materials Article Enhanced Thermoelectric Properties of Misfit Bi2Sr2-xCaxCo2Oy: Isovalent Substitutions and Selective Phonon Scattering Arindom Chatterjee 1, *, Ananya Banik 2 , Alexandros El Sachat 1 , José Manuel Caicedo Roque 1 , Jessica Padilla-Pantoja 1 , Clivia M. Sotomayor Torres 1,3 , Kanishka Biswas 2 , José Santiso 1 and Emigdio Chavez-Angel 1, * 1 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus Universitat Autonoma de Barcelona (UAB), Bellaterra, 08193 Barcelona, Spain 2 New Chemistry Unit, School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur, Bangalore 06484, India 3 ICREA—Catalan Institute for Research and Advanced Studies, 08010 Barcelona, Spain * Correspondence: arindom.chatterjee@icn2.cat (A.C.); emigdio.chavez@icn2.cat (E.C.-A.) Abstract: Layered Bi-misfit cobaltates, such as Bi2 Sr2 Co2 Oy , are the natural superlattice of an elec- trically insulating rocksalt (RS) type Bi2 Sr2 O4 layer and electrically conducting CoO2 layer, stacked along the crystallographic c-axis. RS and CoO2 layers are related through charge compensation reac- tions (or charge transfer). Therefore, thermoelectric transport properties are affected when doping or substitution is carried out in the RS layer. In this work, we have shown improved thermoelectric properties of spark plasma sintered Bi2 Sr2-x Cax Co2 Oy alloys (x = 0, 0.3 and 0.5). The substitution of Ca atoms affects the thermal properties by introducing point-defect phonon scattering, while the electronic conductivity and thermopower remain unaltered. Keywords: misfit cobaltates; thermoelectric properties; misfit-layer; isovalent substitutions Citation: Chatterjee, A.; Banik, A.; El Sachat, A.; Caicedo Roque, J.M.; Padilla-Pantoja, J.; Sotomayor Torres, C.M.; Biswas, K.; Santiso, J.; 1. Introduction Chavez-Angel, E. Enhanced The search for renewable energy sources and energy recovery methods is an active Thermoelectric Properties of Misfit area of research. Direct conversion of waste heat into electricity using the thermoelectric Bi2 Sr2-x Cax Co2 Oy : Isovalent Seebeck effect has received attention in recent years [1]. High efficiency in a thermoelectric Substitutions and Selective Phonon module requires a high “figure of merit” (zT), which is a balance between power factor and Scattering. Materials 2023, 16, 1413. thermal conductivity (zT = (σS2 )T/k, where σ, S, k, and T are the electronic conductivity, https://doi.org/10.3390/ma16041413 Seebeck coefficient, thermal conductivity, and mean operational temperature, respectively). Academic Editors: Shakeel Ahmad For high TE efficiency, a high zT is mandatory, i.e., a large power factor (PF = σS2 ) and Khandy and Ishtihadah Islam low k are essential elements [2]. Recent studies in layered materials based on bismuth telluride, silicene films, tin selenide, and multilayer structures of dissimilar 2D materials Received: 15 December 2022 have demonstrated zT values above 2 at room temperature [3–6]. However, oxide materials Revised: 3 February 2023 will be an alternative solution for high-temperature thermoelectric application because of Accepted: 6 February 2023 their chemical stability at high temperatures, non-toxicity, and less expensive constituent Published: 8 February 2023 elements [7–11]. Soon after the discovery of a large Seebeck coefficient (~100 µV/K) and relatively high electrical conductivity (~5000 S/cm) in Na0.5 CoO2 (NCO) at room temperature, the Copyright: © 2023 by the authors. layered cobaltates are considered as a promising class of compounds for thermoelectric Licensee MDPI, Basel, Switzerland. energy conversion [12]. Aside from cobaltates, BiCuSeO oxyselenides have also been This article is an open access article identified as potential thermoelectric materials, showing a zT close to 1 [13] and Seebeck distributed under the terms and coefficient around 500 µV/K [14]. The misfit cobaltate [15] Bi2 Sr2 Co2 Oy (BSCO) is a p-type conditions of the Creative Commons thermoelectric material and has shown a figure of merit (zT) > 1 at 1000 K [16]. Attribution (CC BY) license (https:// NCO and BSCO share a common CdI2 -type CoO2 layer in their crystal structures [17]. creativecommons.org/licenses/by/ The CoO2 layers in BSCO are separated by the rocksalt (RS)-type Bi2 Sr2 O4-δ layers. RS and 4.0/). CoO2 layers do not fit along the crystallographic b-axis (because the b parameter of RS Materials 2023, 16, 1413. https://doi.org/10.3390/ma16041413 https://www.mdpi.com/journal/materials Materials 2023, 16, 1413 2 of 12 > b-parameter of CoO2), hence the name misfit [18]. The incommensurate nature of the crystal structure