High-Figure-of-Merit Thermoelectric La-Doped A ‑ Site-De ﬁ cient SrTiO 3 Ceramics

: The structure and thermoelectric (TE) properties of La-doped, A-site-de ﬁ cient SrTiO 3 (Sr 1 − 3 x /2 La x TiO 3 ) ceramics sintered in air and N 2 /5% H 2 have been investigated. Air-sintered ceramics with 0.10 ≤ x < 0.30 appear cubic by X-ray di ﬀ raction (XRD) but exhibit superstructure consistent with a tetragonal cell ( a 0 a 0 c − ), according to electron di ﬀ raction (ED) studies. 0.30 ≤ x < 0.50 have additional short-range A-site vacancy ( V A ) ordering, and x ≥ 0.50 are orthorhombic with an a − a − c + tilt system and long-range V A ordering. 0.10 ≤ x ≤ 0.50 reduced in N 2 /5% H 2 are oxygen-de ﬁ cient and appear cubic in XRD patterns but exhibit superstructure compliant with an a 0 a 0 c − tilt system by ED. For x = 0.50, additional short-range V A order is observed, and x > 0.50 are orthorhombic with an a − a − c + tilt system and long-range V A ordering. x = 0.15 sintered in N 2 /5% H 2 shows the largest dimensionless TE ﬁ gure-of-merit ZT = 0.41 at 973 K reported for n-type SrTiO 3 -based ceramics, suggesting that the accommodation of La through formation of ( V Sr ) coupled with reduction in N 2 /5% H 2 represents a new protocol for the development of oxide-based thermoelectrics.


INTRODUCTION
Thermoelectric generators (TEGs) can convert heat into electricity directly and vice versa and have emerged as a promising new technology for energy harvesting and refrigeration. Most state-of-the-art thermoelectrics with high figure-of-merit (ZT = S 2 σ/κ, where S is the Seebeck coefficient, σ is electrical conductivity, and κ is thermal conductivity) values are composed of toxic, naturally rare, and heavy metal elements. 1 As a result, further work is required to develop new, low-cost, stable materials based on oxides. Excellent properties have already been reported for layered cobaltitebased thermoelectrics such as Na x CoO 2 (ZT ∼ 1), which exhibit p-type conductivity. 2 To date, n-type oxides with equivalent ZT values have yet to be discovered. 3 SrTiO 3 -based systems have attracted considerable attention due to their high thermoelectric properties by so-called donor-doping with higher valence ions on the A-or B-site, 4−6 especially lanthanum-doped SrTiO 3 (LST). 4,5 Table 1 summarizes the reported properties for several doped SrTiO 3 thermoelectric materials.
Reports for LST are inconsistent and contradictory with respect to the doping mechanisms, solid solution limits, and crystal symmetry, due, in part, to the sensitivity of LST samples to processing variables such as temperature, P O 2 , and time. To date, the weight of scientific evidence suggests that the extra positive charge from substitution of Sr 2+ by La 3+ is compensated by electrons offered by the creation of an equal number of Ti 3 + from Ti 4 + with a formula of Sr 1−x 2+ La x 3+ Ti 1−x 4+ Ti x 3+ O 3 under highly reducing condi-tions. 19−21 Sr 1−x La x TiO 3 has, therefore, been widely studied as a promising candidate for thermoelectric applications. 22 In contrast, there is little evidence to suggest that ionic compensation for La occurs through the formation of V Ti . Instead, investigators have primarily focused on compositions in which La is compensated through the formation of A-site vacancies, according to the general formula Sr 1−3x/2 La x TiO 3 , for potential use as anodes in solid oxide fuel cells. 23,24 Several structural characterization studies of the SrTiO 3 − La 2/3 TiO 3 system have already been carried out. Battle et al. reported A-site cation-vacancy ordering in Sr 1−3x/2 La x TiO 3 (0.25 ≤ x ≤ 0.60) sintered in air using HRTEM. 