmed the high sensitivity and effectiveness of the method. It has been shown that the defects level β/α characterizes elastic stresses in ferrite ceramics. The data obtained in the work made it possible to evaluate the high efficiency and sensitivity of the method and to recommend its use in controlling non-magnetic phases, as well as other defects in industrial ferrite products. Acknowledgments The research is funded by the Tomsk Polytechnic University Competitiveness Enhancement Program grant. References Fig. 6. Dependence of the width of the reflex (400) on the β/α defects level of model samples. The solid line is an approximation straight line.
level with increasing concentration of the additive Al2O3 (Table 2) and physical broadening δ (Table 4) in the model samples, it follows that the sensitivity of the method for determining the defects level from the analysis of the temperature dependences of μi with respect to phase inclusions is significantly higher than the sensitivity of typical X-ray methods. It is known that the elastic stresses in the material affect the width of the reflexes [20]. To determine the correlation between the elastic stresses and the values of the defects level β/α, a relationship between the width of the reflex (400) and the defects level β/α was constructed in model samples (Fig. 6). From the obtained data, one can see a linear correlation between the indicated parameters, which proves the validity of the interpretation of the defects level β/α as a characteristic of the elastic stress of soft ferrites [17]. Thus it is shown that the introduction of diamagnetic Al2O3 additives (or the detected non-magnetic phases in control samples of ferrite ceramics) causes an increase in the elastic stresses in LiTiZn ferrite ceramics. Elastic stresses of the material, in turn, are proportional to the level of defects. 6. Conclusions An experimental approbation of a method for estimating the defects level based on the mathematical processing of initial permeability temperature dependences has been carried out on model samples containing a controlled amount of a diamagnetic alumina additive. Mathematical processing has shown that the defects level β/α is the most sensitive parameter from other parameters of the phenomenological expression for determining the value of nonmagnetic inclusions in ferrites. It has been experimentally shown that the defects level (the perfection of the structure) can be characterized by the magnitude of the maximum of μi(Т) near the Curie point. The coordinated data on the measurement of the parameters of the magnetic hysteresis loop of model samples, as well as their true physical
[1] A. Verma, R. Chatterjee, Effect of zinc concentration on the structural, electrical and magnetic properties of mixed Mn–Zn and Ni–Zn ferrites synthesized by the citrate precursor technique, J. Magn. Magn. Mater. 306 (2006) 313–320. [2] J. Smith, H.P.J. Wijn, Ferrites: Physical Properties of Ferromagnetic Oxides in Relation to their Technical Application, Phillips Technical Library, Eindhoven, 1959. [3] M. Kestern, Reversible und irreversible magnetisierun-gsanderungerlangs der hystereschleife, Z. Angew. Phys. 7 (1955) 397–407. [4] L. Neel, Energie magnetocrictalline d′ur macrocristal subdivise on crystallites guadretigues, C. R. Acad. Sci. 257 (1963) 2917–2921. [5] L. Neel, Defaults ponetuels dansles solides ferromagnetiques et ordre directional, J. Phys. (Fr.) 24 (1963) 513–516. [6] A. Globus, Influence des dimensions des parois la permeability, C. R. Acad. Sci. 255 (1962) 1709–1711. [7] A. Globus, Some physical consideration about the domain wall sine. theory of magnetization mechanisms, J. Phys. 38 (1977) 1–15. [8] A. Globus, M. Guyot, Wall displacement and bulging in magnetization mechanisms of the hysteresis loop, Phys. Status Solidi В 52 (1972) 427–431. [9] L.Z. Li, Z. Lan, Z. Yu, K. Sun, M. Luo, Z. Xu, H. Ji, Effects of Ta2O5 addition on the microstructure and temperature dependence of magnetic properties of MnZn ferrites, J. Magn. Magn. Mater. 321 (2009) 438–441. [10] M.J. Iqbal, Z. Ahmad, T. Meydan, Y. Melikhov, Temperature and composition dependence of magnetic properties of cobalt–chromium co-substituted magnesium ferrite nanomaterials, J. Magn. Magn. Mater. 