Enhanced thermoelectric performance in Ca-substituted Sr3SnO

Accepted Manuscript Enhanced thermoelectric performance in Ca-substituted Sr3SnO Enamul Haque, M. Anwar Hossain PII:

S0022-3697(18)31013-8

DOI:

10.1016/j.jpcs.2018.08.010

Reference:

PCS 8686

To appear in:

Journal of Physics and Chemistry of Solids

Received Date: 18 April 2018 Revised Date:

9 August 2018

Accepted Date: 10 August 2018

Please cite this article as: E. Haque, M.A. Hossain, Enhanced thermoelectric performance in Casubstituted Sr3SnO, Journal of Physics and Chemistry of Solids (2018), doi: 10.1016/j.jpcs.2018.08.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Enhanced thermoelectric performance in Ca-substituted Sr3SnO Enamul Haque and M. Anwar Hossain* Department of Physics, Mawlana Bhashani Science and Technology University, Santosh, Tangail – 1902, Bangladesh

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Corresponding author: M. Anwar Hossain ([email protected])

Abstract

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First-principles calculations were performed to study the electronic and thermoelectric transport properties of Ca-substituted Sr3SnO (Sr3−xCaxSnO, 3≥x≥0). The effects of Ca substitution on the

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bandgap are studied, and detailed mechanisms are proposed to explain the results obtained. We found that an increase of the hole concentration reduces the effective mass and the Seebeck coefficient of Ca-substituted Sr3SnO. The optimum hole concentration was obtained for Sr2CaSnO, and the corresponding maximum Seebeck coefficient of 219 µV/K was obtained at 500 K. The electrical conductivity of Sr3SnO and its alloys has a semiconducting nature, which contradicts experimental results for Ca3SnO. We found that Ca-deficient Ca3SnO exhibits

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metallic conductivity, and this removes the contradiction with our results. The lattice thermal conductivities (κl) of Sr3SnO and Ca3SnO were calculated by use of both the Perdew-BurkeErnzerhof functional and the GW functional. The total thermal conductivity for Sr3SnO and Ca3SnO at 300 K is 3.03 and 2.06 W/(m K), respectively. The figure of merit (ZT) for Sr2CaSnO

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at 500 K is 0.6, making it promising for thermoelectric applications.

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Keywords: Electronic structure; Bandgap; Electrical conductivity; Seebeck coefficient; Carrier relaxation time; Lattice thermal conductivity

1.

Introduction

Antiperovskite Dirac-metal oxides (ADMOs) have attracted much attention because of their unusual superconductivity [1–3], topological behavior [4], ferromagnetic properties [5–9], and good thermoelectric transport properties [10–13]. In these oxides, the positions of the metal ions and the oxygen ions are reversed, and thus the metal ions have negative valence states [12]. Sr3SnO (SSO), an ADMO, has been experimentally found to exhibit topological

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superconductivity with a superconducting transition temperature of approximately 5 K due to Sr deficiency [1, 3]. However, many theoretical studies reported that SSO exhibits topological insulating and semiconducting behavior due to the band inversion between two quartets [4]. SSO with Si (001) is a dilute magnetic semiconductor [5, 7]. The most recent theoretical studies on

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A3SnO (A=Ca, Sr, Ba) have found that these ADMOs have good thermoelectric properties and are suitable for thermoelectric applications [11]. Ca3SnO (CSO) has been experimentally found to possess a high Seebeck coefficient, approaching about 100 µV/K at room temperature [10]. Since doping can significantly improve the thermoelectric performance by reducing thermal

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conductivity and increasing the Seebeck coefficient [14–17], it is reasonable to study the thermoelectric properties of Ca-substituted SSO. A thermoelectric device requires high-

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performance thermoelectric materials to convert heat energy into electricity efficiently. The performance of thermoelectric materials at a given temperature T can be calculated by use of the equation [18]
 =

  

 

, where S, σ, , and  are the Seebeck coefficient, electrical

conductivity, electronic thermal conductivity, and lattice thermal conductivity, respectively. Thus, ZT will be high for a material possessing high thermopower and low thermal conductivity. However, it is very difficult to optimize these parameters simultaneously. A recent experimental

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study on polycrystalline CSO revealed that the thermal conductivity of CSO is relatively low— 1.7 W/(m K) at 290 K—and that CSO shows metallic conductivity, but it was not mentioned why CSO shows metallic conductivity [10]. Theoretical studies revealed that CSO is a topological insulator [4, 11]. Therefore, it is important to study the electrical conductivity of

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CSO to find the reason for the contradiction between experimental and theoretical results. SSO is a cubic crystal with experimental lattice parameter a=5.1394 Å and space group 3 (no.

