Ferroelectric composites have non-linear dielectric properties, depending on external conditions. Currently, such composite materials are widely used in microelectronics, instrumentation, and materials for space due to their extraordinary physical properties. For example, thermistors with abnormally high positive coefficient of resistance are used in instrumentation engineering as active elements of measuring, signaling, and safety devices . In addition, some ferroelectric materials exhibit high radiation resistance, which allows their use as coatings for spacecraft. Such coatings with inclusion of ferroelectric particles are capable of creating an outer protection of the spacecraft from the excess electric charge during the flight .
Dielectric properties of ferroelectric composites were investigated in Refs. [3, 4]. It is shown that an increase in the volume fraction of particular inclusions in composites (KNO3)1− x /(BaTiO3) x and (KNO 3 )1− x /(PbTiO3) x stabilizes their ferroelectric phase. Therefore, further studies of ferroelectric composites of different compositions and varying percentage of inclusions of particles presents a scientific interest.
In this paper, we investigate the dielectric properties of ferroelectric composite (NH4HSO4) x /(PbTiO3) 1−x . Earlier, it was found that there was an expansion of the temperature interval of the ferroelectric phase existence for ammonium hydrogen sulfate particles in the nanoscale matrices caused by reducing the temperature of the lower phase transition and also increasing the width of the hysteresis lower temperature phase transition [5 and references therein].
Ammonium hydrogen sulfate NH4HSO4 ferroelectric is in the temperature range from 160 K to 270 K at heating and from 154 K to 270 K at cooling. The value of spontaneous polarization at 260 K is 0,4 ∘C/cm2 and reaches its maximum of 0,8 ∘C/cm2 at 154 K. Structure NH4HSO4 belongs to the space group Pc in ferroelectric phase, to the space group P2 1/c at room temperature and to the space group Pc at low temperatures. Both phase transitions are associated with the processes of SO4 tetrahedra ordering .
Lead titanate PbTiO3 is a ferroelectric perovskite. At room temperature, it has a tetragonal structure. The magnitude of the spontaneous polarization is ∼57 ∘C/cm2 . When heated to the Curie temperature of 768 K, the ferroelectric undergoes phase transition from the tetragonal to the cubic nonpolar polar phase .
For research, composite samples (NH4HSO4) x /(PbTiO3)1− x were prepared with x = 0,10; 0,20; 0,30; 0,40; 0,50. Respective volume proportions of ammonium hydrogen and lead titanate powders were mixed and pressed at 6000 kg/cm2 into tablets of 13 mm diameter and ∼1 mm thickness. Measurements of dielectric constant were performed in the heating mode, during cooling in the temperature range from 130 K to 380 K at a rate of 1 deg/min in the frequency range from 0,1 Hz to 10 MHz using a broadband dielectric spectrometer Novocontrol. We used silver paste for the electrodes. To remove adsorbed water, composite samples were pre-warmed to 380 K.
Figure 1 shows the temperature dependence of the permittivity of the composite samples (NH4HSO4) x /(PbTiO3) 1−x of different compositions. As reference, was used a sample of polycrystalline ammonium hydrogen sulfate (x = 0,00). The maxima of the dependence for polycrystalline NH4HSO4 corresponding to phase transitions are located at the points T 1 = 166 K and T 2 = 272 K, which is 6 K and 2 K higher than the phase transition temperature of the single crystal of ammonium hydrogen sulfate. This may be due to the mechanical stress of the sample, crystal deformation, charge on the crystal surface, or air gap between the crystals preventing the propagation of domains and domain wall motion. On the graphs ε'(T) (Fig. 1) for composite samples with a volume fraction of lead titanate particles 0,10≤x≤0,40 there are two peaks of the permittivity. The upper peak corresponding to the transition from paraelectric to ferroelectric phase is near the bottom temperature 270 K. The peak corresponding to the transition between paraelectric and ferroelectric phases is 3-6 degrees less than the temperature of the polycrystalline NH4HSO4. For the composite sample (NH4HSO4) x /(PbTiO3) 1−x with a volume fraction of inclusions x = 0,50 peaks corresponding to phase transitions are not observed as well as for the composite (KNO3)0,50(BaTiO3)0,50 [3, 4].
Figure 2 shows that width temperature interval of the ferroelectric phase ammonium hydrogen sulfate in composite with a volume fraction of particle inclusions from 0,10 to 0,50 by heating is expanded by ∼5 degrees as compared with pure polycrystalline NH4HSO4 and it is independent on the volume fraction of inclusions. In order to explain the stabilization of the ferroelectric phase ammonium hydrogen sulfate in composite, we use the expansion of the free energy in accordance with the Landau theory , where the value of the polarization plays the role of the order parameter. In addition, it is necessary to consider an additional contribution due to an electric dipole interaction of particles PbTiO3 with the surrounding particle matrix NH4HSO4.
Thus, the free energy of the ferroelectric particle systems (in the absence of an external electric field) can be written as:
where , V i , V j and p i , p j – volumes and polarization particles NH4HSO4 and PbTiO3, respectively, r i j – extrapolation a length, which is determined by the distribution of particles in the sample. The energy of the dipole-dipole interaction Δ F d d depending on the location and orientation of the dipole moments of the particles can have both positive and negative values. However, due to general physical considerations we can conclude that the dipole moments are oriented in NH4HSO4 particles so as to compensate field PbTiO3 particles when Δ F d d >0, thus increasing the ferroelectric stability. This can be explained by the fact that each dipole reorientation is difficult, as it requires additional overcoming of the potential barrier formed by the dipole moments of PbTiO3 particles.
The absence of peaks corresponding to phase transitions, for samples x=0,50 can be explained as follows. With increase in the proportion of lead titanate particles in the composite, the distance between the titanate is reduced. This leads to the fact that the field of lead titanate particles closes on itself, and ferroelectric properties of the ammonium hydrogen sulfate in the composite will not appear.
Figure 3 shows the temperature dependence of the permittivity for the composite samples (NH4HSO4) x /(PbTiO3) 1−x in cycle heating-cooling for the upper phase transition. Studies have shown that the inclusion of PbTiO3 particles give rise to the upper temperature hysteresis of the phase transition. In pure NH4HSO4 there is no hysteresis, as this transition is of the second order. The observed temperature hysteresis may indicate a change in the type of phase transition from the second order to the first order one.
Table 1 presents the lower and upper phase transition temperatures during heating and cooling, for the hysteresis width of the samples.
To understand the thermal hysteresis, it should be noted that the Hamiltonian of dipole-dipole interactions above and below the phase transition has a different size, since two systems with ready dipole moments interact in the ferroelectric phase. The interaction energy (energy Keesom) of two oppositely directed dipoles will be determined by the relation:
While in paraelectric phase, ready dipole moments of PbTiO3 microparticles interact with induced dipole moments in NH4HSO4 with energy (Debye energy):
where χ – polarizability. This energy has a lower value and decreases proportionally to the sixth power of the distance. The difference in free energy of expansion when approaching from above and below by the phase transition temperature leads to a jump in energy; therefore, the phase transition changes its order from II to I.
Dielectric studies of ferroelectric composite (NH4HSO4) x /(PbTiO3) 1−x have shown that the value of the temperature interval of existence of the ferroelectric phase increases by ∼5 degrees and it is independent at the volume fraction of particulate inclusions in composites. Revealed temperature hysteresis of the upper phase transition may indicate a change in the type of phase transition from the second order to the first order one.