1 Introduction

Thermoelectric materials can directly transform a temperature difference dT into a voltage U due to the Seebeck effect [1], defined by:

$$ S=\frac{U}{dT} $$
(1)

Materials with a high Seebeck coefficient S, high electrical conductivity and low thermal conductivity can be used in thermoelectric generators for the recovery of heat, which is particularly interesting considering the limited primary energy resources [2]. Although the efficiency of thermoelectric generators is by far smaller than the Carnot efficiency [1], they are used in remote applications because of their high reliability due to no moving parts. Cost-effective thermoelectric generators can improve the efficiency of primary power generators like power plants by converting a part of the waste heat into electrical power [2].

Conventional thermoelectric materials like tellurides and skutterudites have good thermoelectric properties, but are limited to lower temperatures ranges (up to 300 °C) as they melt or decompose at higher temperatures. In addition, their raw materials are toxic, rare and expensive. These conventional thermoelectric materials are also sensitive to oxidation [3].

An interesting alternative are oxide thermoelectric materials. Their thermoelectric performance is not as high as of the non-oxide materials, but they are less toxic, their raw materials are cheaper, and often more abundant. Additionally, they are stable at higher temperature in oxidizing atmosphere. By decreasing the production costs of oxide thermoelectric generators while maintaining or increasing their performance, these oxide generators could become practically relevant, especially for high temperature applications [2].

Two important measures are the power factor, PF, and the figure of merit, ZT, describing the electronic properties with respect to energy conversion. Material with a high PF require a high Seebeck coefficient, S, and a good electrical conductivity, σ.

$$ PF={S}^2\cdotp \sigma $$
(2)

For a high figure of merit, ZT, a low thermal conductivity κ is necessary. ZT increases with the temperature, T, if all other material parameters are constant.

$$ ZT=\frac{PF}{\kappa }T=\frac{S^2\cdotp \sigma }{\kappa }T $$
(3)

Today, doped SrTiO3 [4, 5] and ZnO [6,7,8] show the best performance for n-type thermoelectrics at elevated temperatures. As high-temperature p-type materials, recent studies on delafossites like CuFeO2 indicate good thermoelectric properties [9,10,11]. However cobaltites currently exhibit the highest ZT values among oxide p-type thermoelectrics [12,13,14,15,16,17]. One of the most promising material is calcium cobaltite Ca3Co4O9 [2, 3, 15,16,17,18]. Ca3Co4O9 has a layered crystal structure of alternating CoO2 and Ca2CoO2 [19] and is stable in air up to 926 °C. At higher temperatures, it decomposes into Ca3Co2O6 and CoO [19, 20]. Undoped, pressure-less sintered calcium cobaltite reaches Seebeck coefficients between 120 μV/K and 135 μV/K at room temperature [21,22,23,24,25,26] and 190 μV/K to 220 μV/K at temperatures between 600 °C and 800 °C [23,24,25,26]. The electrical conductivity varies between 1500 S/m and 9000 S/m at room temperature [21,22,23,24,25,26] and between 2500 S/m and 6500 S/m at 600 °C to 800 °C [23,24,25,26,27], respectively. The thermal conductivity amounts to 1 W/mK [28] to 6 W/mK [22]. Altogether, the power factor of undoped Ca3Co4O9 reaches values between 28 μW/K2 m and 90 μW/K2 m at room temperature [23,24,25,26] and between 60 μW/K2 m and 200 μW/K2 m at 600 °C to 800 °C [23,24,25,26]. The figure of merit amounts to approximately 0.008 at 25 °C [21, 22, 28] and 0.09 at 600 °C [27, 28].

The two main synthesis routes for Ca3Co4O9 are soft chemistry [16, 24, 29,30,31] and solid-state reaction [15, 21, 23, 25, 32,33,34], the latter is historically also known as mixed-oxide route. During a thermal process, known as calcination, the final phases are formed. The soft chemistry synthesis, such as co-precipitation of oxalates [29], polymer-solution synthesis [24] or Pecchini method [16, 24], result in Ca3Co4O9 nanoparticles. The high surface area of such small particles increases the driving force for sintering and thus leads to a higher density and increases the electrical conductivity as shown by Sotelo et al. [24]. Soft chemistry synthesis causes higher powder synthesis costs than the mixed-oxide route, due to the expensive raw materials and the associated calcination step [35].

