Crystal structure refinement, dielectric and magnetic properties of Sm modified BiFeO3 multiferroic

Journal of Molecular Structure 1097 (2015) 207–213

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Crystal structure refinement, dielectric and magnetic properties of Sm modified BiFeO3 multiferroic Priyanka Godara, Ashish Agarwal, Neetu Ahlawat, Sujata Sanghi ⇑ Department of Applied Physics, Guru Jambheshwar University of Science & Technology, Hisar 125001, Haryana, India

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Refinement has been done by

XRD patterns of Bi1xSmxFeO3 samples.

assuming hexagonal representation of R3c space group.  Magnetic properties are affected by the suppressed periodic self spinning structure.  Impedance plots have revealed a non-Debye type of relaxation process.

a r t i c l e

i n f o

Article history: Received 11 March 2015 Received in revised form 11 May 2015 Accepted 11 May 2015 Available online 19 May 2015 Keywords: X-ray crystallography Multiferroics Magnetic properties Impedance spectroscopy Dielectric properties

a b s t r a c t Bi1xSmxFeO3 multiferroics (x = 0.0, 0.05 and 0.1 having code BF0/SM0, SM5 and SM10 respectively) were synthesized via stage solid-state reaction method and their detailed structural, magnetic and impedance measurements are performed. X-ray diffraction profile and Rietveld analysis indicates that the crystal structure is rhombohedral (R3c). Due to Sm doping, the weak ferromagnetism in BiFeO3 ceramics may be attributed to the improved crystallinity and non presence of secondary phases. Bi0.9Sm0.1FeO3 ceramic exhibited the highest value of remnant magnetization and coercive field. The values of dielectric constant and dielectric loss of SM5 and SM10 samples showed dispersion at low frequency region. The temperature dependence of electric modulus at different frequencies shows the presence of well defined peaks and thus gives the temperature at which the measuring frequency is equal to conductivity relaxation frequency. The typical features of jump relaxation model are obeyed in ac conductivity analysis. Frequency dependence of the conductivity follows the universal power law. Ó 2015 Elsevier B.V. All rights reserved.

Introduction Ample studies have been done in the area of multiferroics during the last few years because of their potential applications in multiple state memory elements, sensors and spintronic devices. ⇑ Corresponding author. Tel.: +91 1662 263384; fax: +91 1662 276240. E-mail address: [email protected] (S. Sanghi). http://dx.doi.org/10.1016/j.molstruc.2015.05.022 0022-2860/Ó 2015 Elsevier B.V. All rights reserved.

Multiferroic systems are of three types: (i) systems in which magnetism and ferroelectricity have different origins (e.g. BiFeO3); (ii) systems in which incommensurate spiral spin structure breaks down the spatial inversion symmetry giving rise to ferroelectricity (e.g. TbMnO3); and (iii) systems where multiferroicity is governed by the elastic interaction at the interface of ferroelectric–magnetic superlattice structure (e.g. BaTiO3–CoFe2O4 multilayers). Multiferroic materials are quite rare as they possess

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simultaneously two or more primary ferroic properties in same phase [1–3]. BiFeO3 has received sizeable attention due to its high ferroelectric Curie temperature (TC  1100 K) and high antiferromagnetic Neel temperature (TN  640 K) well above RT (room temperature), and makes it suitable for various practical applications. Practical applications of BiFeO3 (BFO) are obstructed by some limitations which include (i) synthesis of single phase BFO as it is often accompanied by the presence of impurity phases due to metastable state of BFO, (ii) problems in disclosing strong ferroelectric behavior and piezoelectric properties due to low electrical resistivity, and (iii) difficulties in attaining net magnetization because the magnetic ordering in BiFeO3 materials is of antiferromagnetic type having a spatially modulated spin cycloid. The first two obstacles can be removed by using specific synthesis techniques [4–6]. In order to improve the magnetic properties of the BFO a lot of work has been done which suggests that the destruction of the space modulated spin structure can be possible either by applying high magnetic field or by doping rare earth ions at Bi-site of the compound. In the rhombohedrally distorted structure of BiFeO3 perovskites, the introduction of rare earth cations increases the anisotropy constant and makes the cycloidal spin structure energetically unfavorable [7]. Previous investigations have revealed an enhancement in magnetization by the chemical substitutions of lanthanides, like La3+ [7,8], Nd3+ [9,4], Sm3+ [10– 13], Eu3+ [6], Gd3+ [14–16], etc. No increase in the leakage current is expected in Sm doped BFO because trivalent Sm3+ have same valence state as that of Bi3+. However, by now, much work has already been reported on the magnetic properties of Sm doped BFO above 10% doping concentration. Below this doping level, a detailed study of the dielectric properties is still missing. Hence, the objective of the present work is to study the dielectric and magnetic properties of BiFeO3 ceramics doped with Sm3+ ions and to correlate these properties with the changes in crystal structure.

