Band gap energy (Eg) for PZTN, determined using the diffuse reflectance principle (Kubelka-Munk expression). Error Eg= ± 0.003 eV. ED values obtained with the Eg and more intense emission band at around 2.56 eV.
The photoluminescence (PL) it is a non thermal origin process, in that a chemical compound absorbs the photons (of the electromagnetic radiation), jumping to an electronic state of more energy, the inverse process happens and so call recombination (when passing to inferior energy level) and the materials radiating photons. The period between absorption and emission occur is in order to 10 nanoseconds. But under special circumstances, this period can extend in minutes or hours. The transition energy is determined by quantum mechanics rules. Different imperfection presents in the materials study will alter the recombination time or frequency.
Simpler PL processes are resonant radiations, in that a photon of a particular longitude wave is absorbed and an equivalent photon is emitted immediately. This process doesn't involve any transition in forbidden energy band and it is extremely quick (10 ns). The most interesting processes happen when the desexcitation energy transition is not direct at the basic level. The most common effect is the fluorescence that is also typically a quick process, but in that the original energy it is dissipated so that the slight photons emitted are of the lower energy that those absorbed. This phenomenon can happen for the isolated atoms, molecules or atoms and molecules in interaction excitement.
1.1. Atomic, molecular and atoms and molecules in interaction luminescence
The isolated atom excitement (making notice that a very rarefied gas can be considered as a group of isolated atoms) it drives to a spectrum of lines. The atom only absorb the frequency of the incident ray that corresponds to the allowed transitions (Figure 1). So all the isolated atoms can be luminescent.
That happens for the isolated atoms is also valid for the isolated molecules, but the laws are more complicated due to the vibrations and rotations molecular than they introduce supplementary energy levels as the sample the following diagram of figure 2.
The pressure of a gas it increases and a new transitions of excitement energy appear by collision, for the appearance of kinetic energy and metastable states. The return to the basic state is with a reduction of the yield of the luminescence and an expansion of the spectrum of the transmission. Then appears spectrum of band. The return to the fundamental state it doesn't always happen with light emission (transitions without radiation).
1.2. Crystalline luminescence
The luminescence of the crystalline bodies is due to the transmission centers (the activators). These centers are:
physical imperfections in crystalline structure (vacancies, interstitial atoms, dislocations), this is intrinsic luminiscence.
chemical imperfections (impurity atoms) in interstitial or substitution position, this is extrinsic luminiscence.
The mechanism of crystalline luminiscence it is explained with the help of energy bands diagram (Figure 3).
Considering that in the perfect crystal any level doesn't exist in forbidden band, the presence of imperfection in the cystal introduces some levels allowed in the forbidden or in the allowed bands. These energy levels they can be:
recombinations levels (h/e -)
metastable levels: the traps of e- (Pe) or h (Pt)
fundamental (F) and excited levels (E) of isolated centers
The spectra of crystalline luminiscence differ notably of the atomic spectra for two fundamental aspects.:
bands are observed and
the emitted radiation appears toward the longitude of big waves, this can made a mistake with the absorbed radiation.
These two aspects are due to the interaction between the emission center and the crystalline lattice.
According to the type of imperfections there are the transitions way and therefore the energy of the transition.
A first transition consists on an electron that leaves a donor level and go toward the valency band. The energy of this transition is given for: E=Egap-Ed
Also, can be observed where an electron leaves to the conduction band to pass at aceptor level. In this case, the energy of the transition is given for: E=Egap-EA
It is known that the energy ED and EA differ according to the chemical nature of the impurity. For this reason is allows to use the photoluminiscence experiments to confirm the presence of a specific type of impurity in a material.
In many cases, the theory of the effective mass is a first valid approach, it predicts the value of the energy ED and EA for a given semiconductor.
In general m * h >>m * e , it is explained, why the bond energy of aceptor levels is bigger than that donors levels.
Broad bands are observed for many optical transitions in the partly filled d-shell of transition metal ions (d - d transitions), but also for transitions between the 5d shell and the 4f shell of rare-earth ions (d - f transitions) and for emission on s2 ions (these ions possess a ‘‘lone pair’’ of s electrons), like Tl+, Pb2+, or Sb3+. Sharp emission bands are characteristic of optical transitions between electronic states with chemical bonding character (almost) the same for ground and excited state, and for the same reason also of optical transitions between electronic states that hardly participate in the chemical bonding (e.g., f - f transitions on rare-earth ions).