The solid-state reaction is cost-effective and easily scalable by using a rotary kiln and is therefore widely used as powder synthesis method for various functional materials like BaTiO3 or PZT in industry [36]. Within literature, a wide range of calcination procedures is used to synthesize Ca3Co4O9. Stoichiometric amounts of the raw material (CaCO3 and mainly Co3O4) were mixed with a planetary ball mill [15, 21, 23, 25, 32,33,34]. The calcination temperature varied between 750 °C [23] and 900 °C [21, 22, 25, 28, 32, 34]. The dwell time was at least 12 h [21, 23, 32] but mostly between 20 h [15] and 24 h [21, 22, 25, 28, 34]. Most authors repeated the calcination with an intermediate grinding step [15, 21,22,23, 27, 32]. Park et al. compacted the powder into pellets before calcination and used a pure oxygen atmosphere instead of air [34].

There are only a few studies examining the influence of the calcination procedure on the properties of Ca3Co4O9. Smaczyński et al. [37] examined the influence of the temperature on the phase formation and showed that no Ca3Co4O9 was formed for temperatures below 750 °C, whereas Ca3Co2O6 was already present at 800 °C. The latter result is not in good accordance with the phase diagram [19, 20] and other studies as mentioned above [21, 22, 25, 28, 32, 34]. Thermoelectric properties were not tested. In a study by Yu et al. [38], the powder was calcined at 800 °C and 900 °C, respectively. They found Ca3Co4O9 at 800 °C and Ca9Co12O28 at 900 °C. The powder produced at 900 °C had a 1.5 times higher electrical conductivity. The influence on the Seebeck coefficient was not measured. Delorme et al. [39] reached a 30% higher electrical conductivity by using nano CaO (<100 nm) as raw material instead of powder with a grain size of 10–20 μm. An influence on the Seebeck coefficient was not observed. Presečnik et al. [40] showed that longer milling times of the raw material mixture improved the electrical conductivity by a factor of 1.6.

In summary, the calcination procedure varies within the different studies. To the authors’ knowledge, a systematic research of the solid-state powder synthesis procedure for Ca3Co4O9 considering the thermoelectric properties has not yet been published.

As a high temperature process, the powder synthesis consumes a lot of energy. To produce cost-effective thermoelectric generators, a good knowledge of the powder synthesis is indispensable. In this study, the influence of the calcination procedure on the thermoelectric properties of Ca3Co4O9 is analyzed using the design of experiment method (DoE).

2 Experimentals

2.1 Design of experiments

Statistical design of experiments allows getting a maximum of information from a minimum number of experiments. Therefore, several parameters p are examined at the same time. With a full factorial design, all effects of the parameter and all interactions of the parameter can be analyzed. The number of experimental points n is given by

$$ n={L}^p $$
(4)

with the parameter levels L. The experimental points are randomized to minimize the effect of disturbances on certain parameters [41].

The main synthesis parameter (particle size of raw material, calcination temperature, and calcination dwell time) were examined with a 23 statistical design of experiments. The applied experimental framework is shown in Table 1. The mean particle size was varied between 1.6 μm and 2.3 μm (for particle size distribution see Fig. 1), the calcination temperature was varied between 800 °C and 900 °C, and the dwell time between 6 h and 9 h. The number of calcination cycles was set to 2. Supplementary to the statistical design of experiments, the influence of the calcination cycles was investigated with additional experimental points (No 9–12). Therefore, the number of calcination cycles was varied between zero and three (0, 1, 2 3) and the other synthesis parameter were set to a constant level (mean particle size of raw materials: 2 μm, calcination temperature: 850 °C, and dwell time: 9 h). The effects of the different parameters within the statistical design of experiments on the target values (linear shrinkage, sinter density, particle size after calcination, Seebeck coefficient and electrical conductivity) were analyzed with the statistics package Minitab 17 (Minitab Inc., State College, Pennsylvania, USA).