and the entire calculated pattern based on the simultaneously refined models for the crystal structure, lattice parameters and instrumental factors as may be desired. We need to minimize the function D given by [19],

D¼

X wi fIiO  IiC g2

ð1Þ

i

where IiO and IiC are observed and calculated intensities for diffraction angle 2hi, wi are the weight parameters which can be written as (1/wi) = ri2, where ri is the standard deviation in companion with the intensity at each 2hi value. Magnetic measurement Magnetic properties of the samples were studied by using Vibrating Sample Magnetometer (Lakeshore VSM 7410) with a maximum applied field of 20 kOe at room temperature. Dielectric measurement Using pellet press the compact discs of the samples were made at room temperature by applying a pressure of 10 tons. An organic binder (PVA) was used for proper shaping. The prepared pellets are of about 13 mm diameter and 1 mm thickness. The two surfaces of the sintered discs were coated with silver paste for making electrodes. The impedance measurement was performed using an impedance/gain phase analyzer (Newton’s 4th Ltd.). Dielectric data was recorded in the frequency range of 10 Hz–5 MHz and temperature range 303–723 K. Results and discussion Crystal structure

Experimental details Sample preparation Bi1xSmxFeO3 ceramics with x = 0.0, 0.05 and 0.1 were synthesized by conventional solid-state reaction route. High purity analytical reagent grade (P99% pure) oxides: Bi2O3, Fe2O3 and Sm2O3 were weighed accurately in stoichiometric proportion. These powders were ground thoroughly in an agate mortar. In order to get the desired crystallinity the samples were calcined at 773 K for 7 h and then slowly cooled to room temperature. The calcined powders were reground again for 30 min to make the mixtures more homogeneous. The final sintering was performed in the furnance at 1073 K. X-ray diffraction The X-ray diffraction (XRD) patterns of the prepared samples were recorded for the phase identification of all the samples. The data was taken by using a Rigaku Miniflex-II diffractometer with Cu Ka radiation at RT in the angular range 10° 6 2h 6 80° at the scanning rate of 2°/min. Rietveld refinement Rietveld refinement of all the samples was performed using GSAS-EXPGUI program [17,18]. The Rietveld method requires a structural model that has an approximation for the actual structure. In this method, the least square refinement is carried out until the best fit is obtained between the entire observed XRD pattern

XRD analysis The room temperature XRD spectra obtained for undoped and Sm3+ doped ceramics are shown in Fig. 1. BiFeO3 is known to have a rhombohedrally distorted perovskite structure described by space group R3c at room temperature. In this structure, the Bi3+ ions occupy the cubo-octahedral positions and Fe3+ ions are present in octahedral coordination. The rhombohedral cell (having a  89.4°) is very close to the cubic cell. The cations are displaced from their center of symmetry along [1 1 1]p direction with anion sub lattice having distortion according to an a a a tilt system. The FeO6 octahedra rotate in antiphase around this direction [20]. All the peaks in the XRD profiles of Bi1xSmxFeO3 ceramics (x = 0.0, 0.05 and 0.1 having code BF0/SM0, SM5 and SM10) samples are clearly related to perovskite-structured phases. Foreign phases of Bi2Fe4O9 and Bi25FeO40 are detected in undoped and 5% Sm3+ doped BiFeO3 samples [21]. These secondary phases are routinely observed in metastable BiFeO3 ceramics due to its chemical kinetics of formation. A single phase BiFeO3 material (as shown in XRD data) is formed by doping 10% Samarium at A-site which indicates that the Sm3+ ions are incorporated very well in the BiFeO3 crystal structure. Pure polycrystalline BiFeO3 samples with rhombohedral structure have clearly separated (1 0 4) and (1 1 0) diffraction peaks around 32°. The existence of these splitted peaks in the prepared samples confirms the distorted R3c rhombohedral structure which is compatible with the earlier reports [22,23]. Due to smaller ionic radius of Sm3+ as compared with Bi3+, the peaks around 32° shifts toward higher diffraction angle. The addition of trivalent Sm in BiFeO3 does not lead to any structural transition up to 10% doping which can be possible at higher concentration as reported in previous investigations [13,24].

