Chemical stability of Ca₃Co_4−xO_9+δ/CaMnO_3−δ p–n junction for oxide-based thermoelectric generators

Abstract

An all-oxide thermoelectric generator for high-temperature operation depends on a low electrical resistance of the direct p–n junction. Ca₃Co_4−xO_9+δ and CaMnO_3−δ exhibit p-type and n-type electronic conductivity, respectively, and the interface between these compounds is the material system investigated here. The effect of heat treatment (at 900 °C for 10 h in air) on the phase and element distribution within this p–n junction was characterized using advanced transmission electron microscopy combined with X-ray diffraction. The heat treatment resulted in counter diffusion of Ca, Mn and Co cations across the junction, and subsequent formation of a Ca₃Co_1+yMn_1−yO₆ interlayer, in addition to precipitation of Co-oxide, and accompanying diffusion and redistribution of Ca across the junction. The Co/Mn ratio in Ca₃Co_1+yMn_1−yO₆ varies and is close to 1 (y = 0) at the Ca₃Co_1+yMn_1−yO₆–CaMnO_3−δ boundary. The existence of a wide homogeneity range of 0 ≤ y ≤ 1 for Ca₃Co_1+yMn_1−yO₆ is corroborated with density functional theory (DFT) calculations showing a small negative mixing energy in the whole range.

---

Introduction

For waste heat harvesting at high temperatures and oxidizing conditions, thermoelectric generators (TEGs) based on oxides represent an interesting technology, enabling increased energy efficiency of any high-temperature process where heat harvesting is viable.¹ Oxide-based thermoelectrics exhibit modest efficiencies compared with state-of-the-art non-oxides, but offer in principle superior stability at high temperatures in air (oxidizing conditions). The stability is however jeopardized by the need for metallic interconnects to form well-conducting contacts between the oxide p- and n-type legs, since the metals are noble (rare and expensive) or they will oxidize over time. Cracking or exfoliation due to differences in coefficients of thermal expansion (CTEs) between ceramic conductors and metal interconnects represent additional challenges.² TEGs with direct contact between the p- and n-type legs without metallic interconnects in between have however been proposed.^3–5 By avoiding the metallic interconnects, manufacturing becomes both simpler and less expensive. Such a direct oxide p–n junction faces however not only challenges in terms of high contact resistances from charge carrier depletion, but also stability issues related to interdiffusion and formation of new phases at the interface region. These stability issues are addressed in the present investigation for the specific case of Ca₃Co_4−xO_9+δ–CaMnO_3−δ.

The recently reported all-oxide TEG made of p-type Ca₃Co_4−xO_9+δ and n-type CaMnO_3−δ introduced a new concept where a new phase with favorable thermoelectric properties is formed in situ at the interface between the p- and n-type conductors.⁶ Herein, we further study the materials and present a detailed analysis of the interdiffusion and formation of the secondary phases at the p–n interface in air and typical operating temperature of 900 °C.

According to Woermann et al., Ca₃Co_4−xO_9+δ is stable up to 926 °C in air, at which it decomposes to Ca₃Co₂O₆ and a Co_1−zCa_zO (ss).⁷ Ca₃Co_4−xO_9+δ is described with a homogeneity range (Ca₃Co_3.9+xO_9+δ) with x between −0.03 and +0.17 at 900 °C.⁸ The homogeneity range increases towards Co-rich compositions with increasing temperatures and becomes narrowly sharp, where it ends at a single point.⁸ The stoichiometry of Ca₃Co_4−xO_9+δ in our investigation corresponds to x within the homogeneity range as mentioned above, giving a maximum operating temperature of 900 °C.^6,8,9

Ca₃Co_4−xO_9+δ has a superlattice-misfit structure consisting of two monoclinic subsystems: a triple rock salt (RS)-type slab of Ca₂CoO₃ and a single CdI₂-type CoO₂ slab. The subsystems have identical a, c, and β parameters, but different b parameters: a = 4.8376 Å, c = 10.833 Å, β = 98.06, b₁ = 4.5565 Å, and b₂ = 2.8189 Å.^10–13

CaMnO_3−δ has an orthorhombic perovskite type structure, with lattice constants a = 5.279 Å, b = 7.448 Å and c = 5.264 Å at room temperature.¹⁴ Upon heating in air, the oxygen content is reduced and structural phase transitions occur at 893 and 913 °C with resulting tetragonal and cubic structural modifications, respectively.¹⁵ However, the phase transition temperatures are strongly dependent on the oxygen stoichiometry.¹⁶ According to the CaMnO_3−δ phase diagram the cubic-to-tetragonal and tetragonal-to-orthorhombic transformations occur when 3 − δ ≈ 2.965 and 2.98, respectively, at 900 °C.¹⁷ Oxygen stoichiometry in air is reported to be 2.94 at 900 °C,¹⁷ and hence CaMnO_3−δ should be in the cubic phase domain considering the heat treatment used in this work.