324 (2012) 3986–3990. [11] M. Rezlescu, L. Rezlescu, P.D. Popa, E. Rezlescu, Influence of additives on the properties of a Ni–Zn ferrite with low Curie point, J. Magn. Magn. Mater. 215–216 (2000) 194–196. [12] R. Parvin, A.A. Momina, A.K.M. Akther Hossain, Improvement of microstructure, initial permeability, magnetization and dielectric properties of nanocrystalline LixCu0.1Co0.1Zn0.8−2xFe2+xO4, J. Magn. Magn. Mater. 401 (2016) 760–769. [13] A.V. Knyazev, I. Zakharchuk, E. Lahderanta, K.V. Baidakov, S.S. Knyazeva, I.V. Ladenkov, Structural and magnetic properties of Ni-Zn and Ni-Zn-Co ferrites, J. Magn. Magn. Mater. 435 (2017) 9–14. [14] M.K. Anupama, N. Srinatha, Sh Matteppanavar, B. Angadi, B. Sahoo, B. Rudraswamy, Effect of Zn substitution on the structural and magnetic properties of nanocrystalline NiFe2O4 ferrites, Ceram. Int. 44 (2018) 4946–4954. [15] A.A. Al-Ghamdi, F.S. Al-Hazmi, L.S. Memesh, F.S. Shokr, L.M. Bronstein, Effect of mechanochemical synthesis on the structure, magnetic and opticalbehavior of Ni1−xZnxFe2O4 spinel ferrites, Ceram. Int. 43 (2017) 6192–6200. [16] H. Bahiraei, C.K. Ong, Microstructural and electromagnetic study of low temperature fired nanocrystalline MgCuZn ferrite with Bi2O3 addition, Ceram. Int. 43 (2017) 4780–4784. [17] A.V. Malyshev, A.B. Petrova, A.N. Sokolovskiy, A.P. Surzhikov, Defects level evaluation of LiTiZn ferrite ceramics using temperature dependence of initial permeability, J. Magn. Magn. Mater. 456 (2018) 186–193. [18] S. Takane, H. Umeda, T. Aoki, T. Murase, Influence of Al2O3 addition on the temperature dependence of initial permeability of NiCuZn ferrites, Key Eng. Mater. 485 (2011) 225–228. [19] J. Selsig, Internal stresses in ceramics, J. Am. Ceram. Soc. 44 (1961) 419–422. [20] R.E. Dinnebier, S.J.L. Billinge, Powder Diffraction: Theory and Practice, the Royal Society of Chemistry, Cambridge, 2008.
20754
Contents lists available at ScienceDirect
Ceramics International journal homepage: www.elsevier.com/locate/ceramint
Influence of Al2O3 addition on microstructure, defects level and magnetic properties of LiTiZn ferrite ceramics
T
⁎
A.V. Malyshev , A.B. Petrova, A.P. Surzhikov Tomsk Polytechnic University, 634050 Tomsk, Russia
A R T I C LE I N FO
A B S T R A C T
Keywords: A. Sintering B. Defects C. Magnetic properties D. Ferrites
In the present work, the results of the influence of diamagnetic additives on the defects level of ferrite ceramics, its microstructure and magnetic properties are presented. A method based on a mathematical analysis of the experimental temperature dependences of the initial permeability was used for estimation of the defects level in the samples. Model samples containing a controlled amount of the diamagnetic additive Al2O3 served to test the possibility of monitoring this method of nonmagnetic phases of ferrite ceramics. It was shown that with an increase in the concentration of the Al2O3 additive in the range of (0–0.5) wt%, a significant increase in the defects level was observed almost 6-fold. The data from SEM micrographs showed that the addition of Al2O3 affects the type of grains of ferrite ceramics, but does not affect their grain size. Grains are highly agglomerated and show large grain size dispersion and also pore. Obtained data were compared to hysteresis loop parameters. It is shown that with an increase in the concentration of the Al2O3 addition, there is a regular decrease in the residual induction and an increase in the coercive force. However, such changes in hysteresis loop parameters are small in comparison to defects level. Investigations of the true physical broadening of the diffraction reflections were performed for the same model samples in order to compare the change in the defects level to the direct X-ray diffraction measurements of micro deformations. The defects level as a characteristic of the elastic stress of a ferrite ceramics is proposed. This assumption follows from a linear relationship between the defects level and the width of the diffraction reflections. The consistency of the obtained results made it possible to evaluate the high efficiency and sensitivity of the method for defects level estimating.