In the case of optical processes involving electronic states which participate in the chemical bonding, the nature of the bonding (covalent, ionic) and the symmetry of the site at which the emitting ion is incorporated play a very important role. This is generally described by the ligand field theory, which we do not treat here.
The emission generated reflects how the optical properties of the ion depend on its chemical environment. This luminescent material can be applied as green phosphor in very high-quality fluorescent lamps and also in plasma display (Ronda, 2008).
2. Luminescence in PZT
The width of luminescent band usually observed at room temperatures in crystals of perovskite type it is associated with the presence of imperfections or defects (Haertling, 1999; Anicete-Santosaet al., 2007), be already oxygen or lead vacancies. But other author explain apparition of PL to order-disorder presence in the structure (Chen et al., 1989; Suárez-Gómez et al., 2009; Shannigrahi, 2007) distortion of oxygen octahedral fundamentally.
Undoped PZT ceramics are seldom used. They are usually substituted in the A or B-sites of the perovskite structure ABO3 in order to improve dielectric, piezoelectric and mechanical properties. For example La3+ and Nb5+ are used satisfactorily (Durruthy et al., 1999, 2002; Bharadwaja et al., 2002). The excess of positive charge in (La/Nb) doped PZT is compensated by lead vacancies and the typical Kröger-Vink notation to describe the electroneutrality, have been reported in many papers previously (Eyraud et al, 2006; Jaffe et al., 1954).
The defects caused by the small dopant concentrations in A or B places of the structure could generate a combination of blue, green and red emission of light which is of great importance for optical devices applied in optoelectronics includes flat-screen, full-colour displays and compact laser devices operating in the blue region (Nakajima et al., 2004; Yang et al., 2008).
Recently M.S. Silva et. al., 2005, reported a theoretical and experimental result, and presents an alternative method to process PL in PZT and aim to explain why this phenomenon depends on the crystalline structure of the material. The wide bands at 2.1 and 2.67 eV respectively in PL emission in perovskite ceramics are associated to the oxygen vacancies provoked during the sintering process (Lines & Glass, 2001) or related to ensure electroneutrality process.
What happens with luminescence effect with A, B or A+B doped PZT?
We will try to respond this question with several examples.
All samples that show were prepared by a conventional processing method using mixed oxide powders. The photoluminescence (PL) spectra were obtained using a Jobin Yvon Horiba Fluoromax-3 spectrometer using the excitation band at 373 nm. The absorption spectra were acquired with an UV-vis Ocean Optics Spectrometer QE650000 using diffuse reflectance measurements the data was processed by using the Kubelka-Munk function:
R∞ = (I/I0) is diffuse reflectance at one wavelength from an opaque sample with infinite thickness (> 2 μm), 0< R∞<1, α is the absorbance in cm-1 and S is the scattering factor which is assumed to be independent of the wavelength for grain sizes greater than the wavelength of the light (Wendlandt & Hecht, 1966; Kottim, 1969).
Crystalline structure (Figure 4), like we will see later, influences in the shift energy of PL in the samples. For this reason it is advisable to carry out this study previously to PL analysis. All samples firth were identify by X-ray diffraction (XRD). The XRD patterns of the polycrystalline samples show the tetragonal (Zr/Ti = 20/80, 40/60) and rhombohedral (Zr/Ti = 60/40, 80/20) PZT phases, and both phase together for Zr/Ti = 53/47. This is a classical behavior for this material and has been reported by some authors (Jaffe et al., 1971; Noheda, 2000, 2001).
In our samples doped the compensation of charge provokes in all cases oxygen vacancies that should increase with the dopant concentration or saturates in a composition that denotes a limit of solubility. However, oxygen vacancies are easily induced during the sintering process because the PbO has low volatile temperature of about 880ºC. This phenomenon takes place in all samples and also promotes lead and oxygen vacancies, which are quenched defects at low temperatures. Lead vacancies can only become mobile at high temperatures with high activation energy greater than oxygen mechanism values.
According to Eyraud et. al. (2006) singly and doubly ionized lead and oxygen vacancies coexist in the PZT ceramic, then they may constitute donor and acceptor sites which are able to exchange electrons according to the following reactions:
in our case at least three types of defects coexist, whose contribution to PL depends on the levels in the band gap.