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221). The Wyckoff positions for the Sr, Sn, and O atoms are 3c (0, 0.5, 0.5), 1a (0, 0, 0), and 1b (0.5, 0.5, 0.5), respectively [19, 20]. In this article, we report the electronic and thermoelectric transport properties of Ca-substituted SSO (Sr3−xCaxSnO, 3≥x≥0) by using first-principles calculations. We also study the effect of Ca deficiency on the thermoelectric transport properties of CSO. We find that the thermoelectric performance is significantly improved by Ca substitution in SSO. We also find that CSO shows metallic conductivity for small Ca deficiency as experimentally observed [10]. Moreover, the GW method provides reasonably accurate lattice thermal conductivity in comparison with the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) method.

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2.

Computational details

Electronic structure was studied by use of a full potential augmented linearized plane wave method in WIEN2k [21]. The structural optimization was performed, and the muffin-tin radii

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were 2.3, 2.5, 2.3, and 2.2 bohr for Sr, Sn, O, and Ca, respectively. For good convergence of the basis set, the kinetic energy cutoff (RKmax) was set to 7.0. To overcome the underestimation of the bandgap (PBE-GGA) [22], the Tran-Blaha–modified Becke-Johnson (TB-mBJ) potential [23, 24] was used for electronic and transport calculations. For self-consistent field (SCF) and density

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of states (DOS) calculations and band structure calculations, 15 × 15 × 15 and 21 × 21 × 21 kpoints were used, respectively. To generate the required data for the calculation of the transport

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properties, the SCF calculation was performed again by use of 47 × 47 × 47 k-points. The transport properties were calculated by our the solving semiclassical Boltzmann transport equation as implemented in BoltzTraP [25]. BoltzTraP calculates the electron transport parameters within the constant relaxation time approximation. The temperature-dependent values of the transport parameters were taken at the Fermi level of 0 K. The lattice thermal conductivity was calculated by our solving the linearized phonon Boltzmann transport equation with the finite

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displacement approach [26] as implemented in Phono3py [27]. In this code, the single-mode relaxation time approximation is used. This calculation was performed by our creating a 2 × 2 × 2 supercell that contains 40 atoms and simultanously displacing one by one atom about 0.06 Å from its original position. To calculate the second-order harmonic and third-order

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anharmonic interatomic force constants (IFCs), the atomic forces for each atomic displacement were calculated by use of the plane wave pseudopotential method and the PBE-GGA functional [28, 29] in Quantum Espresso [30]. For this, the convergence criteria were set to 10 and the

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criterion of force convergence was set to10 eV/Å. A kinetic energy cutoff of 372 eV for wavefunctions and 1088 eV for charge density was used. In the IFC calculation, an ultrasoft pseudopotential (generated by PS library 1.00) was used. Finally, lattice thermal conductivity was calculated by our performing BZ integration in the q-space with a 21 × 21 × 21 mesh and the equation =



# $

∑' &' (' ⊗ (' * , where V is the volume of the unit cell, ( is the group

velocity, τ is the single-mode relaxation time for phonon mode λ, and &' is the mode-dependent phonon heat capacity. The relaxation time (τ) was calculated from the self-energy (Γ(ω)) as

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found in the previously described calculation by use of * =



+,(.)

. This method has successfully

predicted the lattice thermal conductivity of many compounds [31–34]. Since the PBE-GGA method underestimates the lattice thermal conductivity [32], the lattice thermal conductivity was

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also calculated by use of the GW method [35–39]. For this, we used projector augmented wave GW pseudopotentials [40] (provided in VASP 5.4.4) and kept the other settings the same to

3.

Result and discussion

3.1.

Structural optimization

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calculate second-order harmonic and IFCs in VASP [41–43].

