Improving of Thermoelectric Efficiency of Layered Sodium Cobaltite Through its Doping by Different Metal Oxides

1. Introduction

About two-third of energy consumed by factories, transport, and households, is dissipated into environment and, in fact, lost for humanity [1]. This high-potential waste heat can be partially transferred into electrical energy using thermoelectrogenerators (TEGs). To produce TEGs one need so-called thermoelectric materials, which should possess a complex of unique properties, such as low electrical resistivity (ρ) and thermal conductivity (λ), high values of Seebeck coefficient (S) etc. [2,3,4,5]. Traditional thermoelectrics based on the layered chalcogenides of bismuth, lead etc. possess a number of drawbacks as they content toxic, rare and expensive components as well as unstable in air at elevated temperatures. These drawbacks are absent for oxide thermoelectrics [6,7,8,9,10], one of well-known representative of them is layered sodium cobaltite Na_xCoO₂, firstly described by Jansen and Hoppe [11] and characterized as thermoelectric by Terasaki et al. [12]. Its structure consists of [CoO₂] layeres (CdI₂ structure) with sodium atoms in between them [13]. According to Viciu et al. [14], the concentration of oxygen vacancies in [CoO₂] layers is negligible, so oxidation state of cobalt ions in it is only determined by the sodium content (x_Na). Due to its unique transport properties, Na_xCoO₂ is considered as potential material for p-branches of TEGs and ceramic (oxide) thermocouples [15,16], cathode material of sodium-ion batteries (SIBs) [17,18,19,20], and its crystal hydrate, Na_xCoO₂⋅yH₂O, below 4 K indergoes into a superconducting state [21]. Crystal structure, electrotransport, thermal, and functional characteristics of Na_xCoO₂ strongly depend on the sodium content in it [22,23,24,25].

Functional, including thermoelectric, characteristics of the ceramic samples of the layered sodium cobaltite are worse than for moncrystals, but they can be improved using different approaches: i) doping in sublattices of cobalt [26,27,28] or/and sodium [29,30,31], ii) modification by particles of metals [32,33] or semiconductors [34], iii) using so-called soft synthesis methods [7,35,36], iiii) using of special sintering techniques [37] resulting in improving of ceramics microstructure which enhances its electrotransport and mechanical properties.

Partial substitution of cobalt by copper in NaCo_2–xCu_xO₄ ceramics improves its sinterability, lowers electrical resistivity and enhances Seebeck coefficient, resulting in essential increase of power factor values of these solid solutions comparing to the unsubstituted sodium cobaltite [38,39], which reache maximal value for NaCo_1.8Cu_0.2O₄ phase – 3.08 mW/(m⋅K²) at 1073 K [38]. Substitution of cobalt by nickel deteriorates sinterability of NaCo_2–xNi_xO₄ phases, but decreases their ρ and strongly enlarges S, and P value for NaCo_1.9Ni_0.1O₄ at 1073 K reaches 2.36 mW/(m⋅K²), which is 8 times larger than for base NaCo₂O₄ phase [40,41]. When zinc substitutes cobalt in NaCo_2–xZn_xO₄, electrical resistivity and Seebeck coefficient of ceramics increase, and power factor reaches 1.7 mW/(m⋅K²) at 1073 K for NaCo_1.9Zn_0.1O₄ solid solution, which is 4 times larger than for NaCo₂O₄ cobaltite [42].

Earlier we estimated the possibility to improve the thermoelectric performance of Na_xCoO₂ by increasing of sodium content in it [25] as well as by doping of sodium-poor Na_0.55CoO₂ cobaltite with oxides of different transition and non-transition metals [16,43].

In this work the effect of the nature of different transition or heavy metals partially substituting cobalt in the sodium-rich Na_0.89CoO₂ layered cobaltite on its crystal structure, microstructure, thermophysical, electrophysical, and thermoelectric (functional) properties was studied.