1. Introduction The properties of ferrite materials which used in practice can differ significantly from the properties predicted on the basis of crystallochemical composition. This is mainly due to the presence of various crystal structure defects in the material. As a rule, the defectiveness of materials occurs at the stage of their manufacture, and therefore the development of technological regimes for the production of ferrites should provide the possibility of controlling not only the crystallochemical composition, but also the defects level of the material. In general, defects level of ferrite ceramics includes intragranular crystal lattice defects and interface defects of grain boundaries. It is known that in the production of standard ceramic technology, ferrite ceramics often have side phase inclusions and various defects [1]. Such defects, together with intragranular porosity, cause the deterioration of the electromagnetic properties of ferrites. It is known also that such properties are determined by the dynamics of the magnetization reversal processes and the magnetic state of the material, which in turn depend
⁎
not only on its chemical composition but also on the content and distribution of defects in it. Thus, the accumulation of information regarding the relationship of defects with the basic magnetic properties of ferrites is important in the manufacture of products from this material [2]. The processes of magnetization of ferrites are determined by the dynamics of the domain walls motion, which in turn is determined by the action of the braking forces arising from defects in the material. According to Kersten [3] a decrease in the energy of the domain wall due to a decrease in its area at the intersection of nonmagnetic inclusions serves as a source of inhibitory forces. The decrease in the energy of the domain wall occurs under the condition that the domain wall completely contains a dislocation. In this case, the exchange energy of magnetic crystallographic anisotropy will decrease in the places of violation of atomic ordering, which will lead to a decrease in the energy of the domain wall. Neel [4,5] showed that the decrease in the energy of the domain wall in the region of inclusions occurs mainly due to a decrease in the
Corresponding author. E-mail address: [email protected] (A.V. Malyshev).
https://doi.org/10.1016/j.ceramint.2018.08.073 Received 16 July 2018; Received in revised form 7 August 2018; Accepted 7 August 2018 Available online 08 August 2018 0272-8842/ © 2018 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Ceramics International 44 (2018) 20749–20754
A.V. Malyshev et al.
energy of the demagnetizing fields surrounding the defects. The decrease in the energy of the demagnetizing field during the passage of the 100-degree domain wall through the inclusions is due to a change in the polarity of the magnetic charges in the part of the volume surrounding the inclusion. In Globus theory [6–8], the parameters determining the motion of domain walls depend on the dimensions of these walls. In turn, the dimensions of the walls depend on the grain sizes (provided that it does not contain defects). At present, in the area of ferrite ceramics, most of the research is devoted to the temperature and composition dependence of magnetic properties [9–16]. At the same time, there is practically no research about the relationship between the nominal electromagnetic and dielectric parameters of ferrite materials to their defective structure. The ferrite ceramics manufactured in production is tested for a number of the basic parameters that are compared to the reference parameters of ferrite materials from the product catalogue. From their comparison, a conclusion is made about the quality of the products. The defects level of ferrite ceramics caused by intragranular porosity, non-magnetic phases, and defects in the crystal structure is practically not investigated. In our work [17], we proposed a structurally sensitive method for estimating the defects level of ferrite ceramics on the basis of an analysis of the temperature dependences of the initial permeability in a wide temperature range, including the Curie point. For the experimental approbation of the developed ideas regarding the relationship between the parameters of the temperature variation of μi(Т) and the defects level of ferrite ceramics, we studied the results of the investigation of the μi(Т) dependences of model samples containing a controlled amount of intergranular phase inclusions of alumina. The choice of the additive type is due to its diamagnetism, which makes it possible to verify the possibility of monitoring by the indicated method of secondary non-magnetic phases of ferrite ceramics. In addition, a doping of the samples with aluminium oxide provided a predetermined defects level with respect to samples not containing non-magnetic additives. The data of magnetic hysteresis loops are given for comparison of the proposed method with traditional magnetic methods of quality control of ferrites. The data of the true physical broadening of the reflexes served to compare the defects level change in model samples with direct X-ray diffraction measurements of microdeformations, as well as to assess the sensitivity of the method. We also showed that defects level correlates with the elastic stress of a ferrite ceramics. Therefore, this parameter can serve as a characteristic of the elastic stress of a soft ferrite ceramics. 2. Experimental The samples for research were rectangular-shaped toroids sintered in laboratory conditions [17]. Sintering of the samples was carried out at a temperature of 1010 °C for 2 h. In addition to samples without additives, 3 batches of samples with different concentrations of Al2O3 additives – 0.1, 0.25 and 0.5 wt% were produced. In each of the batches, 5–7 samples were made. The X-ray diffraction patterns of these compositions confirmed the formation of the single phase spinel structure. The XRD patterns were measured by ARLX’TRAX-ray diffractometer (Switzerland) with a Peltier Si(Li) semiconductor detector and Cukα radiation for 2θ = (10–80)° with a scan rate of 0.01°/s. The processing of the diffractograms was carried out using the Powder Cell 2.5 program. The measurements and mathematical processing of the temperature dependences of the initial permeability were carried out according to the method proposed in [17]. As a result, the calculated values of the main parameters of the phenomenological expression, including the Curie point (Тс), were obtained. Also, Curie point was obtained graphically from temperature
dependencies of initial permeability μi. The hydraulic press PGr-10 with press mold was used for compaction of ferrite samples. Samples dimensions, toroidal form: 18.4 × 14.1 × 2 mm. We utilized SEM micrographs of polished and chemically etched cross-sections for microstructure and grain size evaluation. The average grain size (D) was calculated by using the intercept method. The defects level (β/α) was determined from mathematical analysis of temperature dependences of initial permeability μi by the phenomenological expression (1) obtained in [17].