We created a 2 × 2 × 2 supercell containg 40 atoms as illustrated in Fig. 1b. Then we replaced

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one Sr atom with one Ca atom (x=0.125) and applied the symmetry operation. The symmetry operation reduced the number of nonequivalent atoms to 13 and lowered the symmetry to space group 4/mmm (no. 123). We optimized the geometry to find the equilibrium configuration. By application of the same procedure for x=0.25, the space group was found to be 4/mmm, for

x=0.375 0.5, 0.62, 1, and 2, it was found to be mmm (no. 47), and for x=3, it was found to be

3 (no. 221). The optimized lattice parameters for x=3 (i.e., CSO) was found to be 4.8373

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Å, in excellent agreement with the experimental value of 4.827Å [20]. Since the PBE-GGA functional is sufficient for structural optimization, geometry optimization was performed with this functional. By using the equilibrium configuration, we performed all other calculations (with

next sections.

Electronic structure

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3.2.

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the TB-mBJ functional, only electronic and electron transport properties) as mentioned in the

The calculated energy band structures of Sr3−xCaxSnO are illustrated in Fig. 2. For x=0, our calculated band structure is consistent with other calculations [1, 4, 44]. However, the Fermi level is slightly (less than 0.05 eV) lower than that obtained by inclusion of spin-orbit coupling [4, 44]. The bandgap of SSO (i.e., x=0) calculated with the TB-mBJ functional is consistent with other theoretical results [11]. Stoichiometric SSO has been found experimentally to exhibit semiconducting resistivity [1, 5, 7]. The “Dirac cone” exists along the Γ-X direction with a direct bandgap of 0.22 eV as shown in Fig. 2a. When one Sr atom is replaced by one Ca atom (x=0.125), the Fermi level significantly shifts to lower energy and the parabolic nature of the

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conduction bands increases with increasing bandgap as shown in Fig. 2b. This behavior is consistent with the behavior of other semiconducting materials [45–49]. To take account of this effect further, we calculated the effective mass of the conduction band minima and valence band maxima by taking the second E-K derivative using the finite difference method. Fonari and

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Sutton [50] describe the calculation details for the effective mass. The calculated results are listed in Table 1. We see that because of Ca substitution (x=0.125), the effective mass of holes increases with the bandgap. When the Ca concentration in Sr3−xCaxSnO increases, the conduction band and the valence band become more parabolic, and maximum parabolicity is obtained for

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x=0.5. At this concentration, we see that the effective mass of electrons significantly increases by reducing the effective mass of holes. For x=0.375 and 0.625, the bandgap decreases

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comparatively to the decrease for x=0.5, 0.25, and 0.125 as does the effective mass of the electrons. The maximum hole effective mass is obtained for x=1.

The hole effective mass of CSO (1.78) is reasonably close to the value (1.96) obtained from the experimental data [10]. The DOS of SSO and its alloys are illustrated in Fig. 3. The DOS is larger for x=0.125, 0.375, and 0.625 than for other concentrations. However, the DOS for x=0.5 is also comparable to the DOS for these concentrations at the Fermi level. We see that the main

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features of the DOS after Ca substitution remain almost the same, and only the Fermi level shifts, findings that are consistent with our band structure calculation. For clarification, the Fermi energy and bandgap at different Ca concentrations are illustrated in the inset in Fig. 3. We see that the Fermi energy of CSO is much lower than that of SSO, while the bandgap of CSO is

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greater than that of SSO. The calculated projected DOS of SSO, CSO, and Sr2CaSnO are shown in Fig. 4. The peak around -1 eV in SSO arises from the strong hybridization between Sr 4d and

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Sn 5p orbitals, while in CSO it is due to Ca 3d and Sn 5p orbitals. The corresponding peak at positive energy comes from the antibonding combinations. The oxygen does not contribute to the DOS around the Fermi level. In the projected DOS of Sr2CaSnO, we see that Sr 4d and Ca 3d orbitals have almost equal contributions to the DOS. The difference of the projected DOS of the Sr 4d and Ca 3d orbitals is due to the energy difference between the Sr 4d and Ca 3d orbitals. The bandgap of SSO is caused by the mixing of Sr 4d and Sn 5p orbitals. In CSO, the bandgap is caused by Ca 3d and Sn 5p states. However, the mixing of Sr 4d and Ca 3d orbitals in Sr2CaSnO may be responsible for the decrease of the Fermi energy and hence the increase of the bandgap. Since both Ca and Sr have equal numbers of valence electrons, the change of electronic

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properties is brought about by the mixing of Sr 4d and Ca 3d states; that is, the difference in energy of 4d and 3d orbitals.

3.3.

