1. X- ray diffraction studies
X- ray diffraction patterns of Co0.7−xNixMn0.3Fe2O4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15, PbZr0.52Ti0.48O3 (PZT) ferroelectric and 30% CNMFO – 70% PZT magneto electric (ME) composites are shown in Fig. 1 (a), (b), and (c) respectively. Figure 1 confirms pure phase formation without any impurity for all compositions of ferrite, ferroelectric and ME composites. From Fig. 1 (a), presence of particular characteristic peaks at certain 2θ positions confirms cubic spinel structure for all four compositions of ferrites. Lattice parameter decreases from 8.40 Å to 8.37 Å with addition of Ni content. This decrease in lattice parameter is due to the replacement of larger Co2+ (0.78 Å) ions by smaller Ni2+ (0.74 Å) ions. Lattice contraction obeys Veegards law which states that, cell volume decreases with addition of smaller cation and vice-versa . Figure 1 (b) shows well defined peaks as well as splitting of peaks which confirms tetragonal pervoskite structure for ferroelectric phase. Lattice parameters (c = 4.14 c and a = 4.03 Å) are in good agreement with reported values .
X-ray diffraction patterns of ME composites in Fig. 1 (c) show characteristicpeaks of both ferrite and ferroelectric phases. Absence of any unidentified peak confirms that, there is no any chemical reaction between two constituent phases. Two distinct phases are maintained as the final sintering temperature of ME compositesis kept lower than that of final sintering temperature of pure phases.
2. Scanning electron microscopy
Figure 2 (a), (b), (c) and (d) shows scanning electron micrographs of Co0.7−xNixMn0.3Fe2O4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15. From SEM it is clearly observed that, grain size decreases with increase in Ni content. This decrease in grain size is due to substitution of Ni2+ (0.74 Å) ions in place of Co2+ (0.78 Å) ions. The results obtained from SEM are in good agreement with results obtained from XRD in which lattice parameter decreases with increase in Ni content.Also, the number of grain boundaries and pores was found to increase with addition of Ni content which may increase the resistivity of ferrite phase and may serve our purpose to increase the resistivity of ferrite phase. With the addition of Ni content grain size was decreased from 4.9 µm to 3.8 µm. Figure 3 shows SEM of PbZr0.52Ti0.48O3 (PZT) ferroelectric phase. The grains are grown and well connected with grain size of nearly 5.1 µm are observed.
Two different regions of large sized well grown grains and smaller sized grains are observed in Fig. 4 (a), (b), (c) and (d) confirming co-existence of two constituent phases in ME composites. In the present work ME composites are synthesized in ferroelectric rich (with 70% PZT) region. Obviously, the grains of major component would grow rapidly and vice-versa, as a result, microstructure becomes heterogeneous. Variation of grain size with Ni content is random as ferrite and ferroelectric are mixed randomly.
Temperature dependent variation of dc resistivity for Co0.7−xNixMn0.3Fe2O4 (CNMFO) ferrites with x = 0.00, 0.05, 0.10 and 0.15 is shown in Fig. 5 (a). All compositions of ferrites show semiconducting behavior but the conduction mechanism is quite different than that of known semiconductors such as silicon and germanium. In semiconductors, carrier concentration increases with increase in temperature and results into decrease of resistivity. Here electron jumps from lower energy state to higher energy state of same ion and then it is available for conduction. Thus, conduction in semiconductors is due to electron hoping and ∆E in Arrhenius equation is the activation energy. In case of ferrites, carrier concentration is almost constant but, mobility of charge carriers increases with increasing temperature. In ferrites electron jumps from one ion to another ion situated at different crystallographic sites, thus ∆E is migration energy. As ferrites are resistive materials, electrons apply strain on the lattice while moving through it. Thus, electron coupled with strain field is called as polaron. If this strain field extends beyond the lattice parameter, polaron is called as large polaron and if the strain field is smaller than lattice parameter, polaron is called as small polaron. Many reports are available on conduction in ferrites due to small polaron . Spatial extent of polaron will be the appropriate term to show size of polaron rather than “polaron radius”. The term polaron radius is quite misleading and confusing, as strain field is not having exactly round shape. The conduction mechanism in ferrites is explained on the basis of Vervy de Bhor theory, which involves electron exchange between ions of the same element present in more than one valance state and randomly distributed over equivalent crystallographic sites. In cubic spinel ferrites iron ions are present in Fe2+ and Fe3+ states. This cubic spinel structure has 64 tetrahedral (A) and 32 octahedral (B) sites out of which iron ions have strong preference for B site. The distance between cation in B-site (0.292) is much smaller than the distance between cation at A-site (0.357). Thus, polaron hoping between Fe2+ and Fe3+ ions present at B-site controls conduction in ferrites. This polaron hoping is thermally activated and with increase in temperature, conductivity increases showing NTCR. Careful observation of Fig. 3 (a) shows increases in resistivity with addition of Ni content. This is obviously due to the fact that, Ni2+ ions have strong preference for B-site . This will displace Fe2+ or Fe3+ions from B-site reducing conduction at B-site. Thus, it can be said that, inverse spinel structures have higher resistivity than normal spinel structures. As observed from SEM grain size decreases with Ni content. Increased number of grain boundaries and pores will act as opposing walls for conduction and will cause resistivity increase. Spatial extent of polaron can roughly calculated by the formula
Rp = ½ [π/6N] 1/3 −−−−−−−−−−−−−−−−−−−−1
Where, N is number of sites per unit volume = 64 (A) + 32 (B)/ (a) 3= 96/a3, where ‘a’ is lattice parameter.
