Microstructure and dielectric properties of BF–PFN ceramics with negative dielectric loss

The object of investigations was multiferroic BiFeO₃–PbFe_1/2Nb_1/2O₃ ceramic solid solutions (BF–PFN) with different content of BiFeO₃ (BF) component in relation to PbFe_1/2Nb_1/2O₃ (PFN) component [35, 36]. Three multiferroic ceramics obtained from simple oxides with percentages contain BF/PFN: 60/40 (BF60–PFN40), 70/30 (BF70–PFN30), 80/20 (BF80–PFN20), respectively were tested. Solid solutions of the BF–PFN were obtained from simple oxides: PbO (99.9%, POCH), Fe₂O₃ (99.9%, POCH), Nb₂O₅ (99.9%, Sigma-Aldrich) and Bi₂O₃ (99.9%, Aldrich). The powders were weighed in a suitable, stoichiometric manner, while the lead oxide PbO was weighed with excess of 3.5 wt% (to compensate lead evaporation during sintering). Then the ceramic powders were mixed and milled in a planetary ball mill for 15 h and next were successively dried and calcined at 1173 K/2 h. The obtained powders were uniaxially pressed into discs with a diameter of 10 mm and the thickness of about 3 mm, using polyvinyl alcohol as a binder. Such prepared ceramic discs have been sintered in alumina crucibles at 1323 K for 2 h, with the heating rate of about 2.5 K/min (for all three compositions of the BF–PFN material). In the next step the ceramic samples were grinded, polished and annealed at 973 K/5 min. to remove mechanical stresses that may have occurred during mechanical machining. For the electrical tests, silver electrodes (P-120 supplier Polish State Mint) were applied on both surfaces of the ceramic samples (burning method).

X-ray powder-diffraction data (XRD) of the BF–PFN ceramic materials were carried out at room temperature (RT) on a diffractometer Phillips X’Pert APD (Cu-Kα radiation). The data were collected in the 2θ range from 10° to 65° in steps of 0.02 degrees with an integration time of 4 s/step. Microscopic investigations were performed on the fracture of samples (after breaking the samples), using the scanning electron microscope (JEOL JSM-7100F TTL LV). The chemical composition analysis in microareas was performed by the standard method, using an energy dispersive spectrometer (EDS). The SEM/EDS studies were performed by the accelerating voltage 15 kV, and with Au sputtering on the surface of samples, using Vacuum Evaporator JEE-4X (JEOL). Au sputtering on the sample was the last stage of sample preparation for imaging and analysis with the electron microscope. Dielectric constant and loss tangent were measured on the 1 V amplitude of the driving signal using LCR meter (QuadTech 1920 Precision) at temperature range from RT to 923 K, for several frequencies of measurement field (range from 20 Hz to 1 MHz). DC electrical conductivity has been measured using a Keithley 6517B electrometer (high resistance meter) in temperature range from RT to 570 K.

The XRD test of the multiferroic BF–PFN ceramic powders after sintering have been presented in Fig. 1. On diffraction patterns for all BF–PFN samples are visible the lines connected with the BiFeO₃ and PbFe_1/2Nb_1/2O₃ materials as well as the lines connected with of foreign phase (Bi₂₅FeO₄₀). A secondary undesirable phase Bi₂₅FeO₄₀ (JCPDS card no. 01-073-9538) is created during the technological process. The largest amount of foreign phase occurs for the BF80–PFN20 sample. In the case of the BiFeO₃ (BF) component the best fit to the measured data was obtained with the pattern JCPDS card no. 86-1518 (a polycrystalline rhombohedral distorted perovskite structure with a space group of R3c). In the case of the PbFe_1/2Nb_1/2O₃ (PFN) component the best fit to the measured data was obtained with the pattern JCPDS card no. 04-009-5124 (a perovskite structure with the tetragonal symmetry and P4mm space group).

Results of morphology studies of breakthrough of the samples have been presented in Fig. 2. Microstructures of BF60–PFN40 and BF70–PFN30 ceramics are characterized by well-shaped grins grains (with clearly visible grain boundaries and with sharp edges of the grains) of different size (Fig. 2a, b, respectively). The microstructure of multiferroic BF80–PFN20 sample (Fig. 2c) is characterized by worse shaped grains, compared to microstructure of BF60–PFN40 and BF70–PFN30 ceramic materials. The microstructure of BF60–PFN40 and BF70–PFN30 multiferroic ceramics reveals clear grains boundaries after breaking the samples. In the case of the BF60–PFN40 ceramic material only one type of fractures appears after breaking the samples, namely along the grain boundaries (Fig. 2a). In the case of the BF70–PFN30 ceramics two types of fracture appears, the first one (main) along the grain boundaries, but also single fractures through grains are present in this material (Fig. 2b). The type of cracks along the grain boundaries is becoming dominating in this ceramic sample. A mixed nature of fracture occurs in BF80–PFN20 material, that is, fractures occur along boundaries as well as through grains (Fig. 2c).