Phonon transport properties

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The phonon relaxation time of SSO and CSO decreases with increasing temperature because of the increase of phonon scattering as shown in Fig. 5a. At low temperature, the phonon relaxation time is long as scattering is significantly low. The theoretical Debye temperature (12 ) of SSO is

276.1 K [2]; therefore, the scattering of electrons above 12 should be almost entirely due to

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phonons as acoustic phonon scattering is dominant in this temperature range [51, 52]. In this temperature range, the relaxation time shows  3/+ dependence [53] as shown in the inset in Fig. 5a. Such a linear dependence implies that acoustic phonon scattering is a predominant process in

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these antiperovskites. González-Romero and Antonelli [54] suggested that the  3/+ dependence may be used to find the relaxation time at different temperatures. Our calculated relaxation times for SSO and CSO are in a reasonable range for typical thermoelectric materials and similarly exhibit a temperature dependence [55, 56]. The calculated lattice thermal conductivities (κl) of SSO and CSO are shown in Fig. 5b. The lattice thermal conductivity calculated with the PBE

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method is small for both compounds, 0.268 and 0.257 W/(m K) at 300 K for SSO and CSO, respectively. The experimental thermal conductivity of CSO is 1.7 W/(m K) at 290 K, and the lattice contribution is predominant [10]. Therefore, the PBE method underestimates the lattice thermal conductivity of CSO. To overcome this underestimation, we calculated it using the GW

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method (Fig. 5b), and κl for both compounds is much larger than that obtained by the PBE method. For SSO and CSO, κl is 1.43 and 1.3 W/(m K), respectively, values about five times

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larger than those obtained with the PBE method. Thus, the lattice thermal conductivity of CSO is consistent with the observation that the contributions of phonons to the thermal conductivity is predominant up to 380 K, as illustrated in Fig. 5b. The Ca substitution should induce lattice distortions by shortening the mean free path of phonons. Thus, the lattice thermal conductivity should be decreased by Ca substitution [57, 58], and hence we did not perform the calculation for other Ca-substituted SSO alloys.

3.4.

Transport properties

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BoltzTraP uses the constant relaxation time approximation to calculate the transport parameters. Thus, we need to evaluate the carrier relaxation time to find the real values of these quantities. Since the conduction is mainly due to holes, we used the hole effective mass calculated earlier. We considered that the conduction carriers are predominantly scattered by acoustic phonons. We

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also considered the pure longitudinal wave along the (100) direction and the elastic constant of SSO from our previous study [2]. The carrier relaxation time can be calculated by [59]

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*4567

3/+ /+  2 = ћ ?@@ =8 ∗ < , … … … … (1) +  :;  3A45

where cii is the direction-dependent cubic elastic constant and Dac is the deformation potential EF

EG

, where E is the change of band energy with the change of lattice

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defined as A45 = D

parameter (a) caused by the applied strain. We calculated E as the change of the minimum conduction band energy and maximum valence band energy caused by the applied strain. For more details of the calculation of these parameters, see [60–62]. The calculated carrier relaxation times are illustrated in Fig. 6.

The transport properties of a material depend mainly on its carrier concentration. For good

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thermoelectric materials, the optimum carrier concentration is required [63–65]. The change of carrier concentration at 300 K with Ca concentration (x) is illustrated in Fig. 7a. The maximum carrier concentration (3.471 × 10I cm3 ) is obtained for x=0.5 and the minimum (0.859 ×

10I cm3 ) is obtained for x=1. The carrier concentration for x=3 (i.e., CSO; 1.37 ×

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10I cm3 ) is in reasonable agreement with the experimental value (1.43 × 10I cm3 ) [10].

However, CSO exhibits metallic behavior because of Ca deficiency, and we will clarify this later

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in this section. Therefore, the experimental carrier concentration should be larger than that in our semiconducting pure single-crystal CSO. The variation of the Seebeck coefficient with Ca concentration (x) is illustrated in Fig. 7b. The maximum Seebeck coefficient (S) is obtained for x=1.0, for which the carrier concentration is a minimum. This indicates that the thermoelectric performance would be significantly increased by reduction of the carrier concentration. Because of the increase of carrier concentration, the Seebeck coefficient is significantly reduced at x=0.5. The positive Seebeck coefficient (S) implies that the holes are the predominant carriers for these compounds. This is consistent with the experimental observation for CSO [10] and also with our calculated effective mass (m*). Such a high value of the effective mass with a low carrier