Table 1 Experimental framework with parameter settings of the varied calcination conditions
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Fig. 1
figure 1

Particle size distribution of the raw material mixture after attrition milling measured with a laser diffraction system. The milling time was set to 15 min for a D50r = 2.3 μm and to 45 min for a D50r = 1.6 μm

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2.2 Material preparation

Stoichiometric amounts of calcium carbonate (99%, low-alkali, Riedel-de Haën, Seelze, Germany) and cobalt (II, III) oxide (99.97+ %, ChemPUR, Karlsruhe, Germany) were attrition milled (rotation speed: 800 min−1) in ethanol with zirconia balls (d = 2.5 mm). The ethanol was evaporated in a rotary evaporator (Rotavapor R-124, Büchi, Essen, Germany). The milling time was varied to reach different particle size distributions (see Table 1 and Fig. 1). The powder mixtures were calcined in alumina sintering boats in air (for temperature and dwell time levels see Table 1), and afterwards dry-milled in a planetary ball mill (Pulverisette, Fritsch, Idar-Oberstein, Germany) with agate grinding bowls for 15 min with a rotation speed of 215 min−1. 1.5 wt% pressing additives (Zusoplast 9002 and Optapix AC 95, Zschimmer & Schwarz, Lahnstein, Germany) were added to a water-based suspension of the powder. After drying, the mixture was grinded to obtain flakes of powder with pressing additives finer than 200 μm. Five test bars (50 mm × 5 mm × 5 mm) of each composition were uniaxially cold pressed (30 MPa) and sintered at 900 °C for 24 h in air.

2.3 Characterization

After each milling step, the particle size distributions of the powders were analyzed with a laser diffraction system (Mastersizer 2000, Malvern Instruments, Malvern, United Kingdom). Before and after sintering, the dimensions of the test bars were measured with a micrometer gauge (height h, width w) and with a caliper gauge (length l). The specimens were weighed (weight m) with an analytical balance with a resolution of 0.1 mg before and after sintering.

The linear shrinkage dl/l0 was calculated according to:

$$ dl/{l}_0=\frac{l_0-{l}_1}{l_0} $$
(5)

with length before sintering l0 and length after sintering l1. The apparent density (geometric density) ρ was calculated according to formula (6).

$$ \rho =\frac{m}{l\cdotp w\cdotp h} $$
(6)

The mass loss of the test bars was determined according to formula (7) with weight before sintering m0 and weight after sintering m1:

$$ dm/{m}_0=\frac{m_0-{m}_1}{m_0}\cdot 100\% $$
(7)

The microstructures of the samples were examined on polished as well as on fractured surfaces using a scanning electron microscope (Gemini Supra 40, ZEISS, Jena, Germany) fitted with an energy-dispersive X-ray spectrometer (EDX). The grain morphology was analyzed with the imaging software PixelFerber (Berlin, Germany) by measuring the maximum feret diameters of at least 100 grains. The phase compositions of the sintered samples were studied with X-ray powder diffraction (XRD) by means of synchrotron radiation because of its excellent intensity and very short required measurement time. These measurements were performed at the microfocus beamline μSpot (BESSY II, Helmholtz Centre Berlin for Materials and Energy, Germany) in transmission geometry. The XRD patterns were collected for 30 s, with a wavelength of 1.0039 Å by a Si (111) double-crystal monochromator and recorded using a two-dimensional MarMosaic CCD X-ray detector. An algorithm from the FIT2D software was used to process the obtained scattering images and to convert them into diagrams of scattered intensities versus scattering vector q (q = 4π sinθ / λ). For a direct comparison to the results by XRD with Cu radiation, the q-values were converted to the diffraction angle 2θ (Cu-Kα1).