Golovkin et al. have reported phase diagrams of the system Ca–Mn–Co–O.¹⁸ Ca₃Co_4−xO_9+δ exhibits a certain solid solubility of Mn,^19,20 and the formation of a quaternary phase Ca₃Co_1+yMn_1−yO₆ is described by several authors.^21–23 This phase has been reported to have a K₄CdCl₆ type of structure, the same as the pristine Ca₃Co₂O₆ phase, with space group R3̄c. Both Hervoches et al.²² and Kanas et al.²⁴ have confirmed a wide homogeneity range for Ca₃Co_1+yMn_1−yO₆, extending from y = 0 to 1.

To establish all-oxide thermoelectric generators for operation in air at high temperatures, a detailed understanding of the processes taking place at the p–n junction at typical operating temperatures is decisive. In this investigation, we present a comprehensive study of the interdiffusion and formation of secondary phases at the Ca₃Co_4−xO_9+δ/CaMnO_3−δ interface in air at 900 °C.

Results and discussion

The SEM cross section view of the specimen in Fig. 1 shows the interface between the relatively dense CaMnO_3−δ and the porous Ca₃Co_4−xO_9+δ layer after heat treatment at 900 °C for 10 h. The distribution of Co (pink), Mn (blue) and Ca (green) at and in the vicinity of the interface between Ca₃Co_4−xO_9+δ and CaMnO_3−δ is visualized in the bottom left inset in Fig. 1.

Fig. 1 SEM micrograph of a cross section of the Ca₃Co_4−xO_9+δ/CaMnO_3−δ interface after heat treatment at 900 °C for 10 h. The bottom insets correspond to a magnification of the rectangular stippled area, where bottom left is the SEM-image and bottom right corresponds to an EDS map of Ca (green), Mn (blue) and Co (pink). Region (a) corresponds to the porous region in the vicinity of the interface, while Region (b) corresponds to the interphase region, in-between the initial phases Ca₃Co_4−xO_9+δ and CaMnO_3−δ.

Two distinctly different regions are identified at the junction: “Region (a)” which is a ∼10 μm thick porous region at the porous Ca₃Co_4−xO_9+δ side with a high density of Co-rich grains (pink in Fig. 1, bottom right inset).

“Region (b)” is a ∼2 μm thick dense interphase region with a significantly higher Ca/Mn ratio compared to the bulk CaMnO_3−δ (green layer in Fig. 1, bottom right inset). Chemical analysis, topographically performed across the junction (Fig. 2), is in agreement with the observations from Fig. 1. The variations in the concentration of Ca, Mn and Co across the interface are given in Fig. 2b. Mn is seen to diffuse far into the porous Ca₃Co_4−xO_9+δ, while the Mn concentration in Region (b) is lower than in the main bulk phase of CaMnO_3−δ. Enhanced level of Ca is observed in Region (b) (interphase region) while a depletion in Ca is obvious in Region (a) (porous region). There is a moderate gradient in the Co concentration all through the Ca₃Co_4−xO_9+δ layer until we reach the boundary between Region (a) and (b), followed by a steep decrease across Region (b).

Fig. 2 (a) SEM micrograph of the area analyzed by EDS. (b) Corresponding EDS diffusion profiles of Co, Mn and Ca. Unit of abscissa in μm and unit of ordinate in at%.

Co is also seen to diffuse rather far into the CaMnO_3−δ phase. This is in agreement with our recent data on bulk and enhanced grain boundary diffusivity of Co into CaMnO_3−δ,²⁵ where the bulk diffusivity at 900 °C would predict a diffusion length of 0.1 μm, while the enhanced grain boundary diffusion can explain the length closer to 10 μm in Fig. 2b. The faster diffusion of Mn into Ca₃Co_4−xO_9+δ is most probably related to the porosity promoting enhanced surface diffusion. After careful surface polishing from the Ca₃Co_4−xO_9+δ side (Fig. 3a), the polished surface was subjected to SEM/EDS analysis.