2. Materials and Methods

Ceramic samples of Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Ni, Mo, W, Pb, and Bi) materials were obtained using solid-state reaction method according to the reaction scheme:

1.335 Na₂CO₃ + 0.3/x Me_xO_y+ 0.9 Co₃O₄+(0.5325 − 0.15 y/x) O₂ =
= 3 Na_0.89Co_0.90Me_0.10O₂ + 1.335 CO₂

(1)

The powders of Na₂CO₃ (99%), Co₃O₄ (99%), Cr₂O₃ (99%), NiO (99.99%), MoO₃ (99.99%), WO₃ (99.99%), PbO (99.99%), and Bi₂O₃ (99.99%) were taken in the ratio of Na : Co : Me = 1.2 : 0.9 : 0.1 (the excess of Na₂CO₃ in the initial mixture is taken to compensate for the loss of Na₂O from the samples during their thermal treatment and allows to obtain ceramics of the specified composition [25,44]). The powdered samples were milled in a planetary mill PM 100 Retsch (material of beakers and grinding balls – ZrO₂) for 90 minutes at 300 rpm with the addition of C₂H₅OH (~3–5 wt.%). The resulting slurries were air-dried at a temperature of 323 K, and then pressed into tablets with a diameter of 19 mm and a thickness of up to 5 mm. After that, the obtained samples were calcined in air for 12 hours at a temperature of 1133 K. Subsequently, after calcination, the blanks were ground in an agate mortar and re-milled in a planetary mill, then pressed into bars measuring 5 × 5 × 30 mm³ and tablets with a diameter of 15 mm and a thickness of 2–3 mm, which were sintered in air for 12 hours at a temperature of 1203 K [43].

The real sodium content (x_Na) and the average oxidation state of cobalt (Co^+Z) in the obtained ceramic materials were determined using iodometric [44] and reverse potentiometric titration [45], as well as spectrophotometrically according to the method described in [46] (see Supplementary Information).

The phase composition of the samples and calculation of the crystal lattice parameters of the Na_0.89Co_0.90Me_0.10O₂ layered cobaltites were performed by means of X-ray diffraction analysis (XRD) using Bruker D8 XRD Advance X-ray diffractometer (CuKα radiation (λ = 1.5406 Å)).

The values of the coherent scattering area for the Na_0.89Co_0.90Me_0.10O₂ ceramics were calculated using the Debye–Scherrer equation (D_S) (2) [47] and the size-strain method (D_SS) (3) [48]

$$D_S={\displaystyle \frac{0.9\cdot \lambda }{\beta \cdot \cos \Theta }},$$

(2)

$$\left(d\cdot \beta \cdot \cos \Theta \right)=\left({\displaystyle \frac{0.9\cdot \lambda }{D_{SS}}}\right)\cdot \left(d^2\cdot \beta \cdot \cos \Theta \right)+{\left({\displaystyle \frac{\epsilon }{2}}\right)}^2,$$

(3)

where d is the interplanar distance, nm; β is the full width of the reflex at its half maxima, rad; Θ is the diffraction angle, °; ε is the microstrain.

The degree of crystallographic orientation of the grains of the Na_0.89Co_0.90Me_0.10O₂ ceramics was evaluated using the Lotgering factor according to Equation (4) [49]:

$$f={\displaystyle \frac{p-p_0}{1-p_0}},$$

(4)

where p= ΣI(00l)/ΣI(hkl) (ΣI is the sum of the counts of X-ray diffraction peaks of the synthesized samples); p₀ = ΣI₀(00l)/ΣI₀(hkl) (ΣI₀ is the sum of the counts of X-ray diffraction peaks of the reference phase JCPDC #00-030-1182).

The apparent density of the Na_0.89Co_0.90Me_0.10O₂ ceramic samples (d_EXP) was determined based on their mass and geometric dimensions, and their total porosity (Π_t) was calculated as follows

$${\Pi }_t=\left(1-{\displaystyle \frac{d_{EXP}}{d_{XRD}}}\right)\cdot 100\%,$$

(5)

where d_XRD is the X-ray density of the samples, g/cm³.

The open porosity of the sintered samples (Π_O) was determined by weighing the ceramic samples of Na_0.89Co_0.90Me_0.10O₂, which were saturated with ethyl acetate for 60 minutes under a vacuum of 25–30 Pa, and then weighed in ethyl acetate according to Equation (6):

$${\Pi }_o={\displaystyle \frac{m_1-m}{m_1-m_2}}\cdot 100\%,$$

(6)

where m is the mass of the dry ceramic sample, g; m₁ and m₂ are the masses of the sample saturated by the liquid ethylacetate at weighing in air and introduced into the liquid ethylacetate, respectively, g.

