Charge-Carrier Hopping in Highly Conductive CaMn1âxMxO3âÎ´

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Charge-Carrier Hopping in Highly Conductive CaMn MO Thermoelectrics Philipp Thiel, Sascha Populoh, Songhak Yoon, Gesine Saucke, Kristaps Rubenis, and Anke Weidenkaff J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b05882 • Publication Date (Web): 18 Aug 2015 Downloaded from http://pubs.acs.org on August 23, 2015

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The Journal of Physical Chemistry

Charge-Carrier Hopping in Highly Conductive CaMn1-xMxO3-δ Thermoelectrics Philipp Thiel1, Sascha Populoh1,a, Songhak Yoon1, Gesine Saucke1, Kristaps Rubenis1,2, Anke Weidenkaff3 1

Laboratory Materials for Energy Conversion, Empa, Swiss Federal Laboratories for Materials

Science and Technology, Überlandstr. 129, CH-8600 Dübendorf, Switzerland 2

Institute of General Chemical Engineering, Faculty of Materials Science and Applied Chemistry,

Riga Technical University, 14/24 Azenes st., LV-1048 Riga, Latvia 3

Materials Chemistry, Institute for Materials Science, University of Stuttgart, Heisenbergstr. 3,

DE-70569 Stuttgart, Germany ABSTRACT Highly dense CaMn1-xMxO3-δ (with M = Nb, Mo, Ta, W and 0 ≤ x ≤ 0.08) n-type thermoelectric materials with low electrical resistivities are prepared from nano-crystalline powders. Their room temperature power factors outperform the best reported results by 30% or more. In combination with the thermal conductivities promising figure-of-merits of ZTM=Ta,x=0.04 = 0.21 and ZTM=W,x=0.04 = 0.20 were achieved at 1160 K. The relative changes and temperature dependencies of the Seebeck coefficient, the electrical resistivity, and the power factor are described with a small-polaronhopping-based mechanism. In the limits of high-temperatures and low substitution levels the Seebeck coefficients are in good agreement with Heikes formula. At high substitutions the efficiency of the doping presumably decreases due to trapping states caused by the formation of bands from Jahn-Teller lowered eg orbitals of Mn3+. Jahn-Teller distortion of Mn3+ also leaves its footprints in the orthorhombic distortion of the crystal structure along the b-axis.

Keywords: Perovskite, Oxide, Transport Properties, Jahn-Teller Effect, Energy Materials,

a

Corresponding author, email: [email protected]; Phone: +41 58 765 4689

ACS Paragon Plus Environment


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I.

INTRODUCTION

Among the green energy technologies thermoelectric waste heat recovery stands out due to its robustness and scalability.1 Thermoelectric converters are solid state devices that convert heat flow between a heat source (TH) and a heat sink (TC) into electric power.1-2 For decades they are competitive power sources in niches such as space applications3-4 or self-powered systems1. Nowadays, automotive applications3-4, industrial heat exchangers1, 5, or solar power conversion4, 6-7 are upcoming for application. The efficiency of thermoelectric converters depends on the dimensionless figure-of-merit ZT=S2T/ρκ, where S is the Seebeck coefficient, ρ the electrical resistivity, and κ the thermal conductivity, and the Carnot efficiency = 1 − / .8-9 Promising for thermoelectric waste heat recovery are applications with a high (T up to 1000 K).10 Therefore, high-temperature and air-stable materials are demanded. Standard thermoelectric materials, like Bi2Te3 (Tmax = 550 K)11, half-Heusler compounds (Tmax = 850 K)12-13 or SiGe (Tmax > 1300 K, but oxidation sensitive) do not fulfill these criteria and moreover some of them contain either critical or expensive elements. Thermoelectric oxides – in particular calcium manganites – master these challenges.7, 10 Pristine calcium manganite CaMnO3-δ crystallizes in a perovskite structure14 and exhibits n-type transport properties with a high Seebeck coefficient S (ST=360K = -448 µV/K) but relatively high electrical resistivity (ρ = 950 mΩ·cm).15 With suitable aliovalent substitution on the Ca-site (A-site) or Mn-site (Bsite) the electrical resistivity can be greatly reduced (ρ < 10 mΩ·cm). The additional charge of the substituent is compensated by changing the ratio of Mn3+/Mn4+.16 The resulting higher carrier concentration affects S adversely and the best compromise for reaching a high power factor S2/ρ needs to be pursued. Substitution also reduces the unfavorably high thermal conductivity κ, which is larger than κ > 5 W/Km at room temperature.17 The substituents provide mass difference and impurity scattering centers that reduce the phonon propagation.18 A further strategy for reduction of κ and high ZT values lies in nanograin sized materials.19-20 Like other thermoelectric transition metal oxides, calcium manganites are semiconductors with narrow bands and large Coulomb interactions causing localized charge carriers at the Mn-sites.21-22 For hole doped


