Pb(Zr,Ti)O₃ (PZT)-based piezoelectric ceramics has been study more than anyone else ferroelectric because of their excellent piezoelectric properties [1]. However, the presence of lead in those materials is about 60 % in weight [2], reconsidering its use in technical applications, due to the high toxicity of lead for the environment as well as for humans.

Recently have been reported some materials as (K_0:44Na_0:52Li_0:04)(Nb_0:84Ta_0:10-Sb_0:06)O₃ [2] and (Na_0.5K_0.5)_l−x (LiSb)_xNb_l−xO₃ [3], showing excellent piezoelectric properties, similar to those corresponding to PZT systems, however, there are still problems such as the use of alkaline metals, their use being very difficult where semiconductor-based technologies are used.

BaTiO₃ (BTO)-based systems have been known to be strong candidates in the race for lead free ferroelectrics materials [4-6]. One of the most reported variants is Ba(Zr_xTi_1-x)O₃ (BZT) [7]. Due to their high permittivity, these materials are used frequently in commercial capacitor applications, at the same time it is a very promising material for DRAM memory and micro-electromechanic systems (MEMS) applications [6]. Some papers suggest A- and B- sites compositional modifications in ABO₃ ferroelectric materials can arise the antiferroelectric double hysteresis loops [8-10], and diffuse phase transitions are caused by the compositional fluctuation of a particular ion at the B site and the concentration of different types of ions in the crystal lattice. The transitions may also become diffused due to grain boundary effects [11, 12].

When Ba ion is substituted by Mg ion in a BZT system, a great structural disorder is espected, arasing changes in dielectric and ferroelectric properties of samples. This motivated us to work on effects off Mg substitution. We present results obtained in the study of phase transition and dielectric properties of B(Zr_0.05Ti_0.95)O₃ by hysteresis loop where Mg²⁺ was added, obtaining Ba_1-xMg_x(Zr_0.005Ti_0.095)O₃ with x = 0.025; 0.050; and 0.075.

The samples were prepared by the conventional solid state reaction procedure. The starting powders MgCO₃, BaCO₃, TiO₂ and ZrO₂ (ALFA AESAR 99.9% pure) were weighed according to the formula (1-x) BaCO₃ + x MgCO₃ + 0.95TiO₂ + 0.05ZrO₂. x was given the values 0.025, 0.050 and 0.075. The powders were mixed in a Zr ball mill and sintered afterward at 1300^oC for 2 hours at a rate of 1C^o/min. For practical purposes the samples will be coded as follows: Ba(Zr_0.05Ti_0.95)O_3, BZT005; Ba_0.975Mg_0.025(Zr_0.05Ti_0.95)O_3, BM0025ZT; Ba_0.950Mg_0.050(Zr_0.05Ti_0.95)O₃, BM0050ZT and Ba_0.925Mg_0.075(Zr_0.05Ti_0.95)O₃, BM0075ZT.

X-ray diffraction (XRD) studies were performed on the samples using Cu K_α radiation between 20 and 70 degrees with a scanning step of 0.5 degree. Dielectric measurements were carried out in the 25-200^oC temperature range, using an HP3238 capacitor analyzer in the 1 kHz to 1 MHz frequency range. The hysteretic loop was obtained with a RT66A (Radiant Technologies).

Fig. (1) shows the XRD patterns obtained for BZT, BM025ZT, BM050ZT and BM075ZT. In all cases the presence of a perovskite structure is observed but not the same crystal phase. The pattern for BZT005 corresponds to a tetragonal perovskite structure whereas for BM0025ZT, BM0050ZT and BM0075ZT a pseudo cubic structure is observed. Due to the differences in length of the ionic diameter between Ba²⁺ and Mg²⁺, mechanical stress was introduced into the lattice during cooling after sintering process, leading the transition from tetragonal structure in BZT005 to a pseudocubic structure in BMZT systems.

Fig. (1) X-ray patterns of BZT005, BM0025ZT, BM0050ZT and BM0075ZT.

Fig. (2) shows SEM images of the BZT005, BM0025ZT, BM0050ZT and BM0075ZT samples. From these images the average grain size and their relative error were estimated. results are 6.3; 1.4; 3.2; 2.8 respectivily.

Fig. (2) SEM images.

