Analytical grade Bismuth nitrate pentahydrate (Bi (NO₃)₃・5H₂O, Alpha Aesar, 98%), Titanium dioxide (TiO₂, Fisher Scientific, 98%), Potassium hydroxide (KOH) and Sodium hydroxide (NaOH) were used as precursors for the hydrothermal synthesis of Potassium and Sodium Bismuth titanates. The alkaline hydroxides were used to adjust the p^H values of the solutions. A stoichiometric ratio of 2 for Titanium to Bismuth (Ti/Bi = 2) was employed in the starting materials of the reaction. Initially KBT and NBT nanopowders were prepared separately following the hydrothermal route.

The procedures followed for the preparation of KBT or NBT nanoparticles were as follows. First, Bismuth nitrate was dissolved in CO₂-free distilled water under vigorous stirring, in to which the corresponding alkali metal hydroxide was added, followed by the addition of Titanium dioxide. After stirring vigorously for about 2 hours, a thin yellow homogeneous solution was formed. The concentrations of Ti⁴⁺ and Bi³⁺ in the suspension were 0.25 and 0.50 mol/dm³ respectively, and the alkali metal hydroxide concentration was adjusted to 12 mol/dm³. The as-prepared mixture was poured in to a Teflon lined autoclave and was then subjected to hydrothermal treatment at 165˚C at a comparatively low pressure of 1.5 bars for 72 hours. The so-obtained product was collected and the sediments were washed three times by dispersing in CO₂-free distilled water followed by centrifuging. The raw powders were then dried overnight at an ambient temperature of 75˚C. The KBT and NBT powders thus prepared were mixed in desired weight ratios and pelletized, with Polyvinyl alcohol used as a binder, to get different solid solutions of KNBT with the general formula (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃, where x = 0, 0.20, 0.25, 0.33, 0.50, 0.75, 0.80, 0.85 and 1.0. Thin discs of diameter 9 mm and thickness 1 mm were calcined at 600˚C and then sintered at 50˚C intervals between 850˚C and 1000˚C for duration of half-hour each. After heat treatment of the samples, the dry weights of the pellets were measured with a balance and the bulk densities of the sintered samples were determined.

The crystalline phases of the prepared composite ceramic discs were determined using X-ray powder diffractometry in the θ - 2θ mode with Cu-Kα radiation of wave length 1.5406 Å (Bruker make, D8 Advance). The lattice parameters (a, b and c) and the unit cell volume (V) were calculated from the obtained XRD data using the MAUD programme.

Scanning Electron Microscopy (SEM) with Energy Dispersive X-Ray measurement has been used to identify and characterize the matrix. The SEM images of all the samples were recorded with a scanning electron microscope (Jeol make, Model 6390 LV) to examine the morphology of the matrix and homogeneity. Energy Dispersive X-ray (EDX) was specifically used to obtain a qualitative information on the full elemental composition of any unknown contaminant in the matrix.

The KNBT ceramics were cut and polished for various physical and electrical measurements reported in this work. Silver paste was used as the electrode for the measurement of dielectric and piezoelectric properties of the samples. The dielectric properties were measured using an Impedance analyzer (Hioki make, IM 3570) with the thinned sample mounted as dielectric medium in parallel-plate capacitor geometry.

The piezoelectric charge coefficient d₃₃ was determined with a conventional Berlin court Piezo D33 Test System (Piezotest make, PM300). The specimens for piezoelectric measurements were polled by applying a DC electric field of 2 kV/mm for 10 minutes in a stirred silicone bath at 150˚C.

The piezoelectric coefficient d₃₃, also known as the piezoelectric strain coefficient, is a very important parameter for piezoelectric actuators. There are, however, other important parameters also to be considered for such materials [21] . The internal polarization for a material is not an easy property to measure. In many materials, the measured variable is the voltage or the electric field (E) that is induced due to an applied stress (σ). The relationship between the field and stress is given by the piezoelectric voltage coefficient g, given as [22] [23] ,

E = g σ (1)

Taking in to account the relationship between electric field and polarization it can readily be shown that,

g = d / ε ε 0 (2)

The above equations are in fact simplified forms of the corresponding tensor relations, which holds good for either homogeneous materials or along the principal axes of the crystal. Both strain and voltage piezoelectric coefficients give the magnitude of the effect. However, the efficiency of the material in converting electrical energy to mechanical energy and vice-versa is given by the electro-mechanical coupling factor which is the ratio of the stored electric energy to the input energy. It can be shown that the electromechanical coupling factor k² is related to the strain constant d and the dielectric constant ε₀ as

k 2 = d 2 / ε ε 0 (3)

The variation of bulk mass density of KNBT samples as a function of NBT concentration is shown in Figure 1. The theoretical density of KBT is 5.929 g/cc and that of NBT is 5.568 g/cc. The theoretical density of various KNBT composition are calculated as the weighted average of their respective KBT and NBT contributions. So, as expected, solid solutions of KNBT composites show a corresponding mean values. Moreover, as is evident from Figure 1, the bulk densities of the samples show good agreement with the corresponding theoretical values and the nature of variation are exactly identical.

