High-Temperature Thermoelectric Properties of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7)

Abstract

Polycrystalline specimens of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) were synthesized using a solid state reaction method. All samples had a typical perovskite structure, where the orthorhombic (Pbnm) phase was dominant at x ≤ 0.5 and the rhombohedral (R-3c) phase was dominant at x ≥ 0.6. Since the B site is in the mixed valence state of Fe³⁺/Fe⁴⁺ and the spin quantum number is in the range of 0.86 ≤ s ≤ 1.15, it is expected that Fe³⁺ is in the spin state of low spin (LS) Fe³⁺ or intermediate spin (IS) Fe³⁺ and Fe⁴⁺ is in the spin state of LS Fe⁴⁺. As x increases, the ratio of IS Fe³⁺ decreases compared to that of LS Fe³⁺ at x ≥ 0.3, so that the P-type Seebeck coefficient is maintained up to x = 0.5. Although ZT = 0.002 (T = 850 K) of x = 0.7 which shows the maximum N-type thermoelectric characteristic is about 8% of ZT = 0.024 (T = 850 K) of x = 0.1 which shows the maximum P-type thermoelectric characteristic, both are the results of relatively high Seebeck coefficient, low electrical resistivity, and low thermal conductivity. Therefore, we strongly suggest that there is a possibility of application of PN elements which compose of the perovskite-type oxides.

 

This Paper was Originally Published in Japanese in J. Thermoelec. Soc. Jpn. 15 (2018) 3–13.

1. Introduction

Thermoelectric conversion materials are expected to be applied as energy harvesting, which directly converts unutilized waste heat discharged from power plants and automobiles to electric energy for effective utilization, and the researches targeting various materials are vigorously pursued. In particular, thermoelectric conversion materials used for recovering electric energy from high-temperature waste heat are required to be chemically stable for a long period of time in a high-temperature atmosphere. At the same time, it is also expected to be a thermoelectric conversion material in recent years. Furthermore, it is required to be a material which is abundant as a resource and composed of elements having relatively low toxicity. From the above point of view, it is an extremely attractive material as a candidate for thermoelectric conversion materials supporting a future sustainable society.

Oxide material has attracted attention as a candidate for thermoelectric conversion material with NaCo₂O₄ discovered by Terasaki et al.¹⁾ in 1997. The reason why NaCo₂O₄ shows high P-type thermoelectric characteristics (ρ = 2 µΩ m and S = 100 µV K⁻¹ at room temperature) is due to the fact that a correlated electron system²⁾ because of the high density of state near the Fermi energy in the narrow bandwidth of the Co t_2g band shows the large Seebeck coefficient S which is one order of magnitude larger than that of general metals in spite of a high carrier density (about 10²⁷ m⁻³) as metal. Then, as the oxide thermoelectric conversion material exhibiting P-type thermoelectric characteristics, a series of misfit layered Co oxides represented by Ca₃Co₄O₉ was reported.^3–14) On the other hand, Al-doped ZnO^15–17) which is a wide gap degenerate semiconductor, and a partially substituted perovskite structure CaMnO₃^18,19) which is a strongly correlated electron system is known for the oxide thermoelectric conversion material exhibiting N-type thermoelectric characteristics. In fact, Urata et al.²⁰⁾ made the oxide thermoelectric module using Ca_2.7Bi_0.3Co₄O₉ for P-type and CaMn_0.98Mo_0.02O₃ for N-type, and estimated the maximum energy conversion efficiency of 2.0%. Furthermore, it is also reported that the N-type element breaks due to the difference in thermal expansion coefficient between PN elements. Urata et al.²⁰⁾ has reported the linear expansion coefficient of P-type and N-type elements to be 8 to 9 µK⁻¹ and 11 to 13 µK⁻¹, respectively in the temperature range from 373 K to 1173 K. Nagasawa et al.²¹⁾ also reported the coefficient of linear expansion of the P-type element to be 9 to 10 µK⁻¹ in the same temperature range.