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concentration normally leads to a high Seebeck coefficient [66–70]. A high effective mass implies low carrier mobility and a high Seebeck coefficient, although the power factor may be reduced [71]. The calculated transport parameters of Ca-substituted SSO alloys at different temperatures are illustrated in Fig. 8. For calculation of the temperature dependency, we took the

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values of the transport parameters at constant chemical potential, at which it is equal to a Fermi energy of 0 K, under the consideration that the Fermi level does not significantly change with increase of temperature. The Seebeck coefficient of p-type material can be expressed as NO − NQ 2:; + , … … … … (2) RS RS

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M=

where EC, EF, kB, and qh are the minimum energy of the conduction band, the Fermi level, the

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Boltzmann constant, and the hole charge, respectively, at absolute temperature. Because of the increase of electron concentration in semiconductors, the Fermi level generally shifts toward the conduction band as the temperature increases. For such a shift of the Fermi level, the energy difference between the minima of the conduction band and the Fermi level (EC−EF) becomes smaller, and thus Eq. (2) says that the minimum Seebeck coefficient will result. When the temperature is increased, the Fermi level shifts toward the middle of the bandgap, and thus the

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energy difference between the minima of the conduction band and the Fermi level increases, resulting in an increase of the absolute Seebeck coefficient. Thus, the Seebeck coefficient for alloys of SSO and CSO increases with increasing temperature as shown in Fig. 8a. However, the Seebeck coefficient of SSO increases up to 350 K and then it become almost constant up to 500

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K. Therefore, for the temperature range from 350 to 500 K, the Seebeck coefficient is constant. The maximum Seebeck coefficient is 219 µV/K at 500 K with Ca concentration of x=1.0. The

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reason for the study of transport properties up to 500 K is that SSO changes its phase from cubic to orthorhombic above 500 K [20]. The electrical conductivity of SSO and its alloys increases with increasing temperature, implying a semiconducting nature. The electrical conductivity for x=0.25 increases very slowly with temperature because of the low carrier concentration (see Fig. 7a). The relaxation time for SSO at 280 K is 5.85 × 10 s, and the corresponding calculated electrical resistivity is 1.08 × 10V Ω m, which is in reasonable agreement with the experimental value of 6.750 × 10 Ω m

measured on polycrystalline chunks. The electronic part of the thermal conductivity increases

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with temperature as usual because of the increase of electrical conductivity, as shown in Fig. 8c. The calculated power factor at different temperatures is illustrated in Fig. 8d. The power factor increases with increasing temperature as expected. The minimum power factor is obtained for x=0.5 because of the low value of the Seebeck coefficient. The thermoelectric figure of merit ZT

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should also be small because of the high electronic thermal conductivity. The question may arise as to why for CSO our calculated electrical conductivity shows semiconducting behavior whereas the experimental sample [10] shows a metallic nature. To find the reason for this, we studied the effect of Ca, Sn, and O deficiency on electrical conductivity. Because of Sn

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deficiency, CSO becomes an n-type material, which is not consistent with the experimental observation. Because of the O vacancy, the material exhibits metallic conductivity but a very

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small Seebeck coefficient. However, Ca deficiency gives rise to metallic conductivity, and also a large Seebeck coefficient as compared with O vacancy. The calculated Seebeck coefficient and electrical conductivity of CSO with Ca deficiency (12.5%, i.e., Ca2.875SnO) are shown in Fig. 9. Our calculated S and σ/τ show a similar trend as the experimentally observed S and σ for CSO [10]. The electrical resistivity at 280 K is 1.98 × 10V Ω m, which agrees fairly well with the

experimental value of resistivity for a polycrystalline sample of 6.348 × 10V Ω m [10].

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Therefore, it is important to synthesize pure CSO to obtain high thermoelectric performance. The calculated total thermal conductivity of SSO and CSO is presented in Fig. 10. The total thermal conductivity decreases with increasing temperature, as the lattice contribution is large. However, the total thermal conductivity obtained by use of the PBE method is much smaller than

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that obtained from the GW method. The total thermal conductivity (κ) of CSO of 2.05 W/(m K) is reasonably close to the experimental value of 1.707 W/(m K). Our calculated value for a single

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crystal is slightly larger because the experimental measurement was performed on a polycrystalline sample, in which phonon scattering is less because of the grain boundary than in a single crystal. We found that κ shows T-1 dependence for both SSO and CSO as experimentally observed in CSO [10]. The κ values for SSO and CSO are relatively larger than those for glasses and amorphous alloys—0.5–1 W/(m K) [72, 73]—but are relatively smaller than for inorganic compounds [74–76]. Low thermal conductivity is essential and a prerequisite for a high thermoelectric figure of merit (ZT).