During synthesis of metallic oxide nanoparticles following hydrothermal route, hydroxide ion concentration is a decisive factor that determines the formation rate as well as crystalline structure of solid particles [15] [24] . In the case of complex perovskite fine particles like KBT and NBT, initial p^H value strongly influences the crystalline structure and shape of the particles [19] [20] . It is found that a highly alkaline condition, with p^H_init > 10, is essential for the formation of NBT in single phase. Decrease in p^H_init induces formation of Bi₂Ti₂O₇ [24] and metallic Bismuth [25] . Figure 2 shows the XRD patterns of hydrothermally treated pure K_0.5Bi_0.5TiO₃, (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃ (with x = 0. 20, 0.25, 0.33, 0.50, 0.75, 0.80 and 0.85) and pure Na_0.5Bi_0.5TiO₃ nanopowders, all sintered at 1000˚C for three hours. As can be seen from the XRD patterns, well crystallized phases are obtained for the samples and the particle sizes estimated using Scherer’s formula are found to be around 18 nm, 28 nm, 29 nm, 31 nm, 30 nm, 32 nm, 30 nm, 29 nm, and 30 nm respectively for the above samples. The presence of broad diffraction peaks in the case of pure KBT, pure NBT and samples with weight ratio adjusted from 0.25 to 0.75 between KBT and NBT in the solid solution, and with x = 0.85 can be assigned as due to the formation of KNBT phase with a rhombohedral crystal structure belonging to R3c space group (JCPDS File No. 01-070-9850) as a major phase [26] . However, in the case of (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃, with x = 0.80, the diffraction peaks are sharp, and using JCPDS matching it is found that the diffraction peaks of this structure correspond to a tetragonal phase belonging to the space group P4 mm with lattice parameters a = b = 3.761 Å and c = 6.112 Å. The additional peaks corresponding to tetragonal phase are also found to appear for this composition. This clearly indicates a change in phase resulting from a change of concentration, which corresponds to a MPB. The composition range of MPB has also been determined using XRD patterns, which show the coexistence of rhombohedral (R3c) and tetragonal (P4 mm) structures in uneven proportion at the composition with x = 0.80.

The lattice parameters (a, b and c) and the unit cell volume (V) were calculated from the obtained XRD data using the MAUD programme for all the samples and are shown in Table 1 and Figure 3. The unit cell volume initially shows an increase and then falls slightly for composition with x = 0.5 and then remains almost constant. This is reflected in the XRD pattern also (Figure 2) as a shift in the peak position for the corresponding compositions. Compared to pure NBT and KBT the lattice parameters a, b and c more or less remain equal and constant for composition with x ≤ 0.5. However, for the composition with x > 0.5, a and b fall slightly whereas c increases considerably. This increase is at its peak for the composition with x = 0.8 at a value of 6.112 A⁰. This indicates that due to the coexistence of NBT and KBT in different weight ratios, the structure starts changing from rhombohedral to tetragonal from x = 0.5 onwards and is distinctly in tetragonal phase for composition with x = 0.8. The tetragonal distortion is also evaluated as shown in Table 1. It is found that the rhombohedral distortion (b/a) almost remains constant as unity for all compositions whereas tetragonal strain constant (c/a), though remains almost unity for x ≤ 0.5, start increasing up to a maximum of almost 63% at composition with x = 0.8. This further indicates that a change of composition result in a change of phase from rhombohedral to tetragonal resulting in an MPB at the composition with x = 0.8. It may also be noted here that the unit cell volume though constant for compositions with x > 0.5 it shows a slight increase for composition with x = 0.75. This is resulted from the simultaneous fall of the lattice parameters a and b along with anelongation for the lattice parameter c, as this composition is reached. However the tetragonal strain constant (c/a) still increase to show a maximum value at x = 0.8. Further, this modification results in lattice distortion which is supposed to lead to enhanced polarizability [12] [27] [28] . It is anticipated to be beneficial to the dielectric and piezoelectric properties of the crystal [29] .

