Structural and Thermoelectric Properties of Gd2−2xSr1+2xMn2O7 Double-Layered Manganites

Double-layered manganites are natural superlattices with low thermal conductivity, which is of importance for potential thermoelectric applications. The Gd2−2xSr1+2xMn2O7 (x = 0.5; 0.625; 0.75) were prepared by the solid-state reaction method. All the samples crystallize in the tetragonal I4/mmm Sr3Ti2O7 type structure. The unit cell volume and the distortion in the MnO6 octahedra increase with increasing Gd content. Their thermoelectric properties were investigated between 300 and 1200 K. All exhibit an n-type semiconducting behavior. The electrical conductivity (σ) increases while the absolute value of the Seebeck coefficient (|S|) decreases with increasing Gd content. Simultaneous increases in σ and |S| with increasing temperature are observed at temperatures approximately higher than 600 K, and the power factor reaches a maximum value of 18.36 μW/(m K²) for x = 0.75 at 1200 K. The thermal conductivity (κ) is lower than 2 W/(m K) over the temperature range of 300–1000 K for all the samples and a maximum dimensionless figure of merit ZT of 0.01 is obtained for x = 0.75 at 1000 K.


Introduction
Since the report of the layered NaCo 2 O 4 showing good thermoelectric (TE) performance with a large Seebeck coefficient of 100 µV/K at 300 K [1], there has been increasing interest in exploring new oxide TE materials in the last two decades because of their high chemical and thermal stability at high temperature, low toxicity, and relatively low-cost starting materials [2,3]. TE materials enable the direct conversion of thermal into electricity and are useful for manufacturing TE devices for power generation from waste heat. The efficiency of a TE material is mainly determined by the dimensionless figure of merit ZT, which is a product of the TE figure of merit Z and the absolute temperature T, given by ZT = S 2 σT/κ, where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively. A good TE material requires large S, high σ, and low κ. As these three parameters are strongly coupled, depending on the carrier concentration and electronic structure, and there is a trade-off between S and σ, it is difficult to enhance them simultaneously. The power factor PF, defined as S 2 σ, is related to the electrical properties of a material. Whilst the performance of most TE oxides is limited by their low ZT values due to low PF and high κ, several layer-structured oxides show outstanding TE properties, such as p-type layered cobaltites Ca 3 Co 4 O 9 and BiCuSeO, and n-type perovskite oxides CaMnO 3 manganates and SrTiO 3 titanates [2][3][4]. Methods to enhance ZT mostly include doping, carrier engineering, defect chemistry engineering, nanostructuring/nanocomposites, band engineering, etc., aiming to improve PF and reduce κ [2,3,[5][6][7].
The Ruddlesden-Popper (RP) compounds with a general formula A m+1 B m O 3m+1 (A = rare earth (RE) and/or alkaline earth elements and B = transition metals) or AO(ABO 3 ) m have a natural superlattice structure consisting of an alternate stacking of multiple (m) perovskite structure BO 2 layers and a single rock-salt A 2 O 2 layer along the c axis direction [8]. The double-layered oxides A 3 B 2 O 7 belong to the m = 2 member and the perovskites ABO 3 correspond to the m = ∞ member of the RP family. The layered structure of the RP compounds would enhance the phonon scattering at the interfaces between the A 2 O 2 layer and perovskite layer and consequently reduce κ, which is of great importance for TE materials. Investigation on thermal conductivity in the thin films of the m = 1-5 and 10 members of the (SrTiO 3 ) m SrO RP superlattices showed that the m = 2 member had the lowest κ in this RP homologous series [9]. Significant reduction of κ values was observed in the layered (Sr 1−x RE x ) m+1 Ti m O 3m+1 (m = 1, 2) [10] and La 2−2x Ca 1+2x Mn 2 O 7 (0.75 ≤ x ≤ 1.0) [11] due to the intrinsic superlattice structure as compared to their perovskite phases. It is desired for a TE material that good electron transport properties PF would be kept while κ is reduced. The structure of the RP oxides allows compositional tailoring, and the TE properties of n-type CaMnO 3 and SrTiO 3 can be improved by substitution at either the A or B sites. It has been found that RE element doping at Ca sites of CaMnO 3 is an effective way to increase σ while keeping a moderate absolute S [6,12]. Studies of the effects of various RE 3+ ions doping at Sr sites of (Sr 0.95 RE 0.05 ) 3 Ti 2 O 7 oxides on their TE properties indicated that the maximum ZT was obtained in Gd-doped (Sr 0.95 Gd 0.05 ) 3 Ti 2 O 7 mainly owing to its lower κ [13] or enhanced S [14].