(
)
g
δ
T ⎡ ⎤ 1− T c ⎢ ⎥ x= γ ⎢ ⎥ T α 1 β − + ⎢ ⎥ Tc ⎣ ⎦
1+x , μi = 1 + N ⋅x
(
)
(1)
The coefficientsα , β , γ and δ are determined by the relations (2), (3), (4):
α=
K1 (0) λ (0) , β = sr ⋅σ , δ = (r − n) f , γ = (m − n) f Msr (0) Ms (0) m
K1 (T ) M (T ) ⎤ λ (T ) M (T ) ⎤ =⎡ s =⎡ s , s ⎢ ⎥ ⎢ K1 (0) M (0) λ (0) s ⎣ s ⎦ ⎣ Ms (0) ⎥ ⎦
T Ms (T ) = Ms (0) ⎡1 − ⎤ ⎢ Tc ⎥ ⎣ ⎦
(2)
n
(3)
f
(4)
Where g= 2 and r = 2 – exponent of power in (1), (2) for model of initial permeability by Smith and Wijn; m, n, f – exponent of power in (3), (4); К1 – crystallographic magnetic anisotropy; λs – magnetostriction constant; σ – average level of elastic stresses; N – the magnitude of the demagnetizing factor; Ms – saturation magnetization; Tc – Curie temperature. Mathematical processing of experimental temperature dependences μi was carried out using the least squares method (LevenbergMarquardt algorithm) of Origin 9.0 software package [17]. The measurement of the magnetic hysteresis loops was carried out using a classical oscilloscope measurement circuit using an oscilloscope Tektronix-2012B. 3. Results and discussion Fig. 1 shows the diffractograms of LiTiZn model samples of ferrite ceramics. The scale of the mapping is the same as for the axis of 2θ and the axis of intensity. It turned out that the addition of even 0.5 wt% Al2O3 to the LiTiZn ferrite mixture was not detected by the XRD method. The concentrations of the Al2O3 additive of more than 0.5% significantly influenced onthe chemical composition of the ferrite, which resulted in a significant increase in the Curie point (by 10 degrees for 1% Al2O3). Therefore, the data with the results of the addition of Al2O3 above 0.5% are not included in this work. Fig. 1 shows that the addition of Al2O3 affects the intensity of the main reflections of the diffractograms. At the same time, the lattice parameter a does not depend on the concentration of the additive. However, crystallite size and microstrain increased significantly with an increase in the concentration of the additive (Table 1). Fig. 2 shows the microstructure of the model samples. As it can be seen from Fig. 2, the shape of grains in LiTiZn samples of ferrite ceramics with additives differs markedly from samples without additives, but the grain size calculated by the method of secants differs insignificantly D = (2.5 ± 0.4) μm. A polycrystalline structure with well-formed grain boundaries is observed for all samples. In addition, grains are highly agglomerated and show large grain size dispersion and also pore. In the next stage of the experimental study, the temperature dependences of the initial permeability were measured for each of the
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Fig. 1. The XRD patterns of model samples: no additives (a); additive Al2O3 0.1% (b); additive Al2O3 0.25% (c); additive Al2O3 0.5% (d). Table 1 Effect of Al2O3 additives on the X-ray structural data of model samples. Samples type
a (nm)
Micro-strain·104
Crystallite size (nm)
No additive Add. 0.1% Add. 0.25% Add. 0.5%
0.83626 0.83638 0.83617 0.83627
3.2 5.8 17 18.4
280 360 445 603
model samples. Fig. 3 shows that the addition of Al2O3 significantly affects both the shape of the curves μi(T) and their maximum, but the Curie points are close (about 270 °C). Each of the temperature curves was mathematically processed by the phenomenological expression (1); the values of the parameters included in this expression were obtained (Table 2). From the data in Table 2, it follows that the Curie point does not depend on the concentration of the Al2O3 additive in the range of (0–0.5) wt%. The demagnetizing factor N increased by almost 50%, and the parameter β increased