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

Abstract

Na₀.₈₉Co_0.90Me_0.10O₂ (Me = Cr, Ni, Mo, W, Pb, and Bi) ceramic samples were prepared using a solid-state reaction method, and their crystal structure, microstructure, and electrical, thermal, and thermoelectric properties were investigated. The effect of the nature of the doping metal (Me = Cr, Ni, Mo, W, and Bi) on the structure and properties of layered sodium cobaltite Na_0.89CoO₂ was analyzed. The largest Seebeck coefficient (616 μV/K at 1073 K) and figure-of-merit (1.74 at 1073 K) values among the samples studied were demonstrated by the Na_0.89Co_0.9Bi_0.1O₂ solid solution, which was also characterized by the lowest value of the dimensionless relative self-compatibility factor of about 8% within the 673–873 K temperature range. The obtained results demonstrate that doping of layered sodium cobaltite by transition and heavy metal oxides improves its microstructure and thermoelectric properties, which shows the prospectiveness of the used doping strategy for the development of new thermoelectric oxides with enhanced thermoelectric characteristics. It was also shown that samples with a higher sodium content (Na:Co = 0.89:1) possessed higher chemical and thermal stability than those with a lower sodium content (Na:Co = 0.55:1), which makes them more suitable for practical applications.

1. Introduction

Approximately two-thirds of the energy consumed by factories, transport, and households is dissipated into the environment and, in fact, lost for humanity [1]. This high-potential waste heat can be partially converted into electrical energy using thermoelectrogenerators (TEGs). To produce TEGs, one needs 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 layered chalcogenides of bismuth and lead possess several drawbacks, including the presence of toxic, rare, and expensive components, as well as instability in air at elevated temperatures. These drawbacks are absent for oxide thermoelectrics [6,7,8,9,10]. One of the well-known representatives of them is layered sodium cobaltite Na_xCoO₂, first described by Jansen and Hoppe [11] and characterized as thermoelectric by Terasaki et al. [12]. Its structure consists of [CoO₂] layers (CdI₂ structure) with sodium atoms in between [13]. According to Viciu et al. [14], the concentration of oxygen vacancies in the [CoO₂] layers is negligible; therefore, the oxidation state of cobalt ions is determined only 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]. The crystal structure, electrotransport, thermal, and functional characteristics of Na_xCoO₂ strongly depend on the sodium content [22,23,24,25].

The functional characteristics of the ceramic samples of the layered sodium cobaltite are worse than those of monocrystals; however, 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], and (iv) using special sintering techniques [37], resulting in the improvement of the ceramic 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 the base NaCo₂O₄ phase [40,41]. When zinc substitutes cobalt in NaCo_2−xZn_xO₄, the electrical resistivity and Seebeck coefficient of ceramics increase, and the 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]. Co-substitution of Na by Bi and Co by Mn in Na_0.81CoO₂ decreases its ρ and increases its S, which results in a strong increase in the p values of ceramics, reaching 0.632 mW/(m·K²) at 781 K for Na_0.66Bi_0.15Co_0.99Mn_0.01O₂ compound, which is three times larger than that of the parent Na_0.81CoO₂ phase [43].

The authors of [44] produced a π-shaped thermoelectric device consisting of Na_0.50Co_0.85Cu_0.15O₂ (p-leg) cobaltite and Ba_0.2Sr_0.8PbO₃ (n-leg) plumbate, which produced an output power of 12 mW when the temperatures of the hot and cold sides were 1045 K and 539 K, respectively [44]. The power generation properties of this element did not change after high-temperature operation for seven days [44].

Earlier, we estimated the possibility of improving the thermoelectric performance of Na_xCoO₂ by increasing the sodium content in it [25] and by doping sodium-poor Na_0.55CoO₂ cobaltite with oxides of different transition and non-transition metals [16,45].

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. The chemical and thermal stabilities of the obtained materials were also studied and compared with those of sodium-poor Na_0.55Co_0.90Me_0.10O₂ layered cobaltites [16]. It was found that the modification of Na_xCoO₂ by different metal oxides, along with an increase in sodium content from x = 0.55 to x = 0.89, resulted in an essential enhancement of its thermoelectric performance and chemical and thermal stabilities. This led us to consider the materials obtained in this work as attractive for practical applications in thermoelectric devices for different purposes. To the best of our knowledge, such complex studies have not been performed earlier, and the results of this work bring new knowledge in the field of thermoelectric materials science compared to previously published works [16,25,28,29,36,37,45].