25 At room temperature, 0.00 ≤ x ≤ 0.40 are cubic and then orthorhombic (Pban) for x = 0.50 and 0.60, with the symmetry being dominated by long-range A-site vacancy ordering. In 2004, Howard et al. additionally concluded the existence of a sequence of octahedral tilt transitions in this system with a cubic room-temperature structure for x < 0.20, tetragonal (I4/ mcm) for x = 0.50 with short-range cation-vacancy occurring for 0.30 ≤ x ≤ 0.50, and then orthorhombic (Cmmm) for x = 0.55 with long-range A-site vacancy ordering present for x ≥ 0.55. 26 Further studies on Sr 1−3x/2 La x TiO 3 suggested glass-like thermal conductivity when Nb is additionally substituted on the B-site and a large increase in power factor reported for Pr-and Nbdoped SrTiO 3 by Bos et al. and Kovalevsky et al.,respectively. 16,17 In previous work, we have highlighted the importance of A-site vacancies in the oxygen-loss mechanism in Sr 1−3x/2 La x TiO 3 , 27 according to eq 1, with A-site deficiency reported to improve the electrical conductivity in Sr 1−3x/2 La x TiO 3 as compared to that in Sr 1−x La x TiO 3 for an equivalent P O 2 and temperature. 28,29 Related studies on other materials such as ZnO have reported the influence of the preparation atmosphere on thermoelectric properties, which suggests that the formation of oxygen vacancies is conducive to the improvement of their n-type thermoelectric properties. 30,31 There is, however, still no definitive report on the influence of cation/vacancy ordering, oxygen loss, and octahedral tilting on the thermoelectric properties of Sr 1−3x/2 La x TiO 3 oxides. Here, we compare the crystal structure of Sr 1−3x/2 La x TiO 3 ceramics sintered in air and N 2 /5% H 2 , with the intention of optimizing their thermoelectric properties at intermediate temperatures (673−973 K).

EXPERIMENTAL SECTION
A solid-state reaction method was used to prepare Sr 1−3x/2 La x TiO 3 ceramics from SrCO 3 (99.90%, Sigma-Aldrich), La 2 O 3 (99.99%, Sigma-Aldrich), and TiO 2 (99.90%, Sigma-Aldrich). Stoichiometric amounts of dry raw powders were weighed and mixed using an attrition mill for 60 min with yttria-stabilized zirconia (YSZ) media in isopropanol. The mixed powders were calcined at 1373 K for 3 h in an alumina crucible after being dried at ∼80°C and sieved. Pellets and bar samples were prepared using an uniaxial press with calcined powders, followed by cold isostatic pressing at 200 MPa and finally sintering in air at a cooling rate of 5°C/min or flowing N 2 /5% H 2 gas at a cooling rate of 30°C/min at 1773 K for 6 h.
A high-resolution STOE STADI-P diffractometer (STOE & Cie GmbH, Darmstadt, Germany) with a linear position sensitive detector (PSD) with Cu Kα (λ = 1.5406 Å) radiation was used for crushed samples. Ceramic microstructures were studied using an FEI Inspect F scanning electron microscope (SEM). Samples for transmission electron microscopy (TEM) were ground and polished using SiC paper and then ion thinned to perforation using a Fischione low-angle ion milling system (model 1010, E.A. Fischione Instruments, Inc., USA). A Philips EM 420 (120 keV) transmission electron microscope was used to obtain electron diffraction (ED) patterns. A double-aberration-corrected microscope, JEM-Z3100F-R005 STEM/TEM, operated at 300 keV was employed to obtain high-angle annular dark field (HAADF) and annular bright field (ABF) images.
A PerkinElmer Pyris 1 TGA was used to measure the weight variation of ceramic samples as a function of temperature in air with a 5°C/min heating rate up to 1000°C and a 5°C/min cooling rate to room temperature.
S and σ were measured simultaneously on ∼20 × 3 × 3 mm 3 bar samples in air from 473 to 973 K by a conventional steady-state method and a four-probe method, respectively. κ measurements were performed on an Anter FlashlineTM 3000 with a high-speed xenon discharge (HSXD) pulse source.