The results of first-principle calculation reported by Ghasemifard et al., (2009) show that the PZT polycrystalline has a direct band gap between the X and Γ points of 3.03 eV (Baedi et al., 2008), then by assuming a direct band gap we can calculate the values of the energy gap (Eg) for all the samples. In general calculating the absorption coefficients of the synthesized powder in the strong absorption region needs both, the transmission and reflection spectra. In our case, we obtained the absorption spectra by diffuse reflectance measurements, and by using the Kubelka-Munk equation for all samples the band gap energy Eg was determined.
2.1. Substitution in A site
The substitution for La3+ in the A site of perovskite structure it’s traditional. It is one of the classic sustituyentes in this system.
The emission spectra (PL) at 273, 325, 373, 413 and 457 nm were characterized to present different bands for PLZT 1-x/x/y (Figure 5), prevailing blue-violet band presence (2.4-2.75 eV), it’s appears at bigger intensity for 413 nm. This evidences that PL effect has the same origin in all cases.
As it has been expressed previously, the energy of the spectra of PL demonstrates the presence of levels in the forbidden band. The calculations of first principles (Longo et al., 2007) have been demonstrated that disorder in perovskite structure and the defects in the same one, they cause states in the forbidden band. On the other hand the experimental evidence of the presence of defects exists (oxygen vacancies) (Mansimenko et al., 1998) starting from mensurations of resonance electronic paramagnética (RPE) in the system PLZT.
If we consider to our materials as semiconductors of big gap, the presence of states in the forbidden band, what causes a contraction of the gap, is the causing of a well-known Burstein-Moss shift of emission spectrum (Yu & Cardona, 1996). It can associate to presence of picks around 2.65 eV to the presence of bands inside of forbiden band in the material, being more intensity when it’s excited with λ= 413 nm.
Analyzing the results associating them with the colors corresponding of the wave longitudes, we see that emissions exist (although of different intensity) in almost the whole visible spectrum, from the red one until the ultra violet, but the bands of very high intensity correspond to the bands of the blue-violet and ultraviolet.
The motive that causes this effect are similar when you doped these materials in B site, this will be explained in the next section.
2.2. Substitution in B site
In perovskita structure (ABO3) N5+ substitute B site, occupied by Zr4+ and Ti4+ ion. The high volatility of lead oxide at elevated temperatures during the powder calcinations and the
sintering stages in the PZT system is known, which provides both fully-ionized cationic lead vacancies and anionic oxygen vacancies. On the other hand, following Eyraud’s model (Sivasubramanian et al., 2007; Chang et al., 2001) the valence of the Niobium is assumed as donor doping in the PZT has a strong influence in the ionization state of extrinsic lead and oxygen vacancies.
Figure 6 shows the PL spectra of PZTN samples for compositions 80/20, 60/40, 53/47, 40/60 and 20/80 which have diverse dopant concentrations. The emission bands (PL response) when fixing the excitation bands (EB) at 373, 457 and 325 nm were observed in three regions: one is at around 1.72 eV (lowest energy region); the second is at around 2.56 – 2.61 eV which shows a higher intensity, and the third is at around 3.35 – 3.45 eV (highest energy region) respectively. The band at 2.56 eV is the most intense and narrow, and the band at 3.35 eV shows greater broadening. The band at 1.72 eV did not show any notable shift in the maximum position peaks for different compositions or dopant concentrations. Nevertheless, the bands at 2.56 and 3.35 eV show a shift in the maximum peak position which depending if the phase is rhombohedral or tetragonal will shift to 2.61 and 3.45 eV, respectively.
Note that in the PZT polycrystalline samples without Nb, the three well resolved emission bands were also shown, in contrast with other reports (Longo et al., 2008; Chang et al., 2001) where the emission for polycrystalline PZT is very low and broad or absent. For these materials (PZTN) the emission is bigger in 1 or 2 order than PLZT. The PLE spectra for samples doped and without doped they present same character, appearing the same line, for what they have the same origin in both cases (Figure 7).
The Eg (in PZTN) values for tetragonal samples 20/80 and 40/60 are between 2.80 to 2.98 eV, the composition 53/47 are near the morphotropic phase boundary which shows a higher variation in Eg, values as a function of the dopant concentration from 2.70 to 3.19 eV. For this composition and rhombohedral phases 60/40 and 80/20 the behavior of Eg values as a function of Nb concentration shows a minimum at 0.8% with values of approximately 2.67 to 2.70 eV. In our case, experimentally it is observed a transition (EPL) at 2.56 eV for samples PZTN 80/20/0.0.