The double-layered manganites RE 2−2x Sr 1+2x Mn 2 O 7 are of significant interest due to the effect of colossal magnetoresistance (CMR) and intensive studies have been focused on their magnetic and magneto-transport properties [15][16][17][18][19][20][21]. However, works on the high-temperature TE properties of RE 2−2x Sr 1+2x Mn 2 O 7 to take advantage of their intrinsic superlattice structures are very scarce. During the course of our systematic research on the phase diagram of the Gd-Sr-Co/Mn-O systems [22,23], a Gd 2−2x Sr 1+2x Mn 2 O 7 solid solution was found. Our magnetic measurements of the Gd 2−2x Sr 1+2x Mn 2 O 7 samples in the temperature range of 2-350 K under an applied magnetic field of 0.02 T show two ferromagnetic transitions, which is in analogy to the temperature-dependent magnetizations of La 1.2 Sr 1.8 Mn 2 O 7 [24] and La 1.4 Sr 1.6 Mn 2 O 7 [25]. In this paper, we report the structural and TE properties of double-layered manganites Gd 2−2x Sr 1+2x Mn 2 O 7 (x = 0.5, 0.625, 0.75). Investigation on their TE properties revealed an n-type semiconducting behavior and a κ of lower than 2 W/(m K) over the temperature range of 300-1000 K. σ increases while the absolute value of S decreases with increasing Gd content.

Materials and Methods
Polycrystalline samples of Gd 2−2x Sr 1+2x Mn 2 O 7 (x = 0.5, 0.625, 0.75) were prepared by the conventional solid-state reaction method in air. Gd 2 O 3 (99.95%, Sinopharm, Beijing, China), SrCO 3 (≥99.0%, Sinopharm, Beijing, China), and MnCO 3 (99.95%, Aladdin, Shanghai, China) were used as starting materials. Gd 2 O 3 and SrCO 3 were dried at 773 K for 24 h, and MnCO 3 at 373 K for 24 h prior to use. Stoichiometric amounts of the preheated powders were thoroughly mixed and ball-milled in anhydrous ethanol medium for 10 h in the agate grinding jars using a planetary ball mill (QM−3SP4, Nanjing, China). The resultant powders were calcined at 1123 K for 24 h in a muffle furnace. Subsequently, the calcined powders were reground, pressed into pellets with diameters of 15 mm and a thickness of~4 mm or pressed into 20 mm long rectangular samples with widths of 4 mm and a thickness of~3 mm, and sintered at 1673 K for 120 h.