The microstructure and chemical composition of the Na_0.89Co_0.90Me_0.10O₂ samples were studied using scanning electron microscopy (SEM) by a Tescan MIRA 3 LMH scanning electron microscope equipped with an AZtecLIVE Advanced energy dispersive microanalysis system with a nitrogen-free Ultim Max 100 standard detector (Oxford Instruments Analytical Ltd., UK).

The thermal expansion, electrical resistivity (ρ) and Seebeck coefficient (S) of the sintered ceramics were measured in air within a temperature range of 323–1073 K using the methodology described in [39,50,51]. Values of the average linear thermal expansion coefficient (α, LTEC) were calculated from the linear parts of Δl/l₀ = f(T) plots.

The thermal diffusivity (η) of the Na_0.89Co_0.90Me_0.10O₂ layered cobaltites was studied in a helium atmosphere over a temperature range of 323–1073 K using the LFA 457 Micro-Flash device (NETZSCH). The thermal conductivity (λ) of the Na_0.89Co_0.90Me_0.10O₂ sintered ceramics was calculated using the Equation (7).

$$\lambda =\eta \cdot d_{EXP}\cdot C_p,$$

(7)

where Ср – is heat capacity, calculated by the Dulong–Petit law, J/(g⋅K). Thus, according to the data of works [16,52], the heat capacity of layered sodium cobaltite near 300 K becomes slightly dependent on temperature and reaches a plateau.

The phonon (λ_ph) and electron (λ_e) parts of the thermal conductivity of the Na_0.89Co_0.90Me_0.10O₂ ceramics were roughly approximated by Equations (8) and (9)

$$\lambda ={\lambda }_e+{\lambda }_{ph}$$

(8)

$${\lambda }_e={\displaystyle \frac{L\cdot T}{\rho }}$$

(9)

where L is Lorentz number (L=2.45∙10^–8 W∙Ω∙K^–2).

The values of the power factor (P) and figure of merit (ZT) of the Na_0.89Co_0.90Me_0.10O₂ solid solutions were calculated as follows

$$P={\displaystyle \frac{S^2}{\rho }}$$

(10)

and

$$ZT={\displaystyle \frac{P\cdot T}{\lambda }}$$

(11)

The self-compability factor (s) and the dimensionless relative self-compatibility factor (Δs) [53] for the Na_0.89Co_0.90Me_0.10O₂ ceramics were calculated using equations (12) and (13)

$$s={\displaystyle \frac{\sqrt{1+ZT}-1}{S\cdot T}}$$

(12)

and

$$\Delta s={\displaystyle \frac{s_{\max }-s_{\min }}{s_{\min }}}\cdot 100\%.$$

(13)

3. Results and Discussion

The sodium content in the obtained samples (x_Na), determined by iodometry, reverse potentiometry, and spectrophotometry methods, was approximately 0.89 for all the investigated samples (Table 1, Table S1). The average oxidation state of cobalt in the Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Co, Ni, Mo, W, and Bi) layered cobaltites varied within 2.78–3.23 (Table 1, Table S1), increasing with the substitution of an acceptor character (Ni instead of Co) and decreasing with the substitution of a donor character (Mo, W, Pb, or Bi instead of Co), which was also observed for the Na_0.55Co_0.90Me_0.10O₂ samples in the study [16].

According to the XRD results, all the ceramic samples were single-phase, within the XRD accuracy. The ceramic samples of Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Ni, Mo, W, Bi) obtained in the study, like the base Na_0.89CoO₂ cobaltite, exhibited a hexagonal structure corresponding to the γ-Na_xCoO₂ phase structure [11,29,54,55,56] (Figure 1а).

The values of the lattice constants for the Na_0.89Co_0.90Me_0.10O₂ solid solutions varied within the ranges of a = 2.822–2.831 Å  and c = 10.92–10.97 Å (Table 1), which are close to the parameters of the Na_0.89CoO₂ base cobaltite (a = 2.826 Å, c = 10.94 Å) [26,57,58]. As a result, the values of volume of the unit cell for the phases of Na_0.89Co_0.90Me_0.10O₂ with partial cobalt substitution by transition or heavy metals changed very little, but their axial ratio significantly decreased only with the substitution of cobalt by nickel in the Na_0.89CoO₂ structure. Thus, partial substitution of cobalt with other metals in the Na_0.89CoO₂ phase does not lead to significant changes in the size and shape of the unit cell for the Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Mo, W, and Bi) solid solutions compared to the unsubstituted phase of layered sodium cobaltite.