results in the ultralow cross plane [19,20] and low in-plane [21] thermal conductivity, which is one of the key factors responsible for the high zT. It is well known that the CoO2 layer governs the electronic transport properties of misfit cobaltates because the RS layer is electrically insulating in nature [17]. Nevertheless, these two layers are intimately related to each other through charge transfer [22]. Given that NCO and BSCO share common triangular CoO2 layers, their electronic structure near Fermi energy (EF ) are quite similar [23]. At room temperature, σ of BSCO is lower (~330 S/cm) than in NCO, but S remains high for both compounds (100–120 µV/K) [24]. At high Na doping in NCO, σ and S remained very high [25], whereas Pb doping in BSCO also showed improved σ, and hence improved PF [26,27]. However, σ decreased drastically in Bi2 M2 Co2 Oy (M = Ba, Sr and Ca) when Ba was substituted by Sr or Ca [28]. Note that even though the RS layer is electrically insulating, doping or substitution in the RS layer produced significant change in the transport properties. In fact, the electronic band structure near the Fermi energy (EF ) was significantly affected (transfer of spectral weight from the broad itinerant band to an incoherent regime was observed) in Bi2 M2 Co2 Oy (M = Ba, Sr, and Ca) when Ba was replaced by Sr or Ca [23]. Therefore, RS layers provide tunable possibilities to understand the charge transfer mechanism and optimize conditions to achieve the best thermoelectric performance. To this aim, several strategies were employed in the single crystal and polycrystals of BSCO. For example, an improved zT (0.023 at 300 K) was reported in Pb-substituted BSCO single crystals [26]. A different set of single crystals of composition Bi2.3-x Pbx Sr2.6 Co2 Oy (0 ≤ x ≤ 0.44) showed enhanced S and σ upon Pb substitution in the RS layer (PF ~ 9 µW/cm.K2 at 100 K) [27]. Polycrystalline Bi2 Sr2 Co2 Oy showed high-temperature stability and zT ~ 0.2 at 1000 K, however this was very much dependent on the composition [29]. Ca-substituted polycrystalline sintered BSCO prepared by the sol-gel method showed lower zT ~ 0.007 at 300 K [30,31]. Modifying the sintering conditions, zT = 0.05 in BSCO was achieved at 150 K [32]. To the best of our knowledge, high-temperature thermoelectric properties of Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) samples have not been reported yet. In this work, we investigate the temperature dependence (340 < T < 750 K) of the thermoelectric properties of spark plasma sintered (SPS) parent Bi2 Sr2 Co2 Oy and their Bi2 Sr2-x Cax Co2 Oy alloys (x = 0.3 and 0.5). Although isovalent ion substitutions (Sr+2 by Ca+2 ) did not significantly impact the electronic properties, a strong decrease in κ was found. This result reflects the selective phonon scattering that occurred by point defects in the misfit cobaltates, which caused an improved zT ~ 0.02 at 300 K and 0.09 at 740 K in Bi2 Sr2-x Cax Co2 Oy alloys (within x = 0.3 and 0.5). 2. Experimental Methods Synthesis: Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) polycrystalline pellets were syn- thesized by conventional high temperature solid-state reactions [29]. A stoichiometric mixture of Co3 O4 , Bi2 O3 , SrCO3 , and CaCO3 were mixed in an agate mortar to obtain a homogeneous powder. The powder was pressed using a stainless-steel die into a pellet under uniaxial pressure. The pellet was slowly heated up to 1070 K and calcined for 40 h at the same temperature in air and then slowly cooled down to room temperature. The calcined pellet was ground into a fine powder and then pressed again into a pellet in uniaxial pressure for 30 min to achieve dense pellets. Then, the pellets were placed into a tubular furnace and sintered at 1160 K for 20 h at 100 sccm pure oxygen flow. Samples were prepared by the SPS method at 920 K in a uniaxial pressure of 3.1 kN (~40 MPa) to achieve high density (~94.3%) for thermoelectric transport measurement. Characterization: Polycrystalline sample quality and θ-2θ diffraction patterns were checked by X-ray diffraction technique at room temperature using a Malvern-Panalytical X’pert Pro MRD (multipurpose X-ray diffractometer, Malvern, UK) tuned at Cu K-alpha radiation of wavelength 1.54598 Å. Out-of-plane lattice parameters were calculated from Materials 2023, 16, 1413 3 of 12 (005) reflections. X-ray photoelectron spectroscopy (XPS) measurements were carried out at room temperature in order to identify the elements and their oxidation states. The Raman spectra were recorded by a T64000 Raman spectrometer manufactured by HORIBA Jobin Yvon (Chilly-Mazarin, France) in single grating mode with 2400 lines and a spectral resolution better than 0.4 cm−1 . The measurements were performed by focusing a diode laser (532 nm) onto the sample with a 100× microscope objective. The power of the laser was kept as low as possible (~0.5 mW) to avoid any possible damage from self-heating of the samples. Transport properties: The Seebeck effect and electronic conductivity measurements were carried out simultaneously from 350 to 750 K in a LINSEIS instrument (in a 1 atm helium pressure). Thermal diffusivity measurements were carried out in a NETZSCH LFA instrument (with continuous N2 gas flow). Pellets were cut into 2 × 2.5 × 8 mm3 and 6 × 6 × 2 mm3 dimensions for the Seebeck effect and thermal diffusivity measurements, respectively. Thermal conductivity was calculated from the relation, κtotal = DCp d , where D, Cp , and d are thermal diffusivities, specific heat capacity, and density of the pellet, re- spectively. It is important to note that due to the polycrystalline nature of the samples, there are no preferred orientations in the crystal structure. Thus, we did not find anisotropies in the thermal and electronic properties of synthesized samples. The measurement of thermal conductivity is subject to an uncertainty of approximately 5%, which is dependent on the chosen characterization method and the underlying assumptions made in the modeling of thermal properties. The three-omega technique is widely regarded as a highly effective method for determining thermal conductivity, and it has been shown to achieve uncertain- ties below 1% when specific experimental conditions are met [33]. In comparison, the flash method is associated with a relatively low uncertainty of around 3 to 5% for the estimation of thermal diffusivity [34]. 3. Results and Discussion 3.1. Structural and Elementary Characterization Figure 1 depicts the powder X-ray diffraction (XRD) patterns of the Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) samples. The power XRD patterns are similar to the polycrystalline samples synthesized by others [26]. No impurity phases were detected within the detection limit of the diffractometer. A systematic shift of (005) reflection in 2θ position can be observed with increasing Ca content, which indicates that the out-of-plane cell parameters decreases with increasing Ca content. As the ionic radii of Ca+2 ion is smaller than Sr+2 ions, the unit cell undergoes a systematic contraction [35]. The change in the c-parameter upon substitution confirms the incorporation of Ca atom in the BSCO unit cell. To prove the incorporation of calcium in the BSCO lattice, Raman spectra measure- ments were also carried out at room temperature. Figure 2 represents the recorded Raman spectra of Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) samples from 500 to 950 cm−1 at 300 K. Two prominent phonon peaks can be observed for all samples at ~618 cm−1 and ~815 cm−1 . The peaks at 618 cm−1 can be assigned to A1g modes, comparing with the Raman spectra of single crystals of similar composition [19]. The A1g modes represent the out-of-plane vibrational mode of oxygen atom. A slight right shift in the position of Raman peak in Figure 2b can be observed with increasing Ca content. This can be explained by the increase in bond strength of the Ca-O bond, with respect to the Sr-O bond. Element detection and oxidation states of cobalt ions were obtained from XPS, as shown in Figure 3. The overall spectrum contains prominent peaks of Bi, Sr, Ca, Co, and O (see Figure 3a). The high-resolution core level XPS spectrum of Ca-2p is depicted in Figure 3b. As can be seen in Figure 3b, the parent composition did not contain Ca, while the alloys showed prominent peaks of Ca-2p. The high-resolution core level spectrum of Co-2p of Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) compositions is depicted in Figure 3c. The Co-2p spectrum was split into two components—Co 2p3/2 and Co 2p1/2 —due to strong spin-orbit coupling at an intensity ratio of ~2:1. The appearance of the satellite peaks from both parts of the 2p components at higher binding energies to the main peaks indicates the Materials 2023, 16, x FOR PEER REVIEW 4 of 13 Materials 2023, 16, 1413 4 of 12 a 005 presence of mixed valence cobalt ions. Misfit cobaltates showed satellite peaks due to the 003 Intensity (a. u.) Bi Sr1,5Ca0,5Co2Oy presence of Co+3 /Co+4 pair. The line shape of the2 Co-2p core-level spectrum indicates the -112 presence of low-spin (LS) Co+3 ions. Valence band spectrums of the parent and alloys are 004 112 001 002 008 006 009 007 depicted in Figure 3d. They are very similar to those obtained in single crystals [36]. The density of states (DOS) near the Fermi energy (EF ) is dominated by the hybrid molecular Bi2Sr1,7Ca0,3Co2Oy orbitals of Co-3d and O-2p. The sharp peak around 1.5 eV is due to the presence of LS Co+3 2023, 16, x FOR PEER REVIEW 4 of 13 ions (t2g 6 eg 0 ). A small amount of DOS is embedded in the EF ; therefore, the compounds were expected to show metallic behavior in their transport Bi Sr Co O properties. 