The electrical resistance R of the test bars at room temperature was measured with a 4-probe-method using a digital multimeter (3458A, Hewlett Packard, Santa Rosa, USA). The measurement was repeated two-times for top surface and bottom surface of the specimen. According to eq. (8) the electrical conductivity σ was calculated using the resistance R, the dimension of the test bars (h, w), and the distance of the two inner probes d.

$$ \sigma =\frac{d}{R\cdotp h\cdotp w} $$
(8)

To determine the Seebeck coefficient S at room temperature, a laboratory setup was used. The two ends of the test bars were heated or cooled with Peltier elements to establish temperature differences from 1.5 K to 3 K between the two test probes. Two thermocouples type K with a distance of approximately 2 cm were used as test probes to measure both temperature difference ΔT and Seebeck voltage U. The Seebeck voltage was measured between the two chromel wires of the thermocouples. The Seebeck coefficients of the specimens STest bar were calculated according to eq. (9), with SChromel = 22.4 μV/K [42].

$$ {S}_{\mathrm{Test}\ \mathrm{bar}}=\frac{U}{\Delta T}+{S}_{\mathrm{Chromel}} $$
(9)

A measurement system analysis type-2 was performed to evaluate the repeatability and the reproducibility of the measurement setup for the Seebeck coefficient. The standard deviation of the total gage repeatability and reproducibility is 0.6%. A validation of the data was conducted with a laboratory setup of the Department of Functional Materials in Bayreuth, Germany. Data showed a systematic difference with the factor of 1.1.

3 Results

All powder synthesis conditions led to the formation of Ca3Co4O9 after sintering. Figure 2 shows as an example the influence of the calcination cycles on the powder XRD pattern of sintered test bars. The XRD pattern of sintered test bars from uncalcined powder (experimental point No. 9) and powder that was calcined one time (No. 10), or three times (No. 12) at 850 °C, for 9 h with a mean particle size of the raw materials D50 ≈ 2 μm are presented, respectively. The powder diffractograms of all samples were similar, with a main phase identified as Ca3Co4O9 [43] and a minor phase identified as Co3O4 (PDF 01–080-1534). The peak intensity of the minor phase was so low that no quantitative XRD analysis was possible. None of the investigated powder synthesis parameters had a significant influence on the phase composition after sintering. The decomposition product Ca3Co2O6 (PDF 00–051-0311) was not found.

Fig. 2
figure 2

Example for XRD pattern (λ = Cu-Kα1) of sintered test bars produced by different calcination routes (Tcalc = 850 °C, tdwell = 9 h, D50 ≈ 2 μm, experimental points No. 9, 10, 12)

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Figure 3 shows the micrographs of fractured surfaces from sintered test bars. For a better illustration of the influence of the calcination procedure on the microstructure, the three examples with the largest differences in the microstructure were chosen. The examples are a reaction sintered test bar (no calcination, experimental point No. 9), a sintered test bar (No. 2) from powder calcined at low temperatures (800 °C) for a short dwell time (6 h) and a sintered test bar (No. 7) from powder calcined at high temperatures (900 °C) for a long dwell time (12 h). As shown in Fig. 3, the grains in the sintered test bars have a mica-like morphology and sinter-necks have formed between the grains. The grains are randomly orientated. The grains from calcined powder are more rounded than the ones in the reaction sintered test bars. Reaction sintered test bars and test bars from calcined powder at low temperatures for a short dwell time (800 °C, 6 h) have a similar mean grain size (ferret diameter) after sintering of about 1.9 μm. Higher calcination temperature and longer dwell time (900 °C, 12 h) increase the mean grain size of the microstructure to 2.7 μm, the anisotropy of the grains is more pronounced.

Fig. 3
figure 3

SEM micrograph of fractured surface of sintered test bars from uncalcined powder (D50r ≈ 2 μm, No. 9), from powder calcined two times at 800 °C for 6 h (D50r ≈ 1.6 μm, No. 2), and from powder calcined two times at 900 °C for 12 h (D50r ≈ 2.3 μm, No. 7)

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Figure 4(a) shows a micrograph of a polished surface with some pores, light-grey areas (marked with an oval), and a dark-grey matrix. For better illustration, a micrograph with an above-average number of light-grey areas was chosen. The corresponding EDX-mapping for Co and Ca is shown in Fig. 4(b, c), respectively. The dark-grey matrix of the microstructure contains both Ca and Co (according to quantitative analysis of EDX spectrum of point 1: approximately 25 mol% Co, 18 mol% Ca and 56 mol% O) The light-grey phase contains Co but indicate no Ca (according to quantitative analysis of EDX spectrum of point 2: approximately 40 mol% Co and 60 mol% O). Such compositional inhomogeneities are found for all tested synthesis conditions. The area fractions of these inhomogeneities do not change regarding for example calcination cycles or calcination temperature.

