CrFe2O4-BiFeO3 Perovskite Multiferroic Nanocomposites – A Review

Though semiconductor technology has advanced significantly in miniaturization and processor speed the “ideal” nonvolatile memory memory that retains information even when the power goes is still elusive. There is a large demand for non-volatile memories with the popularity of portable electronic devices like cell phones and note books. Semiconductor memories like SRAMs and DRAMs are available but, such memories are volatile. After the advent of ferroelectricity many materials with crystal structures of Perovskite, pyrochlore and tungsten bronze have been derived and studied for the applications in memory devices. Ferroelectric Random Access Memories (FeRAM) are most promising. They are nonvolatile and have the greater radiation hardness and higher speed. These devices use the switchable spontaneous polarization arising suitable positional bi-stability of constituent ions and store the information in the form of charge. This paper is focused on the synthesis and characterizations of BiFeO3 and xCrFe2O4-(1-x) BiFeO3 nanoceramics which are most promising FeRAM materials. The effect of various-dopant-induced changes in structural, dielectric, ac impedance, ferroelectric hysteresis, mechanism of the dielectric peak broadening and frequency dispersion have been addressed. It also deals with low temperature processing technique of those nanoceramics which has high dielectric and ferroelectric properties. These studies can be further extended to reinforce BiFeO3 and CrFeO4 materials with carbon nanotubes to obtain conductive composites using appropriate techniques. key words: CrFe2O4 and BiFeO3 nanoceramics; FeRAM material; nanocomposites; sol-gel technique; XRD technique; perovskite materials.


INtROduCtION
Modern engineering systems, like highperformance engines, nuclear reactors, computers and memory devices, require better and new materials than those available today.Better materials and processes have an increasing roll in efforts for environmental protection, development of information infrastructure, improvement in energy efficiency, modern and reliable transportation and civil infrastructure.In certain industries, the need for energy conversion systems, energy efficiency and materials withstanding corrosive chemical and/or thermal environments have sparked a new interest in processing of ceramic materials.Moreover, the continuing trend towards miniaturization in the electronic industry has imposed a growing demand on preparation of semiconductors using innovative processing techniques.Ceramics have been traditionally admired for their mechanical and thermal stability and the unique electrical, optical and magnetic properties.These materials have become very important in many key technologies including communications, energy conversion and storage, electronics and automation.These materials are now classified under electro-ceramics to distinguish them from other functional ceramics like structural ceramics.Historically, developments in the various subclasses of electro-ceramics have indicated the growth of new technologies.Thus advances in materials research, represent and progress across a broad range of scientific disciplines and technological areas, with high impact on society.

Perovskite -Ferroelectric Materials
Many oxide structures are based on close packing of cations and anions.A somewhat different structure occurs where large cations are present, which can form a close packed structure along with the oxygen ions.Calcium titanate (CaTiO 3 ) is the first compound to be classified as a Perovskite invented by Russian geologist Perovsky.The commonly studied ferroelectrics have the cubic Perovskite structure (in paraelectric phase) with chemical formula ABO 3 .For convenience, the structure drawn in Fig. 1 as A-site cations occupying the corners of a cube, and B-site cations on the body center.Three oxygen atoms per unit cell are on the faces.The lattice constant of these Perovskite is always close to 4a (where 'a' is the lattice constant).Because, the rigidity of oxygen octahedral network and well defined oxygen ionic are having radii of 1.350 Å.The A-site cation has 12-and B-site cation has 6-coordinates.The site-A cation is generally bigger than the site-B cation.The oxygen anion has 6 as the coordination number.All the ions assumed as hard spheres, and the lattice parameter 'a' of the cubic Perovskite is given by 2 / ) ( 2 are the ionic radii of the 12-coordinated site-A cation, 6-coordinated site-B cation, and 6 -coordinated oxygen anion respectively.The stability of the Perovskite structure can be described geometrically as the ratio of Eq. (1) to Eq. ( 2), called as the tolerance factor -'t'.It is given by It is advantageous if the A-and B-site cations are in contact with oxygen anions for an ABO 3 compound for forming a steady Perovskite structure.Thus, if the tolerance factor t »1.0, then the Perovskite structure is more stable.An advantage of the Perovskite structure is that different cations could be substituted on both A and B site without any drastic change in the overall structure.Complete solid solution is easily formed between many cations, often across the entire range of composition.Simple solid solutions are basically of two types: substitutional solid solutions and interstitial solid solutions.In substitutional solid solutions, the atom that is being introduced directly replaces an atom of the same charge in the parent structure.In case of interstitial solid solutions, the introduced species occupies a site that is normally empty in the crystal structure.Even though two cations are compatible in the solution, their individual behavior can be radically different when apart.Thus, it is possible to change the properties of the materials like Curie temperature, piezoelectric coefficient etc. with a small substitution of given cation.