3.5.

Figure of merit

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The dimensionless thermoelectric figure of merit (ZT) at different temperatures of SSO and its alloys is presented in Fig. 11. ZT increases with increasing temperature, and the maximum value for SSO is 0.46 at 500 K. As the Ca concentration, x, increases from x=0.125, ZT decreases. However, surprisingly ZT increases for x=0.375 because of the low carrier concentration (high

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Seebeck coefficient). When 33.33% Sr is replaced by Ca, we obtained a low carrier concentration and a high Seebeck coefficient, and this corresponds to the maximum ZT. The maximum ZT obtained (0.6) is 1.3 times higher than that of a pure SSO crystal. Further experimental study is required to confirm the optimum carrier concentration and hence high

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thermoelectric performance, remembering that a pure SSO crystal is the essential criterion for

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high ZT in these compounds.

Conclusions

In summary, we have presented a comprehensive set of first-principles calculations of the electronic and thermoelectric transport properties of Ca-substituted SSO. We found that the Fermi level shifts to lower energy because of Ca substitution. The maximum bandgap, 0.62 eV, was obtained for x=0.5, and the corresponding effective mass of electrons is also a maximum for

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x=0.5. The minimum hole effective mass was obtained for x=0.375. We found that in the case of SSO, the Seebeck coefficient and the effective mass of holes are significantly reduced because of the increase of hole concentration. The optimum hole concentration was obtained for x=1.0, and the corresponding Seebeck coefficient was maximum. The maximum Seebeck coefficient, 219

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µV/K, was obtained at 500 K. The electrical conductivity of SSO and its alloys has a semiconducting nature, which contradicts experimental observations for CSO. To overcome this,

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we studied the Seebeck coefficient and electrical conductivity of defective CSO. We found that because of Ca deficiency, CSO shows metallic conductivity, and this removes this contradiction with our theoretical results. This reveals the importance of synthesizing pure CSO to obtain high thermoelectric performance. The lattice thermal conductivity (κl) of SSO and CSO was calculated by use of both the PBE functional and the GW functional. The lattice thermal conductivity obtained with the PBE functional largely underestimates the experimental value for CSO. The total thermal conductivity (with κl obtained with the GW functional) at 300 K is 3.03 and 2.05 W/(m K) for SSO and CSO, respectively, in excellent agreement with the experimental value of 1.707 W/(m K) for CSO. The maximum thermoelectric figure of merit (ZT) is 0.6 at 500

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K for x=1.0, which is 1.30 times larger than that for pristine SSO (0.46 at 500 K). We conclude that the thermoelectric performance in Ca-substituted SSO could be further improved by nanostructuring and grain refinement to reduce the lattice thermal conductivity without affecting

the thermoelectric properties of Ca-substituted SSO.

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Fig. 1. (a) Crystal structure of Sr3SnO and (b) the 2 × 2 × 2 supercell structure of Sr3SnO. These

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diagrams were sketched with the program XCrysDen [38].

Fig. 2. Energy band structure of (a) Sr3SnO and (b–i) its alloys Sr3−xCaxSnO. The dashed line at zero energy represents the Fermi level. For x=0.125, 0.25, 0.375, 0.5, and 0.62, the band structures are plotted for a 2 × 2 × 2 supercell.

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Fig. 3. Total density of states (DOS) of Sr3−xCaxSnO. The Fermi level is set to zero energy. The inset shows the variations of the Fermi energy and band gap with Ca concentration.

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Fig. 4. Projected density of states of (a–c) Sr3SnO (x=0), (d–f) Ca3SnO (x=3), and (g–j) Sr2CaSnO (x=1). The zero energy represents the Fermi level.

Fig. 5. The calculated (a) relaxation time from the phonon self-energy obtained with the PerdewBurke-Ernzerhof (PBE) functional and (b) lattice thermal conductivity obtained with both the PBE functional and the GW functional. The relaxation time obtained with the GW functional is almost same and thus it is not shown in (a) for clarity.