Fig. 3 (a) A schematic illustration of the polished sample prior to SEM/EDS analysis. The figure is not drawn to scale, and Regions (a) and (b) are extended for the sake of clarity. (b) Plane view of back scattered electron image (uppermost section) followed by corresponding EDS maps of Ca (green), Co (pink), Mn (blue) and O (red). The assessment of the chemical composition was supplemented by spot EDS analysis according to the positions numbered from 1 to 6 in the uppermost section, and the results are given in Table 1.

EDS elemental maps were taken along the surface (4 lowermost sections in Fig. 3b) and quantitative EDS analyses were made at 6 positions (“spots”) according to the numbering given in Fig. 3b (uppermost section). The results of the quantitative EDS analysis are given in Table 1. The compositions in positions 1 and 5 correspond to CaMnO_3−δ and Ca₃Co_4−xO_9+δ, respectively, while position 6 most probably correspond to mixture of Ca₃Co_4−xO_9+δ and Co₃O₄. Position 3 (Region (b)) correspond to the quaternary phase, Ca₃Co_1+yMn_1−yO₆,^22–24 where the ratio between Ca and the sum of Mn and Co is 1.53 which is close to 1.5 as expected in Ca₃Co_1+yMn_1−yO₆. We suggest that position 4 is representative for the porous region (Region (a)) due to the ratio Ca/(Mn + Co) is 1.33, which is between Ca₃Co_4−xO_9+δ (≈0.75) and Ca₃Co_1+yMn_1−yO₆ (1.53), hence a mixture of Ca₃Co_1+yMn_1−yO₆ and Ca₃Co_4−xO_9+δ. Position 2 shows a cation ratio between CaMnO_3−δ and Ca₃Co_1+yMn_1−yO₆ and may be a mix of these two phases. It should be emphasized that there are uncertainties related to these calculations, both in the accuracy of the measurement as well as the fact that spot analysis also may include elements from phases below the point of analysis. Besides Ca redistribution, a thin densified reaction layer of Ca₃Co_1+yMn_1−yO₆ is formed as a result of Co entering into CaMnO_3−δ. Variations in the Co/Mn ratio across the Ca₃Co_1+yMn_1−yO₆ reaction layer is expected as this forms a diffusion barrier for both cations and allows a wide range of mixing ratios, as seen from the steepness of both the Mn- and Co-profiles in Region (b) (Fig. 2).

Table 1 at% of cations at the spots given in Fig. 3. The uncertainties in Ca, Co and Mn are ±1 at%, while for O it is ±5 at% and is due to the inherent accuracy of the EDS method. The phases dominating at the various spots are suggested based on the ratio between the cations. Also included is the expected ratio between the cations (Ca/(Mn + Co)) in stoichiometric CaMnO_3−δ, Ca₃Co_1+yMn_1−yO₆ and Ca₃Co_4−xO_9+δ, respectively

Spot	Ca	Co	Mn	O	Co + Mn	Ca/(Co + Mn)	Phase	Region
1	20	0–1	20	60	20	1.00	CaMnO3−δ	—
2	28	6	14	53	20		CaMnO3−δ/Ca3Co1+yMn1−yO6	—
3	29	11	8	53	19		Ca3Co1+yMn1−yO6	(b)
4	28	13	8	52	21		Ca3Co1+yMn1−yO6/Ca3Co4−xO9+δ	(a)
5	20	22	3	57	25		Ca3Co4−xO9+δ	—
6	16	23	2	60	25		Ca3Co4−xO9+δ	—
CaMnO3−δ						1		—
Ca3Co1+yMn1−yO6						1.5		—
Ca3Co4−xO9+δ						0.75		—

---

Besides, a thermopower across the Ca₃Co_1+yMn_1−yO₆ reaction layer in TEG is directly affected by the Co/Mn ratio in Ca₃Co_1+yMn_1−yO₆, where the thermopower increases as Co/Mn ratio decreases.²⁴

The polished plane view surface was further analyzed by XRD for phase clarification, where the main reflections corresponded to CaMnO_3−δ and Ca₃Co_4−xO_9+δ (Fig. 4).