Ferroelectric And Magnetic Materials
Magnetic and Ferroelectric materials are the customary subjects of research area and have been leading the most significant technological advances in these days.These materials have several applications in modern technology.For example, the consumers' electronic products are generating huge data and are stored as regions of opposite magnetic polarization in ferromagnets.The sensors industry depends mostly on ferroelectrics materials.Many ferroelectric materials are also ferroelectric -i.e., A change in their electric polarization is accompanied by a change in shape.Consequently, they are used to convert sound waves into electrical signals in sonar detectors.In actuators they convert electrical impulses into motion.Ferro-electricity and Magnetism are concerned with off centre structural distortions of the material and local twists.These two apparently unrelated phenomena may coexist in certain odd materials.These materials are known as multiferroics [2][3][4][5][6][7][8][9][10][11][12][13][14] .The word "electromagnetism" derives from the fact that the magnetic and electric fields are interdependent.A changing magnetic field produces an electric field, whereas an electric current, produces a magnetic field (Biot-Savart law).Electromagnets are coiled wire or loops, which are bulky and difficult to fabricate.The magneto-electric effect in a solid i.e., the induction of magnetization by means of an electric field and the induction of an electric polarization (P) by magnetic field are observed by Pierre Curie 15 .He studied the analogy of the electromagnetic phenomena in solids and in vacuum.This analogy is significant from the standpoint of applications.The efficient control of magnetism by an electric field in a solid could help the technology of spintronics used for magnetic random access memory and magnetic storage.