SEM images of as-prepared samples are shown in Figure 4. Morphology and mean sizes of the resulting particles undergo drastic changes with variation in concentration ratio between KBT and NBT in the composite samples. The nearly spherical fine particles are formed in the case of pure KBT and pure NBT (Figure 4(a) and Figure 4(i)), whereas rod-like cubic structures start forming as NBT concentration is increased in the KNBT sample (Figures 4(d)-(h)). As can be seen from Figure 4(g), this rod-like structure formation is at its top end corresponding to the composition (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃, with

x = 0.80, whereas this rod-like structure starts to disappear for the composition (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃, with x = 0.85 and disappear completely for pure NBT. The average grain sizes of the ceramic particles have been calculated by counting 100 particles taken from SEM images, and the mean sizes are found to be around 125 nm, 344 nm, 234 nm, 240 nm, 186 nm, 220 nm, 350 nm, 210 nm, and 320 nm respectively for pure KBT, (1 − x)K_0.5Bi_0.5TiO₃ − xNa_0.5Bi_0.5TiO₃, with x = 0.20, 0.25, 0.33, 0.50, 0.75, 0.80, 0.85 and pure NBT. In the case of the composition with x = 0.80 the rod-like structures have an average diameter around 450 nm and length as high as a few micrometers.

Among the various KNBT ceramics the grain size is found to be minimum in the case of pure KBT and it is found to increase as the concentration of NBT is increased. It appears that higher concentration of KBT in the composite sample generally inhibits the grain growth; however, a considerable population of NBT in the sample enhances grain growth as can be seen in Figures 4(d)-(h). In such NBT dominant ceramics the domains of most of the grains are lamellar or needle-shaped and is an indicator of the formation of tetragonal domains, and this result is in agreement with the studies reported earlier by Octonicar et al. [30] . A more detailed discussion on the actual mechanism of domain formation close to MPB requires neutron scattering or selected area electron diffraction studies of the compositions.

The dielectric constants and dielectric losses of different samples show a normal variation with frequency for phase pure KBT and NBT as well as for different compositions of KNBT, as is evident from Figure 5 and Figure 6. However, the magnitude of dielectric constant, instead of following a mean field approximation, increases in a nonlinear manner for KNBT samples with increase in Sodium

content. This is shown in Figure 7. It is clear that the properties peak to a maximum for the composition with x = 0.80, and is assigned to be as due to this composition being close to a Morphotropic Phase Boundary (MPB) where the ions are subjected to comparatively large remnant polarization.

Owing to the presence of MPB structure in KNBT ceramics at the composition with x = 0.80, the relevant piezoelectric properties of all the samples have been determined. The d₃₃ coefficients of all the prepared compositions have been measured and the piezoelectric figures of merit―the piezoelectric voltage coefficient g₃₃ and the electro-mechanical coupling coefficient K²―have been evaluated using Equations (2) and (3). It is important to note that though the Potassium sodium bismuth titanates with aurivillius phase, prepared following conventional solid state reaction route offer a d₃₃ coefficient about 20 pC/N [20] , KNBT ceramics synthesized following hydrothermal route described above offer a much higher piezoelectric d₃₃ coefficient of about 40 pC/N. Figure 8, shows the variations of the various piezoelectric figures of merit with concentration of NBT/KBT for these samples. It is clear from the figure that these properties are at their threshold maxima at the composition corresponding to x = 0.80, which corresponds to MPB. It may also be noted that the d₃₃coefficient for this composition increases to about 88 pC/N.

Table 2 shows a comparison of the piezoelectric properties of PZT with those of KNBT ceramics at the threshold corresponding to x = 0.80 (MPB). Values available in literature for commercially available PZT-4 have been used for comparison [25] [26] [30] . These values of PZT-4 are comparable to the corresponding values for PZT at MPB [31] . A comparison of the values of dielectric and piezoelectric properties shows that the dielectric constants are of the same order of magnitude while the dielectric loss is smaller for KNBT. The extensional strain coefficient d₃₃ is only about 50% for KNBT, while the extensional voltage coefficient g₃₃ is higher for it. Again, the electro-mechanical coupling coefficient K² is much higher for KNBT. So we see that the lead-free KNBT, synthesized following comparatively simple hydrothermal route, offers a promising alternative to PZT for piezoelectric applications.

Further, it can be anticipated that KNBT ceramics with still smaller grain sizes

(which could be controlled by optimization of sintering conditions)may lead to further enhancement in their piezoelectric properties [32] . However, more detailed investigations are required to reveal the dependence of these properties on the particle size and morphology for the development of potential lead-free piezoceramics for practical applications.