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compounds of the La1-xAxMnO3 series there is consensus about the small adiabatic nature of the polarons.23 Although, the electronic transport phenomena of the electron doped CaMn1-xMxO3-δ compounds are often described by a small adiabatic polaron hopping process,21, 24-26 there is some debate if the polarons are either localized small adiabatic or Fröhlich (continuum or larger) polarons.27-28 Nevertheless, the small adiabatic polaron model provides a good starting point for a further analysis of the transport properties.15 The hopping model depends on the Jahn-Teller active Mn3+O6 octahedra due to their t2g3eg1 electron configuration which renders the transport properties.18, 29 This effect is also essential for properties like the colossal magnetoresistance in highly A-site doped Ca1-xL3+xMnO3-δ (L3+ = lanthanide).30-31 In such oxides charge ordering can be observed, which describes a distinct alinement of the unpaired spins in the eg1 orbitals.32 Structurally, the Jahn-Teller effect causes a distortion of the Mn3+O6 octahedra in three modes, a breathing mode, a basal-plane distortion mode (displacement of the central Mn3+ ion), and an octahedral stretching mode (elongation of the apical Mn-O bonds). The x2-y2 orbitals aligned towards the basal-plane O atoms is shifted upwards and the z2 orbital aligned towards the apical O atoms is below the Fermi level.33 Previous theoretical and experimental studies were devoted to describe the electronic transport taking the splitting of the eg orbitals into account.29, 34 In this study we demonstrate that the Seebeck coefficient, the electrical resistivity and the thermoelectric power factor can be semi-quantitatively determined by taking small polaron hopping into account. We also identify the footprints of the Jahn-Teller effect in the transport as well as in the crystallographic data. Our analysis is accomplished on four series of CaMn1xMxO3-δ

II.

(M = Nb5+, Mo6+, Ta5+, W6+; x ≤ 0.08) samples synthesized by an adapted Pechini method. EXPERIMENTAL

2.1. Sample Preparation Dense CaMn1-xMxO3-δ samples were sintered from nano-crystalline powders synthesized by a tailored soft chemistry synthesis process.35 The CaMn1-xMxO3-δ powders synthesized by a polymeric polynuclear precursor method were calcined for 5 h at 1073 K (heating rate 300 K/h). 1.5 mL commercial



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penetrating fluid (WD-40) has been added as a lubricant to 6.0 g of calcined powders. The mixture was ground and uniaxially pressed into 2.5 cm diameter pellets followed by cold isostatic pressing at 2 kbar. The green bodies were pre-sintered at 1373 K for 5 h (the samples of Mo6+ and W6+ with x ≥ 0.04 at 1453 K). First, they were heated with a heating rate of 1 K/min from 373 to 673 K and dwelled for 2 h to burn off the penetrating fluid and further ramped with 5 K/min. Starting from 1073 K, ramping was decreased to 0.5 K/min up to the sintering temperature. After shaping of the pre-sintered samples, a second sintering step at 1573 K for 5 h (the samples of Mo6+ and W6+ with x ≥ 0.04 at 1623 K) with a ramp of 0.5 K/min was employed. Densities between 92.7% and 99.1% of the theoretical density as calculated from the crystallographic data (Table 1) are achieved. M-x