2. Materials and Methods

Ceramic samples of Na_0.89Co_0.90Me_0.10O₂ (Me = Cr, Ni, Mo, W, Pb, and Bi) were obtained using a solid-state reaction method according to the following 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 substitution level of 10 mol. % was chosen as for lower substitution degree it can be hard to detect the effect of substitution on the structure and properties of the parent phase, but for the higher substitution degrees the solubility level can be exceeded [38,40], which results in the formation of not single-phase but composite ceramics.

The dopants were selected, firstly, to provide neutral (Cr³⁺), acceptor (Ni²⁺), and donor (Mo⁶⁺, W⁶⁺, Pb⁴⁺, Bi⁵⁺) character of substitution without the size factor effect due to the slight difference in the ionic radii values of substituted (Co³⁺, Co⁴⁺ in CoO₆ octahedra (C.N. = 6) of Na_xCoO₂ crystal structure) and substituting ions [46], secondly, to use both transition (Cr,Ni) and heavy metals (W, Pb, Bi), and, thirdly, to demonstrate the effectiveness of some chosen dopants in enhancing the thermoelectric performance of layered sodium cobaltite [16,38,39,40,41,42,43].

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 to obtain ceramics of the specified composition [25,46]). The powdered samples were milled in a planetary mill PM 100 Retsch (material of beakers and grinding balls–ZrO₂) for 90 min 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. Subsequently, the obtained samples were calcined in air for 12 h at a temperature of 1133 K. The calcination temperature of 1133 K was chosen to reduce the calcination time, as at this temperature, one of the initial reagents, Na₂CO₃, melts (T_m = 1127 K [47]). 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 h at a temperature of 1203 K [46]. A sintering temperature of 1203 K was selected based on the results of previous studies [48], as at lower sintering temperatures, samples possessed high porosity values, and at higher sintering temperatures, they partially melted and reacted with the crucible material (alundum).

The real sodium content (x_Na) and average oxidation state of cobalt (Co^+Z) in the obtained ceramic materials were determined using iodometric [48] and reverse potentiometric titrations [49], as well as spectrophotometrically, according to the method described in [50] (see Supplementary Information).

The phase composition of the samples and the 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 a Bruker D8 XRD Advance X-ray diffractometer (Bruker Optik GmbH, Ettlingen (Germany)) (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) [51] and size-strain method (D_SS) (3) [52].

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

(2)

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

(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 (°), and 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, as shown in Equation (4) [53]:

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

(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 using the following formula:

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

(5)

where d_XRD is the X-ray density of the sample (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 min under a vacuum of 25–30 Pa, and then weighed in ethyl acetate, according to Equation (6):

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

(6)

where m is the mass of the dry ceramic sample (g), m₁ and m₂ are the masses of the sample saturated with liquid ethyl acetate during weighing in air and that introduced into liquid ethyl acetate, respectively (g).

The microstructure and chemical composition of the Na_0.89Co_0.90Me_0.10O₂ samples were studied using scanning electron microscopy (SEM) using 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., High Wycombe (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 [39,54,55]. The values of the average linear thermal expansion coefficient (α, LTEC) were calculated from the linear parts of the 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 an LFA 457 Micro-Flash device (NETZSCH, Selb (Germany)). The thermal conductivity (λ) of the Na_0.89Co_0.90Me_0.10O₂ sintered ceramics was calculated using Equation (7).

$$\lambda =\eta ·d_{EXP}·C_p,$$

(7)

where Cp is heat capacity, calculated by the Dulong–Petit law, (J/(g·K)). Thus, according to the data of works [16,56], the heat capacity of layered sodium cobaltite near 300 K becomes slightly dependent on the 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)

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

(9)

where L is the 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 using the following formula:

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

(10)

and

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

(11)

The self-compatibility factor (s) and the dimensionless relative self-compatibility factor (Δs) [57] for the Na_0.89Co_0.90Me_0.10O₂ ceramics were calculated using Equations (12) and (13)

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

(12)

and

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

(13)

