The observed X-ray diffraction pattern for the synthesized BCTN ceramic is shown in Figure 1. The peak position and relative intensity of all diffraction peak are observed to be matching well with the standard powder diffraction file of JCPDS card No. 00-039-0258 and thereby confirming the tetragonal tungsten bronze structure with space group P4bm. Ganguly, P. et al. [16] have reported

the similar diffraction pattern for Ba_5−xCa_xSmTi₃Nb₇O₃₀ (x = 0) synthesized by solid state reaction method. The crystallite size of synthesized BCTN ceramic was calculated by using the Debye Scherer’s equation [17] [18] :

D = 0.9 λ / β c o s θ (1)

where D gives the crystallite size, λ is incident wavelength, β is FWHM, and θ is the glancing angle. The observed crystallite size of BCTN was found to be 14.43 nm. The lattice parameters were calculated by using the relation reported by Ganguly et al. [8] . The values of lattice parameters a, b, & c were observed to be 8.3311 Å, 8.3311 Å and 12.1289 Å respectively.

Room temperature SEM micrographs of gold coated BCTN ceramics sintered at 1300˚C shown in Figure 2. It is observed that specimen has fine grains and

dense microstructure due to high temperature sintering optimized condition. It is well known that with high sintering temperature well developed grain with uniform grain distribution is observed [19] . The grain size of BCTN ceramic is 6 µm. The grain size of BCTN ceramic can be explained on the basis of driving force. This driving force is relative to difference between free energy of strained matrix and strain free crystal. Its result decrease grain boundary area and total boundary energy and increase the grain size of sample. With increasing grain size porosity of specimen decreases [20] [21] . Thus increase in grain and decrease in porosity may be attributed due to small interfacial energy. This interfacial energy is proportional to grain diameter.

The stability of the tetragonal tungsten bronze (TTB) structure compound can be determined by Tolerance factor (t) discussed by Wakiya et al. [22] According to the general formula of TTB, two types of A sites are present, one is A1 site with 12 fold coordination which is identical as perovskite structure and A2 site with 15 fold coordination which occupies pentagonal site. Thus value of tolerance factor (t) can be calculated by following relation [23]

t A 1 = ( R A 1 + R O ) / ( 2 ( R B + R O ) ) (2)

t A 2 = ( R A 2 + R O ) / ( 23 − 12 3 ( R B + R O ) ) (3)

where t_A1 and t_A2 represent the tolerance factor of A₁ and A₂ sites, R_A, R_B and R_O are ionic radius of A sites, B sites and oxygen respectively.

In TTB structure tolerance factor and stability relationship analyzed by the combined relationship of above two equations which can be expressed as:

t = ( t A 1 + 2 t A 2 ) / 3 (4)

The crystal structure is stable when value of t is closer to 1. Since the calculated value of tolerance factor (t) for BCTN ceramic is 0.63640 which is slightly small than 1 hence showing a slight instability of the synthesized TB ceramics.

In order to confirm the chemical composition and stoichiometric proportions of the typical samples of Ba₅CaTi₂Nb₈O₃₀ (BCTN) ceramics, energy dispersive analysis of X-ray (EDAX) study is carried out and the typical EDAX spectra for ceramic is presented in Figure 3. All the ions present in Ba₅CaTi₂Nb₈O₃₀ ceramics are observed to be in good stoichiometric proportions as desired. Table 1 shows the elemental percentage and calculated atomic formula with nominal composition.

It is well known that the dielectric constant and dielectric loss of the ferroelectric

materials depends upon the composition, grain size etc. Figure 4(a) and Figure 4(b) show the temperature dependence of dielectric constant ( ε ′ ) at frequencies of 1 kHz, 10 kHz, 100 kHz. In Ba₅CaTi₂Nb₈O₃₀ compound, shows the sharp transition in dielectric constant at Curie temperature T_c, where dielectric constant is maximum. It is observed that compound has dielectric anomaly at 316˚C (the Curie temperature T_c) depicts the occurrence of ferroelectric-paraelectric phase transition [24] . It is also analyzed that compound has the same transition temperature (T_c) at above revealed frequencies, indicating that compound does not have relax or behavior.

The increase in value of dielectric constant can be understood as: The sintering of compound is carried out in muffle furnace of very high temperature, so there is possibility of re-oxidation around the grain during the cooling process and lattice pick up oxygen vacancies from the ambient. This re-oxidation creates a strong insulating layer around the grain with bulk resistance. Its result can developed very large conductive difference between bulk and grain boundary. And grain boundary is responsible for large capacitance and resistance compared to grain interior subsequent to surface charge accumulation and interfacial polarization therefore leads to increase dielectric constant [25] [26] [27] . Secondly, the value of maximum dielectric constant can be attributed due to well defined or well developed grain and shown in Figure 2. Well defined grain makes the domain wall motion easier and due to this dielectric constant value increase.