Ferroelectricity
Ferroelectrics are the materials that have two or more equilibrium orientations of impulsive polarization vector in the absence of an external electric field.The spontaneous polarization vector may be switched between these two orientations by an electric field 16 .Two main types of a ferroelectric behavior can be distinguished -displacive and orderdisorder.The displacive type behavior is due to an ion getting displaced from the equilibrium position.Hence it acquires a permanent dipole moment.At high temperatures (T > T C , where T C is a ferroelectric Curie temperature), the thermal energy is sufficient to allow the ions to move randomly from one position to another, so there is no fixed asymmetry.When the temperature is below T C , the ion is frozen in an off-center position.This gives a net dipole moment.In an order-disorder ferroelectric, a dipole exists in each unit cell.But at high temperatures, they are pointing in random directions.When the temperature is lowered, the dipoles get arranged in order and become aligned in the same direction within a single domain.
Ferroelectric polarization hysteresis loop shown in (Fig. 2) is the characteristic of ferroelectric material, which arises due to the presence of ferroelectric domains in the crystal.Application of an external DC electric field, E >E C (where E C -coercive field) to a polydomain ferroelectric crystal, causes the polarization.The vectors P, having different orientations in different domains, to align themselves parallel to the field direction via the domain wall movement.The minimum value of the DC field, required to move the domain walls, is a measure of the coercive field.The initial value of the vector P S in a polydomain crystal increases with increasing DC field to a maximum value which is a characteristic of the material.Reversing the electric field reintroduces movement of domain walls.This results in the vector P S in different regions to be reversed.At zero current fields, the crystal will have a remnant polarization, which is smaller than the spontaneous polarization.At fully reversed field, the final Ps will have the same magnitude as the original Ps but with opposite sign.The hysteresis loop is a function of the work required to displace the domain walls, which is closely related to the defect distribution in the crystal and to the energy barrier separating the different orientations.
According to their symmetry, crystals can be divided into the 32 point groups with 11 of them being centrosymmetric (non-polar) and 21 lacking an inversion center (polar).Lack of inversion center is a pre-requisite for the piezoelectric behavior of the crystal.The crystal lacking a centre of symmetry will have a net 6 displacement of the negative and positive ions with respect to each other resulting in an electric dipole.For the centrosymmetric crystals, the centers of the two opposite charges will always coincide, so that there is no electric dipole generated.Out of the twenty piezoelectric classes, only ten, possessing a unique polar axis which can be spontaneously polarized, belong to ferroelectrics.Among all the ferroelectric materials, which are studied the Perovskite ferroelectrics are the most extensively and widely used.A perfect Perovskite structure has a general formula of ABO 3 , where A represents a divalent or trivalent cat-ion, and B is a tetravalent or trivalent cation.The origin of ferroelectricity in this class of materials can be explained using the well-known example of BaTiO 3 .BaTiO 3 is a ferroelectric material with a Perovskite structure as shown in Fig. 3.It is the first discovered piezoelectric ceramic 17 .BaTiO 3 has a cubic structure above Curie temperature Tc, 120ºC.Cubic BaTiO 3 is nonferroelectric because, the centers of negative and positive charges overlap as the ions are symmetrically prearranged in the unit cell.It has tetragonal structure below T C , in which the O -2 ions in the BaTiO 3 crystal are shifted in the negative C-direction, while the Ti +4 ions are shifted in the positive C-direction.It results in an electric dipole along the C-axis.Therefore BaTiO 3 is ferroelectric in tetragonal structure.The behavior of the spontaneous polarization of ferroelectrics can be explained by thermodynamic (Landau-Ginzburg-Devonshire) theory [16, 18].In the basic Landau-Ginzburg-Devonshire theory, one assumes that the free energy may be expanded in a power series of the order parameters of the system.For a ferroelectric, the macroscopic order parameter is polarization P: .......... 6 Where the coefficients á n are temperature dependent.This series does not contain terms in odd powers of P if the un-polarized crystal has a center of inversion symmetry.The value of P in thermal equilibrium is given by the minimum value of F as a function of P; differentiating the equation above with respect to P gives: ... 0 The coefficient á 1 takes the form á 1 = ã (T " T 0 ), where ã is a positive constant and T 0 may be equal to or lower than the phase transition temperature, T C .The assumed form of á 1 is a necessary result of mean field theory and its validity is supported by the experimentally observed Curie-Weiss law.A small positive value of á 1 indicates that the lattice is "soft" and close to instability.A negative value of a 1 indicates that the un-polarized state is unstable.
When a 2 is positive, we can neglect the á 3 term.The polarization for zero fields can be found from Eq.6.
So that either P S = 0 or For, T e" T 0 , P S = 0 since ã and á 2 are positive.Therefore, T 0 is the Curie temperature.For T< T 0 , the minimum of the free energy in zero field is at Which is plotted in Fig. 4(a).Changes in the free energy and polarization at the transition temperature are continuous and it is a second order transition.When á 2 is negative, the transition is of first order.We must retain á 3 and take a positive value to ensure that F converges.The equilibrium condition for E = 0 in this case is: At the transition temperature T C , the free energies of the paraelectric and ferroelectric phases are equal.The existence of meta-stable phases during the phase transition is characteristic of first order transitions.Correspondingly, a sudden jump in polarization occurs at T C as shown in Fig. 2.3 (b).In the present study an attempt is made for the synthesis and characterizations of BiFeO 3 and BiFeO 3 with CrFeO 4 for different percent compositions discussed in chapters 4 and 5 respectively.