Sintering stages in the PZT system is known, which provides both fully-ionized cationic lead vacancies and anionic oxygen vacancies. On the other hand, following Eyraud’s model (Sivasubramanian et al., 2007; Chang et al., 2001) the valence of the Niobium is assumed as donor doping in the PZT has a strong influence in the ionization state of extrinsic lead and oxygen vacancies.
The ED values reported in Table 2 were calculated using Eg and EPL obtained by excitation at EB=457 nm. Even the origins of these luminescence bands are not clearly understood. Figure 8 shows a schematic diagram to represent the recombination process for the three emission bands. The PL at a high energy region of approximately 3.35-3.45 eV, that overcomes the Eg, which is obtained when the excitation is at 3.81 eV.
|% Nb||Egap (Zr/Ti)|
This corresponds to transitions between higher energy states in the conduction band to the valence band (hot luminescence), and the emission intensity shows a strong dependence on the Nb concentration.
The PL at 1.73 eV, the lowest energy region which is obtained with excitation energy of 3.32 eV, it could be follows a recombination mechanism:
from the localized states due to oxygen vacancies below the conduction band () to the localized states above the valence band due to lead vacancies () and/or
by recombination from band conduction to the localized states above the valence band due to lead vacancies ().
The intensity emission of this band also shows a strong dependence on Nb concentration, and is present in all compositions indicating common defect types related to a deep level inside the band gap. In general, the incorporation of Nb5+ increases the PL intensity in this region due to the compensation of charge and induced defects (and), as it was already seen previously.
In this case the simultaneous disorder of lead and oxygen vacancies should be created during the sintering process. The PL at 2.56 eV, which shows the highest intensity in all PZTN compositions and is associated to a transition between a shallow defect in the band gap and the valence band, see Figure 8. These levels are associated to oxygen vacancies, with simple or double ionization which is in accordance with the classification of Longo et al., (2008), vacancies bonded to clusters of TiO5 in disordered regions. In principle, the incorporation of Nb5+ in PZT samples would be producing more lead vacancies than oxygen vacancies. However, the higher intensities observed for peaks at 2.56 eV rather than peaks at around 1.73 eV is an indication that the oxygen vacancy concentration is higher than lead vacancies.
2.3. Substitution in A + B site
We will present results of double substitution in place A and B for “hard” and “soft” well-known ceramic. For “hard” ceramics present Sr2+ + Cr3+ doped PZT ceramics and for “soft” ceramics present La3+ + Nb5+ doped PZT ceramic.
We will only present the behavior in the PZT morphotropic phase boundary region of phase diagram (Zr/Ti=53/47).
In both type of samples (hard and soft) only appear two regions of emission bands, one at around 1.86 eV and other with higher intensity at around 3.00 eV when fixing the excitation band at 373 nm (3.4 eV) (Figure 9). Also, it is possible to observe emission band around 2.5-2.7, to a lot of smaller intensity. When fixing the excitation band at 412 nm (3.01 eV) only appear one signal wide at 3.28-3.31 eV (Figure 10).
PL show in the high energy region, the maximum position is around 3.00 eV for all composition, but the emission band is a broad band composed by two bands, at 2.98eV (414nm) and 3.03eV (408 nm) (Figure 9). PL lower energy region for PSZTC and PLZTN samples show the band at 1.87 eV (659 nm), additionally is observed that band at 1.74 eV is not present in all compositions and its intensity is reduced appreciably with the incorporation of Cr (Durruthy et al, 2010a,b, 2011).
The general effect of the Cr doping is a decrement the PL intensity in both region bands with the increase of dopant. It is noted that the PL of doped La3+ and Nb5+ is larger than of undoped samples and increased with the composition of both ions at least one order of magnitude for PSZTC, but is two and three order to PZTN and PLZT respectively.
It was of waiting that doped La3+ and Nb5+ increase PL intensity in 1.87 eV (659 nm) in PL, it is well known that is associated with lead vacancies, due to the compensation of charge, in this case the disorder or lead vacancy should be associated to the substitution of La3+ by Pb2+ in the host structure and the typical presence of lead vacancy due to the sintering route (Calderón-Piñar et al, 2007; Silva et al., 2005). The presence of the peak at 1.87 eV, in PSZTC 0.2-0.5 mol % and PLZTN 1 mol% indicates a common defect related with a deep level inside the band gap. As we saw in the region of high energy (3.00 eV) results are similar to showed above previously.