Powder X-ray diffraction (XRD) data were collected on an x-ray diffractometer (Rigaku D/Max 2500V, Tokyo, Japan) using Cu Kα radiation over the angular range of 10 • to 110 • 2θ, with a step size of 0.02 • . The XRD data were analyzed with the Rietveld method using the Fullprof program [26]. The microstructure of the sintered samples was examined by a field emission scanning electron microscope (FE-SEM, Hitachi SU8020, Tokyo, Japan) using the secondary electron (SE) mode. The chemical compositions of the samples were determined by the equipped energy-dispersive X-ray spectrometer (EDS, Oxford X-MAX80, Oxford, UK). Specimens for the measurements of σ and S were prepared by grinding and polishing the sintered rectangular samples into a typical dimension of 3.9 mm × 2.0 mm × 19.0 mm. All the surfaces of the specimens were carefully polished with SiC emery papers before measurement to ensure parallel ends. The temperature dependences of σ and S were measured on a multifunctional thermoelectric materials measurement system (Advance Riko ZEM-3M10, Yokohama, Japan) in the temperature range of 300-1200 K in a helium atmosphere. The specimen was placed vertically between the upper and lower Pt block electrodes in the infrared heating furnace, and two probes of the thermocouple were adjusted to attach to the longitudinal side of the specimen. V-I plot measurement was carried out to check whether the specimen was well contacted with the probes before the simultaneous measurements of σ and S. The thermal conductivity κ was calculated using the relationship κ = DC p d, where D is the thermal diffusivity, C P is the specific heat capacity and d is the bulk density. D was measured using the laser flash method (NETZSCH LFA 457, Selb, Germany) on disc specimens with diameters of 12.7 mm and a typical thickness of 1.5 mm. C P was measured using differential scanning calorimetry (NETZSCH STA 449 F3, Selb, Germany) under an argon atmosphere up to 1000 K. The bulk density d of the sintered discs was determined by Archimedes' method (Shimadzu AUW220D, Kyoto, Japan). All the diffraction peaks can be indexed in a tetragonal Sr 3 Ti 2 O 7 type structure with space group I4/mmm (No. 139). A typical Rietveld refinement pattern and the crystal structure for the sample x = 0.625 are demonstrated in Figure 1b. As seen from the structure, two stacked MnO 2 layers (i.e., double perovskite layers) form the quasi-two-dimensional (2D) magnetic layer (called bilayer). Two adjacent MnO 2 bilayers are separated by the (Gd, Sr) 2 O 2 rock salt layers. The refined structural parameters, theoretical density (ρ x ), selected bond lengths, and reliability factors for Gd 2−2x Sr 1+2x Mn 2 O 7 are summarized in Table 1. The measured bulk density d of the sintered samples and the relative density (% T. D.) are also given in Table 1. The relative density for all the samples is about 94%, indicating that the samples are of similar compactness.

Structural and Morphological Analysis
According to the analysis from the neutron powder diffraction data [27], the Sr/RE ions occupy two Wyckoff sites, i.e., 2b (0, 0, 1/2) site in the 12-coordinate perovskite-like block and 4e (0, 0, z) site in the 9-coordinate rock salt layer. As seen in Figure 1b, each Gd 3+ /Sr 2+ ion is labeled by 2b or 4e to indicate its atomic Wyckoff position. Smaller RE ions such as Gd 3+ , Tb 3+ , Dy 3+ , etc., were found to prefer the 4e site [27]. Refinements on the occupancies of Gd 3+ /Sr 2+ ions showed that they co-occupied the 2b and 4e sites with a higher occupation of Gd 3+ ions at the 4e sites. The refined occupancies of Gd 3+ /Sr 2+ ions are given in Table 1. This is in agreement with the results of the refinement of DySr 2 Mn 2 O 7 [27] and (Sr 0.95 RE 0.05 ) 3 Ti 2 O 7 [14]. This preferential occupation of RE 3+ ions at the 4e sites might be due to the smaller ionic radius differences between RE 3+ ions and 9-coordinate Sr 2+ (r = 1.31Å, coordination number (CN) = 9) as compared to 12-coordinate Sr 2+ (r = 1.44Å, CN = 12) [14]. With increasing Gd content, the unit cell volume increases while the unit cell parameter a first increases and then decreases, and c shows the opposite variation with a. These size variations have been found for Nd 0.2 La 1.8−2x Sr 1+2x Mn 2 O 7 (0.3 ≤ x ≤ 0.7) [28], and can be attributed to the simultaneous occurrence of the substitution of Sr 2+ (r = 1.31Å, CN = 9) ions with smaller Gd 3+ ions (r = 1.107Å, CN = 9) and the conversion of Mn 4+ (r = 0.53 Å, CN = 6) to larger Mn 3+ (high spin, r = 0.645 Å, CN = 6) to maintain charge neutrality. It is therefore expected that the increasing amount of the Jahn-Teller active Mn 3+ ions would lead to a stronger MnO 6 octahedral distortion with increasing Gd content in Gd 2−2x Sr 1+2x Mn 2 O 7 . The tolerance factor t describes the structural distortion, defined as where r O is the ionic radius of the O ion and r A and r B are the mean radii of the ions at the A and B sites, respectively. With increasing Gd content, r A decreases and r B increases, a decreasing t is then obtained which confirms the enhancement of the structural distortion. Accordingly, the bond lengths of the apical Mn-O1 bonds (Mn to the apical oxygen atom O1 shared between the two MnO 2 layers within a bilayer) and the in-plane Mn-O3 bonds (Mn to the equatorial oxygen atom O3 in the MnO 2 layers) vary oppositely, with the Mn-O1 bonds along the c axis showing a larger extent of variation. The bond lengths of the apical Mn-O2 bonds (Mn to the apical oxygen atom O2 in the (Gd/Sr) 2 O 2 rock-salt layers) are longer than those of the apical Mn-O1 and in-plane Mn-O3 bonds, and are elongated with increasing Gd content, which indicates the enlargement of the interlayer Mn-Mn distances.
