Effect of Oxygen Nonstoichiometry on Electrical Conductivity and Thermopower of Gd0.2Sr0.8FeO3-δ Ferrite Samples.

The behavior of the resistivity and thermopower of the Gd0.2Sr0.8FeO3-δ ferrite samples with a perovskite structure and the sample stability in an inert gas atmosphere in the temperature range of 300⁻800 K have been examined. It has been established that, in the investigated temperature range, the thermoelectric properties in the heating‒cooling mode are stabilized at δ ≥ 0.21. It is shown that the temperature dependencies of the resistivity obtained at different δ values obey the activation law up to the temperatures corresponding to the intense oxygen removal from a sample. The semiconductor‒semiconductor electronic transitions accompanied by a decrease in the activation energy have been observed with increasing temperature. It is demonstrated that the maximum thermoelectric power factor of 0.1 µW/(cm·K²) corresponds to a temperature of T = 800 K.


Introduction
The major characteristics of a thermoelectric material are its thermoelectric efficiency Z = S 2 σ/κ (S is the Seebeck coefficient, also known as thermopower, σ is the electrical conductivity, and κ is the thermal conductivity) [1], dimensionless thermoelectric quality factor ZT (T is the absolute temperature), and power factor P = S 2 σ = S 2 /ρ (ρ is the resistivity).
Recently, close attention of researchers has been paid to oxide materials [2], since they are stable against high temperatures, nontoxic, and, as a rule, do not contain rare elements. A group of complex oxides of the rare-earth transition metals Ln 1−x A x MO 3−δ (Ln is a lanthanoid, A is an alkali or alkali-earth metal, and M is a transition metal (Co, Fe, or Mn)) with a perovskite structure holding a special place [3][4][5] among the oxides for promising application. The diverse physicochemical properties of these compounds, which belong to strongly correlated electron systems, are interesting both for application [6] and for fundamental research. Along with their thermoelectric characteristics, the stability of these materials against different environmental factors, including the atmospheric composition and temperature, is of great practical importance. In this study, taking into account the significant differences between the low-temperature properties of the Gd 1−x Sr x FeO 3−δ

Results
In contrast to the complex cobalt oxides Re 1−x Sr x CoO 3−δ (Re is the rare-earth ion), which, depending on the cooling rate and synthesis temperature, can form compounds ordered or disordered over A sites of the perovskite structure [13][14][15][16][17][18], the Gd 0.2 Sr 0.8 FeO 3−δ compound synthesized by us is disordered and characterized by the random distribution of oxygen vacancies and cations over the A sites. The X-ray diffraction study revealed no foreign phases. According to the X-ray powder diffraction data (Figure 1), the synthesized Gd 0.2 Sr 0.8 FeO 3−δ samples, similar to the heavily-doped La 1−x Sr x FeO 3−δ (0.8 ≤ x ≤ 1.0) compounds [19], have a form of a disordered perovskite with the cubic symmetry (sp. gr.Pm3m (a = 3.8688(1) Å), in which all the iron sites were identical, as in the mixed-valence iron compounds Sr 2 LaFe 3 O 8.94 [20]. The structural formula derived from the refined occupancies of atomic positions (Table 1) [7] have smaller lattice parameters (3.8665(1) and 3.8582(1) Å), which is consistent with the smaller oxygen stoichiometry estimated from the XRD refinement for our sample.