In all cases, bulks reveals high granular density. It is obviously with the addition of Mg the average granular diameter decrease considerable, in comparison to the granular diameter of BZT005 sample. In bulks where Mg²⁺ ion was added, grains shows faces not well developed as in BZT005, indicating that the growing up process of grains is highly frustrated by short-range forces. Dou to the differences in large of the ionic diameter between Ba²⁺ and Mg²⁺ a mechanical stress was introduced into the lattice during cooling after sintering process, this electromechanical stress increased the energy in the grain boundaries interface, decreasing the kinetic diffusion of ions trough the boundary and as consequence the movement of the grain boundary [13]. Because of the high role played by the short-range forces with the inclusion of Mg, more macrodomains (long–range ordered regions) will breakup into micropolar regions, independent of eachother, in detriment to the ferroelectric response of the ceramic.

Studies of the variation of dielectric permittivity (ε^´) with temperature for BZT005, BM0025ZT, BM0050ZT and BM0075ZT at different frequencies show the presence of two peaks coinciding with those reported in Landolt-Börnstein [14] for BZT005, as can be seen in Fig. (3). The dielectric permittivity shows broad transitions normally associated to diffusive relaxor ferroelectrics. The shift of the peak due to permittivity dispersion with frequency gets smaller with the increase of Mg²⁺ addition.

Fig. (3) Dielectric permittivity for BZT005, BM0025ZT, BM0050ZT and BM0075ZT.

It is known that one characteristic that must be present in a material with diffuse phase transition is a relatively large separation (in temperature) between the maxima of the real (dielectric constant) and imaginary (dielectric loss) part of the dielectric permittivity. Fig. (4) shows the temperature dependence of the dielectric loss of BZT005, BM0025ZT, BM0050ZT and BM0075ZT ceramics. In all cases, it is seen that the values of the temperatures of the maximum of dielectric permittivity and the maximum of the dielectric losses do not coincide. This result corroborates we are in the presence of a diffuse phase transition [15]. Also in Fig. (4) an anomalous behavior is observed in all cases. Such behavior is related to the variation of the dipolar moment originated by the substitution of Mg²⁺ ions at Ba²⁺ sites. The temperature corresponding to the orthorhombic – tetragonal transition varies with the content of Mg²⁺.

Fig. (4) Dielectric loss for BZT005, BM0025ZT, BM0050ZT and BM0075ZT.

Table 1 shows the obtained values of the dielectric constant at 1 KHz and how they decrease with the increase in Mg content. The temperature corresponds to the maximum of the dielectric loss in the BM0075ZT sample (corresponding to the tetragonal-cubic transition) is slightly higher than that of BM0050ZT.

Table 1

Dielectric Parameters as Function of Composition Measured at 1 KHz

The decrease of T_max(^oC) with the increment of the Mg²⁺doping, may be associated to the increment of cationic disorder at the A-site in the perovskite structure as the Mg²⁺ ions are incorporated into the system. Ba²⁺ and Mg²⁺ will occupy the same crystallographic site. However, the ionic radius of Ba²⁺ is much larger than that of Mg²⁺ and the structure will be distorted. Furthermore, B site is occupied by Zr⁴⁺ and Ti⁴⁺ in a random way, with Zr at a fixed percent of 0.05%, generating defects that added to the effects of the Mg²⁺ ions will weaken the long range dipolar interactions [16], reducing the stability of the ferroelectric phase.

In Fig. (5) we can distinguish 3 regions: 1- for the ferroelectric phase, with temperatures below T_m of the dielectric permittivity maximum. 2- Diffuse phase region 3- paraelectric phase up to T_cw, reaffirming the diffuse character of our system.

Fig. (5) 1/ε´-1/ε´max vs T-Tm and the lineal fit of the paraelectric region for BZT005, BM0025ZT, BM0050ZT and BM0075ZT.

Because of the Curie-Weiss law does not explain the diffuse interval of the curve [17]; a modified Curie-Weiss law, Equation 1, was proposed to describe the diffuseness of the phase transition.

where γ (1<γ<2) and C are assumed to be constant. The known forms of Curie-Weiss and squared Curie-Weiss laws are particular cases of the Equation 1 with γ = 1 and γ = 2 respectively. Through some algebraic manipulation and by fitting the experimental measurements the value of γ can be obtained. The procedure is illustrated in Fig. (6) with the respective values of γ obtained for each material.