Fig. 4 XRD diffractogram of the polished top view surface at the interface between CaMnO_3−δ and Ca₃Co_4−xO_9+δ. The reflections marked with “*” and “v” are due to the presence of Ca₃Co_1+yMn_1−yO₆ and Co₃O₄, respectively. CaMnO_3−δ is identified as the low temperature (LT) orthorhombic phase while Ca₃Co_1+yMn_1−yO₆ fits well with a trigonal structure with space group R3̄c. CaMnO_3−δ and Ca₃Co_4−xO_9+δ are marked as (CMO) (CCO), respectively.

With respect to the annealing temperature (900 °C), which is close to the Co₃O₄/CoO phase transition in air,²⁶ Co will definitely be oxidized during cooling and at room temperature to exist as Co₃O₄. The broad and unsymmetrical set of reflections marked with “*” fits well to the trigonal structure of Ca₃Co_1+yMn_1−yO₆ with space group R3̄c.²² These results are in good agreement with our EDS compositional analysis (Fig. 3 and Table 1).

A detailed TEM/EDS analysis of the interface between CaMnO_3−δ and Region (b) is presented in Fig. 5, where (a) to (d) are STEM-image and EDS analysis, while (e) and (f) are TEM-image and SAD zone axis patterns, respectively. The most striking feature is the sharp boundary between CaMnO_3−δ and Region (b) shown by the yellow line in Fig. 5(e). Above the yellow line the Ca₃Co_1+yMn_1−yO₆ phase is confirmed by the SAD [12−1] zone axis patterns shown in (f), and further supported by the EDS analysis in (b)–(d) showing the presence of Ca, Co and Mn. The absence of Co and presence of Ca and Mn below the yellow line ((b)–(d)) confirm the presence of only CaMnO_3−δ in this region. Although we expect some diffusion of Co into the CaMnO_3−δ phase (Fig. 2), the concentration is below the detection limit in (d).

Fig. 5 (a) STEM and (e) TEM images of Region (b) connected to CaMnO_3−δ with the corresponding EDS maps of (b) Ca, (c) Mn and (d) Co. The yellow line in (e) marks the interface between CaMnO_3−δ (lower part) and Ca₃Co_1+yMn_1−yO₆ (upper part). SAD [12−1] zone axis patterns of regions above the yellow line (grain A and B) confirm the presence of Ca₃Co_1+yMn_1−yO₆ and an example is shown in (f).

The CaMnO_3−δ grains are identified as the low temperature (LT) orthorhombic CaMnO_3−δ phase (Fig. 4) and the appearance of the CaMnO_3−δ grains in Fig. 5(e) indicate high defect concentration appearing as a line pattern.

The high defect concentration is probably due to tensile stresses in CaMnO_3−δ originating from the phase transition between the high temperature cubic phase (HT) to the LT phase, which is followed by a significant volume contraction.

A detailed TEM/EDS analysis of Region (a) is given in Fig. 6. The EDS analysis in Fig. 6(c) confirms the formation of a Co-oxide rich phase, however connected to a phase containing Ca, Co and Mn. SAD [12−1] zone axis patterns identified this phase to be Ca₃Co_1+yMn_1−yO₆ (Fig. 6(d)) showing that Ca₃Co_1+yMn_1−yO₆ also may be formed quite far from the initial interface between Ca₃Co_4−xO_9+δ and CaMnO_3−δ. The reason for the formation of Ca₃Co_1+yMn_1−yO₆ far into Region (a) is a combination of Co depletion of the Ca₃Co_4−xO_9+δ phase, due to diffusion of Co towards CaMnO_3−δ, and counter diffusion of Mn into the Ca₃Co_4−xO_9+δ phase (some solid solubility^19,20). At some critical composition, Ca₃Co_4−xO_9+δ will decompose and form Ca₃Co_1+yMn_1−yO₆ and a Co-oxide rich phase. The depletion of Ca in Region (a) (Fig. 2b) suggests that Ca diffuses towards Region (b), which is intuitively surprising since diffusion seemingly takes place against its concentration gradient.

Fig. 6 (a) HAADF STEM and (b) TEM images of connected Ca₃Co_1+yMn_1−yO₆ and CoO core/Co₃O₄ shell grains in Region (a) quite far from the original Ca₃Co_4−xO_9+δ–CaMnO_3−δ interface, with (c) corresponding EDS maps. (d) SAD [12−1] zone axis patterns of Ca₃Co_1+yMn_1−yO₆ from Region (a).

