Spark Plasma Sintering of Tungsten Oxides WO_x (2.50 ≤ x ≤ 3): Phase Analysis and Thermoelectric Properties

Abstract

The solid-state reaction of WO₃ with W was studied in order to clarify the phase formation in the binary system W-O around the composition WO_x (2.50 ≤ x ≤ 3) during spark plasma sintering (SPS). A new phase “WO_2.82” is observed in the range 2.72 ≤ x ≤ 2.90 which might have the composition W₁₂O₃₄. The influence of the composition on the thermoelectric properties was investigated for 2.72 ≤ x ≤ 3. The Seebeck coefficient, electrical conductivity and electronic thermal conductivity are continuously tunable with the oxygen-to-tungsten ratio. The phase formation mainly affects the lattice thermal conductivity κ_lat which is significantly reduced until 700 K for the sample with the composition x = 2.84, which contains the phases W₁₈O₄₉ and “WO_2.82”. In single-phase WO_2.90 and multi-phase WO_x materials (2.90 ≤ x ≤ 3), which contain crystallographic shear plane phases, a similar reduced κ_lat is observed only below 560 K and 550 K, respectively. Therefore, the composition range x < 2.90 in which the pentagonal column structural motif is formed might be more suitable for decreasing the lattice thermal conductivity at high temperatures.

1. Introduction

Transition metal oxides (TMOs) are under debate for high-temperature thermoelectric (TE) applications since NaCo₂O₄ was found to be a p-type material with a thermopower α as high as 100 µV·K⁻¹ at 300 K [1]. By now, TMOs are subject of in-depth investigations [2,3,4] in particular because there is still a lack of appropriate n-type counterparts, although lanthanum-doped SrTiO₃ [5], ZnO [6] or doped TiO_2−x [7,8,9] show promising results.

The enhancement of a TE material’s figure-of-merit ZT (Equation (6)) might be obtained by either increasing the power factor α²σ or decreasing the total thermal conductivity κ_tot = κ_el + κ_lat (Equations (3) and (4)). An interesting approach is the exploitation of crystallographic shear (CS) for the reduction of the lattice thermal conductivity κ_lat due to increased phonon scattering [4,10,11]. CS plane structures occur when a transition metal is partially reduced and oxygen layers are removed from the structure, e.g., of TiO₂, VO₂, MoO₃ and WO₃. In the tungsten-oxygen system (Figure 1a) with decreasing O/W-ratio x the observed phases are the insulating ReO₃-type WO₃, the semiconducting phase W₂₀O₅₈ with CS planes, the metallic phase W₁₈O₄₉ with pentagonal columns (PC) and the metallic rutile-type WO₂, with varying coupling of the [WO₆] octahedra (Figure 1b–e). Such structure modifications result in an increasing charge carrier concentration [12]. A further five observed phases in the range 2 < x < 3 are predicted to be bad metals with charge carrier densities of the order 10²¹–10²² cm⁻¹ according to band structure calculations [13]. Yet, these phases occur only in small domains of single crystals [14,15] or under high pressure conditions [16,17,18]. The fact that they are not observed as bulk materials might be attributed to a microstrain-driven ordering mechanism of the CS planes [19], which should be sensitive to the synthesis conditions.

The vapor-transport preparation route to obtain these phases comprises a high-temperature heating of WO_x powder mixtures over several days and weeks [14,15,21,22,23]. Recently WO_2.72 (W₁₈O₄₉) and WO_2.90 (W₂₀O₅₈) were successfully prepared by spark plasma sintering (SPS) being promising bulk TE materials [11,12,24]. SPS combines the solid-state reaction of powdered precursor mixtures with simultaneous shaping, and provides an effective manufacturing route for TE materials due to low temperatures and short reaction times [8]. The samples around the composition WO_2.90 still showed the formation of a further phase which was interpreted as WO_2.96 [25].

The knowledge on phase formation in the tungsten-oxide system under SPS conditions still appears fragmentary which complicates the evaluation of the system’s potential as a TE material. Thus, we studied the products of the SPS redox reaction dependent on both, the composition x in the range 2.50 ≤ x ≤ 3 (Figure 1a, dashed lines) and the synthesis temperature T_max with powder X-ray diffraction (PXRD). Subsequently, the TE properties of the SPS-prepared WO_x materials with x ≥ 2.72 were investigated.

In this work we use the notation “WO_x” for sample compositions, and “W_aO_b” for phases and their crystal structures.