Multiferroic Materials & Magneto-electric Effect
As per definition, a single-phase Multiferroic 5 material is one, which consists of 2 or all 3 of the 'ferroic' properties: i.e., ferroelectricity, ferroelasticity and ferromagnetism.On the other hand, the current tendency is to eliminate the requirement of ferroelasticity, but to include the possibility of ferrotoroidic order.Furthermore, the classification of a Multiferroic is widening to include antiferroic order.The magneto-electric effect is defined as the induction of polarization by means of a magnetic field and induction of magnetization by an electric field.Magneto-electric coupling may exists, whatever be the nature of magnetic and electrical order parameters.For example this occurs in paramagnetic ferroelectrics 14 .Magneto-electric coupling may occur directly between the two order parameters, or indirectly via strain.The nontrivial spin-lattice coupling in these multiferroics has been manifested through various forms, like linear and bilinear magneto-electric effects 19,20 , polarization change through field-induced phase transition 21,22 , magnetodielectric effect 8,10 , and dielectric anomalies at magnetic transition temperatures 11,12 .
Magnetoelectric multiferroics have all the potential applications of both their parent ferroelectric and ferromagnetic materials 23 .Specific applications, that have been proposed for such materials include multiple-state memory elements, magnetic field sensors, electric-field-controlled ferromagnetic resonance devices, and transducers with magnetically modulated piezoelectricity.The ability to couple with either the magnetic or the electric polarization offers an extra degree of freedom in the design of conventional devices.It was initially proposed that both magnetization and polarization could independently encode information in a single multi-ferroic bit.Four-state memory has recently been demonstrated 24 , but in practice, it is likely that the two order parameters are coupled 20,9 .Coupling could permit data to be written electrically and read magnetically.This is attractive, since it would use the best aspects of magnetic data storage and FeRAM.
In the early 1894, Curie 15 claimed that symmetry conditions enable the bodies containing asymmetric molecules to be polarized in a magnetic field and, magnetized in an electric field.The existence of magneto-electric materials was first experimentally observed in an un-oriented Cr 2 O 3 crystal by Astrov in 1960 25 .Rado and Folen then revealed the anisotropic nature of the magneto-electric effect in oriented Cr 2 O 3 crystals 26,27 .Smolensky et al 28 experimentally proved the existence of magneto-electric effect in a solid solution of PbFe 2/3 W 1/3 O 3 -Pb 2 MgWO 6 .Zhdanov et al. independently confirmed the existence of magneto-electric Perovskite materials based on a study on the PbTiO 3 -BiFeO 3 and BiFeO 3 [29][30][31] systems.Later, a magneto-electric effect was revealed in other structures and more and more systematic studies were undertaken 7,34,32 .BiFeO 3 , with its magnetic and electrical properties has created interest as the material with many applications.It was expected to form a new type memory by the combination of ferromagnetic and ferroelectric properties.Tabares-Munoz et al 33 , observed the ferroelectric/ferroelastic single domain using polarized light microscopy.After this observation, the controversy surrounding the ferroelectric nature in BiFeO 3 was solved.BiFeO 3 is reported to exhibit about a weak ferromagnetic ordering and eight structural transitions 34,35 .The neutron diffraction studies are conducted at room temperature.This revealed that BiFeO 3 has compensated anti-ferromagnetic ordering (T N ~397°C) with a cycloidal spin arrangement, which is disproportionate with its lattice 36 .In BiFeO 3 , the ferroelectric phase is stable up to 836°C.It is very difficult to observe ferroelectric loop at room temperature because of the low resistivity of the sample.The measurements are done at 80KV by Teague et al 37 , to enhance the resistivity and observe a hysteresis loop.They obtained a loop on a single crystal, with a spontaneous polarization of 3.5 mC/ cm 2 in the (100) direction.The existence of Bi 2 Fe 4 O 9 as an additional impurity phase in spite of adopting the improvised method suggested by Sosnowska et al 37 and Achenbach et al 38 is represented by several investigations.Synthesis by microwave-hydrothermal technique is reported to give rise to pure binary oxide 39 .Forming a solid solution of BiFeO 3 with other ABO 3 type of Perovskite helps to reduce the impurity and enhances the resistivity 40,41 .This enables the study of physical properties of BiFeO 3 rich phases and extrapolation of the data to the pure compound.In present work, an attempt is made to study the effect of sintering temperature on electrical and structural properties of BiFeO 3 ceramics, prepared using sol-gel technique.