However, assuming that the thermodynamic activity (chemical potential) of calcium in the Ca₃Co_4−xO_9+δ-phase is much higher than in the Ca₃Co_1+yMn_1−yO₆-phase there will be a thermodynamic driving force for Ca-diffusion from Region (a) to Region (b). This explains the enhanced Ca concentration in Region (b) and Ca depletion in Region (a) (Fig. 2b). However, the formation of Ca₃Co_1+yMn_1-yO₆ depends on diffusion of Mn through the increasing layer of dense Ca₃Co_1+yMn_1−yO₆, which is expected to follow the parabolic law. Hence, the formation of Ca₃Co_1+yMn_1−yO₆ will virtually stop with time, corresponding to a fixed thickness of the Ca₃Co_1+yMn_1−yO₆ layer. The effect of counter diffusion and the formation of Ca₃Co_1+yMn_1−yO₆ on TEG performance is thoroughly elaborated in a previous paper by Kanas et al.⁶ Ca₃Co_1+yMn_1−yO₆ forms together with Ca₃Co_4−xO_9+δ and CaMnO_3−δ a p–p–n junction which exhibits ohmic behavior and a transverse thermoelectric effect, boosting the open-circuit voltage of the module. Furthermore, the electron energy levels of Ca₃Co_1+yMn_1−yO₆ are located intermediate of those of Ca₃Co_4−xO_9+δ and CaMnO_3−δ, which reduces the depletion of charge carriers at the Ca₃Co_4−xO_9+δ–Ca₃Co_1+yMn_1−yO₆ and Ca₃Co_1+yMn_1−yO₆–CaMnO_3−δ interfaces, as compared to initial Ca₃Co_4−xO_9+δ–CaMnO_3−δ p–n interface.⁶

DFT results for the mixing energy of Ca₃Co_1+yMn_1−yO₆ depicted in Fig. 7 show small negative values for the entire composition range, with a shallow minimum at y = 0.25, corresponding to a mixing energy of −5 meV per formula unit. According to the DFT calculations the most stable Ca₃Co_1+yMn_1−yO₆ composition should be in the vicinity of y ∼ 0.25, corresponding to a [Co]/[Mn] ratio of ∼1.67.

Fig. 7 Calculated mixing energies of Ca₃Co_1+yMn_1−yO₆ as a function of y in Ca₃Co_1+yMn_1−yO₆. The scatter may reflect the limited size and number of atoms of the computational cell.

Nevertheless, the negative mixing energy obtained in the entire range from y = 0.1 to 0.9 supports the existence of solid solubility in the whole range from y = 0 to 1, as confirmed by Hervoches et al.²² and Kanas et al.²⁴ A small mixing energy is reasonable given that Co and Mn have similar atom sizes, and the DFT result serves to confirm that the nature of chemical bonding is not greatly affected by the substitution. At finite temperature the free energy would clearly show a broad minimum dominated by the entropy term which was not considered in these 0 K calculations.

All in all, the comprehensive structural analysis of the Ca₃Co_4−xO_9+δ/CaMnO_3−δ p–n junction gives an important overview of the complexity, described by counter diffusion and formation of several reaction products at the interface. In high-temperature applications the hot side of this TEG boosts the overall performance through a high open circuit voltage which occurs due to counter diffusion of cations resulting in formation of Ca₃Co_1+yMn_1−yO₆ with a high thermopower.^6,24

Conclusions

The Ca₃Co_4−xO_9+δ/CaMnO_3−δ p–n junction is not stable at 900 °C as a new Ca₃Co_1+yMn_1−yO₆ intermediate phase forms through counter diffusion of Ca, Co and Mn. On the CaMnO_3−δ side, a thin dense layer of Ca₃Co_1+yMn_1−yO₆ with variable composition forms, in which further in-diffusion of Co is slow. On the Ca₃Co_4−xO_9+δ side, Mn diffusion into Ca₃Co_4−xO_9+δ together with Co deficiency gives decomposition into Ca₃Co_1+yMn_1−yO₆ and Co-oxide. The diffusion profiles are in qualitative agreement with our recently published data on Co diffusion in CaMnO_3−δ. DFT calculations and experimental evidence support the wider homogeneity range (0 ≤ y ≤ 1) of Ca₃Co_1+yMn_1−yO₆.