A-d [g/cm3] 4.45

r-d [%] 96.6

M-x

pristine

c-d [g/cm3] 4.61

Nb-0.01 Nb-0.02 Nb-0.04 Nb-0.08

4.61 4.56 4.69 4.67

4.44 4.48 4.48 4.54

96.2 98.2 95.4 97.3

Ta-0.01 Ta-0.02 Ta -0.04 Ta -0.08

c-d [g/cm3]

A-d [g/cm3]

r-d [%]

4.64 4.70 4.73 4.86

4.49 4.66 4.63 4.75

96.7 99.1 97.9 97.7

Mo-0.01 4.65 4.42 95.1 W-0.01 4.69 4.39 93.5 Mo-0.02 4.58 4.39 95.9 W-0.02 4.68 4.39 93.7 Mo-0.04 4.57 4.35 95.2 W-0.04 4.70 4.36 92.7 Mo-0.08 4.55 4.38 96.4 W-0.08 4.80 4.51 94.0 Table 1 – Theoretical densities from crystallographic data (c-d), by Archimedes method measured densities (A-d), and the relative densities (r-d = A-d / c-d) of the synthesized CaMn1-xMxO3-δ materials.

2.2. Characterization X-ray diffraction was carried out on powder samples with a particle sizes below 150 µm. The patterns were recorded from 20° to 100° in 2θ geometry with a step interval of 0.0167° using a PANalytical X’Pert PRO MRD θ–2θ diffractometer equipped with a Johansson monochromator (Cu Kα1 radiation, λ=1.5406 Å). For Rietveld refinement the Thompson-Cox-Hasting’s function36 was used as implemented in the FullProf suit.37 Bond angles and lengths were calculated from the refined atomic positions by using the program BondStr. The total thermal conductivity κtotal was determined from the measured heat capacity Cp, the thermal diffusivity α and the density d according to the relation κtotal = Cp·α·d. The lattice part of thermal conductivity (κlattice) is approximated according to the relation: κtotal = κlattice + κel. The electrical part of the ACS Paragon Plus Environment

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thermal conductivity κel is derived from the electrical resistivity ρ using the Wiedemann-Franz law, κel = L·T/ρ , where the L corresponds to the Sommerfeld value of the Lorenz number L = 2.45×10-8 W·Ω·K-2.38 The heat capacity was measured on 50-80 mg samples by differential scanning calorimetry (DSC) using a Netzsch DSC 404C Pegasus. For the orthorhombic phase the measured values are approaching the Dulong-Petit-values. Accordingly, in the region of the peak caused by the orthorhombic to cubic phase transition this value was used as the phase-transition temperature. The thermal diffusivity was determined with a Netzsch LFA 457 laser flash apparatus. The detailed experimental procedures are described elsewhere.20 The Seebeck coefficient (S) and electrical conductivity (σ) were measured up to 1273 K in air using an Ozawa Science RZ200li on bar shaped samples. In our previous study we demonstrated that the oxygen contents from the TG-measurements are representative also for highly dense samples.15 An assumption of the experimental error can be found elsewhere.35, 39

2.3. Error Estimation For the substitution level x,y a relative error of ∆(x,y)/(x,y) = 10 % and a minimum absolute error of ∆(x,y) = 0.004 is considered. To assume the error of the bonding distances the XRD measurements were repeated several times. Depending on the background models, the estimated bonding distances were marginally changed. Therefore, we consider an error in the a bonding distances below ∆(Mn-O) = 0.002 Å. The measurement errors for the thermoelectric properties are estimated according to an analysis of Populoh et al.39 The error for the Seebeck coefficient S and the resistivity ρ is ±5%, of the thermal conductivity κ 8%, of the power factor S2/ρ 10%, and of the figure-of-merit ZT 20%. III.