The chemical stability of the Na_0.89Co_0.90Me_0.10O₂ and Na_0.55Co_0.90Me_0.10O₂ [16] samples to the impact of atmospheric water and carbon dioxide was estimated based on the results of their exposure for ten months in wet air at room temperature and a relative moisture of about 75% using optical microscopy (Levenhuk DTX 500 LCD (Levenhuk Inc., Praha (Czech Republic)), XRD (Bruker D8 XRD Advance X-ray diffractometer), infrared absorption spectroscopy (Thermo Nicolet Nexus ESP IR spectrometer (Nicolet Instrument Corporation, Madison (WI, USA)), and gravimetry (RADWAG AS/C/2/N 220 (Radwag Wagi Elektroniczne, Radom (Poland)). According to [16] and the results of XRD and IR-absorption spectroscopy, surface degradation of layered sodium cobaltite is described by Equations (14) and (15)

Na_0.89CoO₂ + 0.445 CO₂ = 0.445 Na₂CO₃ + 1/3 Co₃O₄ + 0.117 O₂

(14)

Na_0.89CoO₂ + 0.89 H₂O = 0.89 NaOH + 1/3 Co₃O₄ + 1/3 O₂

(15)

The intensity of chemical degradation of the samples in air was also estimated by comparing their electrotransport properties (electrical resistivity and Seebeck coefficient) before and after their storage in the measuring set within two weeks.

The thermal stability of the materials was estimated as their durability under operational conditions by comparing their electrical resistivity values after multiple thermocycles within the 323–1073 K temperature interval and after annealing in the measuring set within eight hours at 1073 K in air.

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. Values of sodium content (x_Na), the average oxidation state of cobalt (Co^+Z), lattice constants (a, c, c/a, V), Lotgering factor (f), size of the coherent scattering area obtained using the Debye–Scherrer equation (Ds) and the size-strain method (D_SS), microstrain (ε) and X-ray density (d_XRD) of Na_0.89Co_0.9Me_0.1O₂ (Me = Cr, Co, Ni, Mo, W, Pb, Bi) ceramic samples.

Me	xNa	Co+Z	a, Å	c, Å	c/a	V, Å3	f	Ds, nm	DSS, nm	ε × 104	dXRD, g/cm3
Cr	0.893	3.11	2.825	10.93	3.870	75.53	0.90	69	62	3.43	4.86
Co	0.891	3.11	2.826	10.94	3.872	75.71	0.31	63	45	4.56	4.98
Ni	0.889	3.23	2.831	10.92	3.856	75.75	0.69	70	70	2.61	4.88
Mo	0.894	2.78	2.822	10.96	3.883	75.57	0.87	73	70	1.41	5.06
W	0.889	2.78	2.825	10.97	3.884	75.80	0.92	67	69	1.50	5.43
Pb	0.888	3.01	2.825	10.94	3.873	75.64	0.92	79	60	3.22	5.55
Bi	0.894	2.90	2.823	10.93	3.872	75.45	0.76	77	72	2.49	5.56

and 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 and 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 a previous study [16]. Therefore, Co exists in the Na_0.89Co_0.90Me_0.10O₂ compounds as a mixture of Co³⁺ and Co⁴⁺, Co²⁺ and Co³⁺, and only Co³⁺ for Me = Cr, Co, and Ni; Me = Mo, W, and Bi; and Me = Pb.

According to the XRD results, all 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 this study, similar to the base Na_0.89CoO₂ cobaltite, exhibited a hexagonal structure corresponding to the γ-Na_xCoO₂ phase structure [11,29,58,59,60] (Figure 1a). Note that samples of sodium-poor Na_0.55Co_0.90Me_0.10O₂ cobaltites with the same thermal prehistory [16] contained Co₃O₄ impurities formed by the partial degradation of these phases in air. Our results indicate that increasing the sodium content in Na_xCoO₂ enhances its chemical stability in air. This conclusion is confirmed by the results of long-term exposure of the samples to wet air, according to which the sodium-rich Na_0.89CoO₂ compound degrades according to Equations (14) and (15) two times slower than the sodium-poor Na_0.55CoO₂ phase. The degradation degree of Na_xCo_0.90Me_0.10O₂ cobaltites doped with transition or heavy metal oxides, calculated through their mass change, was 7–27% lower than that of the parent Na_xCoO₂ phases.