The apparent density values of the Na_0.89Co_0.90Me_0.10O₂ ceramic ranged within 3.18–3.47 g/cm³ and decreased with the partial substitution of Co with Cr, Mo, W, or Pb, while they increased with the substitution of Co with Ni and Bi (Table 2). The values of open porosity of the ceramics varied within 16%–22% and were close for samples with different cationic compositions, but values of closed porosity were minimal for the base Na_0.89CoO₂ phase (13%) and Na_0.89Co_0.90Ni_0.10O₂ solid solution (7%) and for other samples varied within 17−24% and were close each other (Table 2).

The values of the Lotgering factor increased from 0.31 for the Na_0.89CoO₂ base cobaltite (moderate orientation) to 0.69–0.76 for the Na_0.89Co_0.90Me_0.10O₂ solid solutions (Me = Ni and Bi) (good orientation) and 0.87–0.92 for the Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Mo, W, and Pb) ceramics of composition (very good orientation) (Table 1). Thus, doping Na_0.89CoO₂ with various transition or heavy metal oxides increases the degree of crystallographic orientation of the ceramic grains (the degree of its texturing). The most pronounced effect among the samples synthesized in this work was observed for Na_0.89Co_0.90W_0.10O₂, with the partial substitution of cobalt by tungsten in the Na_0.55CoO₂ phase leading to a similar effect [16,43].

The coherent scattering area of the Na_0.89Co_0.90Me_0.10O₂ materials, synthesized in the study, calculated using different approaches (Figure 1b), was larger (up to 6–25% and 33 60% according to the Debye−Scherrer and the size-strain method, respectively) comparing to the base layered sodium cobaltite phase (Figure 1b, Table 1). In turn, the values of microstrains for the Na_0.89Co_0.90Me_0.10O₂ ceramics were slightly (Me = Cr and Pb) or significantly (Me = Ni, Mo, W, and Bi) lower compared to the initial Na_0.89CoO₂ cobaltite (Table 1). So, partial substitution of cobalt by transition or heavy metals in Na_0.89CoO₂ results in formation of ceramics possess the grains with larger dimensions and less strained.

According to the results of SEM, the grains of the Na_0.89CoO₂ base unsubstituted cobaltite had a plate-like shape with dimensions (l) of 6 – 15 μm and a thickness of 2.5 – 3 μm (with an average size (l_av) of about 7 μm and an aspect ratio (AR) of approximately 3.9) (Figure 2b). The microstructure of the Na_0.89Co_0.90M_0.10O₂ materials was similar to that of Na_0.89CoO₂, but it differed in the size and aspect ratio (shape) of the grains (Figure 2a, c–f).

The grain sizes of the Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Ni, W) ceramics varied within 6–23 μm with a thickness of 6–10 μm. The average dimension (l_av (AR)) was approximately 17 μm (2.8) for Me = Cr, 22 μm (3.3) for Me = Ni and 14 μm (3.2) for Me = W. Doping of the layered sodium cobaltite ceramics with bismuth or lead oxides resulted in an increase in grain size to 35–60 μm and decrease of the thickness of the grains by up to 1–3 μm. For Na_0.89Co_0.90Pb_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂, the l_av (AR) values were around 43 μm (14.3) and 52 μm (15.6), respectively. Consequently, the anisotropy of the grains in the sodium cobaltite ceramic increased with doping by heavy metal oxides (PbO₂, Bi₂O₃).

Enhancing of Lotgering factor and improving of anisotropy degree (AR) of the grains of Na_0.89Co_0.90Me_0.10O₂ ceramics may causes both by the differences in the sizes of subsituting and substituted ions (size effect) and in their charges (charge redistribution). The first results in localized lattice strain promoting preferential alignment of grains along specific crystallographic planes (in our case, (00l)), but the second alters charge distribution in the structure of Na_0.89Co_0.90Me_0.10O₂ phases, enhances interlayer charge screening, reduces electrostatic repulsion of CoO₂-layers, and stabilizes (00l)-oriented stacking. The maximal values of f and AR were observed, in the whole, for the samples of layered sodium cobaltite, doped by heavy metal oxides (Pb, W etc.) (Table 1, Figure 2), as namely in these cases maximal difference in the sizes and charges of substituting and substituted ions take place.