RESULTS & DISCUSSION

3.1. Crystal Structure



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The unit cells of pristine and substituted CaMnO3-δ are orthorhombic, which is distorted from the ideal cubic perovskite structure.35 In the pseudo-cubic (C) unit cell the lattice parameters of the orthorhombic (O) can be derived as ≈ ≈ √2 × and ≈ 2 × (Figure 1c).14 Accordingly, the orthorombicity O can be used as a measure of the orthorhombic distortion40 and is defined as , [%] = [(( − /√2)) ⁄ (( + /√2) )] × 100

(1)

with respect to the b-axis and as ," [%] = [(( − )) ⁄ (( + ) )] × 100

(2)

with respect to the c-axis. With increasing B-site substitution level x, the orthorhombic distortion of the unit cell increases with respect to both, the b- and the c-axis (Figure 1a). The b-axis orthorombicity Oa,b of the hexavalent (Mo6+, W6+) substituted samples increases more drastically than Oa,b of the pentavalent (Nb5+, Ta5+) substituted samples. This is contrary to the behavior of the c-axis orthorombicity Oa,c which increase similarly for all presented series. Substitution with a hexavalent ion M6+ creates twice the number of Mn3+ ions per substituent atom than with a pentavalent ion M5+. The Mn3+ ions are Jahn-Teller active due to their d4 electronic configuration. The different evolution of the orthorombicities indicates a preferred direction of Jahn-Teller distortion along the b-axis. The observed bond lengths of the Mn to the two crystallographically different O atoms (Figure 1b) support this assumption. The O1 atoms (apical, 4c in Wyckoff position) form the Mn-O1 bonds parallel to the b-axis and the O2 atom (equatorial, 8d in Wyckoff position) form the Mn-O2 bonds in the a-c plane. For pristine CaMnO3-δ the bond lengths and are almost identical with l = 1.9033 Å and l = 1.9021 Å, respectively. With B-site substitution the distance first decreases for low substitution (x ≤ 0.01, xNb = 0.01 makes an exception). But with further increasing substitution both bond lengths and steadily increase with increasing x. Coincidently, the bonds, which are parallel to the b-axis, increase more steeply. Although the measured crystallographic data represent an average over an ensemble of a few Mn3+ among many Mn4+ states, the circumstantial evidences of bond length increase for the bond indirectly indicate a Jahn-Teller distortion of


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the Mn3+O6 octahedrons along the b-axis. This preference direction is in agreement with DFT calculations that predict an elongation of the apical Mn-O bonds.33

Figure 1 – Crystal structure of CaMn1-xMxO3-δ compounds. (a) The orthorhombic distortion of the unit cell as a function of the substitution level. (b) The bond lengths are plotted as a function of the substitution level. The bond lengths are those in the a-c plane and the bond lengths are those along the b-axis. (c) The relationship between the orthorhombic unit cell and pseudo-cubic unit cell. The position of the O1 and O2 atoms are illustrated in (d).

3.2. Seebeck-Coefficient The values of the Seebeck coefficients S are in good agreement with literature data.15, 20, 41-45 With increasing substitution level the absolute Seebeck coefficient |S| (Figure 2a) decreases. As already shown in previous studies the charge-carrier concentration primarily determines the Seebeck coefficient.15 Comparing series with the same valance of the substituent (Nb5+ with Ta5+ and Mo6+ with W6+) the type

of substituting ion shows only minor influence on |S(T)|. Hexavalent substitution decreases |S(T)| more effectively than pentavalent ones and apparently 2×xNb,Ta samples have an almost identical Seebeck coefficient as xMo,W samples. The factor two results from the charge of the ions: The hexavalent substituent contributes twice the amount of additional charge carriers as the pentavalent. Accordingly, an electronic substitution level z is introduced with z = x for Nb and Ta and z = 2×x for Mo and W.