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) [26,61,62]. 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. Values of apparent (d_EXP) density, total (Π_t), open (Π_o) and closed (Π_c) porosity, linear thermal expansion coefficient (α), electrical resistivity (ρ₁₀₇₃), Seebeck coefficient (S₁₀₇₃), power factor (P₁₀₇₃) and figure-of-merit (ZT₁₀₇₃) of Na_0.89Co_0.9Me_0.1O₂ (Me = Cr, Co, Ni, Mo, W, Pb, Bi) ceramics.

M	dEXP, g/cm3	Πt, %	Πo, %	Πc, %	105 × α, K−1	104 × ρ1073, Ω·m	S1073, μV/K	P1073, mW/(m·K2)	λ1073, W/(m·K)	ZT1073
Cr	3.18	35	16	19	1.68	3.28	134	0.055	0.613	0.10
Co	3.38	32	19	13	1.34	2.43	439	0.794	0.536	1.59
Ni	3.46	29	22	7	1.42	1.50	369	0.910	0.591	1.65
Mo	3.22	36	19	17	1.47	5.73	408	0.291	0.323	0.97
W	3.20	41	17	24	1.39	10.9	519	0.320	0.316	1.09
Pb	3.34	40	18	22	1.26	5.58	358	0.230	0.295	0.84
Bi	3.47	38	18	20	1.25	5.97	616	0.636	0.392	1.74

). 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 apparent density of Na-rich samples were 7–8% less than for Na-poor ones [16], which was probably due to the fact that during heat treatment of ceramics, part of Na₂O evaporates into the environment, and this process intensifies with the increase in sodium content in the samples. In fact, porosity values of the Na-rich samples were about two times larger (Table 2) than for Na-poor ones [16].

The Lotgering factor values 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 [16,48].

The coherent scattering area of the Na_0.89Co_0.90Me_0.10O₂ materials, synthesized in this study, calculated using different approaches (Figure 1b), was larger (up to 6–25% and 3360% 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). Therefore, the partial substitution of cobalt by transition or heavy metals in Na_0.89CoO₂ results in the formation of ceramics with larger-grained and less-strained grains.

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 dimensions (l_av (AR)) were 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 a decrease in 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 (PbO and Bi₂O₃).

The enhancement of the Lotgering factor and improvement of the anisotropy degree (AR) of the grains of Na_0.89Co_0.90Me_0.10O₂ ceramics may be caused by the differences in the sizes of the substituting and substituted ions (size effect) and 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 the 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 in these cases, the maximal difference in the sizes and charges of the substituting and substituted ions occurs.

According to the 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 and Figure S2 (see Supplementary Information)).

The Temperature dependence of the relative elongation of the Na_0.89Co_0.9Me_0.1O₂ ceramic samples was practically linear, which proves the absence of structural phase transitions in the complex oxides investigated within all the temperature intervals studied. LTEC values of the Na_0.89Co_0.9Me_0.1O₂ 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 Na_0.89CoO₂ (1.34 × 10⁻⁵ K⁻⁵) (Table 2).

The increase in the LTEC values of the Na_0.89Co_0.90Me_0.10O₂ derivatives compared to those of the Na_0.89CoO₂ base phase is possibly due to the high values of their porosity (Table 2) as well as to the increase in the anharmonicity of the metal–oxygen vibrations in their structure with 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 [63,64]. 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 those for the unsubstituted layered sodium cobaltite (Figure 4a,d). The metallic-like conductivity and low ρ values of the Ni-doped layered cobaltite are in good agreement with the results of [40,41] and are due to the donor nature of the substitution of Co by Ni, resulting in an increase in the concentration of holes, which are the main charge carriers in the layered sodium cobaltites. As can be seen, electrical resistivity values of ceramics increased with the increase in 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 the main charge carriers (holes) as the average oxidation state of the cations in the conducting (Co,Me)O₂ layers of the crystal structure Na_0.89Co_0.90Me_0.10O₂ phases increased (Figure 4a,d, Table 2).

The electrical resistivity of oxide ceramics is affected by their chemical and phase compositions, as well as their microstructural characteristics, such as porosity. In our case, namely larger Π_t values explain the facts, that ρ(Na_0.89Co_0.90Cr_0.10O₂) > ρ(Na_0.89CoO₂), ρ(Na_0.89Co_0.90W_0.10O₂) > ρ(Na_0.89Co_0.90Mo_0.10O₂) (Figure 4a,d, Table 2) though according average oxidation state of cobalt (Table 1) these pairs of Na_0.89Co_0.90Me_0.10O₂ ceramic samples should demonstrate close values of electrical resistivity.