RESULTS
3.1. Phase Assemblage and Grain Structure. Sr 1−3x/2 La x TiO 3 ceramics sintered in air exhibited only peaks associated with a perovskite phase for x ≤ 0.63, above which intensities associated with a La 2 Ti 2 O 7 phase were observed ( Figure 1a). Samples with x ≤ 0.40 appeared cubic by XRD, but for 0.50 ≤ x ≤ 0.63, splitting of the major perovskite peaks along with the appearance of superstructure reflections indicated an orthorhombic structure. Superlattice reflections relating to the orthorhombic structures are labeled O for the air-sintered samples. These peaks became sharper and more intense with increasing x. In contrast, samples sintered in N 2 / 5% H 2 exhibited only peaks associated with the perovskite phase for all compositions within the solid solution ( Figure 1b). Although peak splitting was not observed for any composition, superstructure reflections are indicated for compositions with x ≥ 0.30. Unit cell volume versus x of air-and N 2 /5% H 2 -sintered samples is plotted in Figure 1c. For air-sintered samples, the unit cell volume decreases with increasing x, consistent with the substitution of Sr (1.44 Å in CN12) with the smaller La ion (1.32 Å in CN12), 32 but it then drops precipitously at x ∼ 0.50 and subsequently increases with a positive slope, concomitant with the onset of a transition to an orthorhombic structure. In contrast, the unit cell volume for samples sintered in N 2 /5% H 2 increases from x = 0.00 to 0.20 but then decreases. The initial increase is attributed to oxygen loss from the lattice, eq 1, which results in partial reduction of Ti 4+ (0.605 Å in CN6) to larger Ti 3+ ions (0.67 Å in CN6). The change in slope of cell volume at x ∼ 0.20 may relate to the onset of a structural transition, but the subtle interplay among the concentration of V Sr , V O , and Ti 3+ as x increases and how this might affect unit cell volume cast doubt on such a simplistic interpretation; however, the change in slope is approximately coincident with the appearance of superstructure reflections in the room temperature XRD traces ( Figure 1b).
As shown in Figure 2, all ceramics exhibited dense microstructures with few pores. Grain sizes typically vary from 1 to 10 μm. Although there are clear variations in grain size as a function of composition and processing conditions, the role of A-site and oxygen vacancies in grain growth is complex and beyond the scope of the current study.
3.2. Octahedral Tilting and A-Site Vacancy Ordering. 3.2.1. Air-Sintered Samples. ⟨100⟩, ⟨110⟩, ⟨111⟩ zone-axis electron diffraction patterns (ZADPs) from ceramics with x = 0.30, 0.50, and 0.63 sintered in air are shown in Figure 3. For x = 0.30, sharp discrete superstructure reflections of the type 1 / 2 {ooo} are observed in ⟨110⟩ ZADPs (Figure 3), with no discrete sharp superstructure present in ⟨111⟩ or ⟨001⟩ ZADPs, which has also been observed for x = 0.10 (not shown). According to Woodward and Reaney, 33 the appearance of only 1 / 2 {ooo} reflections indicates a perovskite crystal structure in which the O octahedra are rotated in antiphase only, consistent with the tetragonal symmetry (I4/mcm) and a 0 a 0 c − Glazer tilt system reported for this composition by Howard et al.; 26,34 however, diffuse reflections are also observed for x = 0.30 at 1 / 2 {eeo} positions. These reflections are unlikely to relate to octahedral tilting as 1 / 2 {eeo} occur only when both in-phase and antiphase tilting are present. 33 It is more likely that the diffuse reflections relate to short-range order (SRO) of A-site vacancies on alternate (001) planes first proposed to exist in these compounds by Battle et al. 25 For x = 0.50 and 0.63, superstructure reflections of the type 1 / 2 {ooe} and 1 / 2 {eeo} are observed in ⟨001⟩ and ⟨110⟩, and 1 / 2 {ooe} is observed in ⟨111⟩ ZADPs ( Figure 3). 1 / 2 {ooe} and 1 / 2 {eeo} reflections are conventionally associated with the presence of in-phase rotations of the O-octahedra and antiparallel cation displacements, respectively, 33 but this simplistic interpretation is complicated by the presence of long-range A-site vacancy order which, according to Battle et al., gives rise to primary superstructure reflections at 1 / 2 {eeo}. 25 Moreover, 1 / 2 {eeo} superstructure reflections may undergo complex double diffraction routes to give rise to 1 / 2 {ooe} if diffraction occurs from two domain variants of the vacancyordered structure. Care must be taken, therefore, in deconvoluting these two mechanisms for the generation of superstructure. From their intensity distributions and based on structural data presented by Battle et al. and Howard et al., 25,26 it is reasonable to assume that there are contributions to the 1 / 2 {eeo} reflections from both A-site vacancy ordering and antiparallel cation displacements for compositions with x = 0.50 and 0.63 ( Figure 3).