The peaks that appear in zone (2.65) was associated with oxygen vacancies, simple or double ionized. In the sample PLZTN evidently that ED will be ≥ 0.54 eV, and EPL is lower 2.43-2.74. This is because ED is not exactly one unique value because there are a distribution defects in the structure.
The analysis of the peak at 1.86 eV could be associated to the simultaneous presence of oxygen and lead vacancies (Guiffard et al, 2005; Durruthy et al, 2010a , b, 2011). The PL response in the donor-acceptor mechanism in this case between the levels associated to the oxygen near and below conduction band and the level of lead vacancies above the valence band. Analogously the theoretical quantum mechanical calculation reported by de Lazaro et al. (2007) justify that the presence of disorder associated to the substitution of Zr/Ti or displacement of the ions in the B sites produce an amorphous zone in the ceramic with a direct band gap with a separation near to 1.87eV. Beside this, we are detecting some small peaks whose energy is around of 2.00-2.80 eV which belong to the visible energy spectra too (Figure 9).
The calculated results of the band gap values for the PSZTC samples sintered at 1250 ºC are summarized in Table 2. The figure 11 allows us to affirm that the dependence with Zr/Ti ratio is very strong, and has a maximum in the morphotropic phase boundary and the lowest values are for the composition 80/20, this behavior coincides with the calculations carried out by J. Baedi et al. (2008). Figure 12 shows the way that would be materialize recombination in the PSZTC and PLZTN samples. We supposed that the main way was 1, 5 and 6 for the experimental results obtained, in this work.
|mole %||Egap||mole %||Egap|
3. Dielectric characteristic
Another characteristics of these materials that they are very affected by the presence of oxygen vacancies there are dielectric (ε) and loss (tan δ), for this we present some results in different substitution type in ABO3 perovskite structure.
The dielectric curves reveal anomalies in the neighbor at transition temperatures corresponding to FR(HT) – PC (TC) and FT – PC (TF-P) phase transitions. Strong influence of dopant La, Nb and La+Nb on the phase transition temperature (TC) is confirmed. The comparison of ε(T) curves, obtained for the ceramic samples is shown in Figure 13, dielectric measurement shows a decreasing TC and TF-P when increasing the dopant concentration. The dielectric permittivity decreases for dopant concentration larger than 0.8 mol% (Figure 13), in particularity in Nb-doped ceramics permittivity decreases for concentrations up to about 0.8 mol %, and then it increases slightly, as the grain size behaves. The same as in PL, the permittivity is more intense for substitutions in B and A+B, in this case it is 4 times.
There is good agreement between the transition temperatures obtained from ε and tgδ, respectively, considering the range of measurement error (δt ~ 5 °C), for almost every sample. Those compositions with 0.6 and 1.0 % La have T tgδmax at 50 kHz differing 7.3-8.2 oC from the value obtained at 1 kHz. A possible cause of such differs is the presence of inhomogeneities as a result of compositional fluctuations (Gupta & Viehland, 1998; Garcia et al., 2001).
In those samples doped with La+Nb, there is not a sum of the separate effects of La and Nb. Note that temperatures are not as low as those for Nb, but compared to those for La they are 50 °C below.
Grain size decrement implies domain size decrement (Figure 14). Thus, the domain walls become more movable, so the mechanical friction is small, and then the samples doped with Nb and La+Nb are more compositionally homogenous (the evidence is given by narrow plots of dielectric permittivity vs. temperature, that is, increasing permittivity). On the other hand, grain size increment contributes to higher values of the dielectric constant, as a measurement of the number of polarized unitary cells. The amount of polarization of such cells is related to the presence of Nb5+ and La3+ inside the cristalline structure and contributes to the orientation of the domain walls. An increasing dopant concentration produces the increment of the number of lead vacancies and so the dielectric permittivity grows. The values of ε for PZTN samples are higher and attributed to the higher compositional homogeneity and the existence of only one phase in this composition. But is not the same for PLZTN and PLZT, XRD patterns of samples show the tetragonal and rhombohedral PZT phases together. (Figure 15) in all doped samples, with concentration near to MPB (53/47).
Decrements of Tc might be attributed to the integration of dopants into the cristalline structure.