According to EDX results, the cationic composition of the Na_0.89Co_0.90M_0.10O₂ synthesized compounds was close to the target values, and the distribution of elements within the ceramic was nearly uniform (Figure 3, Figure S2 (see Supplementary Information)).

Temperature dependences of the relative elongation of Na0.89Co0.9Me0.1O2 ceramic samples were linear practically, which proves the absence of the structural phase transitions in the complex oxides investigated within all the temperature interval studied. LTEC values of the Na0.89Co0.9Me0.1O2 solid solutions varied within (1.25–1.68)·10^–5 K^–1 and were lower (for Me = Pb, and Bi), slightly (for Me = W) and essentially larger (for Me = Cr, Ni, and Mo) than for unsubstituted sodium cobaltite Na0.89CoO2 (1.34·10^–5 K^–5) (Table 2).

Obtained increasing of LTEC values of Na0.89Co0.90Me0.10O2 derivatives in comparison to the Na0.89CoO2 base phase possibly is due to the high values of their porosity (Table 2) as well as to the increasing of anharmonicity degree of metal–oxygen vibrations in their structure at partial substitution of cobalt by other metals.

As can be seen from the Figure 4a, the Na_0.89CoO₂ layered sodium cobaltite and its Na_0.89Co_0.90Me_0.10O₂ derivatives exhibited metallic-like conductivity character (∂ρ/∂T>0) (except Na_0.89Co_0.90W_0.10O₂ solid solution, which possesses semiconducting conductivity character within all the temperature interval studied), which for the Na_0.89Co_0.90Bi_0.10O₂ and Na_0.89Co_0.90Mo_0.10O₂ solid solutions near 923 K changed into a semiconducting one (∂ρ/∂T<0) like the conductivity crossover in layered calcium cobaltite of Ca₃Co₄O_9+δ [60,61]. A similar effect was also observed in several Na_0.55Co_0.90Me_0.10O₂ layered sodium cobaltites earlier [16]. The doping of Na_0.89CoO₂ layered sodium cobaltite by different metal oxides results in increasing its electrical resistivity values, except NiO, as ρ values of Na_0.89Co_0.90Ni_0.10O₂ solid solution were essentially less than for the unsubstituted layered sodium cobaltite (Figure 4a, d). As can be seen, electrical resistivity values of ceramics increased at increasing of oxidation state of the substituting cobalt metal Me (ρ(Na_0.89Co_0.90Ni_0.10O₂) < ρ(Na_0.89CoO₂) < ρ(Na_0.89Co_0.90Pb_0.10O₂)). This can be explained by a decrease in the concentration of main charge carriers (holes) as the average oxidation state of cations in the conducting (Co,Me)O₂ layers of the crystal structure Na_0.89Co_0.90Me_0.10O₂ phases increases (Figure 4a, d, Table 2).

The Seebeck coefficient of the Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Ni, Mo, W, Pb, and Bi) solid solutions was positive throughout the temperature range studied, indicating that the main charge carriers are holes, and these materials are classified as p-type conductors. It is also noteworthy that at high temperatures, the change in thermo-EMF for all materials studied was nearly linear. This relationship of the Seebeck coefficient corresponds to Equation (14), which is commonly used to describe the thermoelectric properties of metals and degenerate semiconductors [62]

$$\mathrm{S}=\left({\displaystyle \frac{8\cdot {\pi }^2\cdot k_B^2}{3\cdot e\cdot h}}\right)\cdot m^{\ast }\cdot T\cdot {\left({\displaystyle \frac{\pi }{3\cdot n}}\right)}^{2/3}$$

(14)

where k_B is the Boltzmann constant, J/K; m* is the density of a state effective mass, kg; h is the Planks constant, J∙s; e is the charge of the electron, C; T is the absolute temperature, K; n is the charge carrier’s concentration, cm^–3.