Fig. 4
figure 4

(a) SEM micrograph of polished surface with SE detector. Areas in light grey are marked with an oval. Areas for EDX point analysis are marked with an arrow. (b) Corresponding netto peak areas of Co-L-α X-ray-line (EDX-mapping) in blue and (c) corresponding netto peak areas of Ca-K-α X-ray-line in red with an acceleration voltage of 10 kV

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The specimens produced from uncalcined powder had a mass loss of 18.9%, whereas all other experimental points lead to a mass loss of about 1.1%. Based on the data (physical and thermoelectric properties) gained from the experimental points No. 1–8 of the statistical design of experiments shown in Table 1, the fitted means and standard errors were calculated for the two parameter levels of mean particle size of raw materials (D50r), calcination temperature (T) and calcination dwell time (t), respectively. The corresponding graphs (main effect plots) for the particle size of the calcined powder (D50c), linear shrinkage (dl/l0), electrical conductivity (σ) and Seebeck coefficient (S) are shown in the first three columns of Fig. 5. The last column of Fig. 5 shows the results of the additional experimental points No. 9–12 shown in Table 1 meaning the influence of the calcinations cycles on particle size of the calcined powder (D50c), linear shrinkage (dl/l0), electrical conductivity (σ) and Seebeck coefficient (S), respectively. In summary the influence of the calcination conditions on the physical and thermoelectrical properties at room temperature are shown in Fig. 5. By varying the calcination procedure within the experimental framework, the electrical conductivity can be increased by the factor of 2.1, the linear shrinkage by the factor of 12.6, and the particle size of the calcined powder by the factor of 2.2. The Seebeck coefficient remained almost constant. The power factor can be increased by the factor of 2.1 and reaches a maximum value of 30 μW/mK2. Assuming a thermal conductivity between 1 W/mK [28] and 6 W/mK [22], the figure of merit ZT amounts to 0.002 or 0.009 at room temperature, respectively. As shown in the first column of Fig. 5, a smaller particle size of the raw materials (D50r) decreases the particle size of the calcined powder (D50c) by the factor of 0.9. Simultaneously, it increases the linear shrinkage by the factor of 2.2, the electrical conductivity by the factor of 1.1, as well as the power factor by the factor of 1.1. A higher calcination temperature (second column of Fig. 5) leads to a grain coarsening by the factor of 1.25 and decreases the linear shrinkage by the factor of 0.5. Shorter dwell times (third column of Fig. 5) increase the Seebeck coefficient slightly by the factor of 1.01. As shown in the last column of Fig. 5, the number of calcination cycles had the biggest influence on the thermoelectric and physical properties. In particular, the difference between calcined and uncalcined powder is remarkable. The electrical conductivity is almost 2 times higher for the bars produced from uncalcined powder than for those produced from powder, which was calcined three times; the Seebeck coefficient remains almost constant, the power factor doubles, and the linear shrinkage increases by the factor of 4.5. Test bars produced from uncalcined powder have the smallest grain size (D50 ≈ 2.0 μm), highest shrinkage (dl/l0 = 0.06), highest electrical conductivity (σ = 2000 S/m), highest Seebeck coefficient (S = 123 μV/K), and therefore also the highest power factor (PF = 30 μW/mK2). Within the experimental framework shown in Fig. 5 and Table 1 no significant influence (proofed by analysis of variance, ANOVA, with a level of significance, α = 0.1) was found for the following parameters: particle size of raw materials on Seebeck coefficient; calcination temperature on electrical conductivity, Seebeck coefficient, and power factor; dwell time on particle size of calcined powder, linear shrinkage, electrical conductivity and power factor. No significant interactions (proofed by analysis of variance, ANOVA, with a level of significance, α = 0.1) were found within the statistical design of experiments.