2. Results & Discussion

2.1. Spark Plasma Preparation

The solid-state reaction

x/3 WO₃ + (1 − x/3) W → WO_x

(1)

was performed for different x by spark plasma sintering (SPS) in vacuum (<10 Pa) under an uniaxial pressure of 80 MPa (Figure 2a). Temperature programs included a linear heating with 50 K·min⁻¹, an isothermal dwell time t_dwell at the temperature T_max, and free cooling. Specific experiments in this work are notated by “SPS-T_max/t_dwell”.

For the reference material WO_2.90, the SPS treatment was optimized regarding the phase purity. Systematic variations of the temperature and dwell time in the ranges 1320 K ≤ T_max ≤ 1570 K and 10 min ≤ t_dwell ≤ 4 h, respectively, yielded the optimum regime SPS-1420 K/10 min (Figure 3b). Samples WO_x with x = {2.50, 2.72, 2.80, 2.82, 2.84, 2.86, 2.88, 2.92, 2.95, 2.98} were prepared with the same conditions.

Phase-pure reference material WO_2.72 was obtained via SPS-1420 K/35 min followed by SPS-1420 K/5 min with cleaning of the surface and grinding of the sample between both steps (Figure 2a).

A WO₂ reference sample was directly compacted from the as-purchased material with SPS-1470 K/10 min (green curve in Figure 4).

The compaction of the yellowish as-purchased material WO₃ with SPS-1420 K/10 min resulted in a bluish-violet and multiple-phase product according to PXRD (blue curve in Figure 4). Subsequent annealing performed at 1170 K for 68 h in the open air was supposed to yield the monoclinic γ-WO₃ [26] and resulted in a greyish-yellow specimen (Figure 3c).

2.2. Single-Phase Materials WO₂, WO_2.72, WO_2.90 and WO₃

According to PXRD, phase-pure material WO_2.72 is obtained from the two-step treatment (Figure 3a).

Phase-pure material WO_2.90 is yielded from the routine SPS-1420 K/10 min as seen from the PXRD pattern (Figure 3b), which shows only reflections of W₂₀O₅₈ (x = 2.90). However, all reflections except (0 k 0) show large FWHM values indicating good ordering only in the [010] direction (Figure 1d). Starting from this optimized regime for x = 2.90, the increase of both T_max and t_dwell promotes the formation of W₁₈O₄₉ (x = 2.72), WO₂ and an additional phase. We ascribe the composition x ≈ 2.82 for this phase as seen in the following. Thus, the schematic secondary reaction

W₂₀O₅₈ → W₁₈O₄₉ + WO₂ + “WO_2.82”

(2)

represents a further tungsten reduction below x = 2.90 and is probably a similar SPS-specific reduction effect which is observed for pure WO₃. However, in the case of W₂₀O₅₈ a further decomposition can be kinetically inhibited with a short SPS treatment time t_dwell = 10 min.

The WO₂ does not undergo changes during the SPS treatment. A minor amount of elemental tungsten is observed in both, the as-purchased and SPS-processed material (green curve in Figure 4).

The as-purchased WO₃ sample is confirmed to adopt monoclinic structure (γ-WO₃). In contrast, the PXRD pattern after SPS treatment (SPS-1420 K/10 min, blue curve in Figure 4) shows a mixture of γ-WO₃ (blue triangles), triclinic δ-WO₃ (cyan arrows), W₂₀O₅₈ (x = 2.90, red dots), and an additional phase (green stars) whose reflections resemble those of W₂₅O₇₃ (x = 2.92) [14]. The δ-WO₃ is the stable modification below 290 K [27]. Conventional preparation of WO₃ via high-temperature oxidation usually yields γ-WO₃ [28] whereas the conditions during the free cooling in the SPS processing could promote the further transition γ → δ. After annealing in open air (1170 K, 68 h), only γ- and δ-WO₃ is found in the reference sample (Figure 3c). Most possibly, the annealing time was not sufficient to complete the δ → γ transformation, or the cooling rate afterwards was not sufficient to suppress the γ → δ transition completely. No clear evidence is found for the existence of W₂₅O₇₃ due to strong reflection overlapping. Yet, a reducing influence of the SPS graphite die and lining on the WO₃ starting material is clearly seen from the formation of W₂₀O₅₈. It is supposed to appear at ≈ 1020 K [29] and occurs despite the short t_dwell = 10 min and even 1 min. This SPS specific reduction should be considered additionally to the reaction with W, and will result in WO_x samples with compositions slightly deviating from the nominal O/W-ratio x.