Atomic positions, and their occupancies and thermal parameters in the crystal structure of Sr 0.8 Gd 0.2 FeO 2.79 are given in Table 1.    Figure 2 shows the temperature-programmed reduction data. The change in the mass caused by removal of oxygen from the sample upon heating in the 5%H2-Ar reducing atmosphere started at ≈500 K and depended on the heating rate, which is related to the solid-state reduction kinetics. As the heating rate increased, the thermogravimetric (TG) and derivative thermogravimetric (DTG) curves shifted to the high-temperature region and the maximum reduction rate was observed at 640 and 725 K at heating rates of 2 and 20 K/min, respectively.    Figure 2 shows the temperature-programmed reduction data. The change in the mass caused by removal of oxygen from the sample upon heating in the 5% H 2 -Ar reducing atmosphere started at ≈500 K and depended on the heating rate, which is related to the solid-state reduction kinetics. As the heating rate increased, the thermogravimetric (TG) and derivative thermogravimetric (DTG) curves shifted to the high-temperature region and the maximum reduction rate was observed at 640 and 725 K at heating rates of 2 and 20 K/min, respectively.  The electrical resistivity and thermopower were measured on the rectangular bar samples 0.9 × 4.5 × 9 mm in size at temperatures from 300 to 800 K in the inert Не (99.999%) atmosphere. To examine the changes in the temperature dependences of the resistivity and thermopower, the measurements were performed during the heating-cooling cycles and the courses of the obtained temperature curves were compared. Three thermal cycles were performed. The heating and cooling rates were 5 °C/min. The results obtained are shown in Figure 3. It can be seen that the temperature dependences The electrical resistivity and thermopower were measured on the rectangular bar samples 0.9 × 4.5 × 9 mm in size at temperatures from 300 to 800 K in the inert He (99.999%) atmosphere. To examine the changes in the temperature dependences of the resistivity and thermopower, the measurements were performed during the heating-cooling cycles and the courses of the obtained temperature curves were compared. Three thermal cycles were performed. The heating and cooling rates were 5 • C/min. The results obtained are shown in Figure 3. It can be seen that the temperature dependences of the electrical resistivity and thermopower of the investigated samples in the heating-cooling cycles were essentially different, which is indicative of the strong effect of oxygen on the physical properties of the Gd 0.2 Sr 0.8 FeO 3-δ compound. In the first thermocycle, when oxygen was actively removed from the sample, the behavior of the thermoelectric parameters of the compound was especially anomalous (Figure 4a). For clarity, the electrical resistivity and Seebeck coefficient measured during the first heating with the active oxygen removal (Figure 4a) and the last cooling (Figure 4b), when the sample was almost stable, are plotted. (1, 2) TG and (3, 4) DTG curves of temperature-programmed reduction of the Gd0.2Sr0.8FeO2.87 compound in the 5% Н2-Ar mixture flow at heating rates of 2 (black solid curve) and 20 K/min (red dotted curve).
The electrical resistivity and thermopower were measured on the rectangular bar samples 0.9 × 4.5 × 9 mm in size at temperatures from 300 to 800 K in the inert Не (99.999%) atmosphere. To examine the changes in the temperature dependences of the resistivity and thermopower, the measurements were performed during the heating-cooling cycles and the courses of the obtained temperature curves were compared. Three thermal cycles were performed. The heating and cooling rates were 5 °C/min. The results obtained are shown in Figure 3. It can be seen that the temperature dependences of the electrical resistivity and thermopower of the investigated samples in the heating-cooling cycles were essentially different, which is indicative of the strong effect of oxygen on the physical properties of the Gd0.2Sr0.8FeO3-δ compound. In the first thermocycle, when oxygen was actively removed from the sample, the behavior of the thermoelectric parameters of the compound was especially anomalous (Figure 4а). For clarity, the electrical resistivity and Seebeck coefficient measured during the first heating with the active oxygen removal (Figure 4а) and the last cooling (Figure 4b), when the sample was almost stable, are plotted.   The anomalies in the behavior of the Seebeck coefficient correlated with the data of thermogravimetric analysis of the sample mass loss caused by the removal of oxygen and are observed at much lower temperatures than in the behavior of the resistivity (Figure 4а).
The oxygen nonstoichiometry index δ increased from one heating-cooling cycle to another and the deviation from the semiconductor-type conductivity shifted toward higher temperatures. At δ = 0.21, the temperature dependency of the resistivity was qualitatively consistent with the semiconductor-type conductivity dρ/dT< 0 over the entire temperature range of interest (Figure 4b).