CRFE 2 O 4 -BIFEO 3 Perovskite Multiferroic Materials
It is emphasized that the Multiferroics are a rare class of materials, since ferroelectricity and ferromagnetism make them an exclusive group.Presently, they are a hot research area in view of the many novel applications.Equilibrium contributions of the two phases like ferrite and ferroelectric form magneto-electric composites.These materials are used in sensors, transducers, switching devices and data storage 42 .In addition to the potential application as magneto-electric devices, they are likely to find applications as microwave absorption materials also due to magneto-electric coupling 43 .Perovskite-type BiFeO 3 is one of the multiferroics with both ferroelectric (T c =1103K) and G-Type antiferromagnetic (T N =643 K) nature [44][45][46][47] .In BiFeO 3, Bi-O orbital hybridization due to Bi 6s 2 lone pair is responsible for the ferroelectric instability, while Fe-O-Fe anti-symmetric Dzyaloshinskii-Moriya exchange gives rise to a complicated magnetic order 48 .The low resistivity of the BiFeO 3 ceramics is mainly caused by existence of Fe 2+ and oxygen deficiency 49 .The selection of ferrite and ferroelectric materials depends on factors like high magnetostriction coefficient, piezoelectric coefficient, high dielectric permeability and poling strength.CrFe 2 O 4 is an IIB-type half-metal material.Its molecular magnetic moments are about 5.6ì B which is higher than that of Fe 3 O 4 , 4.0ì B   50   .
From a theoretical study of cat-ion distribution of CrFe 2 O 4 , it is observed that it has Fe 3+ at tetrahedral site, Fe 2+ and Cr 3+ at octahedral site 51 .Till now, scholars have synthesized nanocomposites of ferrites (CuFe 2 O 4, CoFe 2 O 4 and ZnFe 2 O 4 ) with PZT/BaTiO 3 /BiFeO 3 both in bulk and thin films in order to enhance the Multiferroic properties [52][53][54] .An important property is the coupling between electrical and magnetic dipole.The coupling can be induced by magneto-electric effect.understanding the coupling between the magnetic and dielectric properties of nanocomposites is a hot area of research.The ultimate goal of controlling the magnetic/dielectric state using electrical/magnetic field requires that both these properties are coupled.The magnetoelectric couplings of most of the materials are normally weak at room temperature.Hence, it is difficult to find a material with a large magnetoelectric effect at room temperature.To find out the materials which have large magneto-electric effect at room temperature a lot of research is started now 55,56 .Very few papers have been reported on CrFe 2 O 4 -BiFeO 3 spinel-perovskite nanocomposite.Therefore in the present a systematic study is carried out on structural, dielectric, magnetic and magneto-electric properties of nanocomposites xCrFe 2 O 4 -(1-x) BiFeO 3 with x = 0.0, 0.1, 0.2, 0.3 and 0.4 synthesized by sol gel technique.