Experimental

Phase-pure CaMnO_3−δ powder was synthesized by solid-state reaction using a stoichiometric ratio of CaCO₃ (Inframat Advanced Materials, >99% purity) and MnO₂ (Sigma Aldrich, >99% purity) precursors, mixed and heated twice at 1200 °C for 14 h in air with grinding in between. A dense CaMnO_3−δ pellet (diameter 12 mm, thickness 4 mm) was formed by cold isostatic pressing (CIP) at 200 MPa followed by sintering at 1300 °C for 14 h in air using a heating rate of 200 K h⁻¹ and cooling rate of 100 K h⁻¹. The dense CaMnO_3−δ pellet was ground and polished with SiC papers and diamond paste to 1 μm. Ca₃Co_4−xO_9+δ powder, with the nominal stoichiometry Ca₃Co₄O_9+δ, was prepared by spray pyrolysis (CerPoTech AS, Norway), and a Ca₃Co_4−xO_9+δ layer was produced by tape casting according to ref. 6. The tape was cast, laminated, and attached onto the polished CaMnO_3−δ surface by pressing at 10 MPa and 80 °C for 3 min. The sample was then calcined at 450 °C for 1 h in air to remove organics and further heated at 900 °C for 10 h. Firm adhesion between Ca₃Co_4−xO_9+δ and CaMnO_3−δ was obtained after the heat treatment.

The sample was subsequently embedded in epoxy and divided in pieces for both cross section and plane view examinations. The specimens were ground with SiC paper, and final polishing was done with colloidal Al₂O₃ (0.05 μm). For the plane view examination, the specimen was polished down stepwise from the Ca₃Co_4−xO_9+δ side. The exposed area was analyzed by scanning electron microscopy (SEM) with energy dispersive X-ray energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD) in between each polishing step. Cross section specimens were examined by a combination of SEM and transmission electron microscopy (TEM) enabling structural studies at both micro- and nanoscale. The TEM specimen, covering a ∼15 μm long region across the CaMnO_3−δ/Ca₃Co_4−xO_9+δ interface, was cut out by use of a focused ion beam (FIB) and thinned down to about 100 nm. EDS was conducted to map and quantify the elemental composition globally and locally by SEM and TEM, respectively. To improve statistics, line scan data sets were added after aligning the onset of the dense interface region.

A Rigaku MiniFlex600 system using Cu Kα radiation and florescence correction was used for the XRD investigation, while a Hitachi TM3000 SEM, a JEOL2010F TEM operated at 200 kV and a Cs probe corrected FEI Titan G2 60-300 TEM operated at 300 kV were used for the SEM and TEM studies.

The mixing energy of Ca₃Co_1+yMn_1−yO₆ was calculated within the spin-polarized density functional theory (DFT) utilizing the projector-augmented-plane wave method as implemented in VASP,^27,28 and choosing the generalized-gradient approximation functional PBE.²⁹ A supercell consisting of 2 × 2 × 2 primitive unit cells was used to emulate the solid solution, which was set up by randomly replacing 2, 4, 6, 8, 10, 12, and 14 of the 16 Mn atoms with Co atoms in the Ca₃Co_1+yMn_1−yO₆ supercell. To obtain an estimate of the mixing energy, we rely on a ferromagnetic ordering with spin aligned in intra-chain (111) direction. The plane-wave energy cutoff was set to 520 eV with a 2 × 2 × 2 Monkhorst–Pack k-point sampling of the Brillouin zone. Atomic coordinates and unit cell were relaxed until the total energy varied by less than 0.03 meV per formula unit.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support from the Research Council of Norway under the program Nano2021 to the project (number 228854) “Thermoelectric materials: Nanostructuring for improving the energy efficiency of thermoelectric generators and heat-pumps” (THELMA) conducted by NTNU, UiO, SINTEF, FFI, UiS and UiA.