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Up to T = 1000 K with increasing temperature the absolute Seebeck coefficient |S(T)| is increasing. It is linear with 1/T and therefore in good agreement with the theories for hopping conduction for which a suitable description is given by broad band semiconductor theory:29, 46-47 #=±

%& )* ( + +, ' %

(3)

(where %& is the Bolzmann constant, ' the elemental charge, )* the Fermi energy and + a dimensionless constant). With further increasing temperature (T > 1000 K) the samples become oxygen deficient, which causes a rise in the charge-carrier concentration and subsequently a strong decline of |S|.35 The different onsets of reduction cause an equilibration of the Seebeck coefficient at high temperatures.35 Extrapolating the linear part of the S(1/T) plot – which is the temperature region with stoichiometric oxygen content – towards 1/ = 0 results in an high-temperature limit Seebeck coefficient #-→/ . In this case in equation (3) the )* -term approaches zero and the total equation converges to the socalled Heikes’ formula, which quantifies the factor A:21, 48 # 01203 ( → ∞) = ±

%& 9: #∗ (ln 78 ( ,; + , ' %&

(4)

where 8 is a degeneracy factor (for Mn4+/Mn3+ in the low-spin case 8 = 4/9 49-50) and # ∗is an entropy term that is considered to contribute less than 10 µV/K to S and is therefore neglected in the further discussion.21, 47 9: is the number of available hopping sites for itinerant charge carriers, in this case the number of Mn4+ ions. For pentavalent substitution 9: = 1 − 2 × A and for hexavalent substitution 9: = 1 − 1.5 × A. The variable is the charge-carrier concentration that is here tantamount with the Mn3+/Mn4+ ratio. For pentavalent substitution = A/(1 − A) and for hexavalent substitution = A/(1 − 0.5 × A). The high-temperature limit values #-→/ of samples with equal electronic substitution level z only vary in a narrow range of ±20 µV/K, where also fitting and stoichiometry errors contribute (Figure 2b). At low z the #-→/ values are in good agreement with # 01203 (e.g. #-→/;DEF.FG = −262 ± 16 IJ/K vs. # 01203,DEF.FG = −262 IJ/K). With increasing z the extrapolated Seebeck coefficients increasingly differ from the theoretic values (e.g. #-→/;DEF.FL = −162 ± 16 IJ/K vs. # 01203,DEF.FL = −126 IJ/K). At z = 0.16 they are roughly 2.5 times higher than expected. This indicates that with increasing substitution level ACS Paragon Plus Environment

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the electronic doping becomes less effective. According to equation (4) an effective electronic substitution level zeff can be calculated for each nominal electronic substitution level znom. 9: is considered to be 9: = M(AN ) and to be = M(A0OO ). Therefore, it appears that at the highest substitution level the doping is 40% less effective than expected ( A0OO (AN = 0.16) = 0.094 ) (Figure 2c). A possible explanation is that with increasing number of Mn3+ states the split eg-orbitals (Jahn-Teller effect) start to form bands which lie significantly below the Fermi level (approximately 0.75 eV according to Satpathy et al.33) and act as trapping sites. Consequently, less charge carriers than expected would be close to the Fermi level and accordingly a higher absolute Seebeck coefficient would be observed.

Figure 2 – The Seebeck coefficient of CaMn1-xMxO3-δ compounds. In (a) the measured data is plotted against the reciprocal temperature (1/T). The values extrapolated to the high temperature limit 1/T → 0 are shown in (b). The region where the compounds are reduced – and |S| strongly decreases – is neglected. The solid line indicates the expected high temperature limit Seebeck coefficient according to Heikes’ formular. In (c) the effective substitution level zeff derived to Heikes’ formula with the data in (b) is compared with the nominal substitution level znom.