Among oxides having a perovskite structure, Nb-doped SrTiO₃,²²⁾ Ca_1−xA_xMnO₃ (A = Yb, Tb, Nd, Ho),²³⁾ La_1−xSr_xFeO₃,²⁴⁾ La_1−xSr_xCoO₃²⁵⁾ and so on are reported as oxides which show relatively large Seebeck coefficient S. These large S is considered to be the result of strong interaction of the spin state, orbital, charge, and crystal structure of the 3d transition metal element. Koshibae et al.²⁶⁾ extended the Heikes’ formula to a strongly correlated electron system and formulated the high-temperature limit equation of the Seebeck coefficient of 3d transition metal oxide as shown in   

\begin{equation} S_{\infty } \cong - \frac{k_{B}}{e}\ln \left(\frac{g_{3}}{g_{4}}\frac{x}{1 - x}\right), \end{equation} (1)

where k_B is the Boltzmann constant, e is the elementary charge, g₃ and g₄ are the spin and the orbital degrees of freedom of 3d electrons in trivalent and tetravalent transition metal ions, respectively, and x is the concentration of the tetravalent transition metal ion. If the difference between g₃ and g₄ is large, it is expected to be large S_∞ from the formula (1). Therefore, it is expected that the thermoelectric properties of 3d transition metal oxide can be controlled by controlling the spin state of 3d electrons in the transition metal ions. Then, we focused attention on Mn oxide with perovskite structure showing P and N-type thermoelectric characteristics. We searched for oxides having perovskite structure that exhibit thermoelectric properties of P-type comparable to partially substituted CaMnO₃^18,19,25) showing thermoelectric properties of N-type, and found that Pr_0.9Sr_0.1MnO₃ shows ZT = 0.0035 at 468 K which is the P-type thermoelectric characteristics.²⁷⁾ Furthermore, we obtained that Pr_0.9Sr_0.1FeO₃ also shows ZT = 0.024 at T = 850 K which is the P-type thermoelectric characteristics.²⁸⁾

Although it was revealed that Fe-oxide exhibits higher P-type thermoelectric characteristics than Mn-oxide, the correlation between the spin state of Fe ions and the thermoelectric property of Fe-oxide has not yet been clarified. Applying eq. (1) on the assumption that the spin state of Fe ion is in the mixed valence state with low spin Fe³⁺(t_2g⁵); g₃ = 6 and low spin Fe⁴⁺(t_2g⁴); g₄ = 9, the high-temperature limit of Seebeck coefficients are expected to be S_∞ ≅ 224 µV K⁻¹ for x = 0.1 and S_∞ ≅ −38 µV K⁻¹ for x = 0.7. On the other hand, the assumption that the spin state of Fe ion is the mixed valence state with intermediate spin Fe³⁺(t_2g⁴e_g¹); g₃ = 24 and low spin Fe⁴⁺(t_2g⁴); g₄ = 9, the high-temperature limit of Seebeck coefficients are expected to be S_∞ ≅ 105 µV K⁻¹ for x = 0.1 and S_∞ ≅ −158 µV K⁻¹ for x = 0.7. Thus, if we can realize the low spin state of Fe³⁺ or Fe⁴⁺ by partially replacing Sr²⁺ having a smaller ionic radius than Pr³⁺ and releasing the chemical pressure applied to Fe ions by precisely controlling the Fe–O distance and the Fe–O–Fe angle, it is possible to construct a PN element with high thermoelectric characteristics only using the Fe-oxides having the perovskite structure. In this study, the polycrystalline sample of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) was prepared, and the correlation between the crystal structure, the magnetic properties and the thermoelectric characteristics was clarified by considering the spin state of Fe ions. However, Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) avoiding the Sr-rich sample was prepared, the thermoelectric characteristics of P-type and N-type were evaluated and the maximum value of ZT was revealed because SrFeO₃ is easy to take oxygen deficient composition and is required oxygen atmosphere above 500 atm for synthesis.^29–31) Furthermore, applying eq. (1) to the spin states of Fe³⁺ and Fe⁴⁺ obtained from the magnetic properties, we estimated S_∞ and compared it with the high-temperature limit of the Seebeck coefficient. Finally, we determined the spin states of Fe ions.