Experimental Procedure
As discussed in the above sections, the properties of BiFeO 3 phases are studies and extrapolated to set the properties of the pure compound.An attempt is made to estimate the effect of sintering temperature on electrical and structural properties of BiFeO 3 ceramics prepared using solgel technique by Ratnakar Pandu et al 57 .In their experiment, BiFeO 3 is made by sol-gel technique.All reagents are in the analytical grade.Fe(NO 3 ).9H 2 O, Bi(NO 3 ).5H 2 O, citric acid and ethylene glycol are used as starting materials.In the first step, in the distilled water, an aqueous solution of citric acid is made.Then bismuth and ferric nitrates are added to this solution with thoroughly mixing at 60-70 0 C.This is mention to get a homogeneous mixture and to avoid precipitation.Thus a brown color citrate mixture is obtained with clear solution and without precipitation.Then the citric acid/ethylene glycol in the ratio of 60:40 is added to the solution.Subsequently the solution is heated at 600 0 C for 5 hours.Initially this solution was started to swell and filled the beaker by producing a foamy precursor.This foam contains light and homogeneous flakes of tiny particles.The formation of BiFeO 3 is checked by XRD technique with Cu K a radiation (l=0.15418nm), using a BRuKER D8 XRD spectroscope.The surface grain distribution and composition analysis of BiFeO 3 samples were studied using Field Emission Scanning electron micrographs (FESEM), Quanta 200 attached with Energy dispersion X-ray spectrometer (EDAX).Thermo-gravimetric (TG) and differential thermal gravimetric analysis are conducted and checked the stability and phase transformation in the samples.To study ferroelectric hysteresis behavior, a modified Sawyer-Tower circuit is used.Structural characterization and particle morphology study of the synthesized powder is conducted using XRD by monochromatic Cu Ká radiation and TEM respectively.The dielectric measurements are carried out on silver coated pellets using HIKOI-3532 LCR Hi-Tester.Magnetic measurements are carried out at room temperature using a VSM (vibrating sample magnetometer) with a maximum magnetic field of 5kOe.Variations of dielectric constant as a function of magnetic field are also studied.