2 2 2 y a 10 20 30 40 50 60 005 2θ (°) 003 Intensity (a. u.) Bi Sr Ca Co O 2 1,5 0,5 2 y -112 b c 004 112 001 002 14.92 008 006 009 007 Intensity (a. u.) c-parameter (Å) 005 Bi2Sr1,7Ca0,3Co2Oy 14.88 Bi2Sr2Co2Oy 10 20 30 40 50 60 2θ (°) 14.84 b c 29 30 14.92 31 0.0 0.2 0.4 2θ (°) Calcium, % Intensity (a. u.) c-parameter (Å) 005 Figure 1. X-ray diffraction (XRD) patterns. (a) Powder X-ray diffraction patterns of Bi2Sr2-xCaxCo2Oy (x = 0, 0.3 and 0.5) samples, (b) shift of the 005 reflections in 2θ upon substitution, and (c) change of 14.88 the c-parameter with increasing calcium content. To prove the incorporation of calcium in the BSCO lattice, Raman spectra measure- ments were also carried out at room temperature. Figure 2 represents the recorded Raman 14.84 spectra of Bi2Sr2-xCaxCo2Oy (x = 0, 0.3 and 0.5) samples from 500 to 950 cm−1 at 300 K. Two prominent phonon peaks can be observed for all samples at ~ 618 cm−1 and ~ 815 cm−1. The 29 30 31 0.0 0.2 0.4 peaks at 618 cm−1 can be assigned to A1g modes, comparing with the Raman spectra of 2θ (°) Calcium , % represent the out-of-plane vi- single crystals of similar composition [19]. The A1g modes brational Figure 1. X-ray Figuremode diffraction1.(XRD)of oxygen X-ray patterns. atom. diffraction(a) A patterns. (XRD) slight Powder right X-ray (a) shift in patterns Powder diffraction the position X-ray of Bi2of diffraction Raman patterns Sr2-x peak in2-x of Bi2 Sr CaxCo2Oy Figure Cax Co2 Oy 2b can (x = 0, 0.3 and 0.5)(x be observed samples, = 0, 0.3 (b) andshift with 0.5) of increasing the 005(b) samples, Ca reflections content. in 2θ shift of the 005uponThis can be substitution, reflections explained and (c) in 2θ upon by the increase in of change of and (c) change substitution, bond the c-parameter withstrength the of the increasing c-parameter Ca-O calcium with bond, with content. increasing respect calcium to the Sr-O bond. content. To prove the incorporation of calcium in the BSCO lattice, Raman spectra measure- ments were also carried out at room temperature. Figure 2 represents the recorded Raman spectra of Bi2Sr2-xCaxCo2Oy (x = 0, 0.3 and 0.5) samples from 500 to 950 cm−1 at 300 K. Two prominent phonon peaks can be observed for all samples at ~ 618 cm−1 and ~ 815 cm−1. The peaks at 618 cm−1 can be assigned to A1g modes, comparing with the Raman spectra of single crystals of similar composition [19]. The A1g modes represent the out-of-plane vi- brational mode of oxygen atom. A slight right shift in the position of Raman peak in Figure 2b can be observed with increasing Ca content. This can be explained by the increase in bond strength of the Ca-O bond, with respect to the Sr-O bond. Figure 2. (a) Raman spectra of Bi Sr Cax Co2 Oy (x = 0, 0.3 and 0.5) samples at 300 K−1cm−1 . (b) Peak Figure 2. (a) Raman spectra of Bi2Sr2-x2Ca2-x xCo2Oy (x = 0, 0.3 and 0.5) samples at 300 K cm . (b) Peak positions positions of Raman of Raman bandband marked marked with with arrows. arrows. Materials 2023, 16, x2023, Materials FOR 16, PEER REVIEW 1413 8 of 16 5 of 12 Figure 3. X-ray photoelectron spectroscopy. (a) Overview of the XPS spectra of Bi Sr Cax Co2 Oy for Figure 3. X-ray photoelectron spectroscopy. (a) Overview of the XPS spectra of Bi2Sr2-xCax2Co22-x Oy for x = 0 (black=line), x 0 (black line), 0.3 0.3 (blue) and(blue) and 0.5 0.5 (red). (b)(red). (b) High-resolution High-resolution core core level XPS level XPS spectra spectra of Ca-2poffor Ca-2p x = for x = 0 (black line), 0.3 (blue) and 0.5 (red), (c) high-resolution core level XPS of Co-2p 0 (black line), 0.3 (blue) and 0.5 (red), (c) high-resolution core level XPS of Co-2p for x = 0 (black for x = 0 (black line), line), 0.3 (blue) and 0.5 (red).(d) valence band-XPS spectra of Bi2Sr2-xCa 0.3 (blue) and 0.5 (red). (d) valence band-XPS spectra of Bi2 xCo Sr2-x2Oyxfor 2x = 0.3 (black) and Ca Co Oy for x = 0.3 (black) and 0.5 (red) samples. 0.5 (red) samples. 