3.3. Electrical Resistivity The electrical resistivity for T < 1000 K exhibits a metallic behavior (Figure 3a). Remarkably low electrical resistivities, in particular at room temperature, are obtained. Ta substituted samples are by a factor of 4-10 more conductive than the highest reported values in literature.44 Also the Nb 20, 44-45, Mo 43



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and W 15, 41 substitutions outperform previously reported samples partly by more than a factor of two. The low electrical resistivity is most likely due to the obtained high relative densities (see Table 1). Furthermore, the slow and step-wise sintering procedure of the nano-crystalline powders might cause a better grain connectivity and prevent the formation of cracks. Samples with the same electronic substitution level z exhibit a similar resistivity ρ behavior regarding absolute values and temperature dependency (Figure 3a). At temperatures exceeding 1000 K the ρ(T) curves align. Like in case of the Seebeck coefficient, this is a consequence of equilibration of the charge-carrier concentration due to the reduction at high temperatures. Below the reduction onset the logarithmic plot against 1/T reveals a linear dependency PQR(S/) ∝ 1/ (Figure 3c). This is in good agreement with the expectations for an adiabatic small polaron hopping transport process:21, 51 S() = QUVW

2XY' Z 9:

(5)

with 9: and as defined above, an activation energy ) ,46 and a transport constant (const) which is explained in detail by Nell et al.51 A comparison of the isothermal electrical resistivities shows that the pentavalently substituted samples tend to be more resistive than the hexavalently substituted at the same z (Figure 3b). Since for the creation of the same number of Mn3+ states double of the concentration of pentavalent dopants compared to hexavalent dopants is necessary, the product 9: × is larger for the latter and consequently a lower resistivity can be expected. Further electronic doping does not decrease the resistivity: The z = 0.16 samples are less conductive up to 400 K and 550 K than the z = 0.08 samples of the Mo-series and W-series, respectively. Likewise, the activation energy ) , according to equation (5), of these samples is (23 meV and 30 meV, respectively) significantly larger than the corresponding ) of the lower substituted samples (~13 ± 2 meV for Mo and W). These activation energies are significantly lower than for other substituted CaMnO3-δ compounds, e.g. Yang et al. reported activation energies between 40 meV and 80 meV.29 The lower values are probably as well due to the better grain connectivity as stated above. Its impact on the activation energies is even more pronounced when compared with our previous study, where we reported activation energies (25-28 meV) by more than a factor of two higher for 0.01 ≤ yW ≤ 0.05 compounds.15 ACS Paragon Plus Environment

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According to the adiabatic small polaron model the highest electrical conductivity is expected at 9: = if half the conductive sites are occupied by charge carriers.51 This corresponds to z = 0.29 for pentavalent substitution and z = 0.37 for hexavalent substitution. The intersect of the zMo,W = 0.08 and and zMo,W = 0.16 curves indicate that at room temperature minimum ρRT(z) for Mo6+ and W6+ is between 0.08 < z > 0.16 and shifts to higher z with increasing T. The deviation of the observed and calculated maximum electrical conductivity is well-known: For instance Schrade et al. observed a minimum in electrical conductivity at z = 0.25 for highly oxygen deficient CaMnO3-δ (maximum in the small polaron hopping model is z = 0.5).26 They explained the decrease in mobility by a decrease in the number Mn-O-Mn bonds with increasing oxygen deficiency δ. The same model is not applicable in our case as the oxygen deficiency is close to δ = 0 within the analyzed temperature region.35 The deviation from the hopping model might as well originate from the formation of trapping states as discussed earlier for the Seebeck coefficient. Alternatively, for Asite substituted CaMnO3-δ Yang et al. claim that reminiscence of charge ordering affects the transport properties also at high temperatures.29 According to Martin et al. this argumentation can be also transferred to the samples in this study as they proved charge ordering also for in B-site substituted CaMnO3-δ at T < RT measurements.52 Trapping states and charge-ordering effects are thermal barriers which agrees with the fact that the resistivity of the z = 0.16 samples at the highest temperatures is lower compared to samples with z < 0.16.



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Figure 3 – The resistivity of CaMn1-xMxO3-δ compounds. (a) The electrical resistivity is plotted as a function of the temperature T, (b) the isothermal electrical resistivity as a function of the nominal electronic substitution level znom and (c) ρ/T as a function of 1/T in a logarithmic scale.