RESuLtS ANd dISCuSSIONS
BiFeO 3 is the rhombohedrally indistinct perovskite material.This is belong to the space class R3c, with rhombohedral lattice parameters a R =5. since BiFeO 3 is metastable with respect to Bi 2 Fe 4 O 9 (mullite phase) and Bi 25 FeO 39 (sillenite phase) 62,63 .The presence of these impurities results in leakage current in BiFeO 3. It results in poor ferroelectric property and thus causes to be this material is not suitable for practical applications.The available methods, for formation of phase-pure BiFeO 3 with improved multi-ferroic properties are (a) forming solid solution of BiFeO 3 with other ABO 3 type of perovskites like PbTiO 3 64,65 (b) calcinations of stoichiometric mixture of Bi 2 O 3 and Fe 2 O 3 followed by discharging with nitric acid [66] and (c) rapid liquid phase sintering of BiFeO 3 67, 68   .S e l b a c h e t a l ., o n t h e b a s i s o f thermodynamics have suggested that isovalent substitution with a larger cat-ion on the A site or a smaller cation on the B site would increase the stability of BiFeO 3 relating to the binary oxides and possibly also relating to the Bi 2 Fe 4 O 9 mullite and Bi 25 FeO 39 sillenite phase 69,70 .Substitution of a more acidic cation on the B site or a more basic cation on the A site is also expected to stabilize the perovskite phase.They also reported that La 3+ is about the same size as Bi 3+ , and although the space group changes with high substitution levels, perovskite phase is obtained with up to 40% La 3+ .Rare earth ions are smaller than Bi 3+ , but more basic cat-ions, hence the stable solid solutions prepared at ambient pressure have been reported up to 15-20% substitution [71][72][73][74] .Fig. 6. shows the XRD patterns of BiFeO 3 , sintered at 650, 700, 750, 800, 825 and 850°C.From the XRD pattern, it is noted that the major peaks of all sintered samples belong to rhombohedrally fuzzy perovskite BiFeO 3 (R-phase), although tiny amounts of Bi 2 O 3 were detected due to excessive Bi used for compensating volatilization during synthesis.Moreover, the formation of BFO (R-phase), the formation of the minor impure phases, like Bi 46 Fe 2 O 72 (non perovskite paramagnetic phase shown by * symbol) was detected from the XRD analysis.BiFeO 3 is a metastable composite and because of its chemical kinetics of formation.It is always associated with some impurities which do not contribute for the observed magnetic and dielectric properties, as reported by several research scholars 75,76 .The phase analysis is carried out by taking into account the hexagonal BFO unit cell.This unit cell of BFO system consist two formula pseudocubic units cells of BiFeO 3 .The lattice parameters for rhombohedral unit cell of BiFeO 3 are calculated from the indexed XRD pattern for BFO samples sintered at 850 0 C   cos(q) sinq as shown in Fig. 6. using 2q values from the XRD graph and (hkl) values from the standard JCPD-86-1518 card the lattice parameters for the unit cell are generated.The calculated values of the lattice parameters for the hexagonal unit cell of BiFeO 3 matched well with the values reported in the literature [60, 61] which is in the range of which is in the range of 5.5575 -13.861Å.
The variation of lattice parameter 'a R ' with sintering temperature is given in Fig. 7. From the plot of lattice parameter, it is found that with increasing sintering temperature the lattice parameter 'a R ' decreases for BiFeO 3. In this research work the Williamson-Hall approach is used for de-convoluting crystallite size and strain contribution to the X-ray line broadening (â 1/2 ) in the present materials since the Scherrer's formula does not take the strain contribution into account.According to this approach, the X-ray line broadening is a sum of the contribution from small crystallite size and the broadening caused by the lattice strain present in the material 77 , i.e.
where β size = l/Lcosq (from Scherrer's formula) and β strain = 4h tanq; where h is strain Therefore Eq.10 becomes β 1/2 = l/L cosq + 4h tanq ... (11)   β 1/2 cosq/l = 1/L + T sinq/l, where T = 4h, is a measure of strain present in the lattice.Hence by plotting â 1/2 cosq vs. sinq, it is found that the crystallite size from the intercept of the line at x = 0.The lattice strain and crystallite size is calculated from Fig. 8. using the above explained expression From the plot of crystallite size verses sintering temperature, it is found that with increasing sintering temperature crystallite size increases and strain decreases.Fig. 10.shows the FESEM micrographs of BiFeO 3 sintered at different temperature.The microstructures of the sintered BiFeO 3 pellets specified spherical grains, which are uniformly and homogeneously distributed.These microstructures also reveal that the sintered pellets are reasonably dense.Also, it was found that the edges of the grains are not sharp, which shows melting like behavior resembling liquid phase sintering.
The Fig. 11 is shown the variation of grain size with sintering temperature.Grain size measurement is complicated by a number of factors.First, the three-dimensional size of the grains is not constant and the sectioning plane will cut through the grains at random.Thus, on a cross-section it is observed a range of sizes, none larger than the cross section of the largest grain sampled.Grain shape also varies, particularly as a function of grain size.So the intercept approach is applied for measuring grain size.In this method, one or more lines are superimposed over the structure at a known magnification.The true line length is divided by the number of grains intercepted by the line.This gives the average length of the line within the intercepted grains.This average intercept length will be less than the average grain diameter but the two are interrelated.Grain size was observed to increase