To determine the primary origin of the 1 / 2 {ooe} reflections, ⟨111⟩ zone axes ( Figure 3) are particularly useful since these reflections cannot be generated by any known mechanism of double diffraction (NB 1 / 2 {eeo} reflections are forbidden according to the Weiss zone law in ⟨111⟩ ZADPs). 33 It can therefore be concluded that the discrete sharp reflections in ⟨111⟩ ZADPs from x = 0.63 arise uniquely from in-phase rotations of the octahedra, consistent with the proposed tilt system (a − a − c + ) by Howard et al. 26 According to Glazer and Woodward and Reaney, 33,34 if one axis of the perovskite structure is tilted in-phase, e.g., 1 / 2 (312) and 1 / 2 (132) reflections (N.B. these reflections are the allowed reflections of the type 1 / 2 {ooe} in ⟨111⟩ ZADPs) are observed in ⟨111⟩ zone axes, but 1 / 2 (321), 1 / 2 (123), 1 / 2 (213), and 1 / 2 (231)    33 The small ferroelastic twin domain width (20−50 nm) associated with x = 0.50 is shown in Figure 4. For x = 0.63, sharp, discrete reflections are observed only at 1 / 2 (312), indicating diffraction from a single variant, the structure of which has one axis tilted in-phase, consistent with the tilt system (a − a − c + ) reported by Howard et al. 26 Singledomain diffraction patterns may be obtained from samples with x = 0.63 due to their larger domain width (0.5 μm) ( Figure 4).  25 which generates superstructure reflections only of the type 1 / 2 {eeo}. The origin of these reflections, therefore, requires further explanation. A calculation of the proportion of A-site vacancies with respect to the available A-sites with increasing x points to a simple scenario to explain the initial appearance of 1 / 2 {eeo} followed by diffuse reflections at 1 / 2 {ooe}. As x increases (x < 0.50, < 25% A-site vacancies), A-site vacancies accrete randomly onto alternate (001) planes, resulting in the appearance of 1 / 2 {eeo} superstructure reflections. The cell doubling mechanism is the scattering power difference between the alternate partially vacated and the essentially fully occupied (001) A-site planes. As x increases (x ≥ 0.50, ≥ 25% A-site vacancies), the A-site vacancies not only order on alternate (001) planes but also begin to undergo short-range order, SRO, within the partially vacated planes that gives rise to weak diffuse intensities at 1 / 2 {ooe} positions in ED patterns in addition to strong discrete reflections at 1 / 2 {eeo}.    (DF) clearly illustrates the antiphase boundaries that form due to impingement of regions of antiphase tilt that have nucleated out of phase. Note also that there is a cross-hatched background contrast in Figure 4 (DF) that arises from ferroelastic twin domains. The twin domains are approximately 20−50 nm and give rise to the multidomain electron diffraction patterns discussed above in the context of the ⟨111⟩ zone axis in Figure 3. In contrast, the twin domains for x = 0.63 are much larger and permit single-domain diffraction data (Figure 4). Also visible in Figure 4 (BF) are antiphase boundaries that arise primarily from the impingement of regions of antiparallel cation displacements that have nucleated out of phase (a contribution to the image from regions of A-site vacancy order cannot be excluded since the 1 / 2 {eeo} reflection that is dominant under the two-beam condition for the image contains intensities arising from both mechanisms for the generation of superstructure). Note that the antiphase domain width associated with antiparallel cation displacements (∼500 nm) is typically less than that observed for antiphase domains that arise from antiphase tilting. Due to the complexity of the inter-relation between A-site vacancy ordering and octahedral tilting, aberration-corrected scanning transmission electron microscopy (STEM) was performed on Sr 0.055 La 0.63 TiO 3 ceramics sintered in air. Aberration correction atomic resolution images obtained using a high-angle annular dark field (HAADF) detector are capable of imaging columns of atoms with a contrast that relates directly to the average mass of the nuclei. Hence, regions of antiparallel cation displacement and A-site vacancy order may be distinguished unambiguously since the latter will exhibit atomic columns in which the partially vacated {001} have lighter contrast than the fully occupied A-site planes.