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Fig. 1. XRD patterns of Bi1xSmxFeO3 samples. The impurity phases are marked by stars.

Rietveld analysis To know the structure in detail and the lattice parameters of the prepared samples, the experimental XRD data was simulated. Fig. 2(a and b) shows the Rietveld refinement data of SM5 and SM10 samples, respectively. The refined structural parameters and lattice constants (‘‘a’’ and ‘‘c’’) are summarized in Table 1. In order to make the refinement more effective certain residuals are defined used to obtain convergence. The profile residual (Rp)

P Rp ¼

i jI iO

P

 IiC j

and, weighted profile residual (Rwp) are

"P Rwp ¼

i wi ðI iO

P

Fig. 2. Rietveld refined XRD patterns of SM5 and SM10 samples.

ð2Þ

i IiO

 IiC Þ2

2 i wi I iO

Table 1 Structural parameters and profile R-factors of Bi1xSmxFeO3 samples obtained from Rietveld refinement with crystal structure R3c.

#1=2 ð3Þ

These residuals leads to the value of v2 (goodness of fit quality factor) approaching (1). The low values of these parameters (as listed in Table 1) conclude that the structure fit well to the rhombohedral R3c structure. The lattice parameters a = 5.58 Å and c = 13.86 Å obtained from refinement of BiFeO3 ceramic agreed well with that reported in previous work [25]. Initially the Rietveld refinement was performed by zero point shift, after that the unit cell and background parameters were refined. A ‘best fit’ of the entire simulated pattern to the entire experimental pattern was observed. Using Cosine Fourier series the background was modeled and peak shapes were fitted by pseudo-Voigt function. On Sm doping, the value of ‘‘a’’ remains almost same but the value of ‘‘c’’ decreases. The bond length and bond angles resulted from Rietveld refinement are presented in Table 2.

Parameters

BFO

SM5

SM10

a (Å) b (Å) V (Å3)

5.58 13.862 62.21

5.574 13.839 62.06

5.572 13.815 61.91

Bi/Sm

x: 0 y: 0 z: 0.002

0 0 0.276

0 0 0.273

Fe

x: 0 y: 0 z: 0.221

0 0 0

0 0 0

O

x: 0.447 y: 0.026 z: 0.961

0.82 0.62 0.49

0.889 0.647 0.485

Rp (%) Rwp (%)

6.15 8.22 4.89 0.839

4.53 5.95 2.99 0.836

4.00 5.19 2.57 0.832

v2 t

Magnetization analysis The hysteresis loops of Sm doped BFO samples at room temperature are shown in Fig. 3. For BiFeO3 samples the M–H loop is linear at RT [26]. A similar linear contribution is observed in BFO doped with 5% Sm3+ contents which illustrates the basic anti-ferromagnetic nature. It is well known that Lanthanide substitution in BiFeO3 reduce the threshold field of the magnetic phase transformation. Such a behavior is mainly associated with the doping driven increase of the magnetic anisotropy [2]. The anisotropy by the dopants can be directly affected by inducing changes in the crystal field of ligands through the doping with ions having different ionic radius, or indirectly by magneto electric coupling. For

Sm10 sample, an opened magnetic hysteresis loop is observed showing considerable deviation from linearity. In BFO samples, Bi atoms controls the crystalline structure which leads to spiral arrangement of spins of Fe atoms and do not directly affect the magnetic properties [6]. Even at higher addition (>10%) of Samarium substitution did not much influence the linear contribution of BiFeO3 ceramics because Sm3+ ions are not much magnetically active ions having smaller effective magnetic moment of 1.5 lB. Previous investigations on the magnetization measurements of Bi1xLnxFeO3 samples suggest that there is a correlation between the ionic radius of the doping element and the magnetic properties of a corresponding compound. To induce

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Table 2 Bond distances and bond angles of all samples determined through the Rietveld refinement. Bond distances (Å)

Bond angles (°)