An EDS analysis of investigated multiferroic ceramic samples qualitatively confirmed the assumed share of the specific components and it showed that the materials do not contain any impurities (Fig. 3). The results of the percentage of individual components of the BF–PFN ceramic samples are the averaging of 10 randomly-chosen areas from the surface of the sample. The tested materials showed quite stable chemical composition. The Nb₂O₅ and BiO₂ are the most stable behavior in both BF60–PFN40 and BF80–PFN20 ceramic samples, while Fe₂O₃ and BiO₂ are the most stable behavior in BF70–PFN30 ceramic sample (Table 1).

The analysis of the elements distribution showed some differences in the chemical composition but all deviations between the theoretical content of chemical elements in the tested materials and their real content are within the acceptable range.

The temperature dependencies of dielectric constant ε′ for the BF60–PFN40 ceramic sample is shown in Fig. 4a. The dielectric constant increases with increasing temperature up to 643 K, and then decreases with further growth of temperature. The dielectric constant reaches a value of zero at a temperature of 743 K, for all frequencies of the measuring electric field. A further increase in temperature causes the dielectric constant value to drop below zero. The dielectric constant takes negative values. The location of the maximum of the dielectric constant does not depend on the frequency of the measuring electric field and it may correspond to the ferroelectric—paraelectric phase transition. The second maximum of dielectric constant for frequencies in the range from 20 to 500 kHz appears below the phase transition temperature (the inset of Fig. 4a). The location of this maximum depends on the frequency of measuring field, i.e. the relaxation processes are responsible for its origin. The part of Fe³⁺ ions which present in the material could be reduced to Fe²⁺ ions during the sintering process. The potential barrier between these two types of ions affects the movement of charges, causing the relaxation process to appear in tested BF–PFN ceramic material [37].

Figure 4b shows the temperature dependencies of dielectric constant ε′ for BF70–PFN40 ceramic sample. The dielectric constant increases with increasing temperature similar to dielectric constant for BF60–PFN40 sample. The maximum of dielectric constant appears at 628 K for all frequencies of the measuring electric field. This maximum is independent of frequencies of measuring field. The ferroelectric–paraelectric phase transition may be responsible for its appearance. A further increase in temperature causes the dielectric constant to decrease to negative values. The second maximum of dielectric constant, for frequencies in the range from 500 Hz to 20 kHz appears below the phase transition temperature similar to the BF60–PFN40 material (the inset of Fig. 4b). The reason for the creation of this maximum, are the relaxation processes that take place in the tested material.

The temperature dependencies of dielectric constant ε′ for BF80–PFN20 ceramic material is shown in Fig. 4c. The values of dielectric constant increase with increasing temperature and reach the maximum value at 793 K. The clear maximum of dielectric constant occurs in the same temperature for all measuring frequencies. Therefore the temperature of this maximum corresponds to the ferroelectric—paraelectric phase transition in BF80–PFN20 material. A further increase in temperature causes decreasing of the dielectric constant. The values of the dielectric constant, in the tested temperature range, decrease up to negative values for the frequency of measuring electric field in the range from 20 to 500 kHz, while the value of dielectric constant remains positive for remaining frequencies (i.e. from 500 Hz to 10 kHz).

The inset of Fig. 4c shows the dielectric anomaly at temperatures below phase transition temperature (the dielectric anomaly appears at the range from 433 to 583 K). The critical temperature increases with increasing frequency of measuring electric field. The position change of this maximum from the temperature (at different measuring frequencies), indicates the occurrence of dielectric relaxation in the material under study. This relaxation behavior may come from the properties of the BF component of the final BF–PFN solid solution [38].

Negative values of dielectric constant, which clearly appear, in the tested temperature range, for both BF60–PFN40 and BF70–PFN30 materials, may indicate a change in the electrical character of these materials. Namely the electrical character of tested materials is changing from capacitive to inductive one [39]. It can be assumed, by analogy with a diamagnetics in the magnetic field that the material with negative dielectric constant has dia-electric properties [40, 41], i.e. the electric field inside the material has the opposite direction to the applied external electric field.