the mean radii of the ions at the A and B sites, respectively. With increasi 〈 〉 decreases and 〈 〉 increases, a decreasing t is then obtained whic enhancement of the structural distortion. Accordingly, the bond lengths of O1 bonds (Mn to the apical oxygen atom O1 shared between the two MnO a bilayer) and the in-plane Mn-O3 bonds (Mn to the equatorial oxygen MnO2 layers) vary oppositely, with the Mn-O1 bonds along the c axis sh extent of variation. The bond lengths of the apical Mn-O2 bonds (Mn to th atom O2 in the (Gd/Sr)2O2 rock-salt layers) are longer than those of the api in-plane Mn-O3 bonds, and are elongated with increasing Gd content, w the enlargement of the interlayer Mn-Mn distances.  It is evident from the fractured morphology evolves from slightly aggregated spherical shap 0.5 to lath-like or even flake-shaped grains for x = 0.625 and x = 0.75, re fractured morphologies of all the samples show a dense structure, which is the relative density of 94% obtained from Archimedes' method (Table 1). F the EDS mapping images of the cations for x = 0.625, indicating distributions of the elements Gd, Sr, and Mn. The compositions measur given in Table 2. It is shown that the molar ratios of the cations correspo nominal compositions.  It is evident from the insets that the fractured morphology evolves from slightly aggregated spherical shape grains for x = 0.5 to lath-like or even flake-shaped grains for x = 0.625 and x = 0.75, respectively. The fractured morphologies of all the samples show a dense structure, which is consistent with the relative density of 94% obtained from Archimedes' method (Table 1). Figure 2d shows the EDS mapping images of the cations for x = 0.625, indicating homogeneous distributions of the elements Gd, Sr, and Mn. The compositions measured by EDS are given in Table 2. It is shown that the molar ratios of the cations correspond well to the nominal compositions.  . 139), atomic Wyckoff positions: Gd1/Sr1, 2b (0, 0, 1/2), Gd2/Sr2, 4e (0, 0, z), Mn, 4e (0, 0, z), O1, 2a (0, 0, 0), O2, 4e (0, 0, z), O3, 8g (0, 1/2, z). (5) 3.83642 (7) 3.83446 (10) . 139), atomic Wyckoff positions: Gd1/Sr1, 2b (0, 0, 1/2), Gd2/Sr2, 4e (0, 0, z), Mn, 4e (0, 0, z), O1, 2a (0, 0, 0), O2, 4e (0, 0, z), O3, 8g (0, 1/2, z).