Chemistry of Materials
Atomic resolution STEM images taken from two domains along pseudocubic ⟨110⟩ zone axes are shown in Figure 5. The A-and B-site cations can be readily identified in both HAADF and the corresponding annular bright field (ABF) images. Oxygen anions on each side of the B-site cations can also be identified in the ABF images. A-site vacancy ordering was not apparent in one of the two domains, presumably due to orientation of the ordered structure (Figure 5a,b), but in the other twin, {100} planes deficient in A-site cations can be readily identified. The alternate layers of greater and lesser occupancy of A-site cations on the {100} planes give rise to a doubling of the periodic spacing along the corresponding ⟨100⟩ direction (Figure 5c,d), which unambiguously illustrates the formation of long-range A-site vacancy order. To confirm this observation, A-site vacancy ordering was further studied along ⟨001⟩ zone axes.
HAADF and ABF images of two domains taken along the ⟨001⟩ zone axes are shown in Figure 6. An atomic resolution HAADF image of one of the two domains is shown in Figure  6a, and a corresponding ABF image shown in Figure 6b. Besides the A/B sites, the oxygen site on the four sides of B-site cations can be readily identified in the ABF image, as shown by the O symbols in Figure 6b. There are some fluctuations in the intensity of the A-site columns, which may originate from the SRO that gives rise to diffuse 1 / 2 {ooe} reflections in ⟨111⟩ zone axes, but no clear vacancy ordering that doubles {001} may be observed in this orientation of the lattice. In contrast, Figure  6c,d shows HAADF and ABF images of a second domain in which alternate A-site planes exhibit atomic columns of greater and lesser contrast, thereby indicating a doubling of periodic spacing along the corresponding ⟨100⟩ directions, which gives rise to 1 / 2 {eeo} superstructure reflections in ED patterns. Once again, no evidence was observed to explain the weak, diffuse 1 / 2 {ooe} reflections in ⟨111⟩ zone axes from samples with x = 0.63, but from their diffuse character and intensity, a clear   contribution to an HAADF or ABF image is unlikely since nanometer scale SRO will average out through the thickness of the foil (5−10 nm).

Chemistry of Materials
Combining electron diffraction data with aberrationcorrected images, a model of Sr 1−3x/2 La x TiO 3 (x = 0.63) can be constructed in which the tilt system is a − a − c + and in which alternate A-site planes contain a higher proportion of A-site vacancies (Figure 7).

N 2 /5% H 2 -Sintered Samples. ⟨100⟩, ⟨110⟩, and ⟨111⟩
ZADPs obtained from x = 0.30, 0.50, and 0.63 sintered in N 2 / 5% H 2 are shown in Figure 8. For x = 0.30 and 0.50, the ⟨110⟩ ZADP exhibits strong, discrete 1 / 2 {ooo} reflections with no other discrete superstructure reflections present in other major ZADPs. The tilt system is thus defined as being in antiphase only and is consistent with I4/mcm symmetry (a 0 a 0 c − ) proposed by Howard et al. and also with the extra peak in XRD data at ∼25.2°at x ≥ 0.30. 26 Weak 1 / 2 {ooo} reflections associated with antiphase tilting are also observed in ⟨110⟩ ZADPs of x = 0.10 and 0.15 (not shown here), indicating that the onset of octahedral tilting occurs at relatively low La concentrations. Diffuse intensities are also observed at 1 / 2 {eeo} positions in ⟨001⟩ and ⟨110⟩ ZADPs (Figure 8). These reflections are associated with A-site vacancy ordering, but the onset of SRO occurs at x = 0.50 for N 2 /5% H 2 , in comparison with x = 0.30 for air-sintered samples.