The electrical resistivity values of the Na_0.89Co_0.90Me_0.10O₂ ceramic samples did not change after several thermocycles, exposure to wet air for two weeks, and annealing in air at 1073 K for eight hours. Note that the ρ values of Na_0.55Co_0.90Me_0.10O₂ compounds [16] aged under the same schemes increased by 15–25% depending on their composition. These facts prove the enhancement of the chemical and thermal stability of layered sodium cobaltite and its derivatives with increasing sodium content, and allow us to consider the sodium-rich Na_0.89Co_0.90Me_0.10O₂ compounds as more suitable for different practical purposes than sodium-poor ones.

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 were holes, and these materials were classified as p-type conductors. Notably, at high temperatures, the change in the thermo-EMF for all materials studied was nearly linear. This relationship of the Seebeck coefficient corresponds to Equation (16), which is commonly used to describe the thermoelectric properties of metals and degenerate semiconductors [65]

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

(16)

where k_B is the Boltzmann constant (J/K), m* is the density of the effective mass (kg), h is the Planck’s constant (J∙s), e is the charge of the electron (C), T is the absolute temperature (K), and n is the charge carrier concentration (cm⁻³).

The partial substitution of cobalt with ions of various transition or heavy metals in the structure of Na_0.89CoO₂ led to an increase in the Seebeck coefficient, which was 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 with different charges (Co²⁺, Co³⁺, and Co⁴⁺) and spin states (high, intermediate, and low spin). The fact that the Seebeek coefficient values of the Na_0.89Co_0.90W_0.10O₂ phase are larger than those of the Na_0.89Co_0.90Mo_0.10O₂ cobaltite, in which cobalt possesses the same oxidation state and spin state, may be due to its larger porosity. 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). Therefore, these phases can be considered as prospective materials for the 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]. The Seebeck coefficient of the Na_0.89Co_0.90Me_0.10O₂ phases after exposure to wet air for two weeks remained the same within the accuracy of the measurements. In contrast, aged under the same conditions, Na_0.55Co_0.90Me_0.10O₂ samples demonstrated an increase in their S value up to 15–25% depending on their composition, which looks like the results of ρ measurements proved their lower chemical stability.

The weighted mobility (μ_p) and concentration (p) of the main charge carriers («holes») in the samples studied, calculated based on the experimentally determined ρ and S values according to the method described in [66] (see Supplementary Information, Equations (S8) and (S9)), varied with temperature change and essentially and nonmonotonously changed when Na_0.89CoO₂ was doped with different metal oxides. For the base Na_0.89CoO₂ cobaltite at 1073 K, the values of μ_p and p were ~48 cm²/(V∙s) and ~5 × 10⁻²⁰ cm⁻³, respectively, which is in good agreement with the literature data [67]. The weighted mobility values of the Na_0.89Co_0.90Me_0.10O₂ solid solutions were less than, close to, and larger than those of 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 coefficient of ceramics, for example, with the sharp increasing of S values of the layered 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 the 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 by both the 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 associated with an increase in the grain size of the ceramics, which leads to a decrease in the density of grain boundaries that serve as effective phonon scattering regions. The latter occurs due to the partial replacement of lighter cobalt ions by heavier ions of molybdenum, tungsten, lead, or bismuth, serving as effective scattering centers. The electronic component of the thermal conductivity of the ceramics was relatively small (λ_e/λ = 0.03–0.13) and increased with increasing temperature, and for the Na_0.89Co_0.10Me_0.10O₂ solid solutions, except Na_0.89Co_0.90Ni_0.10O₂, 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 shown in Figure 5, the thermal diffusivity and conductivity values of the doped cobaltites (except Cr- and Ni-doped) are lower than those of the base Na_0.89CoO₂ phase. It should be noted that for sodium-poor samples (Na_0.55Co_0.90Me_0.10O₂), the converse effect was found, namely an increase in η and λ values of doped with transition or heavy metal oxides ceramics compared to the undoped Na_0.55CoO₂ phase [16,38].

Although the porosity values of the Na_0.89Co_0.90Me_0.10O₂ ceramic samples were similar (Table 2), some effects of Π_t on the thermal properties of the layered sodium cobaltite derivatives were observed and should be noted. Therefore, the fact that the Na_0.89Co_0.90Bi_0.10O₂ sample demonstrates larger η, λ, and λ_ph values than the Na_0.89Co_0.90Pb_0.10O₂ solid solution (Figure 5) is probably due to its lower porosity.