Values of polaron field extent (Table 1.1) are smaller than lattice parameter. Thus, conduction due to small polaron hoping is confirmed. At certain higher temperature there is change in slope of graphs indicating phase transition from ferromagnetic to paramagnetic state. Figure 5 (b) shows variation of dc resistivity with temperature for PbZr0.52Ti0.48O3 (PZT) ferroelectric phase. In resemblance with the ferrites conduction in ferroelectric can also be explained with the help of Vervy de Bhor mechanism. With increase in temperature polaron hoping between Zr3+-Zr4+, Pb2+-Pb3+and Ti3+-Ti4+. Polaron extent is calculated by using Eq. 1.
Where, N = number of sites per unit volume = (1 B + 8 A)/a3 = 9/ a3 fromthe Table 1.1 it can be seen that for PZT also charge carriers are small polaron. But polaron extent is much bigger than ferrites as ferroelectrics are more resistive.
Variation of dc resistivity with temperature for ME composites with 30% CNMFO and 70% PZT is shown in Fig. 5 (c). All compositions of ME composites show semiconducting behavior due to polaron hoping between Zr3+-Zr4+, Pb2+-Pb3+and Ti3+-Ti4+ and Fe2+-Fe3+.
Values of polaron radius of Co0.7-xNixMn0.3Fe2O4pellets with X = 0.00,0.05,0.10 and 0.15
Polaron Radius (Rp)
4. Dielectric Constant
Dielectric constant decreases with increase in frequency showing regular dielectric dispersion behavior for all compositions of ferrites, ferroelectrics and ME composites as shown in Fig. 6 (a), (b), and (c) respectively. High values of dielectric constants at lower frequencies are sum of four types of polarizations; electronic, ionic, orientational and space charge polarization. Each polarization has different dimensions e. g. electronic polarization is smallest and its dimensions are nearly 1019 Å. Ionic polarization is slightly sluggish and has dimensions of nearly 1015 Å. whereas dimensions of orientational polarization are approximately 109 Å and so on. Due to different dimensions, they are active in different frequency regions. At lower frequency all polarizations are present but with increase infrequency contribution of each polarization decreases and dielectric constant also decreases . Thus, all compositions show dielectric dispersion behavior. With the present instrument we can measure dielectric constant up to107 Hz. Thus, only space charge and orientational polarizations are reduced and observed due to limitations of instrument. Resultant value due to sum of electronic and ionic polarization is called as static value of dielectric constant.
Figure6 (a) shows variation of dielectric constant with frequency for all compositions of ferrites. According to Maxwell Wanger theory and Koops phenomenological theory inhomogeneous dielectric is made up of conducting grains, less conducting grain boundaries and non-conducting cracks, pores and defects . Polarization in ferrites is similar process to the conduction. Conduction of polaron in Fe2+-Fe3+ ions present at B-site leads to local displacement of charges responsible for polarization. Due to higher resistivity of grain boundaries these charges pile up at grain boundaries and contribute for higher dielectric constant. As observed from resistivity section, resistivity increases with addition of Ni content in ferrites. Due to increased resistivity of grains, charges reaching the grain boundaries are reduced and as a result dielectric constant decrease. Thus, with increase in resistivity dielectric constant decreases and it can be said that, resistivity and dielectric have inverse proportion .
Variation of dielectric constant with frequency for PZT is shown in Fig. 6 (b). Polaron hoping between Zr3+-Zr4+, Pb2+-Pb3+and Ti3+-Ti4+ is responsible for displacement of charges . PZT shows much higher dielectric constant as compared to ferrites. Figure 6 (c) shows variation of dielectric constant with frequency for all compositions of ME composites. Random variation of dielectric constant with Ni content was observed as ferrite and ferroelectric grains are randomly mixed.