For x = 0.63, superstructure reflections of the type 1 / 2 {ooe} are observed in Figure 8, revealing the presence of in-phase rotations of O octahedra, consistent with an a − a − c + tilt system. The appearance of sharp, discrete 1 / 2 {ooe} reflections and thus the onset of in-phase tilting occurs at lower values of x in air (x = 0.50) compared with that for N 2 /5% H 2 (x = 0.63) sintered samples. The presence of SRO A-site vacancies for x = 0.50 (N 2 /5% H 2 ) suggests that long-range order, LRO, should have developed for x = 0.63. However, the coincidence of reflections at 1 / 2 (eeo) positions due to antiparallel cation displacements and A-site vacancy order prevents the presence of the latter from being unambiguously determined. Nonetheless, the weight of evidence suggests that A-site vacancy ordering occurs in N 2 /5% H 2 but at higher values of x than in air-sintered samples.
The displacement of the onset of both in-phase tilting and Asite vacancy order to high values of x for N 2 /5% H 2 compared with that of air-sintered samples is directly related to the    23,37 Dark and bright field images obtained under similar conditions to those described in Figure 4 were also obtained for samples that had been sintered in N 2 /5% H 2 . Antiphase boundaries associated with antiphase rotations of the O octahedra were routinely observed, but strong contrast arising from large ferroelastic twin domains could not be routinely observed, suggesting that, even for x = 0.63, samples sintered in N 2 /5% H 2 are not strongly distorted away from cubic, consistent with the XRD data shown in Figure 1.

Chemistry of Materials
A summary of electron diffraction results on Sr 1−3x/2 La x TiO 3 ceramics sintered in air and N 2 /5% H 2 is shown in Table 2. 3.3. Thermogravimetric Data. The onset temperature of oxygen uptake decreased with increasing La concentration ( Figure 9). x ≤ 0.20 prepared in N 2 /5% H 2 were extremely stable in air even at 1000°C. Therefore, only TGA data for x = 0.00 and 0.20 are reported here. x ≤ 0.20 remained black after analysis, consistent with limited O 2 uptake; however, x ≥ 0.30 became white (Table 3). After TGA, x = 0.30, 0.40, 0.50, and 0.60 all exsolved TiO 2 , consistent with Irvine et al., who reported that Sr 1−3x/2 La x TiO 3 perovskites with A-site vacancies are more inclined to exsolve B-site species. 37 This would imply that at least some La 3+ has been compensated locally in the perovksite lattice through the formation of Ti 3+ and not entirely through the formation of A-site vacancies, consistent with the observation in ED data (Figure 8) that the onset of the appearance of SRO superstructure occurs at higher values of x for samples sintered in N 2 /5% H 2 (x = 0.50) compared with those in air (x = 0.30).
3.4. Thermoelectric Data for the N 2 /5% H 2 -Sintered Samples. S, σ, κ, and ZT for Sr 1−3x/2 La x TiO 3-δ ceramics sintered in N 2 /5% H 2 at 1773 K for 6 h over a range of different temperature and values of x are shown in Figure 10. Negative S values suggested that all samples are n-type semiconductors. The undoped SrTiO 3 sample had very high absolute S; however, it had low σ. |S| became smaller with increasing x (Figure 10a), possibly due to an increase in the carrier concentration ( Figure 10b). σ increased at first, reached a maximum, and then decreased with increasing x at x ≤ 0.30 (Figure 10b). κ decreased with increasing temperature and was ∼3 W m −1 K −1 at 973 K for x ≤ 0.30 (Figure 10c).
Comparison of ZT at 973 K showed the same trend as σ with temperature and reached a maximum of 0.41 at 973 K for x = 0.15 due to its high σ (Figure 10e). For x ≥ 0.40, S and σ decreased and became too low for thermoelectric applications (Figure 10f,g). A steep decline in σ was observed for x = 0.40 and 0.50 (Figure 10g).
The Ti 3+ content of x ≤ 0.40 was calculated from an empirical equation for cubic SrTiO 3 perovskites as follows where a and a 0 are the cell parameters for N 2 /5% H 2 -and airsintered samples, respectively. 23 As shown in Figure 11, the Ti 3+ content was found to increase with increasing La concentration up to x = 0.20 and then reaches a plateau at x = 0.30 and 0.40, whereas σ at 473 K kept rising to x = 0.175 and then decreased with increasing La content, suggesting that the σ increase of cubic perovskites with low La content (x ≤ 0.175) is mainly due to an increase in the carrier concentration.