Fig. (6) ln(1/ε´-1/ε´max) vs (T-Tm) for BZT005, BM0025ZT, BM0050ZT and BM0075ZT.

In the studied ceramics the values of γ are found to be higher than 1.5 and for those with Mg higher than 1.6 at 1 KHz, indicating diffuse transitions. The increase of the diffuseness as measured by the value of γ evidently increases with the increase of Mg²⁺ concentration.

Fig. (7) shows the hysteresis loops corresponding to the BZT005, BM0025ZT, BM0050ZT and BM0075ZT samples. In all of them typical hysteresis loop behavior is notable in the materials polarization (P) vs electric field (E) response.

Fig. (7) Hysteresis loops corresponding to BZT005, BM0025ZT, BM0050ZT and BM0075ZT samples obtained at different fields.

Fig. (8) shows the hysteresis loops measured for a field maximum of 6.2 KV cm^-1, resulted to be the rupture field for the BM0050ZT sample. This value is significantly inferior to those obtained for the rest of the studied materials. The tendency for the formation of a double hysteresis loop in the BM0050ZT sample is appreciable but not so in the BM0025ZT and BM0075ZT, where these are, moreover, the least dielectric losses. In a first grade phase transition materials, it is common to see in the vicinity of the transition temperature the hysteretic loop change from simple to a double loop closed in the center [13, 14], but in a previous result obtained by us, it was determined that BMZT system has a diffuse phase transition, putting off consideration the previous option as explication for the phenomenon in sample BM0050ZT.

Fig. (8) Hysteresis loops corresponding to BM0025ZT, BM0050ZT and BM0075ZT samples obtained at 6.2 KV cm-1.

We observe the low polarization values that characterize the BM0025ZT, BM0050ZT and BM0075ZT sample respect to BZT005. Nevertheless, what we have are very poor responses compared to those of BZT005. This behaviour must be associated with an increase in the ionic disorder of the perovskita structure site given by the inclusion of the Mg ion in the system that will occupy the same crystallographic than the Mg in our system. Due to the difference in their ionic radii, a distortion takes place, if we add to this, that location B is occupied by the elements Zr and Ti in a random manner (Zr presents a fixed percentage of 0.05%), we obtain as consequence of these two defects in the network, a weakening in the dipolar long range interactions [16, 18], consequently reducing the stability of the ferroelectric phase. These results suggest that at room temperature small antiferroelectric regions appear in the ferroelectric matrix, as consequence, the dielectric losses became smaller, due to the weak hysteretic nature of the antiferroelectric state [19, 20]. The shape of the hysteresis loop corresponding to the BM0050ZT sample, suggests the coexistence of anti-ferroelectric and ferroelectric phases in the material, with predominance of the latter. We cannot say the same about the BM0025ZT and BM0075ZT samples, this may be explained as: by the decreasing grain size, antiferroelectric domain walls become difficult to form in the grain, and the domain rotation contribution to the strain becomes smaller [21], The decrease of strain with the grain size greater than 5 μm is attributed to the grain boundary which could clamp the transformation strain. The average diameter of our samples are closed to the frontier where two diferents procces clamp the transformation strain, explaining why a presense of an antiferrolectric phase is suggested in BM0050ZT sample, and not in BM0025ZT and BM0075ZT samples. However a thin dielectric hysteretic is a desirable response for electro-optics applications, characterized by a birefringence when an electric field is applied, but relaxing to an isotropic state (non- birefringence) when the electric field is removed, showing a poor remnant [22].

Through the conventional ceramic the Ba_1-x Mg_x(Ti_0.95Zr_0.05) O₃ systems was obtained, where x has the values 0.025, 0.05 and 0.075. From the X-ray the presence of a pseudocubic phase corresponding to a perovskita structure was determined with the inclusion of Mg in BZT005 system. The diffuse phase transition observed in BZT remains when Mg is used, and increases with Mg concentration in the 0<Mg% <0,075 range. The temperature for the maximum dielectric permittivity shift closer to room temperature when Mg adding is increased. A low response in terms of the remnant polarization was found. A discussion around some appears evidences of the presence of antiferroelectrics regions in the matrix was carried out, given that the Ba²⁺ ion substituted by Mg²⁺ ion in the A-site provoke an electromechanical stress, increasing the short-range interaction forces, and not well appreciate given the small values of the grain size obtained. A more complete work is proposed, where the size of the grain must be regulated, and a temperature study is suggested.