2. Experimental

Polycrystalline specimens of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) were synthesized using a general solid reaction method. The compounds starting from stoichiometric mixtures 5 g of Pr₆O₁₁ (99.9%, 3 N, Wako Pure Chemical Industries, Ltd.), SrCO₃ (99.99%, 4 N, Wako Pure Chemical Industries, Ltd.), Fe₂O₃ (99.9%, 3 N, Wako Pure Chemical Industries, Ltd.) in an agate mortar with ethanol 20 ml for 1 h were calcinated at 1273 K for 24 h in air. The calcined powder samples were pressed into pellets under a pressure of 16 MPa and sintered for 48 h in an oxygen atmosphere at 1573 K. X-ray diffraction (XRD) data were measured using a diffractometer (RINT 2500, Rigaku Corporation) using a CuKα (λ = 1.542 Å) radiation with a pyrolytic graphite monochromator at room temperature. Crystal structure parameters were refined by the Rietveld analysis using the RIETAN-FP program³²⁾ with XRD data in a 2θ range from 10° to 90° in a scanning step of 0.02°. The microstructures of the samples were observed using a scanning electron microscope (VE-8800, KEYENCE).

The magnetic susceptibility with increasing temperature was measured in the temperature range from 5 K to 700 K using a direct-current type superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design, Inc.) under zero magnetic field cooling (ZFC) condition at a magnetic field of 1 T in a warming process. The electric resistivity ρ was measured by a direct-current four-probe method in a temperature range from room temperature to 850 K using a homemade apparatus. The Seebeck coefficient S was measured using a steady-state technique in a temperature range from 80 K to room temperature by the ResiTest8300 apparatus (TOYO Co.), and in the temperature range from room temperature to 850 K by the homemade apparatus. Thermal conductivity κ was calculated using the relationship of κ = dαC_V with a bulk density d, a thermal diffusivity α, and a specific heat C_V. The bulk density d was measured at room temperature by the Archimedes method using a specific gravity measurement kit (SMK-401, SHIMADZU Co.), and the relative density of all samples was measured in the range from 86% to 97%. The specific heat C_V was measured in a temperature range from room temperature to 323 K using a differential scanning calorimetry using an X-DSC 7000 apparatus (Hitachi High-Tech Science Co.). In addition, the thermal diffusivity α was measured with a temperature range from room temperature to 973 K using the laser flash method (TC-7000, ULVAC-RIKO Co.).

3. Results and Discussion

The XRD pattern of the polycrystalline samples Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) at room temperature are shown in Fig. 1. All the samples have a typical single-phase perovskite structure at room temperature, but it was thought that the change of crystal structure at 850 K or less does not have a big influence on physical properties. The crystal structure analysis was carried out using an orthorhombic structure (Pbnm) for x ≤ 0.5 and a rhombohedral structure (R-3c) for x ≥ 0.6. The crystal structure parameters refined by the Rietveld analysis using the RIETAN-FP program³²⁾ are summarized in Table 1. In this study, the isotropic atomic displacement parameters B in the analysis were fixed to 0.5 Ų for the cation and to 1.0 Ų for the oxygen ions, and a split pseudo-Voigt function was used to fit the Bragg peak shapes for the Rietveld analysis. The reliability factor of the weighted diffraction pattern R_wp is 10% < R_wp < 15% at 0.1 ≤ x ≤ 0.7, and the index S = R_wp/R_e indicating a comparison with R_e corresponding to the statistically expected minimum R_wp is 1.4 < S < 2.2. Thus, it is judged that some good fitting has been obtained. Furthermore, Fe–O1 and Fe–O2 distances, Fe–O1–Fe and Fe–O2–Fe angles, Goldschmidt tolerance factor³³⁾ indicating the degree of distortion of the octahedral FeO1₂O2₄ of the perovskite ABO₃ structure, and the bond valence sum (BVS)³⁴⁾ showing the valence of cations in the A and B sites are summarized in Table 1, where O1 is the oxygen in the principal axis direction of the orthorhombic system and O2 is the direction perpendicular to the principal axis of the orthorhombic system. The Goldschmidt tolerance factor of the perovskite ABO₃ structure is defined as $(r_{A} + r_{O})/\sqrt{2} (r_{B} + r_{O})$, where r_A, r_B, r_O are the average ion radius of the cations of the A and B sites and the oxygen ions, respectively. Furthermore, BVS indicating the valence of the cations is defined as $\sum\nolimits_{j}\exp [(r_{0} - r_{ij})/0.37\,\text{Å}]$, where r₀ is the bond valence parameter and r_ij is the interionic distance between the i-th cation and the j-th oxygen ion. Here, r₀ of Pr³⁺, Sr²⁺, Fe³, and Fe⁴⁺ were calculated using 2.138 Å, 2.118 Å, 1.750 Å, and 1.765 Å, respectively. As shown in Table 1, as x increases, the average ion radius of the A site increases and the average ion radius of B site decreases, so that the Goldschmidt tolerance factor increases and approaches 1 which is an ideal perovskite ABO₃ structure. This strongly suggests that the octahedral distortion is relaxed with increasing x. On the other hand, as x increases, the BVS at the A site decreases from 2.89 to 2.41 and the BVS at the B site increases from 3.13 to 3.73, so that a part of Fe³⁺ is oxidized to Fe⁴⁺ as Pr³⁺ is partially substituted with Sr²⁺, which suggests that the cations at the B site are in a mixed valence state of Fe³⁺/Fe⁴⁺. The x dependency on Fe–O1 and Fe–O2 distances are shown in Fig. 2(a) and the x dependency on Fe–O1–Fe and Fe–O2–Fe angles are shown in Fig. 2(b). As x increases, the Fe–O1 distance and the Fe–O2 distance tend to decrease and the Fe–O1–Fe and Fe–O2–Fe angles tend to increase, but the FeO₆ octahedron is most distorted at x = 0.3. On the other hand, in the rhombohedral phase (x ≥ 0.6), it is understood that the FeO₆ octahedron is isotropic, the Fe–O–Fe angle approaches 180°, and the Fe–O–Fe is linearly arranged. Since this Fe–O–Fe distance corresponds to the hopping distance a₀ of the small polaron, twice the average value of Fe–O1 and Fe–O2 distances for x ≤ 0.5, and twice the Fe–O1 distance for x ≥ 0.6 are defined as a₀ of each sample. The X-ray Rietveld analysis pattern of x = 0.1 and 0.7 and the crystal structure of both samples are shown in Fig. 3(a) and 3(b), respectively. Both of them show good Rietveld analysis results of S = R_wp/R_e ∼ 1.7. SEM images of x = 0.4 and 0.7 are shown in Fig. 4(a) and 4(b), respectively. A crystal grain size of about 50 µm is confirmed at x = 0.7, whereas the crystal grain size of about 5 µm is confirmed at x = 0.4, so that coarsening of the crystal grains due to the increase of x is confirmed. This suggests an increasing tendency of the electrical and the thermal conductivity with increasing x.