DISCUSSION
X-ray diffraction and TEM data revealed a phase transition from a metrically cubic phase to a distorted orthorhombic phase (tilt system a − a − c + ) at x = 0.50 and 0.63 in air-and N 2 / 5% H 2 -sintered samples, respectively. However, ED patterns revealed all samples with 0.10 ≤ x < 0.50 and 0.10 ≤ x < 0.63 in air and N 2 /5% H 2 , respectively, exhibited reflections consistent with a structure in which the octahedra are rotated in antiphase only, presumably a 0 a 0 c − (I4/mcm), as proposed by Howard et al. 26 The onset of octahedral tilting has been shown to be sensitive to the concentration of V O by several authors. 36    order in the onset of structural transitions is less clear. A-site vacancies in the context of tilting may be considered an effective ionic radius that influences the onset of tilting through simple tolerance factor considerations. 38 Ubic et al. have discussed at length the role of A-site vacancies in the onset of structural transitions, and they concluded that the effective ionic radius of the vacancy was similar to the constituent A-site ion and that no significant lowering of tolerance factor was evident and hence there is little effect on the tilt transition temperature. 39 In addition to the onset of tilting, air-sintered samples revealed a transition from SRO to LRO A-site vacancies as x increased from 0.30 to 0.63, in agreement with work presented by Battle et al. 25 SRO A-site vacancies were evidenced by unique weak diffuse reflections at 1 / 2 {eeo} for samples with x = 0.30. Direct evidence for LRO of A-site vacancies was obtained using atomic resolution HAADF and ABF imaging and inferred through the unusually strong intensities associated with the 1 / 2 {eeo} reflections (in comparison with 1 / 2 {ooe}) in ED patterns for samples with x ≥ 0.50 sintered in air. The 1 / 2 {eeo} reflections are an amalgam of intensity associated with antiparallel cation displacements and A-site vacancy order, whereas discrete 1 / 2 {ooe} reflections arise uniquely from inphase tilting.

Chemistry of Materials
The appearance of A-site vacancy order in samples sintered in N 2 /5% H 2 was less clear, with the driving forces for cation/ vacancy order (charge and strain) potentially disrupted by additional B-(Ti 3+ ) and O-site (V O ) defects. However, the appearance of TiO 2 and SrTiO 3 phases after reoxidation suggests that the concentration of A-site vacancies is lower in samples sintered in N 2 /5% H 2 and implies at least some La 3+ has been incorporated into the lattice through compensation by the formation of Ti 3+ (electronic compensation). This observation is consistent with the appearance of SRO A-site vacancies for x = 0.50 rather than x = 0.30 for N 2 /5% H 2 -and air-sintered samples, respectively. To understand this fully, extensive atomistic simulation is required since the experimental data presented strongly suggest that enhancement of thermoelectric properties occurs when all three sites are likely to exhibit charge and strain defects of the type described (A-site and anion vacancies and Ti 3+ ions).
Optimum thermoelectric properties for Sr 1−3x/2 La x TiO 3-δ sintered in N 2 /5% H 2 occur for ceramics with x ≈ 0.15, which represents the best combination of S, σ, and κ. On the basis of an estimated Ti 3+ content from Figure 11, this corresponds to an approximate composition of Sr 0.775 La 0.15 Ti 0.86 4+ Ti 0.14 3+ O 2.93 . Importantly for applications, compositions with x ≤ 0.20 are not subject to easy reoxidation, as illustrated by the thermogravimetric data presented in Figure  9, suggesting they are considerably more stable as A-site and oxygen-deficient perovskites and are less prone to exsolving TiO 2 on oxidation compared to that for compositions based on x > 0.20.