To determine the factor most influential in dielectric permittivity behaviour with the dopant concentration, the influence of porosity was analyzed. As it was seen in Table 3 it varies in an appreciable way (~ 14%) in the studied composition interval.
Among the models proposed to evaluate the properties of porous materials, applicable to systems with inferior porosity values at 0.6, it (the model) stands out the Bruggeman model. This model offers a satisfactory description of the properties of piezoelectric porous ceramic, in particular those based on PZT. A detailed explanation can it turns in works from Wersing et al (1986).
The model establishes a peculiar relationship between experimental permittivity [ε(p0)] and the theoretical [εpo=0], through of porosity fraction (p0) given by the equation (5), considering connectivity (3-0).
Table 3 shows the results for the dielectric permittivity theoretical and experimental at room temperature. A marked difference exists among both, being bigger for the Nb and the La+Nb, what indicates the influence of this impurity in the evolution of the porosity, also Δε to diminish with the frequency
It is important to make notice that this model considers a materials as a not homogeneous médium and it start with two components: material and pores. In the material component there are all that is not pore, that doesn't have to be necessarily homogeneous, due to the procedure method.
The porosity is not the only factor that determines the permittivity variation with dopant concentration. The analysis for dopant type shows that to smaller concentration bigger porosity, but also bigger grain size, therefore is this last one the most influential in the variations of the dielectric parameter. For example, 0.6% of Nb, the smallest difference exists among the theoretical and experimental results, and the porosity has the fundamental rol, for this concentration "po" it is minimized; in the other concentrations exists a cooperative effect of the porosity and the grain size (Sundar et al. 1996), noted how for 1.0% "po" slightly increases the grain size and Δε (Table 3). In La3+ case, Δε diminishes with the frequency and increases with dopant concentration (Table 3), but ε is increasing with grain size decrement, therefore both factors will contribute in a cooperative way in the relative permittivity (Figure 16). The samples doped with La+Nb have a grain size between 1 and 2 microns, in addition the contribution of the porosity is strong in the behavior of dielectric permittivity, being greater even for the composition 0.8. The factors that determined the variation of the permittivity with increasing dopant concentration are the grain size (Cancarevic et al., 2006) and porosity, fundamentally.
The used of PL and diffuse reflectance measurement in polycrystalline ceramics to determine the band gap and the mechanism of the recombination in samples is possible. The experimental results agree with those calculated.
All system present show mainly two region of emission bands around 1.8 and 3 eV, the presence of broad band (1.8 eV) at the band gap can be associated to the vacancy defect common in all (containing lead) ceramics sintered at high temperatures, the emission at around 3eV correspond to direct recombination from CB to VB.
The emission at 2.56 eV, this present but it is not very intense in all the analyzed materials. Shows the highest intensity and a shift to higher energies in the tetragonal phases. The Nb concentration produces appreciably intensity changes and is associated to a transition from oxygen vacancy levels to valence band. PZTN presents the biggest intensity in this band, what indicates that the oxygen vacancy concentration is higher than lead vacancies.
But not all the dopant has same behavior, in all zone of PL spectra Cr diminish PL intensity with increase concentration, while La3+, Nb5+ and La3++Nb5+ increase PL intensity with the increase dopant concentration.
Another interesting aspect is that A+B doped produces an increment to 2-3 order in PL intensity, principally for “soft” doped.
On the other hand, a strong influence of dopants on the decrement of grain size as concentration grows is observed. The substitution in the A place and the simultaneous substitutions in the A and B places provokes mixture of (tetragonal and rombohedral) phases, while substitution in the B place the structure is tetragonal at least in 95 %. A texture effect is also noticed, as it grows with the dopant concentration.
XRD results are confirmed by the obtained dielectric characteristics. In the PLZT, PLZTN and PSZTC samples which present phase mixture, two peaks in the 1/ε curves are observed and associated to Ferro-Ferro (rombohedral-tetragonal) and Ferro-Para (tetragonal-cubic) phase transitions. Substitutions in the B place contribute more significantly to the Curie temperature drop, with a minimum for PZTN 0.8 %.
This work was supported by project PNCB 10/04, Cuba, Sabbatical program CONACYT, Mexico. The author appreciate work of Ing. M. Hernandez, Ing. F. Melgarejo, Ing. M. Landaverde and Ing. E. Urbina. And to Cybernetic, Mathematical and Physics Instituted.