Fig. 1

X-ray diffraction patterns of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) at room temperature.

Table 1 Crystal structure parameters of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) at room temperature.

Fig. 2

Fe–O distances and Fe–O–Fe angles of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) at room temperature.

Fig. 3

X-ray Rietveld analysis patterns and crystal structures of Pr_1−xSr_xFeO₃ (x = 0.1 and 0.7) at room temperature.

Fig. 4

SEM images of Pr_1−xSr_xFeO₃ (x = 0.4 and 0.7) at room temperature.

Figure 5 shows the temperature dependence of the magnetic susceptibility χ − χ₀ for the polycrystalline sample of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) measured in the temperature range from 5 K to 700 K under ZFC condition at a magnetic field of 1 T in a warming process, where χ₀ is the contribution of temperature-independent magnetic susceptibility. In all specimens, on the high-temperature side, the decreasing tendency of χ − χ₀ is shown with increasing x, and the paramagnetism is confirmed. As shown in the inset of Fig. 5, χ₀ is estimated from the magnetic susceptibility value extrapolated at the high-temperature limit from the relation of magnetic susceptibility χ and the inverse of temperature T⁻¹. Furthermore, the temperature dependence of (χ − χ₀)⁻¹ is shown in Fig. 6. Here, the solid line shows the linear relationship with the slope for the reciprocal of the Curie constant C⁻¹ in the paramagnetic region of 670 K or more. In general, the temperature dependence of paramagnetic magnetic susceptibility is inversely proportional to temperature according to χ = χ₀ + C⁻¹/(T − Θ), so that the reciprocal of magnetic susceptibility (χ − χ₀)⁻¹ is proportional to temperature T. Here, Θ is the Curie temperature and the effective magnetic moment μ_eff of the B site is defined from   

\begin{equation} \mu_{\textit{eff}} = 2\sqrt{s(s + 1)}\mu_{B} = \sqrt{\frac{3k_{B}C}{N_{A}}}, \end{equation} (2)