3.2. Thermoelectric TransportTransport 3.2. Thermoelectric Properties Properties Temperature dependence Temperature of S andofσSofand dependence Bi2σ Srof 2-xCa Bi2xCo 2O Sr2-x y (x Ca = 20,O0.3 x Co y (xand = 0,0.5) samples 0.3 and 0.5) samples are depicted in Figure 4. σ is ~90 S/cm at 340 K for the parent composition (see in Figure are depicted in Figure 4. σ is ~90 S/cm at 340 K for the parent composition (see in Figure 4a). 4a). We found that σ decreases linearly with increasing temperature from 340–750 K,K, which We found that σ decreases linearly with increasing temperature from 340–750 which isistypically typicallyobserved observed inin metallic metallic conductors. conductors. This result This resultis consistent is consistent with the the with pre-previous vious valence valenceband XPS band XPSmeasurements, measurements, where wherea small amount a small amount of DOS of DOS waswas found foundnearnear EF EF (see (see Figure 3d). The positive value of S for the parent composition and their alloys indi- Figure 3d). The positive value of S for the parent composition and their alloys indicates the p-type nature of the compounds (Figure 4b). This also points out the presence of Co +3 /Co+4 cates the p-type nature of the compounds (Figure 4b). This also points out the presence of Co+3/Co+4mixed mixedvalence valencestates inin states thetheCoOCoO2 layer. The S reached a value of +108 µV/K for the parent 2 layer. The S reached a value of +108 μV/K for composition and increased linearly the parent composition and increased linearly with with increasing temperature increasing temperatureup to 145 to 145 at 750 K. up µV/K This is a typical metallic-like behavior. μV/K at 750 K. This is a typical metallic-like behavior. vious valence band XPS measurements, where a small amount of DOS was found near EF (see Figure 3d). The positive value of S for the parent composition and their alloys indi- cates the p-type nature of the compounds (Figure 4b). This also points out the presence of Co+3/Co+4 mixed valence states in the CoO2 layer. The S reached a value of +108 μV/K for the parent composition and increased linearly with increasing temperature up to 145 Materials 2023, 16, 1413 6 of 12 μV/K at 750 K. This is a typical metallic-like behavior. Figure 4. Electronic conductivity and thermoelectric Seebeck effect. Temperature dependent (a) electronic conductivity, (c) thermoelectric power, and (e) power factor of Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) samples. Effect of calcium substitution on (b) electronic conductivity and (d) Seebeck coefficient at 330 K. The influence of calcium substitution on the electronic conductivity and Seebeck coefficient of the BSCO lattice is displayed in Figure 4b,d. The conductivity decreases by a small margin (2.2% drop within the range of x = 0–0.5 of Ca substitution) while the Seebeck coefficient increases slightly (3.7% increase within x = 0–0.5). These changes are driven by variations in the concentration of p-type charge carriers caused by Ca2+ substitution for Sr2+ ions, which is isovalent and should not affect carrier concentration. However, the valence of cobalt ions in the CoO2 layer, which controls the carrier concentration, is linked to the misfit ratio in BSCO single crystals, as revealed in the literature [37]. Typically, in standard semiconductors or semimetals, the electronic conductivity and Seebeck coefficient exhibit opposing behavior with doping or substitution, as observed in our samples. However, in Materials 2023, 16, 1413 7 of 12 the literature [37], it was shown that the valence of cobalt ions in the CoO2 layer is related to the misfit ratio in the single crystals of BSCO, as follows; α b vCo = 4 − ; q = RS (1) q bCoO2 where, vCo , α , and q are the valence of cobalt ion, charge of electrically insulating RS layer, and the misfit ratio of bRS to bCoO2 (bRS and bCoO2 are the b-lattice parameters of the rock salt type and CoO2 layer), respectively. We found that the value of “α” remained constant despite isovalent substitutions. Hence, the alteration in “v” “Co” is expected to be minimal due to the substitution of Ca for Ca+2 in Bi2 Sr2-x Cax Co2 Oy , within the range of x = 0.3 to 0.5. This may result from either decreased p-type carrier concentration in the CoO2 layer due to oxygen vacancy formation or minimal change in the misfit ratio. To uncover the dominant factor affecting the lattice parameters, we performed a calculation of the average in-plane lattice parameters of Bi2Sr2-x Cax Co2 Oy (x = 0, 0.3, and 0.5) using X-ray diffraction (XRD) patterns. The results revealed a decrease in the in-plane parameters from 5.036 to 5.026 Å (a contraction of 0.19%) for x = 0–0.5, while the out-of-plane parameters showed a more significant drop from 14.918 to 14.812 Å (a reduction of 0.71%). This