Fig. 5
figure 5

Physical and thermoelectrical properties at room temperature as a function of the varied calcination parameters described in Table 1. This means Seebeck coefficient (S), electrical conductivity (σ), linear shrinkage (dl/l0) and particle size of calcined powder (D50c)) as function of particle size raw materials (D50r), calcination temperature (T), dwell time (t) and calcination cycles. The first three columns (D50r, T, t) show the fitted means and corresponding standard errors from the statistical design of experiments (No. 1–8). The last column (Calcinations) shows the means and standard deviation from the additional experimental points (No. 9–12). Please pay attention to the different ordinate scales on the right hand side (Calcinations)

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4 Discussion

Considering the XRD-pattern, the EDX-mapping, and EDX-analysis, the dark-grey matrix in Fig. 4 consist of Ca3Co4O9, whereas the light-grey phase is Co3O4. We assume that Co3O4 are remains of unreacted starting material. For all synthesis conditions, we find minor inhomogeneities in the XRD pattern and EDX-mapping probably caused by an incomplete solid-state reaction. According to phase and microstructural analysis, a more energy intensive powder synthesis like repeated calcination cycles, or higher calcination temperatures does not increase the phase content of Ca3Co4O9 remarkably. In contrast to Smaczyński et al. [37], no Ca3Co2O6 was found, even at calcination temperatures of 900 °C.

The calcination procedure has only a minor effect on the Seebeck coefficient in comparison to the other investigated properties. The Seebeck coefficient is an integral material property and is mainly dependent on the carrier concentration and carrier mobility in the low-resistive volume of the Ca3Co4O9 grains [44]. They may change in the equilibrium with the oxygen partial pressure of the calcination atmosphere [11] but this has not been investigated here.

The electrical conductivity of the specimen rises if the raw material grain size gets smaller, if the calcination temperature gets lower, and if the material is less often calcined. The linear shrinkage shows a similar dependency to theses parameters. Figure 6(a) shows an increase of the electrical conductivity with increasing shrinkage of the specimens. A linear regression to the data shows a good adjusted coefficient of determination (R2(adj.) = 84.2%), especially with respect to the standard deviation of the underlying conductivity measurements. In contrast, the electrical conductivity is not dependent on the bulk sinter density of the specimens within the experimental framework (R2(adj.) = 0%, for linear correlation) as shown in Fig. 6(b). In theory with increasing sinter density, the density of the charge carriers per volume increases [45]. Therefore, a higher sinter density should lead to a higher electrical conductivity. Calcium cobaltite is known for very low shrinkage rates [46] and low relative densities after sintering [27, 46, 47]. Within the experimental framework, the sinter density varied only in the range of 8% of the absolute value, whereas the electrical conductivity varied in the range of 50% of the absolute value. Combined with the high standard deviation of the electrical conductivity measurements (repeatability amounts to about 10% of the absolute value), the variations in sinter density are probably not high enough to show an increase in electrical conductivity with increasing sinter density as published in literature [45].

Fig. 6
figure 6

(a) Electrical conductivity as a function of linear shrinkage with linear regression, confidence interval and prediction interval. (b) Electrical conductivity as a function of sinter density

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Regarding the given experimental framework with a generally low level of densification and only slight density variations between the different experimental points, it can be concluded that the electrical conductivity is mainly depending on the connection between the particles. Specimens with a higher shrinkage are in a more advanced sintering state. An advanced sintering state is characterized by stronger rearrangement of the particles and larger contact areas. Due to the increased intergranular contact area, charge transport between grains is enhanced, resulting in higher electrical conductivity.