where s, μ_B, k_B, N_A are the spin quantum number of the B site, the Bohr magneton, the Boltzmann’s constant, and the Avogadro’s number. Thus, from C estimated from the slope of the solid line in Fig. 6, the mixed valence state of Fe³⁺/Fe⁴⁺ is clarified. Table 2 summarizes χ₀ estimated from the inset of Fig. 5, Θ and C estimated from Fig. 6, and μ_eff and s calculated from eq. (2). In all samples, since the spin quantum number is in the range of 0.86 ≤ s ≤ 1.15, it is expected that Fe³⁺ is in a spin state of low spin (LS) Fe³⁺ (t_2g⁵); s = 0.5 or intermediate spin (IS) Fe³⁺ (t_2g⁴e_g¹); s = 1.5 and Fe⁴⁺ is in a spin state of low spin (LS) Fe⁴⁺ (t_2g⁴); s = 1.0. Therefore, assuming that the mixed valence state of Fe³⁺/Fe⁴⁺ at the B site is (LS Fe³⁺_y IS Fe³⁺_1−y)_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7), the spin quantum number is estimated to be s = 1.5 − 0.5x − y + xy. If s is estimated from eq. (2), the ratio of LS Fe³⁺ to IS Fe³⁺, i.e., y:1 − y is determined from   

\begin{equation} y = 1.5 - \frac{s - x}{1 - x}. \end{equation} (3)

Table 2 summarizes the mixed valence state of Fe³⁺/Fe⁴⁺ at the B site. As x increases, the ratio of IS Fe³⁺ increases with x = 0.2 rather than x = 0.1, but y increases at x ≥ 0.3 and IS Fe³⁺ decreases relative to LS Fe³⁺. This strongly suggests that the number of e_g electrons in the B site tends to decrease with increasing x.

Fig. 5

Temperature dependence of magnetic dc-susceptibility (χ − χ₀) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) under zero-field cooling conditions at a magnetic field of 1 T during the warming process, where the temperature-independent term, χ₀, is evaluated from χ (T → ∞) as shown in the inset.

Fig. 6

Temperature dependence of inverse magnetic susceptibility (χ − χ₀)⁻¹ for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7). The straight lines represent the Curie-Weiss laws above 670 K.

Table 2 Temperature-independent magnetic susceptibilities (χ₀), paramagnetic Curie temperatures (Θ), Curie constants (C), effective magnetic moments (μ_eff), spin quantum number (s), ionic ratios of B-site ions for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7).

Figure 7 shows the temperature dependence of the electrical resistivity ρ of the polycrystalline sample Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) in the temperature range from room temperature to 850 K. All samples show semiconductive behavior over the entire temperature range and a decrease in electrical resistivity was confirmed with increasing x. As shown in Table 2, since the mixed-valence state of the B site at x = 0.1 is LS Fe³⁺_0.43 IS Fe³⁺_0.47 LS Fe⁴⁺_0.1, it is expected that the P-type conduction is due to the t_2g hole moving between LS Fe³⁺(t_2g⁵)–LS Fe⁴⁺(t_2g⁴) or the e_g hole moving between IS Fe³⁺(t_2g⁴e_g¹)–LS Fe⁴⁺(t_2g⁴). On the other hand, since the mixed-valence state of the B site at x = 0.7 is LS Fe³⁺_0.22 IS Fe³⁺_0.08 LS Fe⁴⁺_0.7, it is mainly expected that the N-type conduction is due to the t_2g electron moving between LS Fe³⁺(t_2g⁵)–LS Fe⁴⁺(t_2g⁴). As shown in Fig. 8, in addition, all samples show temperature dependence of small polaron hopping conduction at high temperature. According to Polaron theory,^35–37) the hopping conduction of the small polaron shows a thermal activation that the carrier mobility μ is more remarkable than the carrier concentration n and exhibits a temperature dependence such as μ ∝ exp(−W_H/k_BT). Here, W_H is the hopping energy of small polarons and the carrier concentration n is defined as the number of hopping of small polarons per unit volume, i.e., n ∝ exp(−E_g/2k_BT), where E_g corresponds to the band gap. Therefore, the temperature dependence of the electric conductivity σ = enμ is expressed by   

\begin{align} \sigma T &= \sigma_{0}\exp\left(-\frac{E_{\sigma}}{k_{B}T}\right),\quad \sigma_{0} = \frac{e^{2}n_{0}\omega_{LO}a_{0}^{2}}{k_{B}},\\ E_{\sigma} &= W_{H} + \frac{E_{g}}{2}, \end{align} (4)

where n₀ is the Fe⁴⁺ concentration per unit volume, ω_LO is the optical phonon frequency, a₀ is the hopping distance of the small polaron, i.e., corresponding to the Fe–O–Fe distance, and E_σ is the activation energy of the small polaron conduction.