The refined lattice parameters of the as-purchased materials and obtained single-phase products are given in

Table 1. Lattice parameters of phases in the tungsten–oxygen binary system refined from PXRD patterns in this work in comparison to literature data (iv—long-term heating in vacuo, SPS—spark plasma sintering, n.a.—not specified in the reference).

x	Phase	Source	Space Group	Lattice Parameters					Ref.
				a	b	c	β	V
				Å	Å	Å	deg	Å3
2	WO2	n.a.	P21/c	5.58	4.90	5.664	120.7	133.1	[30]
		commercial		5.574(1)	4.898(1)	5.662(1)	120.69(1)	132.9(2)	this work
		SPS		5.575(1)	4.900(1)	5.663(1)	120.70(1)	133.0(1)	this work
2.72	W18O49	n.a.	P2/m	18.32	3.79	14.04	115.0	883.3	[31]
		iv		18.33	3.79	14.04	115.2	882.1	[32]
		n.a.		18.32	3.78	14.03	115.2	879.5	[33]
		SPS		18.32	3.79	14.04	n/a	---	[11]
		SPS		18.329(1)	3.784(1)	14.037(1)	115.20(1)	880.9(4)	this work
2.83	W12O34	n.a.	P2/m	17.0	3.8	19.4	105.3		[34]
		SPS a		17.229(1)	3.782(1)	19.496(1)	105.77(1)	1223(3)	this work
2.90	W20O58	iv	P2/m	12.1	3.78	23.4	85	1066.2	[21]
		calculated		12.05	3.77	23.59	85.3	1067.2	[35]
		SPS		12.08	3.78	23.59	n/a	---	[11]
		SPS		12.00	3.78	23.51	84.8	1062.0	[24]
		SPS		12.080(3)	3.782(1)	23.62(1)	85.36(1)	1075.6(7)	this work
2.92	W25O73	iv	P2/c	11.93	3.82	59.72	98.3	2693.1	[14]
3	γ-WO3	commercial	P21/n	7.33	7.56	7.73	90.5	428.3	[36]
		commercial		7.299(1)	7.537(1)	7.689(1)	90.88(1)	422.9(1)	this work

^a Parameters determined from only 10 main reflections.

together with the respective literature data.

2.2.1. Crystal Structure on Atomic Resolution

From high-resolution transmission electron microscopy (HR-TEM) along [001] of the single-phase WO_2.90, large ordering areas are observed (Figure 5a). The zoomed and Fourier-filtered image from the top-left area (Figure 5b), and the corresponding fast Fourier transform (FFT) reveal the expected values of the lattice parameters a and b, but also some superstructure reflections indicating the doubling of the lattice parameter c (Figure 5c). In [010] direction, CS planes are visible but massively disordered with varying alignments and spacing (Figure 5d) which are consistent with the large FWHM values in the PXRD pattern (Figure 4a). The zoomed and filtered image (Figure 5e) shows low ordering along [001], where only the (001) reflection is present, whereas along [100], reflections of the fifth- and even higher order are observed in the FFT image (Figure 5f).

2.2.2. Thermoelectric Properties

Among the known phases, the lowest electrical conductivity σ(T) values are measured for WO_2.90 with 77(3) × 10³ S·m⁻¹ over the whole temperature range, which is on the level of a heavily doped semiconductor (Figure S1a). A local maximum at 635 K is in good accordance with previous records [11,12,24]. The electrical conductivity of WO₂ and WO_2.72 indicates typical metallic behaviour with σ(T) ∝ 1/T dependency (Figure S1b). No electrical transport measurement was possible for the compacted and annealed WO₃ sample due to its insulating behaviour. This indicates the absence of oxygen vacancies after SPS and annealing, which would promote the electrical conductivity [37].

Both metallic samples (WO₂ and WO_2.72) reveal a relative high thermal conductivity κ_tot(T) > 10 W·m⁻¹·K⁻¹ (Figure 6a). However, in the dense WO₂ structure (Figure 1b), where strong tungsten–tungsten interactions are expected, this arises mainly from the lattice contribution κ_lat, whereas in WO_2.72 κ_el and κ_lat contribute equally (Figure 6b). For the electrically insulating WO₃ sample (κ_lat = κ_tot), the temperature dependence κ_lat(T) appears similar to that of WO_2.72. However, for WO_2.72 the approximation of κ_lat shows uncertainty of maximum 45% and a significant difference regarding WO₃ cannot be determined.

WO_2.90 shows κ_tot ≈ 3.5–4.5 W·m⁻¹·K⁻¹ over the whole temperature range (Figure 6a), which is close to previously published values [11,24]. With respect to errors its lattice contribution κ_lat equals that of WO₃ for T > 560 K (Figure 6b). Thus, the effect of CS planes in the W₂₀O₅₈ structure on the lattice thermal conductivity appears insignificant at high temperatures. The pentagonal column (PC) structural motif of the W₁₈O₄₉ phase (Figure 1c) in WO_2.72 might be an alternative phonon scattering center but proof requires a determination method for κ_lat which is more precise than our approximation from the Wiedemann-Franz law.