The figure of merit values of the investigated materials sharply increased with increasing temperature, and doping of layered sodium cobaltite with various transition and heavy metal oxides had different effects: ZT increased at substitution in Na_0.89CoO₂ of cobalt by nickel and bismuth and decreased when cobalt was partially substituted by chromium, molybdenum, 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 are about 4% and 9% higher, respectively, than that of the Na_0.89CoO₂ phase (Figure 6c). It should be noted that although 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 that of the 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 [68] 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.

Comparing the results obtained in this study with the data published in [16], we can conclude that the modification of layered sodium cobaltite by different metal oxides similarly affects its structure and properties for both sodium-rich (Na_0.89Co_0.90Me_0.10O₂) and sodium-poor (Na_0.55Co_0.90Me_0.10O₂) samples. However, for the latter, the effect is more pronounced due to the larger ρ and smaller S values for the Na_0.55CoO₂ phase. In contrast, sodium-rich Na_0.89Co_0.90Me_0.10O₂ compounds demonstrate higher chemical and thermal stabilities than sodium-poor Na_0.55Co_0.90Me_0.10O₂ phases under both storage and operating conditions. This fact, along with their superior thermoelectric characteristics, makes Na_0.89Co_0.90Me_0.10O₂ cobaltites more suitable for practical applications in different thermoelectric devices (ceramic thermocouples, thermoelectric generators, and industrial waste heat recovery systems).

It should also be noted that layered sodium cobaltite and its derivatives demonstrate significantly larger Seebeck coefficients, power factors, and figure-of-merit values than other layered cobaltites (Ca₃Co₄O_9+δ, Bi₂Ca₂Co_1,7O_y, etc.) [6,9,69,70,71]; therefore, they can be considered more promising thermoelectric materials.

4. Conclusions

Combining the results obtained in this study, one can conclude that doping (up to 10 mol.%) of Na_0.89CoO₂ sodium-rich layered cobaltite by different transition (Cr₂O₃, NiO) and heavy metal oxides (MoO₃, WO₃, PbO, Bi₂O₃) do not change its crystal structure and slightly affects its lattice constants values, but increases coherent scattering area values, grains 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 doping leads to a decrease in the electrical resistivity of the samples and complex changes in the Seebeck coefficient and thermal properties of the ceramics, which are determined by the nature of the metal substituting cobalt in Na_0.89CoO₂ and the peculiarities of the microstructure of the ceramics. The highest values of S possessed by the Na_0.89Co_0.90W_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ cobaltites (519 and 616 µV/K, respectively, at 1073 K), which are 18% and 40% higher than that of the parent Na_0.89CoO₂ phase.

The maximal power factor was observed for the Na_0.89Co_0.90Ni_0.10O₂ compound (0.910 mW/(m⋅K²) at 1073 K), which was 15% higher than that of the base Na_0.89CoO₂ layered sodium cobaltite, which was attributed to both the low values of its electrical resistivity and high values of its Seebeck coefficient. The largest thermoelectric performance was demonstrated by the Na_0.89Co_0.90Ni_0.10O₂ and Na_0.89Co_0.90Bi_0.10O₂ phases, with ZT values of 1.65 and 1.74 at 1073 K, which were about 4% and 9% higher, respectively, than that of the Na_0.89CoO₂ phase.

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 cobaltite derivatives. It was also found that the dimensionless relative self-compatibility factor of Na_0.89CoO₂ layered sodium cobaltite is essentially reduced by doping with transition or heavy metal oxides.

The high sodium content (Na:Co:Me = 0.89:0.90:0.10) in these phases provides enhanced thermal and chemical stability compared to the phases with low sodium content (Na:Co:Me = 0.55:0.90:0.10), which makes the former more promising candidates for thermoelectric devices. Materials possessing high Seebeck coefficient values (Na_0.89Co_0.90Me_0.10O₂ (Me = W, Bi)) are suitable for use in thermocouples, but compounds with large values of power factors and figure-of-merit (Na_0.89Co_0.90Me_0.10O₂ (Me = Ni, Bi)) can be used as components of thermoelectric generators and industrial waste heat recovery systems.