Partial substitution of cobalt with ions of various transition or heavy metals in the structure of Na_0.89CoO₂ leads to an increase in its Seebeck coefficient, which is more pronounced at high temperatures for tungsten- or bismuth-substituted solid solutions (Figure 4b,e and Table 2). This is likely due to the increase in configurational entropy provided by the presence of cobalt ions in different charge (Co²⁺, Co³⁺, and Co⁴⁺) and spin states (high-, intermediate-, and low-spin). The highest values of S among all investigated samples were demonstrated by the Na_0.89Co_0.90W_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ oxides (519 and 616 µV/K at 1073 K, respectively), which are 1.18 and 1.40 times larger than that of the parent Na_0.89CoO₂ phase (Figure 4e and Table 2). So, these phases can be considered as prospective materials for p-legs of ceramic (oxide) thermocouples. It should also be noted that similar results were obtained when studying the Seebeck coefficient of cobalt-substituted derivatives of the Na_0.55CoO₂ layered cobaltite [16,38].

Value of weighted mobility (μ_p) and concentration (p) of the main charge carriers («holes») in the samples studied, calculated on the base of experimentally determined ρ and S values according to the methodics described in [63] (see Supplementary Information, Equations (S8) and (S9)), varied with temperature changing and essentially and nonmonotonusly changed when Na_0.89CoO₂ was doped by different metal oxides. For the base Na_0.89CoO₂ cobaltite at 1073 K values of μ_p and p were equal ~48 cm²/(V∙s) and ~5∙10^–20 cm^–3 respectively which is in a good accordance with the literature date [63]. Weighted mobility values of the Na_0.89Co_0.90Me_0.10O₂ solid solutions were less, close to, end large, than for Na_0.89CoO₂ for Me = Cr, Mo, Pb, Me = Ni, W, and Me = Bi respectively. Charge carriers concentration in Na_0.89Co_0.90Me_0.10O₂ cobaltites was large, close to, and less, than for Na_0.89CoO₂ phase for Me = Cr, Me = Mo, Ni, Pb, and Me = W, Bi respectively, that is in good accordance with the results of measurements of Seebeck coeffisient of ceramics, for example, with the sharp increasing of S values of the layred sodium cobaltite at partical substitution of cobalt by bismuth or tungsten in it, and with the scharp decreasing of S at partical substitution of cobalt by chromium in Na_0.89CoO₂ (Figure 4b,e).

The power factor values of Na_0.89Co_0.90Me_0.10O₂ sintered ceramics increased with rising temperature and changed non-monotonically with the changing of nature of metal substituting cobalt in the Na_0.89CoO₂ structure (Figure 4c,f and Table 2). The maximum P value was achieved for the Na_0.89Co_0.90Ni_0.10O₂ nickel-substituted solid solution (0.910 mW/(m⋅K²) at 1073 K), which is 1.15 times larger than that of the undoped Na_0.89CoO₂ layered sodium cobaltite, and was determined both by low values of its electrical resistivity and high values of its Seebeck’s coefficient.

The thermal diffusivity and thermal conductivity values of the Na_0.89Co_0.10Me_0.10O₂ ceramics decreased with increasing of temperature (Figure 5a,b) and changed nonmonotonously at the doping of Na_0.89CoO₂ by various metal oxides, increasing at substitution of Co by Cr, and Ni, and decreasing at substitution of Co by Mo, W, Pb, and Bi (Figure 5d,e). The first is perhaps associated with an increase in the grain size of the ceramics, which led to a decrease in the density of grain boundaries that serve as effective phonon scattering regions, but the last took place due to the partial replacing of lighter cobalt ion by heavier ions of molibdenium, tungsten, lead, or bismuth, serving as effective scattering centers. The electronic part of the thermal conductivity of the ceramics was relatively small (λ_e/λ=0.03–0.13) and increased with the rising of temperature, and for the Na_0.89Co_0.10Me_0.10O₂ solid solutions, except Na_0.89Co_0.90Ni_0.10O₂ one, it was lower than that of the Na_0.89CoO₂ base oxide. Thus, the main part of the heat in the Na_0.89Co_0.10Me_0.10O₂ phases was carried by lattice vibrations (phonons) (λ_ph/λ ≈(0.87–0.97)) (Figure 5c,f). As can be seen from the Figure 5, both thermal diffusivity and conductivity values of the doped cobaltites (except Cr- and Ni-doped) are less than that of the base Na_0.89CoO₂ phase. It should be noted, that for sodium-poor samples (Na_0.55Co_0.90Me_0.10O₂) the contraversal effect was found, namely increasing of η and λ values of doped with transition or heavy metal oxides ceramics comparing to the undoped Na_0.55CoO₂ phase [16,38].

