The XRD patterns for ceramic and co-precipitation samples of Pb_1-xNi_xTiO₃ which (x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5) are shown in Figure 1 and Figure 2 show a well resolved peaks. The values of the full width at half maximum intensity indicate that the polycrystallite has nano sites. This result confirms that the Ni ions occupied the Pb ions site with smaller ionic radius. The reduced c/a ratio suggests that the samples have perovskite phase with tetragonal structure with improved mechanical stability [5] [6] .

The patterns correspond well to PbTiO₃ phase with a typical tetragonal symmetry showing splitted (001/100), (101/110), (002/200) and (112/211) peaks. When Ni content increases, no change for the patterns is observed, whereas the other phases of Ni previously mentioned and PbO disappeared with increasing Ni content and the two peaks in each group of the tetragonal phase patterns approached to each other, indicating decrease in tetragonality. This phenomenon is observed from XRD patterns from the decreasing of the ratio c/a. The appearance of pre-mentioned diffraction peaks demonstrates that the perovskite nano crystallites of PbTiO₃ can be formed successfully at 600˚C [6] .With increasing Ni content the tetragonality c/a decrease from 1.049 to 1.0276 for ceramic samples and decrease from 1.06519 to 1.0365 for co-precipitation samples. The lattice deformation has high a tetragonality which is a very important factor for piezoelectric performance [7] .

The XRD pattern prove that a single which tetragonal phase was obtained for all compositions with different Ni content with a = 4˚A, c = 3.875˚A and c/a = 0.96875, the crystallite size was determined from the line width using Scherer's equation. It is noticed that the samples with low value line width has higher crystallite size as given in Table 1. There is a correlation between line width and crystallite size as shown in Figure 3 between crystallite diameter and h_1/2. This result is consistent with the correlation

between the crystallite size and the peak width which widely discussed and reported on PT ceramics [8] [9] and Barium Titanate ceramics [10] [11] .

The influence of Ni content on the lattice constant of the prepared materials is shown in Figure 4. The lattice constant (a) shows slight increase by 0.72% while the constant (c) decrease by 13.8% for ceramic samples. The lattice constant (a) shows slight increase by 0.61% while the constant (c) decrease by 10.78% for the co-precipitation samples.

The variation of lattice parameter (a) and (c) by increasing Ni content has low values for co-precipitation sample than the ceramic sample. Although the ionic radius of Ni²⁺ is smaller than the Pb²⁺ ionic radius the lattice parameter (a) increase by increasing Ni concentration which is related to the increase of internal strain which cause the lattice to expand in the (a) direction. The decrease of the lattice parameter (c) by increasing Ni content may be due to the low value of the Ni²⁺ ionic radius compared with ionic radius of Pb²⁺. Figure 5 also shows decrease of c/a ratio which means that the tetragonality feature of the samples decreases by increasing Ni content. Characteristic peak of around 2θ = 31.46˚ and the splitted peaks (001/100) indicate the presence of tetragonal phase [12] .

Figure 6 shows the porosity of the samples. From the figure it is shown that the samples prepared by co-precipitation have small porosity than ceramic samples and the porosity increased noticeably for increasing Ni contents.

The PbTiO₃ doped with Ni are exposed to annealing process at 600˚C, 800˚C and 1000˚C for 2hours to ensure complete crystallization and remove of any foreign phases.

Figure 7 shows the XRD patterns of samples Pb_1-xNi_xTiO₃ (x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5) annealed at 600˚C, 800˚C and 1000˚C Show an increase in the peak intensity by increasing annealing temperature up to 1000˚C. The calculated values of crystallite size for each composition at different annealing temperature were calculated using Scherer’s equation. It is noticed that the crystallite size for each composition increases by increasing annealing temperature as given in Table 2. In comparison small crystallite size is observed for PbTiO₃ doped with Ni powder prepared by co-precipitation method. The crystallite size for co-precipitation samples still in the nano range after annealing at 1000˚C. It is noticed that the diffraction peak at 2θ = 30˚ belong to precursor. Raw materials disappeared at higher annealing temperature due to the complete formation of Pb_1-xNi_xTiO₃.

From Table 3 it is evident that the average crystallite size of the samples prepared by

co-precipitation method smaller than that of prepared by ceramic method. The crystallite size derived from XRD has higher value than that derived from TEM since. The XRD is a bulk technical and the crystallites lower than 20 nm are too low to be detected carefully by X-ray.

IR spectra carried out in lead titanate doped with Ni prepared by both ceramic and co-precipitation methods are shown in Figure 8(a) and Figure 8(b). The IR spectra showed two vibrational absorption bands one at 377 cm⁻¹ and the other at 573 cm⁻¹, another two vibrational peaks appear at 1400 and 1600 for co-precipitation samples and ceramic samples. Additional peak appears at1385 for ceramic sample. The first two peaks around 377 to 573 cm⁻¹ are due to metal oxide binding [13] .

The wide band appearing at 377, 573 cm⁻¹ corresponds to vibrational frequency of Ni-O bond at tetrahedral and octahedral coordination. We can say that the peak appeared around 1400 - 1600 is attributed to the symmetrical H-O-H and as symmetrical H-O-H bond vibration these results are confirmed with the pervious reported data [14] . The presence of the absorption bands in the far infrared region confirms the formation of Pb_1-xNi_xTiO₃ structure.