3.82705 (5) 3.83642 (7) 3.83446 (10) Figure 3a shows the temperature dependence of σ for Gd 2−2x Sr 1+2x Mn 2 O 7 (x = 0.5, 0.625, 0.75) in the temperature range of 300-1200 K. All the samples exhibit a semiconducting behavior with dσ/dT > 0. σ increases gradually with increasing Gd content at the high-temperature region, and a maximum value of 6.1 × 10 3 S/m at 1200 K is observed for x = 0.5, which is of the same order of magnitude as those for Ca 0.96 Dy 0.02 RE 0.02 MnO 3 [29]. As the substitution of Gd 3+ ions for Sr 2+ ions induces Mn 3+ ions and donates electrons, where the nominal amount of Mn 3+ ions (i.e., nominal electron concentration) can be estimated from the composition subscript (2−2x) while the nominal amount of Mn 4+ ions (nominal hole concentration) estimated from the composition subscript (2x), the Jahn-Teller distortion of the Mn 3+ ions leads to the formation of polarons where the electrons are localized due to the strong electron-phonon coupling. The electrical transport of Gd 2−2x Sr 1+2x Mn 2 O 7 is thought to be dominated by the hopping motions of electrons or small polaron between Mn 3+ and Mn 4+ ions. The small polaron hopping conduction can be expressed by the equation [30]:

Thermoelectric Properties
where σ 0 is the pre-exponential constant, E a is the activation energy of small polaron hopping, k B is Boltzmann constant, and T is the absolute temperature. The values of E a were deduced from the slope of the plot of ln (σT) versus 1000/T. As shown in Figure 3b, good linear fittings were obtained over the whole temperature range for x = 0.625 and 0.75, and E a was found to be 0.187 and 0.157 eV, respectively. A change in slope was observed for x = 0.5, with an E a of 0.198 eV at the 300-600 K region and 0.167 eV at the 600-1200 K region. It is found that E a increases with Gd content below 600 K, that is, 0.198, 0.187, and 0.157 eV for x = 0.5, 0.625, and 0.75, respectively. This may be attributed to the increasing concentration of Mn 3+ Jahn-Teller ions which is favorable for the formation of small polarons in this temperature range [31].  Figure 3a shows the temperature dependence of σ for Gd2−2xSr1+2xMn2O7 (x = 0.5, 0.625, 0.75) in the temperature range of 300-1200 K. All the samples exhibit a semiconducting behavior with dσ/dT > 0. σ increases gradually with increasing Gd content at the hightemperature region, and a maximum value of 6.1 × 10 3 S/m at 1200 K is observed for x = 0.5, which is of the same order of magnitude as those for Ca0.96Dy0.02RE0.02MnO3 [29]. As the substitution of Gd 3+ ions for Sr 2+ ions induces Mn 3+ ions and donates electrons, where the nominal amount of Mn 3+ ions (i.e., nominal electron concentration) can be estimated from the composition subscript (2−2x) while the nominal amount of Mn 4+ ions (nominal hole concentration) estimated from the composition subscript (2x), the Jahn-Teller distortion of the Mn 3+ ions leads to the formation of polarons where the electrons are localized due to the strong electron-phonon coupling. The electrical transport of Gd2−2xSr1+2xMn2O7 is thought to be dominated by the hopping motions of electrons or small polaron between Mn 3+ and Mn 4+ ions. The small polaron hopping conduction can be expressed by the equation [30]:

Thermoelectric Properties
where is the pre-exponential constant, Ea is the activation energy of small polaron hopping, kB is Boltzmann constant, and T is the absolute temperature. The values of Ea were deduced from the slope of the plot of ln (σT) versus 1000/T. As shown in Figure 3b, good linear fittings were obtained over the whole temperature range for x = 0.625 and 0.75, and Ea was found to be 0.187 and 0.157 eV, respectively. A change in slope was observed for x = 0.5, with an Ea of 0.198 eV at the 300-600 K region and 0.167 eV at the 600-1200 K region. It is found that Ea increases with Gd content below 600 K, that is, 0.198, 0.187, and 0.157 eV for x = 0.5, 0.625, and 0.75, respectively. This may be attributed to the increasing concentration of Mn 3+ Jahn-Teller ions which is favorable for the formation of small polarons in this temperature range [31].  