Figure of merit values of the investigated materials sharply increased with rising temperature, and doping of layered sodium cobaltite with various transition and heavy metal oxides had different effect – ZT increased at substitution in Na_0.89CoO₂ of cobalt by nickel and bismuth and decreased when cobalt was partially substituted by chromium, molibdenium, tungsten, and lead (Figure 6a and Table 2). The highest thermoelectric characteristics were demonstrated by Na_0.89Co_0.90Ni_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ solid solutions, with ZT values reaching 1.65 and 1.74 at 1073 K, which is about 4% and 9% respectively higher than that of the Na_0.89CoO₂ phase (Figure 6c). It should be noted, that though for the Na_0.89Co_0.90W_0.10O₂, Na_0.89Co_0.90Mo_0.10O₂ and Na_0.89Co_0.90Pb_0.10O₂ ceramics ZT values were less than for Na_0.89CoO₂ phase, at 1073 K they were equal to 1.09, 0.97, and 0.84 respectively, which is close to the theoretical criterion (ZT > 1) that defines materials of practical interest for thermoelectric conversion (Figure 6a and Table 2).

The self-compatibility factor values (s) of the ceramics studied increased at temperature increasing and within temperature interval 673–873 K slightly vary (except for Na_0.89Co_0.90Cr_0.10O₂ compound) (Figure 6b), and dimensionless relative self-compatibility factor (Δs) of Na_0.89Co_0.90Me_0.10O₂ layered cobaltites within 673–873 K varies within 8–29% (Figure 6d), which is, in the whole, less than for the Mg₂Si_0.6–ySn_0.4Sb_y (25-40%) thermoelectric alloy [64] and states the good self-compatibility of the obtained in this work thermoelectric oxide ceramics. Note, that Δs values for the doped sodium cobaltites, except Na_0.89Co_0.90Mo_0.10O₂, were less (8–21%) than for the base layered sodium cobaltite (26%), which shows the effectiveness of doping of Na_0.89CoO₂ by transition or heavy metal oxides in increasing of its self-compatibility.

4. Conclusions

Combining the obtained in this study results one can conclude that doping (up to 10 mol.%) of Na_0.89CoO₂ layered soldium cobaltite by different transition (Cr₂O₃, NiO) and heavy metal oxides (MoO₃, WO₃, PbO, Bi₂O₃) did not changed its crystal structure and slightly affects its lattice constants values, but increasing coherent scattering area, grain size as well as grain orientation degree of Na_0.89Co_0.10Me_0.10O₂ solid solutions comparing to the parent Na_0.89CoO₂ phase.

Such a doping lead, in the whole, to the decrease of elecrical resistivity of the samples and complex changing of Seebeck cofficient and thermal properties of the ceramics, which determined both the nature of metal substituting cobalt in the Na_0.89CoO₂ and the peculiarities of the microstructure of the ceramics. The maximal values of S possess the Na_0.89Co_0.90W_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ cobaltites (519 and 616 µV/K at 1073 K, respectively), which are 18% and 40% higher than that of the parent Na_0.89CoO₂ phase. So, these materials can be recommended as potential materials for p-legs of ceramic thermocouples.

Maximal power factor was observed for the Na_0.89Co_0.90Ni_0.10O₂ compound (0.910 mW/(m⋅K²) at 1073 K), which is 15% higher than that of the base Na_0.89CoO₂ layered sodium cobaltite, and was determined both by low values of its electrical resistivity and high values of its Seebeck’s coefficient. The maximal thermoelectric performance demonstrate the Na_0.89Co_0.90Ni_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ phases, which ZT values is equal 1.65 and 1.74 at 1073 K, that is about 4% and 9% respectively higher than for Na_0.89CoO₂ phase. So, these materials can be considered as potential materials for the p-branches of the modules of high-temperature thermoelectrogenerators.

The obtained results demonstrate the effectiveness of the doping strategy of cobalt by heavy metals in layered sodium cobaltite for the enhancement of the thermoelectric performance of its derivatives. It was also found that dimensionless relative self-compatibility factor of the Na_0.89CoO₂ layered sodium cobaltite essentially reduced at its doping by transition or heavy metal oxides.