Diffuse phase transition

The dielectric peak is broadened indicating the existence of diffuse phase transition. The quantitative evaluation of the diffusivity or disorderness in a sample can be calculated by modified Curie-Weiss law [28] :

ln ( 1 / ε r − 1 / ε max ) = γ ln ( T − T c ) + constant (5)

where, ε_r is relative permittivity at temperature T and ε_max is maximum relative permittivity at temperature T_c, C’ is Curie constant. The parameter γ is regarded as a measure of the diffuseness or disorderness of the ferroelectric to paraelectric phase transition. γ = 1 corresponds to the normal ferroelectric behavior while γ lies between 1 (normal Curie-Weiss behavior) and 2 (for completely disordered system) confirming the diffuse type phase transition in the sample [29] . In present work value of γ observed in between 1 < γ < 2, that is correspond to diffuse phase transition. This observation is in conformity with observed phase transition in Figure 4(a).

The plots of ln(1/ε_r − 1/ε_max) as a function of ln(T − T_c) at 1 kHz, 10 kHz and 100 kHz are shown in Figure 4(c). The calculated value of diffusivity was found to be γ = 1.54 in the material which show the existence of diffuse phase transition in the material.

Figure 4(b) shows the temperature variation of dielectric loss (tanδ) from room temperature to 500˚C at the frequencies of 1 kHz, 10 kHz and 100 kHz. This anomaly in tanδ (of diffuse type material) may be accepted due to dielectric relaxation in the material. At above mentioned frequencies, the variation of dielectric loss with temperature show that dielectric loss has smaller value at lower temperature but its value increase sharply at higher temperature [30] . This sharp increase in tanδ at higher temperature may be attributed due to ferroelectric domain wall contribution and space charge polarization. It is observed that Ba₅CaTi₂Nb₈O₃₀ (BCTN) ceramic has large dielectric constant and low dielectric loss which make it suitable material for tunable device applications.

Raman spectroscopy is powerful tool to study the local distortion, strain and any disorder present in crystalline solids because vibrational spectrum having shorter length scale characteristic. In Figure 5 Raman spectra plotted intensity versus the difference in wave number between incident beam and scattered beam and peak observed in correspondence to phonon frequency [31] . In present work Raman scattering used to study the change in degree of ordering and any distortion present in the sample [32] [33] . Recently this spectroscopy used for the study of multiferroic materials. Room temperature Raman spectra of BCTN compound studied in frequency range 50 - 1600 cm⁻¹ which depicts various mode of vibrations i.e. A₁(TO₁), A₁(TO₂), A₁(TO₃) and A₁(LO₁) at 265.958 cm⁻¹, 628.33 cm⁻¹, 1010.94 cm⁻¹ and 1124.84 cm⁻¹. Peak at low wave number < 200 cm⁻¹ in Raman spectra rise due to external lattice vibration involving motion of cations relative to oxygen octahedron frame work of NbO₆. The sharp A₁(TO₂) band at 628.33 cm⁻¹ which correspond to vibration of A site against NbO6 octahedral ion at B site. A₁(TO₃) mode is due to vibration of Nb and O ions which are located in plane perpendicular to it. A₁(LO₃) mode is due to phonon propagating along c axis which is characteristic feature of tetragonal tungsten bronze structure in BCTN compound. The modes at 265.958 cm⁻¹, 628.33 cm⁻¹ and 1010.94 cm⁻¹ signifies long range ferroelectric ordering [34] .

Figure 6 shows the P-E hysteresis loop of sintered sample recorded at room temperature. The observed value of remenant polarization (P_r) is 0.742 μC∙cm⁻² and coercive field (E_c) is 11.805 kV∙cm⁻¹.

The variation of magnetization as a function of applied field is shown in Figure 7. The values of magnetic parameters such as saturation magnetization, remanence magnetization, coercivity H_c (Oe), and squareness ratio M_r/M_s are observed to be 7.65 × 10⁻⁴ emu/g, 7.22 × 10⁻⁵ emu/g, 65.51 Oe and 0.09 respectively.

The ferroelectric ceramic show a strong makeover of diamagnetism to weak ferromagnetism [35] [36] . So the existence of ferromagnetism in BCTN ceramic is as per expectation.