BFO Bi–O Fe–O Bi–Fe

2.479, 2.358 2.048, 1.998 3.082, 3.311

O–Bi–O O–Fe–O Bi–O–Fe

139.2, 115.80, 92.20, 71.28 169.8, 90.60, 88.35, 83.0 103.6, 97.2, 94.8, 89.7

SM5 Bi–O Fe–O Bi–Fe

2.157, 2.925, 2.817 1.840 3.097, 3.314

O–Bi–O O–Fe–O Bi–O–Fe

67.55 119.44 125.57

SM10 Bi–O Fe–O Bi–Fe

2.293, 2.502 1.756 3.125, 3.321

O–Bi–O O–Fe–O Bi–O–Fe

143.5, 114.12, 93.06, 71.9 118.65 121.4, 101.0

spontaneous magnetization small amount of substituting element is required if the difference between the ionic radii of Bi3+ and substituting ions is larger. As there is not much larger difference between the ionic radii of Bi3+ and Sm3+, greater amount of Sm3+ substitution (as compared to that reported in present study) is necessary for inducing magnetization. A-site substitution results in a gradual suppression of the spin modulation within the initial R3c structure and complete destruction of the spin cycloid takes place only at composition driven phase transformation consistent with that reported [13]. Sm substitution (up to 10%) in BFO does not result in any phase transformation, but only partial change in unit cell volume and lattice parameters is observed due to difference of ionic radii of Bi3+ and Sm3+ ions. The Fe–O perovskite octahedron gets distorted and this internal structure distortion is related to the changes in Bi–O, Fe–O bond length and Bi–O–Fe, Fe–O–Fe bond angles (Table 2). The phase pure SM10 sample exhibited a higher remnant magnetization. A similar type of behavior is also reported in Anthonyraj et al. [27] for the same composition. The measurement of how well the ions fit into a perovskite unit cell is estimated by the ratio (rBi + rO)/l where r is the ionic radius of the respective ions and l is the length of the octahedral edge [28]. This ratio completely resembles to the Goldschmid tolerance factor ‘t’. In perovskite compounds with formula ABO3 the structure stability can be interpreted by this factor ‘t’ whose value was calculated for all samples by using the formula reported by Wang et al. [29]. The value of ‘t’ decreases (Table 1) with progressive

Fig. 4. Nyquist plots of impedance data at various temperatures for SM5 sample.

doping of Sm content as the driving force for octahedral rotation increases resulting in structural distortion [20]. Impedance spectra Fig. 4 illustrates the Cole–Cole formalism for SM5 sample at different temperatures. Complex impedance spectroscopy is a technique used to establish the correlation between the microstructure and electrical properties. A semicircle arc is observed at low temperature (323 K) and with increase in temperature this arc becomes a whole semicircle. The impedance spectra at 353 K presents a depressed semicircle along with a spike (part of a second semicircle) in the low frequency region which can be easily assigned to dielectric polarization between the sample surface and the electrode thus being extrinsic to the sample (Maxwell–Wagner effect) [30]. Further increasing the temperature up to 423 K the original semicircle degenerates and the spike continued to strengthen. This mainly corresponds to the situation of imaginary impedance spectra, where two semicircles coexisted. The impedance value decreased with increase in temperature which suggests thermally activated conduction mechanism. It is clear from the figure that the centers of semicircular arcs are located below the real impedance axis revealing a non Debye relaxation. In the present ceramic materials, the semicircles are ascribed to grain (bulk) mechanism and distribution of grain boundaries. The low temperature semicircle is attributed to the grain effect and with increase in temperature the grains effect is replaced by grain boundaries effect. Dielectric analysis Fig. 5 presents the frequency dependent response of the dielectric constant (e0 ) and dielectric loss (tan d) (inset) for SM5 and SM10 samples at 553 K. These quantities are important for engineering applications and calculated by using the formulas

e0 ¼

e00 ¼ Fig. 3. Magnetic hysteresis loops for SM5 and SM10 ceramics measured at RT.