A combination of a near linear increase in unit cell volume and Ti 3+ ion content with x for x ≤ 0.20 (Figures 1c and 11, respectively) indicates the defect chemistry in these compositions is primarily based on the creation of A-site vacancies by La replacing Sr on the A-sites combined with oxygen loss under reducing conditions to create Ti 3+ ions. The A-site vacancies assist with reducing κ compared to SrTiO 3 (Figure 10c), and the Ti 3+ content is responsible for the strong enhancement of σ, thus resulting in high ZT values of ∼0.40 (at 973) for compositions in the range 0.125 ≤ x ≤ 0.175. The decrease in unit cell volume (Figure 1c) combined with a leveling off of Ti 3+ content and a decrease in σ for x > 0.20 ( Figure 11) are strong indicators of more complex defect chemistry and suggest these perovskites may be kinetically stabilized under the reducing conditions employed to produce the ceramics. The sintering periods were short (ca. 6 h at 1773 K), and there was no evidence of TiO 2 via XRD, ED, or TEM for any of the ceramics sintered under reducing conditions. The rapid oxidation of reduced samples with x > 0.20 in air with TiO 2 exsolution below 1000°C is consistent with the proposal from Irvine et al. that perovskites with significant levels of A-site and O-vacancies are prone to exsolve B-site species and form a perovskite with a composition closer to ABO 3 . 37 In the case of the series presented here, reduced ceramics of x = 0. 20  The high degree of reoxidation associated with samples with x > 0.20 may relate to the onset of A-site vacancy ordering observed in ED patterns, which, in principle, could create highly favorable diffusion paths for the egress and ingress of oxygen. We note, however, that in N 2 /5% H 2 -sintered samples there is no significant evidence of SRO for x = 0.30 and superstructure reflections appear only for x ≥ 0.30. Despite the absence of detectable A-site vacancy superstructure reflections for x = 0.30, it is nonetheless reasonable to consider the increase in concentration of A-site vacancies plays a significant role in reoxidation. According to stoichiometry, reduced x = 0.30 produces 15% A-site vacancies. The development of SRO within the solid solution suggests that, statistically, these vacancies reside on alternate (001) planes, so their effective concentration on the partially vacated planes is > 15%. For x ≥ 0.50, the concentration of A-site vacancies on the partially vacated (001) planes can exceed 50% for ordered regions. We propose the A-site and anion vacancies create an interconnected 2D array of short circuit diffusion paths through comparatively empty AO 3 perovskite {111} pseudo-closepacked stacking planes, resulting in a rapid increase in the diffusion rate of O. Increasing the La concentration, therefore, increases the number and interconnectivity of these short circuit paths, resulting in rapid reoxidation. In perovskites, grain Figure 11. σ versus x at 473 K and Ti 3+ content versus x in Sr 1−3x/2 La x TiO 3-δ ceramics sintered at 1773 K for 6 h in N 2 /5% H 2 . Ti 3+ content was calculated from an empirical equation: a = a o + 0.063y Ti 3+ , where a and a 0 are the cell parameters for N 2 /5% H 2 -and air-sintered samples, respectively. 23 boundary O diffusion is often considered to dominate over bulk particularly at temperatures significantly lower than that of sintering (e.g., ∼573 K lower), as described extensively for BaTiO 3 -based positive temperature coefficient thermistors. 40,41 Doubtless, grain boundaries play a role in reoxidation within the present study, but comparison of the thermogravimetric data with grain size does not reveal a systematic trend, and the increase in La concentration (and A-site vacancies) is, therefore, considered to dominate. At high temperatures, values of thermal conductivity for Ladoped composition converge, with only the undoped compositions being significantly higher. There are many factors that influence thermal conductivity, such as point defects, dislocations, and grain boundaries. We note that all of the measured La-doped compositions exhibit octahedral rotations of the O octahedra at room temperature, but it is unclear whether long-or short-range superstructure exists at the temperature at which the thermoelectric properties are optimized. Nonetheless, at 973 K, optimized compositions contain cation and anion vacancies and a distribution of Ti 3+ / Ti 4+ that enhance phonon scattering and decrease thermal conductivity.

CONCLUSIONS
In conclusion, we report optimized ZT values of 0.41 (at 973 K) for n-type Sr 1−3x/2 La x TiO 3-δ ceramics with 0.125 ≤ x ≤ 0.175. This represents the highest reported TE ZT values to date for any perovskite-based SrTiO 3 ceramics. This was achieved by careful selection of the starting compositions and close control of the ceramic processing conditions to create defective perovskite lattices containing a combination of A-and O-site vacancies with mixed valent Ti 3+ and Ti 4+ on the B-site. Although the optimized materials are highly defective nonstoichiometric perovskites, they are resistant to rapid reoxidation in air up to 1273 K, thus demonstrating their potential for TE applications, e.g., as n-type legs in thermoelectric generators operating at high temperatures. This approach provides a highly promising route to further improve the TE properties of titanate-based perovskites.