Intensity (a.u) Bragg angle (2q )
with increase in sintering temperature.This happens because as the sintering process continues at higher temperatures, the individual powder particles lose their identity completely and grain boundaries move across prior particle boundaries.Larger grains replace the original fine particle structure which influences the dielectric and electrical properties of the samples..The high values of dielectric constant at lower frequencies may be explained on the basis of space charge polarization due to inhomogeneites present in dielectric structure viz.porosity in the nanocomposite system.Decrement of dielectric constant for nanocomposites with x=0.10, 0.20, 0.30 and 0.40 may be accepted on the basis of Ginzburg-Landau theory.This explains the origin of anomaly in dielectric constant (å) on the magnetic order of ferroelectromagnets with T M << T E .The difference of the dielectric constant (äå) below temperature T M will be proportional to square of the magnetic order parameter i.e., äå ~ ãM 2 , where M is magnetization.The sign of äå depends on the sign of the constant magneto-electric interaction (ã).It can be either positive or negative 83 .
The dielectric constant variation (Fig: 18(a)) with the applied external magnetic field (0-9kOe) is found to be above 0.05% for x=0.2, 0.3, which is high compared to other reported values [84].This indicates the presence of coupling effect at room temperature for nanocomposite xCrFe change in lattice parameters on applying magnetic field.The change in the sample dimension by the magnetic order, i.e., magnetostriction, might be considered as the origin of the observed magnetocapacitance.This factor may be considered for x=0.4.Also, It has been reported that the magnetic domain rotation least affects the dielectric constant at low temperature 85 .
Fig: 18(b) and (c) illustrates the temperature dependence of dielectric loss and dielectric constant at 1 kHz frequency for nanocomposites respectively.One broad peak ('!) is observed at around 180 0 C for x=0.4 nanocomposite.This peak is shifted to lower temperature as concentration of CrFe 2 O 4 increased.This peak shift may be ascribed to structure distortion due to ferrite phase.This peak could be one of the six transitions reported by Khijch et al 86 and Pajak et al 87 .BiFeO 3 has the transition at T N = 397 0 C.This is not clearly evident in the Fig: 18(b) because of the high dielectric loss in the samples.These losses could be due the conducting behavior of the nanocomposites at higher temperatures, possibly due to the thermally activated conductivity.In BiFeO 3 , oxygen deficiency is an inherent problem.Hence space charge polarization is always present.However, due to the thermally activated process, there is considerable increase in space charge polarization and material conductivity at higher temperature 88 .Hence, the peak at 397 0 C is not clearly marked in the nanocomposites with x=0.1, 0.2, 0.3 and 0.4.

CONCLuSIONS
The following conclusions are drawn from the present research work.1.
Synthesis of BiFeO 3 is carried out at low temperature using sol-gel method.

2.
From the X-ray Diffraction pattern it is seen that i) The crystallite size increases with increase in sintering temperature. ii) The strain in the crystallite decreases with increase in sintering temperature. iii) The crystallite size increases with increasing temperature the lattice parameter decreases.

3.
From an SEM micrograph, it is shown that the samples are homogeneous and that the grain size increases with increasing sintering temperature and the particle size follows the Gaussian distribution.

4.
The DTA analysis shows that the Curie temperature of pure BiFeO 3 is 814°C which is closer to that of ideal temperature 827°C. 5.
In the experiment xCrFe 2 O 4 -(1-x) BiFeO 3 with x = 0.0, 0.1, 0.2, 0.3 and 0.4, the XRD and thermal analysis confirmed that at 700 0 C the phase was formed.The particle size observed in TEM is about ~100nm.6.
The change of dielectric loss and dielectric constant with frequency confirmed distribution in the range of low frequency.7.
The Magnetization is estimated and observed the ferrite concentration and annealing temperature.Dielectric analysis confirms the conducting behavior at high temperatures.8.
Magneto-capacitance is estimated in the prepared nano-composites.This approves the presence of magneto-electric coupling in the synthesized nano-composites at room temperature.

Scope for the Future Work
The research work reported in this paper mainly deals with the preparation by an economical methods and characterizations of some BiFeO 3 , CeFe 2 O 3 -BiFeO 3 nanocomposites and Carbon Nanotubes.Multiferroics are the potential keystones in upcoming magnetic data storage and spintronics devices provided a simple and fast way can be found to turn their electric and magnetic properties on and off.The present experimental study on synthesis and characterizations of xCrFe 2 O 4 -(1-x) BiFeO 3 Multiferroic nanocomposites, with x = 0.0, 0.1, 0.2, 0.3 and 0.4 can be used as reference work and be extended for further studies with different 'x' values for different properties.Further, this work can be extended to study the carbon nanotubes may be reinforced into BiFeO 3 nanoceramics and convert to metallically conductive composites.By using sparkplasma-sintering method [89], we can fabricate nanocrystalline BiFeO 3 matrices that retain the integrity of SWCNT in the matrix.The conductivity of these composites increases with increasing content of CNTs.

Fig. 17 :
Fig. 17: Variation of dielectric constant and dielectric loss with frequency (at room temperature)

Fig. 18 :
Fig. 18: Variation of magnto-capacitance (a) with magnetic field at room temperature, dielectric loss (b) and dielectric constant (c) with temperature respectively