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Fig. 6. Temperature dependence of the hole relaxation time (*4567 ) of Sr3−xCaxSnO. Fig. 7. (a) Change in carrier concentration with Ca concentration (x) at 300 K, and (b) change in Seebeck coefficient with doping concentration at 300 K and 500 K. Fig. 8. Electronic transport properties of Sr3−xCaxSnO: (a) Seebeck coefficient, (b) electrical

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conductivity (σ/τ), (c) electronic part of the thermal conductivity (κe/τ), and (d) power factor (S2σ).

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Fig. 9. (a) Seebeck coefficient (S) and (b) electrical conductivity (σ/τ) of Ca3SnO with Ca deficiency (12.5%, i.e., Ca2.875SnO). Fig. 10. Total thermal conductivity of (a) Sr3SnO and (b) Ca3SnO obtained with the lattice thermal conductivity obtained through the Perdew-Burke-Ernzerhof (PBE) and GW methods. The experimental data are taken from [10]. Fig. 11. Temperature dependence of the dimensionless thermoelectric figure of merit (ZT) of Sr3−xCaxSnO.

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Table 1. The calculated energy bandgap, effective mass of electrons, and effective mass of holes in the unit of m0, where m0 is the bare electron mass, for different concentrations of Ca in Casubstituted Sr3SnO.

Eg (eV)

x=0.125

0.22 0.37

m* Electrons 0.14 0.694 1.42 1.638

x=0.375

x=0.5

x=0.625

x=1

x=2

x=3

0.49

0.35

0.62

0.33

0.30

0.37

0.32

0.629

0.47

0.75

0.25

0.0101 0.2

0.09

1.802

1.11

0.88

1.37

2.01

1.78

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Holes

x=0.25

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x=0

1.55

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Figure

Fig.1: Crystal structure of (a) Sr3SnO (SSO) and (b) 2 × 2 × 2 supercell structure of Sr3SnO.

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These figures are sketched by using XCrysDen program[38].

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(c) x=0.25

(b) x=0.125

(a) x=0

3

(d) x=0.375

1

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Energy (eV)

2

0 -1

Γ (e) x=0.5

3

X

ΓR

M

(f) x=0.625

1 0 -1 -2 Γ

XR

Γ

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-3 R

(g) x=1

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Energy (eV)

2

Γ

X R

Γ

XR

Γ

X

(i) x=3

(h) x=2

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-3 R

SC

-2

XR

Γ

XR

Γ

XR

Γ

X

Fig. 2: Energy band structure of: (a) Sr3SnO and (b-i) its alloys Sr3-xCaxSnO. The dash line at the

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zero energy represents the Fermi level. For x=0.125, 0.25, 0.375, 0.5, 0.62, the band structures are plotted for 2 × 2 × 2 supercell.

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16

12 10

x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.62 x=1 x=2 x=3

Total DOS

EF Eg

0

1

2

x

3

8

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DOS/eV f.u.

14

0.6 0.5 0.4 0.3 0.2

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EF(Ry), Eg (eV)

18

6

2 0 -3

-2

-1

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4

0

1

2

Energy (eV)

Fig. 3: Total density of states (TDOS) of Sr3-xCaxSnO. The Fermi level is set to zero energy.

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Inset figure shows the variations of Fermi energy and band gap with Ca-concentration.

3

1.6 1.2

(a)

Sr-4d

(b)

Sn-5p

(c)

O-2p

2 0 4 (g) Sr-4d

(i) Sn-5p

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4

3 2 1

1.5 1.0 0.5

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0.0 1.6 1.2 0.8 0.4 0.0 6

x=1

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Density of states (states/eV f.u.)

0.8 0.4

3.2 (d) Ca-3d 2.4 1.6 0.8 0.0 1.6 (e) Sn-5p 1.2 0.8 0.4 0.0 O-2p 8 (f) 6 4 2 0 2.0

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0.0 6

0 3 (h) Ca-3d

2 1 0

-4

-2

0

EP

-6

2

4

2 0

6

Energy (eV)

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(j) O-2p

4

-6

-4

-2 0 2 Energy (eV)

4

6

Fig. 4: Projected density of states of (a-c) Sr3SnO (x=0), (d-f) Ca3SnO (x=3) and (g-j) Sr2CaSnO (x=1). The zero energy represents the Fermi level.