by 5.3 times. The maximum value of the initial permeability on the temperature dependence (μmax) (Table 2) was determined from the dependence graphs on (Fig. 3). With an increase in the concentration of the additive, the μmax falls by almost 70%, hence this parameter characterizes the defects level of ferrite ceramics. A similar result was obtained in [18] for NiCuZn ferrites. In this paper, it was shown that the decrease in the temperature dependence of the initial magnetic permeability is due to the effect of the Al2O3 additives on the domain wall motion. Then, the decrease in μmax is probably due to the effect of additives on domain wall motionin our material. As the concentration of the Al2O3 additive increases, the level of β/ α defects increases almost 6-fold. From the analysis of the data in
Table 1, it follows that the most sensitive parameter of the phenomenological expression with respect to diamagnetic additives is the ratio β/α. Consequently, as a result of mathematical processing of the experimental curves, it was confirmed that the ratio β/α is the most sensitive characteristic of defects level [17]. The appearance of elastic stress fields at the introduction of Al2O3 additives into ferrite is explained by the baking of the oxide particles with the ferrite matrix grains and the difference in the coefficients of thermal expansion, the structure of the lattices of both phases. In this case, the value of the residual stresses can be estimated according to the scheme proposed in [19]. At sufficiently moderate inclusions concentrations, the overlapping of the elastic stress fields can be neglected, and in this case, the total volume of the sample that underwent deformation effects will be proportional to the amount of introduced additive. Such exact behavior is observed in the model samples of ferrite ceramics studied in this work (Fig. 4).
4. Magnetic characterization For comparing the effectiveness of the proposed method with traditional magnetic methods of the ferrites quality control for the same model samples, the measurements of the parameters of the magnetic hysteresis loop were made. Fig. 5 shows the effect of diamagnetic inclusions on the shape and parameters of the magnetic hysteresis loop (Table 3). The amplitude of the magnetizing field is chosen on the basis of saturation of the dependence of the maximum induction on the magnetic field strength Bm(H). The introduction of Al2O3 additives affects the values of the residual induction Br, the maximum induction Bm and the coercive force Hc. It can be seen from Table 3 while the concentration of Al2O3
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Fig. 2. SEM micrographs of model samples: no additives (a); additive Al2O3 0.1% (b); additive Al2O3 0.25% (c); additive Al2O3 0.5% (d).
proportional to the fraction of the sample volume to which the internal stresses propagate [2]. Obviously, this volume will be proportional to the concentration of the introduced inclusions. It should be noted that according to the model of Kersten inclusions, Hc is also proportional to the relative volume of inclusions. Thus, a change in the parameters of the hysteresis loop makes it possible to control the presence of nonmagnetic inclusions in the sample of ferrite ceramics. However, in comparison to the defects level β/α given above, such changes are much weaker.
5. X-ray diffraction reflections broadening
Fig. 3. The temperature dependences of the initial permeability of LiTiZn model samples of ferrite ceramics: no additives (a); with additive Al2O3 0.1% (b); with additive Al2O3 0.25% (c); with additive Al2O3 0.5% (d). Symbols – experimental data, solid lines – calculated curves.