3.4. Thermal Conductivity

Substitution decreases the lattice thermal conductivity κlattice with increasing substitution level most efficiently at low temperatures (Figure 4 top). At room temperature the z = 0.08-0.16 samples show about 40% lower thermal conductivity than the pristine CaMnO3-δ sample due to phonon scattering by mass-difference and point-defects.53 With increasing temperature this deviation becomes minor and at T > 800 K κlattice only differs slightly since Umklapp scattering becomes more crucial in this temperature region.54 According to the Wiedemann-Franz law the electronic thermal conductivity κel of the more heavily substituted compounds is larger due to their lower resistivity. As at high T κlattice is nearly independent of the substitution, the differences in the total thermal conductivity κtotal (κtotal = κlattice + κel) are determined by [0\ . Thus, the highest [\ at high temperatures is found for the highest substitution levels of the Nb5+ and Mo6+ ACS Paragon Plus Environment

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series. Above the stability limit of the orthorhombic phase κlattice rises significantly mostly due to the higher specific heat capacity Cp of the resulting cubic phase. Additionally, the thermal diffusivity d increases as a consequence of the higher crystal symmetry which results in a smaller unit cell. 3.5. Power factor The power factor is the quotient of Seebeck coefficient and electrical resistivity S2/ρ (Figure 4 middle). As a direct consequence of the remarkably low electrical resistivity values the observed power factors in this study are found to be the highest among all the reported calcium manganites (Table 2). ]Y

Considering the comparable small activation energy ) , the exponential term ' ^Z_ in equation (5) only slightly affects S2/ρ, the combination of the equation (3) and (5) reveals a S2/ρ ∝ T-1 dependency. Accordingly, for 0.01 ≤ z ≤ 0.04 a decrease of S2/ρ with increasing T is observed. As shown earlier at higher substitution levels the activation energy ) is increased and subsequently, the exponential term in equation (5) cannot be neglected anymore. As a result, S2/ρ tends to increase with T. Combining the equations for the terms for S from equation (3) and ρ from equation (5) and disregarding any dependencies of the activation energies, geometric factors, mobilities, etc. from the substitution level, it is found: (# G /S) - ∝ PUG (9: /) × 9: ×

(6)

2

Hence, a maximum in S /ρ is expected at z = 0.06 and z = 0.07 for penta- and hexavalent substitution, respectively (Figure 4 inset in the middle). The highest power factors S2/ρ are observed for zTa = 0.04 and zW = 0.04 with S2/ρ ≈ 5 µW/K2·cm at room temperature. Significantly higher substituted samples (z = 0.16) exhibit the lowest power factors. Both observations are in accordance with the theoretical considerations. The comparably small S2/ρ for at z = 0.08 and that the z = 0.01 samples perform among the best samples, indicates that in the real system (S2/ρ(z))max is shifted towards lower z as with increasing substitution level the number of localized electrons is increased. The decay in S2/ρ at T > 1000 K suits the concept again as the reduction results in a higher electron doping, which has a negative impact on S2/ρ. In



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contrast, this “self-doping” makes the pristine sample the best performing at T = 1120 K (S2/ρ = 3.70 µW/K2·cm). A-site

ρRT

SRT

S2/ρRT

[mΩ·cm]

[µV/K]

[µW/cm·K2]