indicates that the substitution of Sr2+ ions by Ca2+ ions has a dominant effect on the out-of-plane direction, while the in-plane parameters remain largely unaffected. Since the rock-salt layer is the primary contributor to the unit cell and XRD pattern, we consider the average in-plane parameters as the average b-parameter of the rock-salt layer. This leads us to the conclusion that the substitution of Sr2+ ions by Ca2+ ions does not significantly impact the misfit ratio or the valence of cobalt, as reflected in their transport and thermoelectric properties. It is also unlikely that the misfit ratio changes due to oxygen vacancies, as all of our samples were sintered under the same conditions and with high oxygen flow. The electrical conductivity of the undoped sample exhibits slight fluctuations around 400 K, as depicted in Figure 4a. These variations could be a result of slight fluctuations in the experimental setup. Nevertheless, similar variations are also observed in the k measurements (Figure 5a), indicating a potential correlation between the two. However, we do not know the exact underlying mechanism behind these fluctuations. Moreover, the S in the single crystal [38] and polycrystals [30] of BSCO below 300 K shows an interesting behavior. It increases in the temperature range between 3–150 K and then remains constant above 200 K. The temperature-independent S is an indication of the contribution of narrowband (i.e., incoherent charge carriers) to the thermopower [39]. 0 Due to the triangular distortion in the CoO2 layer, t2g orbital splits into in-plane Co e g and out-of-plane Co a1g orbitals [23]. The states near EF have a1g symmetry, and elec- trons undergo hopping transport in the neighbouring Co a1g states [40]. Therefore, for localized interacting charge carriers (at the high-temperature limit, i.e., when bandwidth, W << thermal energy, kB T), S is governed by the statistical distribution of charge carriers over available sites, given by Heike’s formula [39] as follows;   k c S = − B ln , (2) e 1−c where, kB , e, and c are the Boltzmann constant, electron charge, and the ratio of particles (holes in this case) to sites, respectively. Although the polycrystalline samples in this work did not show any sign of saturation of S above 340 K, a rough estimation of c = 0.22 was obtained from the measured average S = +110 µV/K by using Equation (2). Here, c is directly related to the oxidation state of cobalt. From the framework of Heike’s formula, c can be simplified to the number of charge carriers per unit cell. Therefore, roughly, an oxidation state of +3.22 can be estimated for cobalt, which is slightly less than the reported valence of cobalt in BSCO (of composition Bi2.1 Sr2.15 Co2 O8+δ ) [41]. Although the possibility of spin and orbital degrees of freedom (β) Materials 2023, 16, 1413 8 of 12 was proposed to contribute to the S in misfit cobaltates [42,43], recent reports in the thin films of misfit cobaltates showed that the use of β factor overestimates the measured S at 300 K [44]. The temperature-dependence of the PF of BSCO and their alloys are depicted in Materials 2023, 16, x FOR PEER REVIEW Figure 4c. The σS2 of all the samples are ~1.1 µW/cmK2 at room temperature and8increased of 13 2 to a maximum value ~1.55 µW/cmK at 775 K. Figure 5. Thermal Figure transport 5. Thermal and thermoelectric transport figure of and thermoelectric merit. figure of(a) Thermal merit. conductivity (a) Thermal as a func- as a conductivity tion of temperature, (b) calculated electronic part of the thermal conductivity from the electrical function of temperature, (b) calculated electronic part of the thermal conductivity from the electrical conductivity and Lorentz number by using the Wiedemann-Franz law, (c) subtracted lattice part of conductivity and Lorentz number by using the Wiedemann-Franz law, (c) subtracted lattice part of the thermal conductivity, and (d) temperature dependence of the thermoelectric figure of merit of Bi2Srthe thermal conductivity, and (d) temperature dependence of the thermoelectric figure of merit of 2-xCaxCo2Oy (x = 0, 0.3 and 0.5) samples. Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) samples. Moreover, the S in the single crystal [38] and polycrystals [30] of BSCO below 300 K Figure 5a depicts κ as a function of the temperature of Bi2 Sr2-x Cax Co2 Oy (x = 0, shows an interesting behavior. It increases in the temperature range between 3–150 K and 0.3 and, 0.5) compounds from 340–750 K. The κ of the parent BSCO polycrystalline pellet is then remains constant above 200 K. The temperature-independent S is an indication of the ~ 1.6 W/mK at 340 K, which is lower than the thermal conductivity value reported in contribution of narrowband (i.e., incoherent charge carriers) to the thermopower [39]. Due a single crystal [21]. Moreover, we observe that k exhibits a very weak temperature- to the triangular distortion in the CoO2 layer, t2g orbital splits into in-plane Co e′g and out- dependence. The low κ of the misfit cobaltates is mainly attributed to the phonon scattering of-plane Co a1g orbitals [23]. The states near EF have a1g symmetry, and electrons undergo at the CoO2 and RS interfaces and the highly ordered RS layer [20]. However, the lower hopping transport in the neighbouring Co a1g states [40]. Therefore, for localized interact- κ for polycrystalline samples reflects the important contribution of phonon scattering at ing charge carriers (at the high-temperature limit, i.e., when bandwidth, W << thermal the grain boundaries. In the literature, a large discrepancy in the absolute value of the energy, kBT), S is governed by the statistical distribution of charge carriers over available thermal conductivity of BSCO polycrystals and single crystal is observed, which varies sites,from given by to ~0.8 Heike’s formula ~4 W/mK [39]K. at 300 asThis follows; variation is attributed to the different methods of kB techniques sample preparation [19,27], measurement c [20,21,45], as well as the sintering S = − ln , (2) e 1−c where, kB , e, and c are the Boltzmann constant, electron charge, and the ratio of particles (holes in this case) to sites, respectively. Although the polycrystalline samples in this work did not show any sign of satura- Materials 2023, 16, 1413 9 of 12 process followed before measurements [32]. A comparison of the reported κ at 300 K is presented in Table 1. The temperature-independent nature of κ suggests that the grain boundaries and impurities mainly dominate the phonon scattering in the samples. The measured κ of the parent Bi2 Sr2 Co2 Oy at 340 K is comparable with previous reports in polycrystalline samples [29,32] prepared by similar high-temperature solid state reactions and sol-gel methods, respectively. Table 1. Comparison of the measured thermal conductivity of Bi2 Sr2 Co2 Oy polycrystalline samples with the reported values in the literature. Sintering Method of Composition Crystallinity Method of Synthesis κ (W/mK) T (K) Reference Method Measurement 4 probe method Diao, et al. Bi2 Sr2 Co2 Oy Single crystal Floating zone technique 1.8 300 - in PPMS [45] Sintered precursor (SP) Funahashi, et al. Bi2 Sr2 Co2 Oy Whisker 2.2 (in-plane) 300 - Diffusivity method [16] traveling-solvent 2.0 (b-axis) Bi2 Sr2 Co2 Oy Single crystal 300 - Herman method Satake, et al. [21] floating-zone method 2.4 (a-axis) Time domain Bi2 Sr2 Co2 Oy Single crystal Flux method 0.24 (ab-plane) 300 - thermore- Li, et al. [19] flectance 0.45 (along traveling-solvent- a-axis) Steady state Bi2-x Pbx Sr2 Co2 Oy Single crystal floating-zone 300 - Terasaki, et al. [20] 3.0 (along b & method technique c-axes) Closed cycle 4.4 (x = 0) optical floating- refrigerator Bi2-x Pbx Sr2 Co2 Oy Single crystal 3.0 (x = 0.35) 300 - Hsu, et al. [26] zone method (direct heat 2.8 (x = 0.55) pulse) Solid state heat Sintered at 1113 Funahashi, et al. Bi2 Sr2 Co2 Oy Polycrystalline 0.8–1.4 400 Laser flash treatment K in air [29] 3.5 (x = 0) Sintered at 4 probe method Yin, et al. Bi2 Sr2-x Cax Co2 Oy Polycrystalline Sol-gel 2.0 (x = 0.3) 300 1073 K in PPMS [30,31] 2.8 (x = 0.5) 1.8 (0 Tesla) high magnetic 4 probe method Bi2 Sr2 Co2 Oy Polycrystalline Sol-gel 1.6 (4 Tesla) 300 Huang, et al. [32] field sintering in PPMS 1.5 (8 Tesla) 1.6 (x = 0) Solid state reactions at Spark plasma Bi2 Sr2-x Cax Co2 Oy polycrystalline 1.2 (x = 0.3) 340 Laser flash This work high temperature sintered 1.3 (x = 0.5) A drop in thermal conductivity (κ) from 1.6 to 1.2 W/mK was observed at 340 K due to the substitution of Sr atoms with Ca atoms, linked to changes in the crystal structure. Despite typical phonon–phonon scattering in thin film semiconductors at high tempera- tures [46,47], the polycrystalline nature of the samples limits phonon MFP at grain bound- aries, resulting in temperature-independent κ. The addition of dopants with varying ionic radii also reduces thermal conductivity through impurity scattering. It is well known that the measured κ consist of two different parts; one is the electronic part (κel ) and the other the lattice part (κLatt ). The κel is directly proportional to the electronic conductivity (σ) according to the Wiedeman-Frentz law. The relation can be mathematically