The conductivity in the regions corresponding to the semiconductor type obeyed the thermal activation law: where is the coefficient weakly dependent on temperature, is the activation energy, and is the Boltzmann constant. The dependences of the logarithmic resistivity of the sample on the reciprocal temperature in the corresponding temperature ranges for several heating and cooling processes are presented in Figure 5. For all the thermal cycles, the ln(ρ)(1/T) curves contain two The anomalies in the behavior of the Seebeck coefficient correlated with the data of thermogravimetric analysis of the sample mass loss caused by the removal of oxygen and are observed at much lower temperatures than in the behavior of the resistivity (Figure 4a).
The oxygen nonstoichiometry index δ increased from one heating-cooling cycle to another and the deviation from the semiconductor-type conductivity shifted toward higher temperatures. At δ = 0.21, the temperature dependency of the resistivity was qualitatively consistent with the semiconductor-type conductivity dρ/dT < 0 over the entire temperature range of interest (Figure 4b). The conductivity in the regions corresponding to the semiconductor type obeyed the thermal activation law: where ρ 0 is the coefficient weakly dependent on temperature, E a is the activation energy, and k B is the Boltzmann constant. The dependences of the logarithmic resistivity of the sample on the reciprocal temperature in the corresponding temperature ranges for several heating and cooling processes are presented in Figure 5. For all the thermal cycles, the ln(ρ)(1/T) curves contain two portions that are described well by the thermal activation law with different activation energies E a . At each specific δ value, the activation energy decreased with increasing temperature. At the same time, the activation energy grew with the oxygen nonstoichiometric index. The absolute values of the oxygen nonstoichiometry indices and activation energies for different temperature ranges and electronic transition temperatures were determined by the crossing points of the approximation curves are given in Table 2.
0.21, the temperature dependency of the resistivity was qualitatively consistent with the semiconductor-type conductivity dρ/dT< 0 over the entire temperature range of interest (Figure 4b).
The conductivity in the regions corresponding to the semiconductor type obeyed the thermal activation law: where is the coefficient weakly dependent on temperature, is the activation energy, and is the Boltzmann constant. The dependences of the logarithmic resistivity of the sample on the reciprocal temperature in the corresponding temperature ranges for several heating and cooling processes are presented in Figure 5. For all the thermal cycles, the ln(ρ)(1/T) curves contain two portions that are described well by the thermal activation law with different activation energies . At each specific δ value, the activation energy decreased with increasing temperature. At the same time, the activation energy grew with the oxygen nonstoichiometric index. The absolute values of the oxygen nonstoichiometry indices and activation energies for different temperature ranges and electronic transition temperatures were determined by the crossing points of the approximation curves are given in Table 2.    Figure 6 presents the plots of activation energy E a in the low-temperature (below the temperature of the electronic transition, T < T p-p ) and high-temperature (above the transition temperature, T > T p-p ) regions and semiconductor-semiconductor transition temperature T p-p as functions of the oxygen content in the sample. It can be seen that, in the investigated temperature and δ ranges, all the dependencies are linear.

Regime δ E a (T < T p-p ) (eV) T p-p (K) E a (T > T p-p ) (eV)
The E a value in the low-temperature range was several times higher than in the high-temperature range; the difference slightly decreased with increasing δ. The electrical conductivity of the materials under study was implemented using impurity carriers induced by different-valence Gd+3/Sr+2 cation substitutions and holes related to oxygen vacancies. At high temperatures, we observed the properties of an almost degenerate semiconductor, while at low temperatures, the activation energy increased. The temperature T p-p of the asymptotic change weakly depended on the vacancy concentration. The fact that the activation energy depended on the vacancy concentration is evidence for the shift of the impurity level from the allowed state band extremum. It is worth noting that the concentration dependences of the activation energies (straights 1 and 2 in Figure 6) are almost parallel. activation energy increased. The temperature Tp-p of the asymptotic change weakly depended on the vacancy concentration. The fact that the activation energy depended on the vacancy concentration is evidence for the shift of the impurity level from the allowed state band extremum. It is worth noting that the concentration dependences of the activation energies (straights 1 and 2 in Figure 6) are almost parallel.   Figure 7 shows the temperature dependencies of the power factor P for the first and last temperature cycles. It can be seen that, as the temperature increased, the power factor of the samples grew, but did not attain its maximum, in the investigated temperature range. In the sample stability region, the increase was monotonic, without jumps, and almost linear for the sample with δ = 0.21. At a temperature of T = 500 K, the power factor of the sample with δ = 0.21 exceeded almost fourfold the power factor of the samples with δ = 0.13 (0.052 µW/(K 2 ·cm) and 0.013 µW/(K 2 ·cm)) and the maximum P value obtained at T = 800 K was 0.1 µW/(K 2 ·cm).