References

1. S. Twaha, J. Zhu, Y. Yan and B. Li, Renewable Sustainable Energy Rev., 2016, 65, 698–726.
2. W. Liu, Q. Jie, S. E. Kim and Z. Ren, Acta Mater., 2015, 87, 357–376.
3. A. Becker, R. Chavez, N. Petermann, G. Schierning and R. Schmechel, J. Electron. Mater., 2013, 42, 2297–2300.
4. R. Chavez, S. Angst, J. Hall, F. Maculewicz, J. Stoetzel, H. Wiggers, L. T. Hung, N. Van Nong, N. Pryds, G. Span, D. E. Wolf, R. Schmechel and G. Schierning, J. Phys. D Appl. Phys., 2018, 51, 014005.
5. G. Span, M. Wagner, S. Holzer and T. Grasser, 25^th International Conference on Thermoelectrics, ICT, Vienna, 6–10 August, 2006.
6. N. Kanas, M. Bittner, S. P. Singh, T. D. Desissa, T. Norby, A. Feldhoff, T. Grande, K. Wiik and M.-A. Einarsrud, ACS Omega, 2018, 3, 9899–9906.
7. E. Woermann and A. Muan, J. Inorg. Nucl. Chem., 1970, 32, 1455–1459.
8. D. Sedmidubsky, V. Jakes, O. Jankovsky, J. Leitner, Z. Sofer and J. Hejtmanek, J. Solid State Chem., 2012, 194, 199–205.
9. N. Kanas, S. P. Singh, M. Rotan, M. Saleemi, M. Bittner, A. Feldhoff, T. Norby, K. Wiik, T. Grande and M.-A. Einarsrud, J. Eur. Ceram. Soc., 2018, 38, 1592–1599.
10. Y. Miyazaki, Solid State Ionics, 2004, 172, 463–467.
11. Y. Miyazaki, M. Onoda, T. Oku, M. Kikichi, Y. Ishii, Y. Ono, Y. Morii and T. Kajitani, J. Phys. Soc. Jpn., 2002, 71, 491–497.
12. A. C. Masset, C. Michel, A. Maignan, M. Hervieu, O. Toulemonde, F. Studer and B. Raveau, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 62, 166–175.
13. M. Schrade, H. Fjeld, T. G. Finstad and T. Norby, J. Phys. Chem. C, 2014, 118, 2908–2918.
14. K. R. Poeppelmeier, M. E. Leonowicz, J. C. Scanlon, J. M. Longo and W. B. Yelon, J. Solid State Chem., 1982, 45, 71–79.
15. H. Taguchi, M. Nagao, T. Sato and M. Shimada, J. Solid State Chem., 1989, 78, 312–315.
16. E. I. Goldyreva, I. A. Leonidov, M. V. Patrakeev and V. L. Kozhevnikov, J. Solid State Electrochem., 2016, 16, 1187–1191.
17. E. I. Leonidova, I. A. Leonidov, M. V. Patrakeev and V. L. Kozhevnikov, J. Solid State Electrochem., 2011, 15, 1071–1075.
18. B. V. Golovkin and G. V. Bazuev, Russ. J. Gen. Chem., 2010, 80, 213–218.
19. A. Bhaskar, C.-J. Liu and L.-C. Huang, J. Electroceram., 2013, 31, 129–133.
20. J. L. Chen, Y. S. Liu, C.-J. Liu, L.-C. Huang, C. L. Dong, S. S. Chen and C. L. Chang, J. Phys. D: Appl. Phys., 2009, 42, 135418–135423.
21. V. G. Zubkov, G. V. Bazuev, A. P. Tyutyunnik and I. F. Berger, J. Solid State Chem., 2001, 160, 293–301.
22. C. H. Hervoches, H. Okamoto, A. Kjekshus, H. Fjellvåg and B. C. Hauback, J. Solid State Chem., 2009, 182, 331–338.
23. G. V. Bazuev, V. G. Zubkov, I. F. Berger and V. N. Krasil’nikov, Russ. J. Inorg. Chem., 2001, 46, 317–322.
24. N. Kanas, S. P. Singh, T. D. Desissa, T. Norby, K. Wiik, T. Grande and M.-A. Einarsrud, Materials, 2019, 12, 497–507.
25. T. D. Desissa, N. Kanas, S. P. Singh, K. Wiik, M.-A. Einarsrud and T. Norby, Phys. Chem. Chem. Phys., 2018, 20, 2754–2760.
26. M. Chen, B. Hallstedt and L. J. Gauckler, J. Phase Equilib., 2003, 24, 212–227.
27. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
28. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
29. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.

---