expressed as; κel = LσT, where L is the Lorentz number. Therefore, κLatt can be separated from the measured κ if L is known. One possibility is to consider the standard value of L, which is ~2.45 × 10−8 W/S−1 K−2 , and another possibility is to estimate L from measured ther- mopower data. L is directly related to the scattering factor (ξ) and the reduced Fermi energy (η) by the following mathematical relation [48];   2  5  2 (ξ + 7/2)F 5 (η)  k ξ+ 2 ξ + 2 F 3 ξ+ 2 ( η ) L= B  − , (3)    3  e (ξ + 3/2)Fξ+ 1 (η) ξ+ 2 Fξ+ 1 (η) 2 2 Materials 2023, 16, 1413 10 of 12 However, η is needed to calculate L from Equation (2). η can be obtained from the measured Seebeck data from Figure 3b by using the single parabolic band model given by; ! k (ξ + 5/2)Fξ+ 3 (η) S=± B 2 − η , (4) e (ξ + 3/2)Fξ+ 1 (η) 2 R∞ n where, Fn (η) is nth order Fermi integral: Fn (η) = 0 1+χeχ−η dχ and η = kEFT , where EF is the B Fermi energy and kB is the Boltzmann constant. Here, we assume that acoustic phonon is the main scattering mechanism of electrons, i.e., ξ = − 12 . Although the Seebeck coefficient was expressed by the single parabolic model (in Equation (4)), the actual electronic band structure of the misfit cobaltates is rather complex (as has been described before). All the above calculations with simple assumptions were carried out only in order to obtain L. The calculated L from the measured S is within the range of ~1.61 × 10−8 WS−1 K−2 . The separated kel is shown in Figure 5b, which is two orders of magnitude lower than the κLatt part (see Figure 5c). Therefore, the reduced κ at 340 K is mainly due to phonons scattering at the point defects in the RS layer originated from the substitution of Sr ions by Ca. Figure 5d represents the zT value of parent Bi2 Sr2 Co2 Oy and Bi2 Sr2-x Cax Co2 Oy (x = 0.3, 0.5) compounds. The highest zT value of 0.09 at 750 K was achieved for the Bi2 Sr2-x Cax Co2 Oy (x = 0.3 and 0.5) samples. A fair comparison of the estimated zT values of our samples with the reported values in the literature is difficult due to that fact that measured thermal conductivity values varies significantly, as described in Table 1. 4. Summary In summary, polycrystalline bulk samples of Bi2 Sr2-x Cax Co2 Oy (x = 0, 0.3 and 0.5) were synthesized by conventional solid-state reactions. The substitution of Sr2+ ions by Ca2+ ions was confirmed through X-ray diffraction, X-ray photoelectron spectroscopy, and Raman spectroscopy. The isovalent substitutions of Sr2+ ions in the BSCO lattice results in a negligible impact on electronic and thermoelectric transport properties, but a significant effect on lattice thermal conductivity due to selective phonon scattering. This reduction leads to a marked improvement in the overall thermoelectric figure- of-merit. Our findings highlight that selective phonon scattering can play a crucial role in enhancing the thermoelectric performance of misfit layer compounds, such as Bi2 Sr2-x Cax Co2 Oy . Author Contributions: Conceptualization, C.M.S.T., J.S. and E.C.-A.; Methodology, A.C.; Validation, A.E.S.; Formal analysis, A.C., A.B., A.E.S., J.M.C.R., J.P.-P. and K.B.; Investigation, A.C., A.B., J.M.C.R., J.P.-P. and K.B.; Resources, C.M.S.T. and J.S.; Data curation, A.C., A.B. and K.B.; Writing—original draft, A.C. and E.C.-A.; Writing—review & editing, A.C., A.E.S. and E.C.-A.; Supervision, C.M.S.T. and J.S.; Funding acquisition, C.M.S.T. and J.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by MINECO ref. MAT2016-77100-C2-1-P; CNRS-CSIC PICS Project ref. 261091, the EU for funding through project H2020-MSCA-RISE-2014 ref. 645658, and the AGAUR agency for 2017SGR. ICN2 is funded by the CERCA programme/Generalitat de Catalunya and by the Severo Ochoa programme of the Spanish Ministry of Economy, Industry and Compet- itiveness (MINECO, grant no. SEV-2017-0706). C.M.S.T. and E.C.-A. acknowledge support from Spanish Ministry MINECO/FEDER: FIS2015-70862-P PHENTOM. A.E.S. acknowledges funding from the EU-H2020 research and innovation programme under the Marie Sklodowska Curie Individual Fellowship THERMIC (Grant No. 101029727). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Raw data can be provided by the corresponding and first author (A.C.) on reasonable request. Materials 2023, 16, 1413 11 of 12 Acknowledgments: A.C. thanks Francisco Rivadulla (from CiQUS, University of Santiago de Com- postela, Spain) for the inspiring discussions about thermoelectric properties of narrow band materials. Conflicts of Interest: The authors declare no conflict of interest. References 1. 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