Conclusions
The behavior of electrical resistivity and thermopower of the disordered Gd0.2Sr0.8FeO3−δ perovskite in the temperature range of 300-800 K and its stability in the helium atmosphere were investigated. It was established that the stability of thermoelectric parameters strongly depends on the oxygen content in a sample and is obtained at temperatures from 300 to 800 K at an oxygen nonstoichiometric index of δ ≥ 0.21.
In the sample stability region, the temperature dependences of electrical resistivity for all δ values contained portions that were described well by the thermal activation law; as the temperature increased, spread semiconductor-semiconductor transitions were observed, which are accompanied by a decrease in the activation energy. The latter grows with decreasing oxygen content in a sample. In this case, the temperature of electronic transition depends linearly on the oxygen nonstoichiometry. The power factors obtained in this work for the sample Gd 0.2 Sr 0.8 FeO 3-δ (P = 0.1 µW/(cm·K 2 )) are consistent with those presented in Reference [21] for the LaCo 1−x Ni x O 3 (P = 0,12 µW/(cm·K 2 ), LaCo 1−x Ti x O 3−δ (P = 0.28 µW/(cm·K 2 )) [22], La 1−x Sr x Co 0.8 Ni 0.1 Fe 0.1 O 3 (P = 0.76 µW/(cm·K 2 )) [5], and La 1−x Na x CoO 3 (P = 0.1 µW/(cm·K 2 )) polycrystalline samples [23], although our data are inferior to the value of P ≈ 3 µW/(cm·K 2 ) for the Ca 3−x Bi x Co 4 O 9+δ samples from study [24].

Conclusions
The behavior of electrical resistivity and thermopower of the disordered Gd 0.2 Sr 0.8 FeO 3−δ perovskite in the temperature range of 300-800 K and its stability in the helium atmosphere were investigated. It was established that the stability of thermoelectric parameters strongly depends on the oxygen content in a sample and is obtained at temperatures from 300 to 800 K at an oxygen nonstoichiometric index of δ ≥ 0.21.
In the sample stability region, the temperature dependences of electrical resistivity for all δ values contained portions that were described well by the thermal activation law; as the temperature increased, spread semiconductor-semiconductor transitions were observed, which are accompanied by a decrease in the activation energy. The latter grows with decreasing oxygen content in a sample. In this case, the temperature of electronic transition depends linearly on the oxygen nonstoichiometry.
We explained the nature of the semiconductor transitions as the result of occupancy/deoccupancy by the oxygen ions of different positions in the nonstoichiometry lattice. The electron bands near the Fermi level substantially changed and led to significant changes in the band gap and the activation energy. The activation energies in the low-and high-temperature regions depended similarly on the δ value. The increase in the δ value led to the significant enhancement of the power factor P. In particular, at a temperature of T = 500 K, the power factor of the sample with δ = 0.21 was almost fourfold higher than the power factor of the samples with δ = 0.13 (0.052 µW/(K 2 ·cm) and 0.013 µW/(K 2 ·cm). In the sample with δ = 0.21, the power factor increased with temperature almost linearly and attained its maximum value of 0.1 µW/(cm·K 2 ) at T = 800 K. Thus, varying the oxygen content in a sample, one can control the temperature ranges of stability and the power factor of the complex transition metal oxides.