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-3/2

T

-4

(10 )

40

Sr3SnO (PBE)

4

Sr3SnO (GW) Ca3SnO (PBE)

3

Ca3SnO (GW)

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60

Sr3SnO 40 Ca3SnO 30 20 10 0 0.8 1.2 1.6 2.0 2.4

κl (W/m K)

τ (fs)

Sr3SnO Ca3SnO

80

2

1

20 0

0 200

300 T(K)

400

500

100

200

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100

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τ (fs)

(b)

(a)

100

300

400

500

T(K)

Fig. 5: The calculated: (a) relaxation time from phonon self-energy by using PBE functional, and (b) lattice thermal conductivity by using both PBE and GW functional. The relaxation time

140 120

x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.625 x=1 x=2 x=3

80 60

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τacps(fs)

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100

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obtained by GW is almost same and thus it is not shown in the Fig. 5(a) for clarity.

40 20 0

200

250

300

350

400

450

500

T(K)

Fig. 6: Temperature dependent hole ( ) relaxation time of Sr3-xCaxSnO.

4.0

220

2.5 2.0 1.5

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200

3.0

180 160 140

300K 500

120

1.0 0.5 0.0

(b)

100 0.5

1.0

1.5

2.0

2.5

3.0

80 0.0

Ca-concentration (x)

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3.5

240

(a)

S(µV/K)

Carrier concentration (ρh1019/cm3)

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0.5

1.0

1.5

2.0

2.5

3.0

Ca-concentration (x)

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Fig.7: (a) Change in carrier concentration with Ca concentration (x) at 300K, and (b) Seebeck

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coefficient with doping concentration at 300 K and 500 K.

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300

S(µV/K)

250 z

200

(a)

10

z

z

z

z

z

z

z

z

z

z

z

z

z

z

150

z z z z

8 z

6 4

z

100

z z

2

SC

0

20

(d)

x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.62 x=1 x=2 x=3

Z

Z

Z Z Z

2

Z

Z

3

zzzzzzzzzzzzzzzzzzzz 2 z z

Z

5

Z

Z

Z

0

S σ(mW/m K2)

Z

4

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κe/τ(1013 W/m K s)

10

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5

(c)

(b)

z z z z z z z z z z z z z z z z z z z z z

50

15

x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.62 x=1 x=2 x=3

12

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x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.62 x=1 x=2 x=3

σ/τ(1018S/m s)

350

Z

Z

Z

Z

Z

200

Z

Z

Z

300 T(K)

400

500

0 100

200

300

400

500

T(K)

EP

100

Z

Z

1

x=0 x=0.125 x=0.25 x=0.375 x=0.5 x=0.62 x=1 x=2 x=3

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Fig. 8: Electronic transport properties of Sr3-xCaxSnO: (a) Seebeck coefficient, (b) electrical conductivity (σ/τ), (c) electronic part of the thermal conductivity (κe/τ), and (d) power factor (S2σ).

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30

15 10

(b)

11.70 11.65 11.60 11.55 11.50 11.45

5 200

300 T(K)

400

100

500

200

300 T(K)

400

500

SC

100

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20

19

S (µV/K)

σ/τ (10 S/ms)

(a)

25

deficiency (12.5%, i.e., Ca2.875SnO).

5 (a)

(b)

PBE GW

κ(W/m K)

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3

1 200

300

AC C

100

EP

2

T(K)

PBE GW

4

4 κ(W/m K)

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Fig. 9: (a) Seebeck coefficient (S) and (b) electrical conductivity (σ/τ) of Ca3SnO with Ca-

400

Exp.

3

2

1 500

100

200

300

400

500

T(K)

Fig. 10: Total thermal conductivity of (a) Sr3SnO and (b) Ca3SnO by using the lattice thermal conductivity obtained through PBE and GW methods. The experimental data are taken from the reference [10].

0.60

0.30

z

0.15 z

z

z

z

z

z

z

0.00 100

200

z

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ZT

0.45

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x=0 x=0.125 x=0.25 x=0.375 z z z z x=0.5 z z z x=0.62 z z x=1 z z x=2 z x=3 z

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300

400

500

T(K)

AC C

EP

Sr3-xCaxSnO.

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Fig. 11: Temperature dependence of dimensionless thermoelectric figure of merit of

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Highlights •

The effects of Ca substitution on the bandgap are studied, and detailed mechanisms are proposed to explain the results obtained. The electrical conductivity of Sr3SnO and its alloys has a semiconducting nature.

•

A large Seebeck coefficient for Sr2CaSnO of 219 µV/K was obtained at 500 K.

•

The thermoelectric figure of merit (ZT) for Sr2CaSnO at 500 K is 0.6, making it

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promising for thermoelectric applications.

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•