additives increases the values of the Bs parameters decrease monotonically, and Hc increase. This behavior is due to the occurrence of demagnetizing fields, as well as an increase in the fraction of the ferrite volume subjected to the action of elastic stress fields. The latter follows from the near-linear form of the concentration dependence for the coercive force Hc, which, according to the Neel formula, is directly
In order to compare the changes in the defects level β/α in model samples with direct X-ray diffraction measurements of microdeformations, the investigations of the physical broadening of diffraction reflections from planes (400) (800) were performed. The method of X-ray measurements and calculation of the true width of the reflections W and the physical broadening δ with respect to the standard sample is described in [17]. The widths of the reflections were determined by taking into account the doublet reflections on the spectral line with the method of decomposition into Gaussian components. According to XRF data, an increase in the concentration of the Al2O3 additive up to 0.5% shows an increase in the true physical broadening of the reflex δ (400) by 38% (Table 4). A similar behavior was observed in other reflexes, for example, (800). From the data comparison in terms of the increase in the defects
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Table 2 Fitting results. Effect of Al2O3 additives on the parameters of the temperature dependence of the initial permeability. Samples type
α
No additive Add. 0.1% Add. 0.25% Add. 0.5%
0.13315 0.12768 0.13378 0.11941
± ± ± ±
0.0003 0.0002 0.0003 0.0004
β·104
N·103
6.5 ± 0.2 11.3 ± 0.4 25.2 ± 0.5 34.5 ± 0.6
1.79 1.96 2.28 2.65
± ± ± ±
Tc(°C) 0.03 0.04 0.06 0.05
269.2 271.8 269.8 267.3
± ± ± ±
0.3 0.3 0.3 0.2
µmax
β/α·103
430.7 400.3 325 299.6
4.9 8.9 18.8 28.9
Table 3 Hysteresis loop parameters of model ferrite ceramic samples. Samples type
Bs (mT)
Br (mT)
Hc (A/m)
No additives Add. 0.1% Add. 0.25% Add. 0.5%
170 154 143 160
127 129 114 108
77.8 80 81.8 82.7
Table 4 Effect of Al2O3 additives on the true physical broadening δ for diffraction reflection (400).
Fig. 4. Concentration dependence of defects level β/α for model samples. The solid line is an approximation straight line.
Samples type
W (degree)
δ (degree)
Standard No additives Add 0.1% Add 0.25% Add 0.5%
0.083 0.150 0.169 0.171 0.191
– 0.125 0.147 0.150 0.172
Fig. 5. The ac hysteresis loops for model samples: no additives (a); with additive Al2O3 0.1% (b); with additive Al2O3 0.25% (c); with additive Al2O3 0.5% (d). 20753
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broadening of the reflex by the X-ray diffraction method, have confirmed the high sensitivity and effectiveness of the method. It has been shown that the defects level β/α characterizes elastic stresses in ferrite ceramics. The data obtained in the work made it possible to evaluate the high efficiency and sensitivity of the method and to recommend its use in controlling non-magnetic phases, as well as other defects in industrial ferrite products. Acknowledgments The research is funded by the Tomsk Polytechnic University Competitiveness Enhancement Program grant. References Fig. 6. Dependence of the width of the reflex (400) on the β/α defects level of model samples. The solid line is an approximation straight line.
level with increasing concentration of the additive Al2O3 (Table 2) and physical broadening δ (Table 4) in the model samples, it follows that the sensitivity of the method for determining the defects level from the analysis of the temperature dependences of μi with respect to phase inclusions is significantly higher than the sensitivity of typical X-ray methods. It is known that the elastic stresses in the material affect the width of the reflexes [20]. To determine the correlation between the elastic stresses and the values of the defects level β/α, a relationship between the width of the reflex (400) and the defects level β/α was constructed in model samples (Fig. 6). From the obtained data, one can see a linear correlation between the indicated parameters, which proves the validity of the interpretation of the defects level β/α as a characteristic of the elastic stress of soft ferrites [17]. Thus it is shown that the introduction of diamagnetic Al2O3 additives (or the detected non-magnetic phases in control samples of ferrite ceramics) causes an increase in the elastic stresses in LiTiZn ferrite ceramics. Elastic stresses of the material, in turn, are proportional to the level of defects. 6. Conclusions An experimental approbation of a method for estimating the defects level based on the mathematical processing of initial permeability temperature dependences has been carried out on model samples containing a controlled amount of a diamagnetic alumina additive. Mathematical processing has shown that the defects level β/α is the most sensitive parameter from other parameters of the phenomenological expression for determining the value of nonmagnetic inclusions in ferrites. It has been experimentally shown that the defects level (the perfection of the structure) can be characterized by the magnitude of the maximum of μi(Т) near the Curie point. The coordinated data on the measurement of the parameters of the magnetic hysteresis loop of model samples, as well as their true physical
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