A schematic diagram of the influence of the calcination procedure on the driving force for sintering is shown in Fig. 7. The calcination process leads to reaction (10) by reducing the chemical potential of the CaCO3 and Co3O4 powder mixture.

$$ 9\ {\mathrm{Ca}\mathrm{CO}}_3+4\ {\mathrm{Co}}_3{\mathrm{O}}_4+{\mathrm{O}}_2\to 3\ {\mathrm{Ca}}_3{\mathrm{Co}}_4{\mathrm{O}}_9+9\ {\mathrm{CO}}_2 $$
(10)
Fig. 7
figure 7

Influence of calcination procedure on driving force for sintering. Raw materials with stripes pattern, calcium cobaltite with chess pattern. Contact areas are marked in red

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Calcium cobaltite is known to form anisotropic mica-like crystals due to its layered crystal structure [43]. The calcination process triggers surface diffusion, which promotes idiomorphic grain growth (Figs. 3 and 7) by minimizing lattice defects and surface energy [48]. The diffusion process during calcination minimizes the driving force for sintering of the powder. Therefore, the shrinkage during sintering is decreased and fewer intergranular contact areas (marked as thick interfaces in Fig. 7) are formed. This reduces the electrical conductivity of the specimens. Although it is common practice to calcine at high temperatures for long dwell times [15, 21, 23, 25, 32,33,34], for a high PF such a high energy input during calcination is not favorable.

Comparing the reaction sintered test bars with the test bars produced from calcined powder, they have the highest shrinkage (see Fig. 5), the highest mass loss, the lowest sinter density (see Fig. 6(b)) and the highest electrical conductivity (see Figs. 5 and 6(a)). Having the highest electrical conductivity and at the same time the lowest density seems like a contradiction as the charge carrier density should decrease with decreasing density. But the improved properties of sintered test bars from uncalcined powder can be attributed to the different sinter mechanism in comparison to calcined powder. Solid state sintering is the densification mechanism for test bars from calcined Ca3Co4O9 powder. Due to the decomposition temperature of Ca3Co4O9, the sinter temperature is limited to 926 °C. As known, this leads to very low shrinkage (below 5%) even for long dwell times (over 24 h) [46]. By using calcium carbonate and cobalt (II, III) oxide as raw materials for the production of test bars, reaction sintering under the formation of Ca3Co4O9 occurs. CaCO3 dissociates into CaO and CO at about 825 °C and Co3O4 into CoO and O2 at about 900 °C [49]. Therefore, the Hedvall-effect of enhanced chemical reactivity around phase changes [50] supports the sintering at 900 °C. This goes along with higher mass loss and higher shrinkage rates, as the reduction of the chemical potential during Ca3Co4O9 formation is effective as additional driving force for sintering [51]. The higher mass loss during reaction sintering (19% for uncalcined powder to 1% for calcined powder) leads to the lower sinter density compared to the test bars from calcined powder. At the same time the higher driving force for sintering increases the linear shrinkage and the intergranular contact areas. The larger intergranular contact area would increase the charge carrier transport although the sinter density is lower. In conclusion, with respect to the generally low level of densification at 900 °C, reaction sintering of non-calcined raw materials results in a more interconnected Ca3Co4O9 microstructure than sintering of any calcined Ca3Co4O9 powder, thus giving higher electrical conductivity and better thermoelectric performance.

5 Summary

The influence of the calcination temperature, dwell time, calcination cycles and particle size of raw materials on the properties of Ca3Co4O9 were successfully studied with a statistical design of experiments (DoE). The calcination procedure had no influence on the phase content of the sintered test bars. Sintered test bars from uncalcined powder had the highest thermoelectric properties (σ ≈ 2000 S/m, S ≈ 123 μV/K, PF ≈ 30 μW/mK2 at 22 °C) within the examined parameter settings. Repeated calcinations, higher calcination temperatures, and longer dwell times result in decreased thermoelectric properties and shrinkage. The electrical conductivity is correlated linearly with the shrinkage, but no correlation was found between density and thermoelectric properties. The calcination procedure barely influenced the Seebeck coefficient. In summary, a higher linear shrinkage leads to a higher power factor. Therefore, a powder with large driving force for sintering should be used to reach high shrinkage. Thermal processes that cause grain growth without densification should not be used during powder synthesis. Ca3Co4O9 can efficiently be synthesized by direct reactive sintering of raw materials, without any additional calcination procedure. Thereby, the energy demand for the powder synthesis is reduced, which is an important step towards a cost-effective production of oxide thermoelectric generators.