Fig. 7

Temperature dependence of electric resistivity (ρ) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7).

Fig. 8

Arrhenius relationship between σT and T⁻¹ for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7), where the straight lines represent the linear portions of the Arrhenius plots.

As shown in Fig. 8, in all samples, the Arrhenius plot of σT and T⁻¹ shows a linear relationship of the slope E_σ/k_B above 670 K. As summarized in Table 3, σ₀ shown in eq. (4) is obtained by extrapolating the linear relationship of σT shown in Fig. 8 to T⁻¹ → 0 and performing porosity correction in the range from 2.08 × 10⁷ Ω⁻¹ m⁻¹ K to 8.39 × 10⁷ Ω⁻¹ m⁻¹ K. Therefore, by obtaining n₀ and a₀ from the crystal structure parameters summarized in Table 1, ω_LO with the porosity correction was calculated in the range from 8.4 THz to 85.2 THz (Table 3), which is consistent with typical optical phonon frequency values, i.e., 10 THz ≤ ω_LO ≤ 100 THz.

Table 3 Activation energy of electrical conduction (E_σ), pre-exponential term (σ₀), concentration of tetravalent ions per unit volume (n₀), intersite hopping distance (a₀), optical phonon frequency (ω_LO), characteristic energy of Seebeck coefficient (E_S), hopping energy of small polarons (W_H), Seebeck coefficient in the high-temperature limit (S_∞), S_∞ evaluated from Heikes formula, bulk density at room temperature (d), relative density at room temperature, specific heat at room temperature (C_V), thermal diffusivity at room temperature (α), and thermal conductivity at room temperature (κ) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7), where * means porosity-corrected physical quantity.

Figure 9 shows the temperature dependence of the Seebeck coefficient S of the polycrystalline sample Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) below 850 K. The absolute value |S| of the P-type Seebeck coefficient shows a decreasing trend with increasing x, and a change to N-type Seebeck coefficient is confirmed at x = 0.6, showing the minimum |S|, whereas the N-type |S| shows a slight increasing trend at x = 0.7. As shown in Fig. 10, in order to estimate the Seebeck coefficient at the high-temperature limit, the Seebeck coefficient S is extrapolated to T⁻¹ → 0 at high-temperature, and a good linear relationship is obtained for all samples above 670 K. In hopping conduction of small polaron, the T⁻¹ dependence of S is given by the following equation.³⁸⁾   

\begin{equation} S = S_{\infty} \pm \frac{k_{B}}{e}\frac{E_{S}}{k_{B}T}, \end{equation} (5)

where E_S (≪ E_σ) is the characteristic energy of the Seebeck coefficient, and S_∞ is the Seebeck coefficient at the high-temperature limit. Table 3 summarizes E_S and S_∞ for all samples. Assuming that E_S corresponds to E_g/2 in eq. (4), the hopping energy of the small polaron is defined as W_H = E_σ − E_S. Table 3 summarizes W_H for all samples.

Fig. 9

Temperature dependence of Seebeck coefficient (S) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7).

Fig. 10

Temperature dependence of Seebeck coefficient (S) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7), where the straight lines represent the theoretical relationship of eq. (5).

If the mixed valence state of Fe³⁺/Fe⁴⁺ of the B site is LS Fe³⁺_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7), the Seebeck coefficient at the high-temperature limit is expressed as   

\begin{equation} S_{\infty} \cong - \frac{k_{B}}{e}\ln \left(\frac{6}{9}\frac{x}{1 - x}\right) \end{equation} (6)

from eq. (1). As shown in Fig. 11, S_∞ for LS Fe³⁺_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7) monotonously decreases as x increases and changes from P-type to N-type at x = 0.6. On the other hand, if the mixed valence state of Fe³⁺/Fe⁴⁺ of the B site is IS Fe³⁺_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7), S_∞ is expressed as   

\begin{equation} S_{\infty} \cong - \frac{k_{B}}{e}\ln\left(\frac{24}{9}\frac{x}{1 - x}\right) \end{equation} (7)