The values of S are negative in the whole measured temperature range as seen in Figure 3c, indicating that electrons are the dominant charge carriers. σ increases while the absolute value of S decreases with increasing Gd content due to the increase in electron carrier concentration, which is similar to those for La 2−2x Ca 1+2x Mn 2 O 7 (0.75 ≤ x ≤ 1.0) [11], La 2−2x Sr 1+2x Mn 2 O 7 [32], and Gd 1−x Sr x MnO 3 (x = 0.5, 0.6, 0.7, 0.8) [33]. The absolute values |S| at 1200 K are found to be decreased by 44% from 67.5 µV/K for x = 0.75 to 37.5 µV/K for x = 0.5. It is observed that the absolute values |S| initially decrease and then increase with temperature, showing a change from a typical semiconducting behavior to a metallic or degenerate semiconducting behavior, which does not coincide with the temperature dependence of σ. The mechanism behind this phenomenon is not clear at present. The temperature Ts which are marked in Figure 3c corresponding to the minimum |S| value, or the so-called metal-insulator transition temperature, was found to shift to higher temperature with increasing Gd content owing to higher electron carrier concentration. Above Ts, all the samples exhibit a metallic or degenerate semiconducting behavior arising from the enhanced scattering of electrons at high temperatures. The dependence of S on the carrier concentration n and temperature T for degenerate semiconductors can be expressed as [34]: where m* is the effective mass of the carrier, k B is the Boltzmann constant, e is the elementary charge, and h is Plank's constant. It is seen from Figure 3a that as T increases from room temperature to 600 K, σ increases sharply from ca. 1.0 × 10 2 S/m to 2.0 × 10 3 S/m, implying a rapid increase in electron carrier concentration n. This rapid increasing n at low temperatures is the dominant factor for the initial decrease in |S| because |S| is inversely proportional to the electron concentration. Then |S| gradually increases with further increasing temperature for an approximately given carrier concentration. Simultaneous increases in σ and |S| with increasing temperature are observed above Ts. This phenomenon was also found in CaMnO 3−δ [12] and Yb 0.1 Ca 0.9 Mn 1−x Nb x O 3 (x = 0.08, 0.1) [35], and was explained by using a two-band model of S which consists of contributions from the hole (Mn 4+ ) and electron (Mn 3+ ) due to the existence of mixed-valence Mn 3+ and Mn 4+ . This model may be applicable to the present Gd 2−2x Sr 1+2x Mn 2 O 7 . Figure 3d shows the temperature dependence of the power factor PF. The monotonic increase in PF with temperature for all the samples is obtained due to the increases in both σ and |S| at high temperatures. The PF increases with decreasing Gd content and a maximum value of 18.36 µW/(m K 2 ) is observed for x = 0.75 at 1200 K. The measured κ was obtained using the relationship κ = DC p d. Measurements for D and C P were carried out from 300 to 1000 K. As seen from Figure 4a, D increases with increasing temperature and with Gd content. C P also increases with increasing temperature, ranging from 0.46, 0.51, 0.36 J/(g K) at 300 K to 0.58, 0.69, 0.50 J/(g K) at 1000 K for x = 0.5, 0.625, 0.75, respectively. The values of D and C P at 300 K are comparable to those for La 2−2x Ca 1+2x Mn 2 O 7 in Ref. [11]. Figure 4b shows the temperature dependence of measured κ for Gd 2−2x Sr 1+2x Mn 2 O 7 (x = 0.5, 0.625, 0.75). κ is lower than 2 W/(m K) over the measured temperature range. κ increases slightly with temperature and with increasing Gd content, which is constant with those for La 2−2x Ca 1+2x Mn 2 O 7 in Ref. [11]. The measured κ consists of two contributions from phonons and electron carriers, i.e., κ = κ L + κ e , the lattice thermal conductivity κ L , and the electronic thermal conductivity κ e . κ e can be calculated according to the Wiedemann-Franz law, κ e = LσT, where L is the Lorentz number (2.45 × 10 −8 W Ω/K 2 ). Increasing σ is accompanied by an increase in κ e . Temperature-dependent κ e and κ L are presented in Figure 4c,d. The values of κ e are seen to be one order of magnitude smaller than those of κ L , indicating that a significant contribution