Nb-0.01

13.7

-239

4.37

Mo-0.02

4.26

-176

4.07

B-site

Ta-0.04

4.25

-143

4.24

W-0.02

4.64

-176

4.23

Nb-0.02

19

-190

1.90

Bocher et al.45

Mo-0.04

6.5

-120

2.22

Pi et al.43

Ru-0.02

10

-170

2.89

Zhou et al.42

W-0.01

9.8

-180

3.5

Kabir et al.41

W-0.02

10.2

-130

1.8

Kabir et al.41

16.9

-114

0.77

Wang et al.55

7

-84

1.01

Wang et al.55

Ce-0.05

10.6

-81

0.62

Wang et al.55

Yb-0.1

4

-80

1.60

Flahaut et al.56

Dy-0.02

22

-180

1.47

Liu et al.57

Dy-0.1

5

-87

1.45

Wang et al. 58

Pr-0.08

6

-110

2.40

Zhang et al.59

Dy-0.02 Y-0.02

0.44

-130

3.8

Zhu et al.60

Dy-0.02 Sm-0.02

5.5

-145

3.8

Zhu et al.61

22

-182

1.49

Bhaskar et al.62

La-0.08 Y-0.1

Bi-0.02

Si-0.02

Y-0.1 Fe-0.05 11.4 -118 1.2 Le Thanh et al.63 2 Table 2 – Best power factors S /ρ at room temperature with corresponding ρ and S from this study in comparison with representative publications. The best performing samples are presented from literatures on CaMnO3. An error of at least 10% has to be considered. To our knowledge there are no S2/ρ values exceeding the ones in our study.

3.6. Figure-of-Merit (ZT) The dimensionless figure-of-merit ZT was calculated in the temperature range 320 K < T < 1277 K. ZT increases with the temperature until T reaches the upper stability limit of the orthorhombic phase. Depending on z the stability limit is at 1000 K or higher.35 Almost linear increase of the ZT-curves is a consequence of low electrical resistivity due to the improved sintering procedure. The z = 0.04 samples with the substituents from the 6th period (Ta, W) exhibit the best ZT values originated from their high power factors. With peak values of ZTTa = 0.21 and ZTW = 0.20 at 1160 K they are among the best thermoelectric CaMnO3-δ based ceramics15, 19, 58, 60-61. Although the highest substituted samples (z = 0.16) exhibit the most attractive thermal conductivities, due to the low thermoelectric power factors their maximum ZT values reaches only ~0.10. The thermoelectric performance of the pristine CaMnO3-δ sample ACS Paragon Plus Environment

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is strongly influenced by the oxygen deficiency at high temperatures.15 Above 600 K it outperforms the z = 0.16 samples and at 1160 K it shows the third best peak performance with ZTpristine = 0.19. All the other samples exhibit almost identical performances and the different substitution levels only exhibits minor impact on this combined thermoelectric property.

Figure 4 – Total and lattice thermal conductivity (top), power factor (middle), and ZT (bottom) of CaMn1-xMxO3-δ compounds.

IV.

CONCLUSION

Within this study we are reporting room temperature (RT) power factors for calcium manganites outperforming the best reported results by 30% or more. The stepwise sintering procedure results in extraordinarily low electrical resistivity values. They are even below reported resistivities of A-site substituted materials. For the application in thermoelectric converters average ZT is more important than peak ZT-values as they work under a temperature gradient.64 Subsequently, the presented top materials (xTa = 0.04 and xW = 0.02) are very attractive for applications in thermoelectric all-oxide converters sustaining



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Page 16 of 25

T > 1000K in air as they exhibit comparably high room temperature ZT values (ZT ≈ 0.04), a linear increase of ZT, and peak values (ZT > 0.2) ranking them among the best performing oxides. Resistivity and Seebeck coefficient data confirm that the electronic transport can be explained by the small adiabatic polaron hopping model. Nevertheless, with increasing substitution level the number of Jahn-Teller active Mn3+-ions increases and the applied model indicates that the number of itinerant charge carriers does not increase to the same extend. This concurs with an over-proportional stretching of the crystal lattice along the b-axis. The formation of bands from the lowered z2 orbitals below the Fermi level act as trapping states and evolve charge-ordering of the unpaired spins which can originate the decreasing efficiency of electronic doping with increasing substitution level.33 Accordingly, the best power-factors are found for substitutions level z = 0.04 slightly below the theoretical maximum (z = 0.06 or 0.07). Aiming on high power-factors a further increase of the charge-carrier concentration is not advised. ACKNOWLEDGEMENT The present work was financially supported by Competence Centre Energy and Mobility (HITTEC Project), the Swiss Federal Office of Energy (BfE), and Empa. The authors also thank Gion Pirovino for his help synthesizing the powders. REFERENCES

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