from eq. (1). As shown in Fig. 11, S_∞ for IS Fe³⁺_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7) also monotonously decreases as x increases and changes from P-type to N-type at x = 0.3. In addition, if the mixed valence state of Fe³⁺/Fe⁴⁺ of the B site is (LS Fe³⁺_y IS Fe³⁺_1−y)_1−x LS Fe⁴⁺_x (0.1 ≤ x ≤ 0.7), S_∞ is expressed as   

\begin{equation} S_{\infty}\cong - \frac{k_{B}}{e}\left[y\ln\left(\frac{6}{9}\frac{x}{1 - x}\right) + (1 - y)\ln \left(\frac{24}{9}\frac{x}{1 - x}\right)\right] \end{equation} (8)

from eq. (1). From the ratio of LS Fe³⁺ and IS Fe³⁺ summarized in Table 2, the result of eq. (8) is plotted in Fig. 11 with “×” marks. As shown in Fig. 11, the Seebeck coefficient at the high-temperature limit is expected to change from P-type to N-type at x = 0.55. Similarly, S_∞ obtained by extrapolating the straight line of eq. (5) by T⁻¹ → 0 (Table 3) also changed from P-type to N-type at x = 0.58 as shown by the dotted line plotted in Fig. 11. Therefore, the main factor of showing the P-type thermoelectric characteristics at x ≤ 0.5 is that the spin state of Fe³⁺ ions in Pr_1−xSr_xFe³⁺_1−x LS Fe⁴⁺_x O₃ (0.1 ≤ x ≤ 0.7) changes from the mixed state of LS Fe³⁺/IS Fe³⁺ to the predominant state of LS Fe³⁺ with increasing x.

Fig. 11

Seebeck coefficient in the high-temperature limit (S_∞) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7), where the solid lines represent relationships of eqs. (6), (7), and (8). On the other hand, the dotted line is evaluated from S (T → ∞) as shown in Fig. 10.

Figure 12 shows the temperature dependence of the power factor S²σ of the polycrystalline sample Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) calculated from Fig. 7 and Fig. 9 below 850 K. In all samples, S²σ monotonically increases with increasing temperature. In 0.1 ≤ x ≤ 0.5 showing P-type thermoelectric characteristics, S²σ at T = 850 K shows a maximum value of 2.0 × 10⁻⁵ W m⁻¹ K⁻² at x = 0.1 and decreases as x increases. On the other hand, in x ≥ 0.6 showing N-type thermoelectric characteristics, S²σ at T = 850 K shows the minimum value at x = 0.6 but increases to 2.8 × 10⁻⁶ W m⁻¹ K⁻² at x = 0.7, which is almost the same value as x = 0.4. Although S²σ (T = 850 K) at x = 0.7 shows the maximum N-type thermoelectric characteristic which is about 14% of S²σ (T = 850 K) at x = 0.1 showing the maximum P-type thermoelectric characteristics, this suggests that it is possible to construct a PN thermoelectric device using only perovskite Fe-oxides.

Fig. 12

Temperature dependence of power factor (S²σ) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7).

The temperature dependence of the total thermal conductivity κ (= κ_L + κ_e) and the electric thermal conductivity κ_e for the polycrystalline samples of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) above 300 K is shown in Fig. 13. Here, κ_L is the lattice thermal conductivity and κ_e = L₀σT is calculated using well-known the Wiedemann Franz law, where L₀ = 2.45 × 10⁻⁸ V² K⁻² is the Lorenz number. In all samples, κ_e monotonically increases with increasing temperature, but the proportion of κ_e to κ is smaller than that of κ_L to κ. In other words, in all samples, κ_L plays a more important role than κ_e, and can be regarded as κ ≅ κ_L. Therefore, as shown in Fig. 13, in all the samples, κ maintains a relatively small value, i.e., it shows a value of about 2 W m⁻¹ K⁻¹ or less in the temperature range of T ≥ 300 K.

Fig. 13

Temperature dependence of the total thermal conductivity (κ = κ_L + κ_e) above room temperature for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7). The temperature dependence of the electric thermal conductivity (κ_e = L₀σT) for all samples are also shown by using the Wiedemann-Frantz law.