The absorption peak at 500 (υ2) which due to M-O bond shifted to lower frequency from 573 to 553 cm⁻¹ which confirming the formation of more perovskite phase at higher Ni concentration. The band near 573 cm⁻¹ is associated to octahedral bond and indicates the formation of a perovskite phase.

In conclusion the studies of IR spectroscopy confirm the formation of a perovskite structure.

Figure 9(a) and Figure 9(b) show SEM micrograph of PbTiO₃ doped with Ni content. The micrograph show good densification and homogenous grain size. Some degree of porosity is clearly seen in ceramic samples micrograph where the porosity is very small for the micrograph of co-precipitation samples. The PbTiO₃ powder derived from ceramic method consists of particles with size ranged from 3.3 to 0.7 μm. In comparison small particle size is observed for PbTiO₃ doped with Ni powder prepared by co-precip- itation method. There is correlation between the grain size and the density. The larger grain size has lower density makes density for samples prepared by co-precipitation method higher than that prepared by ceramic method, So the high value of grain size leads to the decrease in density. The density for both samples decrease by increasing Ni content due to the lower atomic weight of Ni compared with Pb. The SEM micrograph for co-precipitation samples have very smaller grain size, grain appearance and regular grain morphology than the SEM for ceramic samples [15] . The grain size was obtained from SEM micrograph which is given in Table 4. The Ni ions can concentrate near the grain boundaries and reduce their mobility so they are considered to be as grain growth inhibitor [16] . The SEM morphology of all samples indicated spherical and tetragonal shape of the grains and that the tetragonality appeared clearly in the co-precipitation samples. Using the line intercept method the average grain size of the samples was determined.

Correlating the micrometer grain size reviled by SEM with the nanometer size of the ferroelectric domain determined by XRD and TEM images one can conclude that ceramic grains have multi domain structure [1] .

The Pb_1-xNi_xTiO₃ powder for ceramic and co-precipitation samples treated at 1200˚C and 1000˚C respectively were subjected to TEM microstructure analysis to determine the average particle size. Figure 10(a) and Figure 10(b) show TEM images of the PbTiO₃ doped with Ni prepared by ceramic and co-precipitation method. This image reviles that the nanoparticle were not agglomerated for all location of the images with

an average particle size ranged from 14.47 to 3.244 nm for co-precipitation samples. There is some agglomeration appears for ceramic sample at some location. Also TEM images show small ferroelectric domains of about 3 to 14 nm for the co-precipitation sample and 26 to 48 nm for the ceramic samples as given in Table 3. Figure 10(a) and Figure 10(b) show spherical and tetragonal crystallites for PbTiO₃ phase.

The crystallite size derived from XRD has higher value than that derived from TEM since. The XRD is a bulk technical and the crystallites lower than 20 nm are too low to be detected carefully by X-ray. For the sample x = 0.5 the identification of d spacing d = 0.13nm suggest the tetragonal crystallite as shown in Figure11 corresponding to 212 plane of PbTiO₃ phase [17] . This demonstrates that the nanocrystalite of perovskite PbTiO₃ phase was successfully formed by the co-precipitation method.

Figure 12 shows the temperature dependence of dielectric constant (ε) at 1 kHz and 10 kHz for both samples prepared by co-precipitation and ceramic methods.

The samples have a first order phase transition from tetragonal to cubic phase at certain curie temperature T_c. The material converted from ferroelectric to Para electric state. The variation of curie temperature T_c and the value of dielectric constant are shown in the Figure 13. The behavior of ε identifies that our samples are nonrelaxor. Maximum ε at T_c are achieved in pure and Ni content samples increasing the Ni concentration increase the value of dielectric constant where T_c is shifted to lower temperature. The ε shows weak temperature dependents in the temperature rang (300 - 450 ˚k) for all samples. This range shifts to lower temperature by increasing Ni content. The presence of ferroelectric to paraelectric phase transition peaks of ε in the temperature range (560 - 700 ˚k) are clearly seen in Figure 12 which is an evidence for the existence of ferroelectricity for all fabricated ceramic and co-precipitation samples. It is also shown from Figure 12 that the value of ε for samples prepared by co-precipitation method is higher than samples prepared by ceramic method. It may be recognized to the fact that the decrease in grain size leads to the increase of dielectric constant [18] . This can be attributed to the fact that as the grain size increases the grain boundaries get smaller and clamp the domain wall to some extent.

It is clearly depicted that all the dielectric constant show a distinct phase transition point characterized by narrow curie peak, Which may be due to the absence of heterogeneity [19] . The dielectric constant increase by increasing Ni contents due to the increase of space charge contribution [20] . The dielectric constant is increased by increasing temperature, but is nearly independent of frequency especially in the vicinity of the phase transition temperature. The dielectric constant peak at the transition temperature systematically increase as the grain size decrease for both systems prepared by ceramic and co-precipitation methods, however there is a decrease in T_c with decreasing grain size for both systems, which is consistent with the observation [9] . All compositions show narrow peak in dielectric constant which indicate sharp phase transition.