The value of temperature of ferroelectric—paraelectric phase transition is different for various chemical compositions of the BF–PFN ceramics (Fig. 4a–c). The lowest phase transition temperature (628 K) reveals the BF70–PFN30 material, while the highest (793 K) reveals the BF80–PFN20 sample. The BF60–PFN40 sample is characterized by a phase transition temperature equal to 643 K. The results of these studies show that the percentage of BF and PFN components in ceramics affects the value of the phase transition temperature. Increasing the amount of BF (only to a certain value) in relation to PFN affects the reduction of the phase transition temperature. There is a limit ratio of the content of BF and PFN in ceramics above which the temperature of the phase transition increases. The dependence of the phase transition temperature on the percentage of the BF and PFN components, in tested ceramic materials, can be related to influence the BF and PFN components on the anchored of the ferroelectric domain walls. In the BF70–PFN30 ceramics, the ferroelectric domain walls are the least anchored. The least energy is required to release them therefore the phase transition temperature is the lowest among the materials tested. While in the BF80–PFN20 material, the ferroelectric domain walls are most strongly anchored. In order to free the domain walls, the largest energy, in relation to the other studied materials, is required. The confirmation of this fact may be the highest temperature of ferroelectric—paraelectric phase transition (in relation to the other materials tested).

Temperature dependencies of dielectric loss tangent for all tested materials are presented in Fig. 5. Comparing the results for all BF–PFN ceramic samples may be observed that the negative loss phenomenon takes place at different temperature regions, as shown in Fig. 5.

Figure 5a shows that dielectric loss tangent for BF60–PFN40 sample increases with increasing temperature. The first maximum of dielectric loss appears at 623 K (the inset of Fig. 5a), the second one occurs at 723 K. Next, dielectric loss decrease with further increasing temperature and at above 743 K they reach negative values, for all frequencies of the measuring field.

Temperature dependencies of dielectric loss tangent for BF70–PFN30 sample are presented in Fig. 5b. The value of dielectric loss tangent increases with the temperature rise to a certain value, and next with further increasing temperature the value of the tanδ begins to decrease up to the negative values. A small maximum appears on the temperature dependencies of dielectric loss tangent at 523 K (the inset of Fig. 5b). This small maximum of dielectric loss is related with the relaxation processes taking place in the tested BF–PFN material. Further increasing temperature causes decreasing of the values of dielectric loss tangent up to negative values. Negative values of the tanδ occur at different temperatures for different frequencies of measuring field (Fig. 5c).

Temperature dependencies of dielectric loss tangent for BF80–PFN20 sample were presented in Fig. 5c. There is only one maximum on temperature dependencies of dielectric loss tangent for BF80–PFN20 material. The values of the tanδ increasing with the temperature and reach a maximum in the temperature range from 583 to 653 K (depending on the frequency of the measuring field). Next, with further increasing temperature, the values of the tanδ begin to decreases. Dielectric loss reach negative values, in the studied temperature range, only for several frequencies of measuring field (Fig. 5c).

Positive dielectric loss corresponds to the normal relaxation processes that are associated with process of absorption and emission of energy. Axelrod et al. showed in their work [22] that a negative loss phenomenon is related to the fact that more energy must be released than absorbed. According to, the principle of energy conservation, the total energy in the ceramic sample must be conserved. Therefore, there must be some mechanism in this material that allows you to store energy and release it only at certain temperatures and at certain frequencies. The negative loss phenomenon may be attributed to local non-compensated charges, which may accumulate inside the real porous material on the interface of the pores. These charges may be anchored via non-bonding orbitals, full or empty for positive or negative ions, respectively. This assumption allows explain the mechanism of separation of the space charges. The separation of charge leads to the accumulation of energy and this is a metastable state. This metastable state may be eliminated under certain conditions such us temperature and frequency. The specified temperature and frequency may cause avalanche recombination of charges, which results in the effect of energy emission [22].

Figure 6 shows the Arrhenius plot i.e. the dependence of the logarithm of the maximum value of dielectric constant (for the relaxation maximum) against the inverse of the temperature. The Arrhenius plot was used to analyze relaxation processes. To analyze the dielectric relaxation process, the activation energy has been calculated for tested BF–PFN ceramic samples. The activation energy was calculated by fitting the Arrhenius law [42] to the results shown in Fig. 6. The activation energies, which were determined from straight fitting lines, are equal: 1.18 eV, 1.29 eV and 1.38 eV, for BF60–PFN40, BF70–PFN30 and BF80–PFN20 ceramic samples, respectively. Such values of activation energy correspond to the relaxation process, which may be related to the occurrence of ionization of oxygen vacancies [43].

Temperature measurements of the DC electrical conductivity of the multiferroic BF–PFN ceramic samples are show in Fig. 7. At lower temperatures, the lowest electrical conductivity has BF60–PFN40 sample, while the highest electrical conductivity has BF80–PFN20 sample. At higher temperatures, the temperature plots have a similar shape for all BF–PFN ceramic samples.