The temperature dependence of the dimensionless figure of merit ZT for the polycrystalline samples of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) at T ≤ 850 K is shown in Fig. 14. In all the samples, ZT monotonically increases with increasing temperature. In particular, for 0.1 ≤ x ≤ 0.5 indicating P-type thermoelectric characteristics, ZT at T = 850 K shows the maximum value of ZT = 0.024 at x = 0.1 and decreases with increasing x. On the other hand, for x ≥ 0.6 indicating N-type thermoelectric characteristics, the ZT value is shown the minimum at x = 0.6, but increases to ZT = 0.002 at x = 0.7. Although ZT (T = 850 K) at x = 0.7 shows the maximum N-type thermoelectric characteristics which is about 8% of ZT (T = 850 K) at x = 0.1 showing the maximum P-type thermoelectric characteristics, both are the results of a high Seebeck coefficient |S|, a relatively low electric resistivity ρ, and a low thermal conductivity κ, suggesting the possibility of constructing a PN thermoelectric device by using only perovskite Fe-oxides.

Fig. 14

Temperature dependence of the dimensionless figure of merit (ZT) for Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7).

4. Conclusions

In this study, polycrystalline samples of Pr_1−xSr_xFeO₃ (0.1 ≤ x ≤ 0.7) were synthesized using a conventional solid-state reaction method in order to clarify the correlation between their crystal structures, magnetic properties and thermoelectric properties. All samples had a typical single-phase perovskite structure, where the orthorhombic (Pbnm) phase was dominant at x ≤ 0.5, and the rhombohedral (R-3c) phase was dominant at x ≥ 0.6. As x increases, the Goldschmidt tolerance factor increases, the Fe–O1 and Fe–O2 distances tend to decrease, the Fe–O1–Fe and Fe–O2–Fe angles tend to increase, so that it is confirmed that the strain of the FeO₆ octahedron which is the maximum at x = 0.3 is gradually relaxed in the rhombohedral phase at x ≥ 0.6. Also, since the B site is in the mixed valence state of Fe³⁺/Fe⁴⁺ and the spin quantum number is in the range of 0.86 ≤ s ≤ 1.15 in all the samples, it is expected that Fe³⁺ ions are in the spin state of LS Fe³⁺ or IS Fe³⁺ and Fe⁴⁺ ions are in the spin state of LS Fe⁴⁺. The ratio of IS Fe³⁺ increases with x = 0.2 rather than x = 0.1, but that of IS Fe³⁺ decreases compared with LS Fe³⁺ at x ≥ 0.3 so that it is conceivable that the e_g electrons of the B site tend to decrease with increasing x. On the other hand, all samples show the temperature dependence of small polaron hopping conduction at high-temperature, and the electrical resistivity ρ and the absolute value of the P-type Seebeck coefficient |S| decreases with increasing x. Also, |S| changes from P-type to N-type with increasing temperature at x = 0.6, and N-type |S| shows a slight increase with increasing temperature at x = 0.7. In addition, it is suggested from the Seebeck coefficient at the high-temperature limit S_∞ that the P-type thermoelectric properties at x ≤ 0.5 are exhibited because the spin state of Fe³⁺ ions in Pr_1−xSr_xFe³⁺_1−x LS Fe⁴⁺_x O₃ changes from the mixed state of LS Fe³⁺/IS Fe³⁺ to the predominant state of LS Fe³⁺ with increasing x. The thermal conductivity κ maintains a relatively small value in all samples, i.e., it shows a value of about 2 Wm⁻¹ K⁻¹ or less in the temperature range of T ≥ 300 K. Although ZT = 0.002 (T = 850 K) at x = 0.7 shows the maximum N-type thermoelectric properties which is about 8% of ZT = 0.024 (T = 850 K) at x = 0.1 showing the maximum P-type thermoelectric properties, both are the results of a high |S|, a relatively low ρ, and a low κ. Therefore, these results strongly suggest the possibility of application to high-temperature PN thermoelectric devices composed of only perovskite-type Fe-oxides of the same crystal structure.

Acknowledgments

This work was partly supported by the support of Grants-in-Aid for Scientific Research (15K06479). In addition, the magnetization measurement experiment below room temperature and observation of microstructure by scanning electron microscope were carried out using equipment of Yokohama National University Instrumental Analysis and Evaluation Center. Magnetization measurement experiment above room temperature was carried out using the MPMS equipment in the electromagnetic measurement room as a joint use (Approval number: AG68) of the University of Tokyo Physical Institute Laboratory. In addition, the authors would like to express appreciation to Mr. Yoshiki Ishikawa for cooperating in preparing samples for this study.

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