Z 00 h i 2 2 2pfC o ðZ 0 Þ þ ðZ 00 Þ h

Z0 2

2pfC o ðZ 0 Þ þ ðZ 00 Þ

2

i

ð4Þ

ð5Þ

P. Godara et al. / Journal of Molecular Structure 1097 (2015) 207–213

tan d ¼

e00 e0

211

ð6Þ

where Z0 and Z00 are real and imaginary impedances, f is the frequency and Co is the geometrical capacitance. Figs. 6 and 7 illustrate the real and imaginary parts of dielectric constant (e0 and e00 ) for SM10 sample plotted against frequency at different temperatures. With increase in temperature both e0 and e00 values increases in the low frequency region. All plots exhibit a frequency dispersion behavior which is consistent with the previous studies on BFO materials [31,32]. At lower frequencies, the dielectric constant shows a larger dispersion and attains a constant value at higher frequencies. On the basis of space charge polarization model of Maxwell–Wagner [33,34] this behavior can be well explained which is also in agreement with Koop’s phenomenological theory [35]. The polycrystalline ceramics consist of perfectly conducting grains separated by insulating grain boundaries. When field is applied the displacements of charge carriers takes place and they align themselves at grain boundaries if the resistances of grain boundaries are large. At grain boundaries space charge polarization is built up governed by the available free charges. This results in the large value of dielectric constant. The variation of e0 (Fig. 8) and e00 (inset of Fig. 7) with temperature for SM10 sample at different frequencies are presented. The dielectric constant (e0 and e00 ) is found to increase sharply with temperature due to thermally induced hopping conduction. In high temperature region, e0 becomes constantly stable at higher frequencies (P450 kHz) due to the fact that any species which contribute to polarization lags behind the applied field at higher and higher frequencies.

Fig. 6. The variation of real part of dielectric constant (e0 ) with frequency for SM10 sample at different temperatures.

Electric modulus formalism The electric modulus can be expressed as [36]: 00

M  ¼ M 0 þ jM ¼ jxC o Z  ¼ jxC o ðZ 0  Z 00 Þ

ð7Þ

where x is the angular frequency and Co is the capacitance. The values of M0 and M00 can be obtained using the relationship M0 = xCoZ00 and M00 = xCoZ0 . The behavior of electric modulus for both doped samples is almost similar. In the electric modulus spectra, it is known that the smaller capacitance value will dominate which enlarge the grain effects depicting them easier to analyze. The complex electric modulus plot (M00 versus M0 ) at 343 K for SM10 sample is shown in Fig. 9. The plot clearly shows the existence of two resolved semicircles.

Fig. 7. Frequency dependence of imaginary part of dielectric constant (e00 ) for SM10 sample at different temperatures. Inset depicts the temperature dependence.

The variation of M00 with temperature at various frequencies is depicted in Fig. 10. The imaginary part (M00 ) indicates the energy loss under electric field. At a particular temperature M00 values at all frequencies exhibits a well defined peak (M00 max) giving the temperature at which the measured frequency is equal to the conductivity relaxation frequency. Below the M00 max, the frequency region represents the range in which successful hopping of charge carriers takes place and above this frequency region the charge carriers are spatially confined to potential wells and free to move only within the wells. With increasing frequency these peaks are found to shift toward higher temperature similar to that reported in Meena et al. [37]. AC conductivity studies

Fig. 5. Frequency dependence of dielectric constant and dissipation factor (inset) for Samarium doped samples at 553 K.

The phenomenon of conductivity dispersion is the most eminent representation as it influences the dielectric behavior of materials directly. The frequency dependence of ac conductivity for SM10 samples at various temperatures are shown in Fig. 11. The analysis of conductivity dispersion is generally well explained by

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Fig. 8. Temperature dependence of dielectric constant (e0 ) at different frequencies for SM10 sample.

Fig. 9. The complex modulus plot of SM10 at 343 K.

Fig. 11. Frequency dependence of the ac conductivity for SM10 at elevated temperatures.

the power-law proposed by Jonscher [38]. At 553 K, a tedious increase in conductivity curve is observed and above this temperature range a frequency independent dc plateau in the low frequency side comes into view which is attributed to the long-range translational motion of ions (contributing to dc conductivity rdc). This behavior can be well explained by jump relaxation model (JRM). According to this, at lower frequencies ac conductivity is associated with the successful hopping from one site to its neighborhood vacant sites due to the available long time period. These successful jumps result in a long range translational motion of ions contributing to the value of rdc while at higher frequencies two competing relaxation processes may appear simultaneously: (i) the jumping ion jumps back to its initial position, i.e. unsuccessful hopping and (ii) ions become relaxed in neighborhood position, i.e. successful hopping. At high frequencies the more dispersive conductivity is the result of increase in the ratio of successful to unsuccessful hopping [39]. It can be clearly observed from the figure that above 533 K the conductivity become a strong function of temperature and saturates to a constant value which is a common feature for ionic conductors. At higher temperature (633 K) a constant conductivity plateau exists in the measured frequency window consistent with that reported by Zhao et al. [40]. Sample SM5 shows the similar conductivity behavior with frequency. A gradual increase is observed in the value of conductivity with increasing temperature. The trapped charges gets liberated at higher temperatures further increasing the exchange of electrons between Fe2+ and Fe3+ ions resulting in an increased rac values.