is related to the lattice vibration for the heat transport in Gd 2−2x Sr 1+2x Mn 2 O 7 . Figure 5 shows the temperature dependence of ZT. A similar trend is observed for ZT and PF. The x = 0.75 compound Gd 0.5 Sr 2.5 Mn 2 O 7 shows better performances than the other ones due to the simultaneously enhanced S and reduced κ, with a σ of 3.6 × 10 3 S/m, a S of −60.8 µV/K, and a κ of 1.4 W/(m K) at 1000 K. A maximum ZT of 0.01 is thus obtained for x = 0.75, which is comparable to that of n-type La 2−2x Ca 1+2x Mn 2 O 7 (0.75 ≤ x ≤ 1.0) [11] and p-type Ca 3 Co 2−x Mn x O 6 [36]. The ZT value is very low for practical TE applications. These results reveal that efforts should be made to enhance σ and/or S through compositional and processing optimizations in order to obtain high ZT for these double layered manganites to be used as potential candidates for n-type TE materials. contribution is related to the lattice vibration for the heat transport in Gd2−2xSr1+2xMn2O7. Figure 5 shows the temperature dependence of ZT. A similar trend is observed for ZT and PF. The x = 0.75 compound Gd0.5Sr2.5Mn2O7 shows better performances than the other ones due to the simultaneously enhanced S and reduced κ, with a σ of 3.6 × 10 3 S/m, a S of −60.8 µV/K, and a κ of 1.4 W/(m K) at 1000 K. A maximum ZT of 0.01 is thus obtained for x = 0.75, which is comparable to that of n-type La2−2xCa1+2xMn2O7 (0.75 ≤ x ≤ 1.0) [11] and p-type Ca3Co2−xMnxO6 [36]. The ZT value is very low for practical TE applications. These results reveal that efforts should be made to enhance σ and/or S through compositional and processing optimizations in order to obtain high ZT for these double layered manganites to be used as potential candidates for n-type TE materials.   contribution is related to the lattice vibration for the heat transport in Gd2−2xSr1+2xMn2O7. Figure 5 shows the temperature dependence of ZT. A similar trend is observed for ZT and PF. The x = 0.75 compound Gd0.5Sr2.5Mn2O7 shows better performances than the other ones due to the simultaneously enhanced S and reduced κ, with a σ of 3.6 × 10 3 S/m, a S of −60.8 µV/K, and a κ of 1.4 W/(m K) at 1000 K. A maximum ZT of 0.01 is thus obtained for x = 0.75, which is comparable to that of n-type La2−2xCa1+2xMn2O7 (0.75 ≤ x ≤ 1.0) [11] and p-type Ca3Co2−xMnxO6 [36]. The ZT value is very low for practical TE applications. These results reveal that efforts should be made to enhance σ and/or S through compositional and processing optimizations in order to obtain high ZT for these double layered manganites to be used as potential candidates for n-type TE materials.

Conclusions
The structure and TE properties of Mn 3+ /Mn 4+ mixed-valence double-layered manganites Gd 2−2x Sr 1+2x Mn 2 O 7 (x = 0.5, 0.625, 0.75) were studied. XRD patterns of the samples were consistent with a tetragonal Sr 3 Ti 2 O 7 type structure with space group I4/mmm (No. 139). The Rietveld refinements indicated that the unit cell volume and the distortion in the MnO 6 octahedra increase with increasing Gd content. SEM micrographs and EDS measurements of all the samples show dense and uniform microstructures. All the samples are n-type semiconductors, and σ can be fitted well by the small polaron hopping model in the whole temperature range. With increasing Gd content, σ increases while |S| decreases due to the increasing electron carrier concentration. It is found that the absolute values |S| initially decrease and then increase with temperature, and both σ and |S| increase with temperature approximately above 600 K, resulting in a monotonic increase in PF. These phenomena are interesting, and the physical mechanisms are worthy of further study. κ increases with increasing Gd content, and is lower than 2 W/(m K) over the temperature range of 300-1000 K. A maximum ZT of 0.01 is obtained for x = 0.75 at 1000 K. Although the ZT of Gd 2−2x Sr 1+2x Mn 2 O 7 does not yet reach the performance required for practical TE materials, the present study sheds light on their electrical and thermal transport properties and the relevant mechanisms and lays a foundation for seeking new applications for these double-layered manganites.