Conclusions

Fig. 10. Temperature dependence of dielectric modulus for SM10 at different frequencies.

Ceramic samples with composition Bi1xSmxFeO3 (x = 0.0, 0.05 and 0.1) were fabricated by conventional solid-state reaction technique and their structural, magnetic, impedance and dielectric studies are carried out in view of possible applications. In the XRD patterns, the sharp and well defined peaks show that the samples have a degree of crystallinity in the whole 2h range. Refinement of all the samples has been done on the basis of hexagonal representation of R3c space group. The magnetic properties are found to be affected by the spin interaction between Sm3+ and Fe3+ or Fe2+ ions. Samarium substitution in BFO results in narrow hysteresis loops may be desirable for transformer and motor cores to minimize the energy dissipation with the alternating fields

P. Godara et al. / Journal of Molecular Structure 1097 (2015) 207–213

associated with AC electrical applications. The impedance plot revealed a non-Debye type of relaxation process and the coexistence of two semicircles which are attributed to the grain and grain boundary effects. The frequency dispersion of e and tan d is well explained by the Maxwell–Wagner type relaxation. The peak existence in the frequency response of imaginary electric modulus clearly represents the conductivity relaxation. Up to the temperature range of 533 K, the conductivity plot shows dispersion and above this a transition is observed from frequency dependent region to dc plateau. Acknowledgments Authors are thankful to DST, New Delhi for providing XRD facilities through FIST scheme. One of the authors (A. Agarwal) is thankful to the UGC, New Delhi for providing financial assistance (F. 42-829/2013 (SR)). Another author (N. Ahlawat) is thankful to the AICTE (Ref. No. 8023/RID/RPS/006/11/12), New Delhi for providing financial assistance. References [1] R. Majumder, P.S. Devi, D. Bhattacharya, P. Chaoudhury, A. Sen, M. Raja, Appl. Phys. Lett. 91 (2007) 062510. [2] V.A. Khomchenko, I.O. Troyanchuk, M.I. Kovetskaya, M. Kopcewicz, J.A. Paixao, J. Phys. D Appl. Phys. 45 (2012) 045302. [3] M.B. Bellakki, V. Manivannam, J. Sol–Gel Technol. 53 (2010) 184. [4] G.L. Yuan, S.W. Or, J.M. Liu, Z.G. Liu, Appl. Phys. Lett. 89 (2006) 052905. [5] V.A. Khomchenko, D.A. Kiselev, J.M. Vieria, L. Jian, A.L. Kholkin, A.M.L. Lopes, Y.G. Pogorelov, J.P. Araujo, M. Maglione, J. Appl. Phys. 103 (2008) 024105. [6] K. Chakrabati, K. Das, B. Sarkar, S.K. De, J. Appl. Phys. 110 (2011) 103905. [7] G.L. Bras, P. Bonville, D. Colson, A. Forget, N. Genard-Riondet, R. Tourbot, Physica B 406 (2011) 1492. [8] S. Kazhugasalamoorthy, P. Jegatheesan, R. Mohandoss, N.V. Giridharan, B. Karthikeyan, R.J. Joseyphus, S. Dhanuskodi, J. Alloys Compd. 493 (2010) 569. [9] A. Gautam, K. Singh, K. Sen, R.K. Kotnala, M. Singh, Mater. Lett. 65 (2011) 591. [10] I.O. Troyanchuk, D.V. Karpinsky, M.V. Bushinsky, O.S. Mantytskaya, N.V. Tereshko, V.N. Shut, J. Am. Ceram. Soc. 94 (2011) 4502. [11] K.S. Nalwa, A. Garg, J. Appl. Phys. 103 (2008) 44101.

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