A direct property comparison of WO₂, WO_2.72, WO_2.90 and WO₃ can be conducted up to the maximum temperature T = 863 K at which WO_2.72 was investigated. Here WO_2.90 exhibits the highest Seebeck coefficient with α = −55 µV·K⁻¹ in contrast to WO_2.72 and WO₂ with −24 µV·K⁻¹ and −22 µV·K⁻¹ respectively (Figure S2a).

The figures of merit ZT at T = 860 K are low (0.006, 0.017 and 0.045 for WO₂, WO_2.72 and WO_2.90, respectively, Figure S2b). Maximum ZT = 0.061 is found for WO_2.90 at 963 K. The low Seebeck coefficient is a drawback for WO_2.72 and WO₂, together with the high κ_lat of WO₂. However, in the measured temperature range none of the materials shows a ZT maximum as of yet.

2.3. Compositions WO_x

The phase formation in WO_x samples with varying x is established from the PXRD patterns after the SPS-1420 K/10 min treatment (Figure 4). Semi-logarithmic plotting emphasizes reflections with low intensity. In

Table 2. Phases observed from PXRD in WO_x samples prepared with SPS-1420 K/10 min (●—observed, □—not observed).

x	Phases
	WO2	W18O49	“WO2.82” a	W20O58	W25O73 b	γ/δ-WO3
2	●	□	□	□	□	□
2.50	●	●	□	□	□	□
2.72–2.80	□	●	●	□	□	□
2.82–2.88	□	●	●	●	□	□
2.90	□	□	□	●	□	□
2.92–3	□	□	□	●	●	●

^a Presumed composition of the new phase. Synchrotron data suggests this to be W₁₂O₃₄. ^b Phase hard to detect due to strong reflection overlapping.

the observed phases are listed.

For x = 2.50 (Figure 4) only WO₂ (green squares) and W₁₈O₄₉ (x = 2.72, brown rhombs) phases are observed as predicted from the phase diagram (Figure 1a).

In the range 2.72 ≤ x ≤ 2.90, only W₁₈O₄₉ (x = 2.72) and W₂₀O₅₈ (x = 2.90) are expected according to the phase diagram. For 2.72 ≤ x ≤ 2.80, W₁₈O₄₉ and an additional phase (black arrows) are observed. With increasing O/W-ratio (2.82 ≤ x ≤ 2.88) the expected reflections of W₂₀O₅₈ (x = 2.90, red dots) appear. The unindexed reflections are most intense for x = 2.82. From diffraction data of this sample containing only W₁₈O₄₉ and the additional phase, we find many reflection positions fitting to the pentagonal column phase W₁₂O₃₄ (x = 2.83) [34]. In our case, the parameters of the monoclinic unit cell are slightly changed to a = 17.229(1) Å, b = 3.782(1) Å, c = 19.496(1) Å and β = 105.77(1) (Table 1). This is just a rough suggestion; a structure refinement was not successful yet. Distinct reflections of this phase are found also after a comparative synthesis in evacuated silica tubes, which rules out the SPS as cause for its formation (Figure S3). Attempts on synthesis of this phase as single-phase bulk material and further investigations on the structure are pending.

For 2.92 ≤ x ≤ 2.98, the PXRD patterns resemble that of pure WO₃ processed in the SPS: reflections of γ-WO₃, δ-WO₃, W₂₀O₅₈ (x = 2.90) and possibly W₂₅O₇₃ (x = 2.92) occur. A bluish-violet color of all samples with 2.92 ≤ x ≤ 2.98 supports the existence of the latter since W₂₀O₅₈ and W₂₅O₇₃ are colored deeply blue and violet respectively [14,21]. However, samples with the nominal composition (x = 2.92) do not yield single-phase materials. Under SPS conditions, W₂₅O₇₃ might not be stable.

2.3.1. Microstructure

From polarized light microscopy (PLM), the grain size of all synthesized WO_x samples is found to be of the order 10–30 µm (Figure 7). A color variation from yellow to red to blue with increasing O/W-ratio x is caused by the different optical reflectivity of the occurring phases. According to SEM images with backscattered electron (BSE) contrast, the samples are homogeneous. Distinct porosity is found only for x = 2 and 2.98. Energy dispersive X-ray spectroscopy (EDX) reveals tungsten and oxygen only, but differences of the oxygen content are below the detection limit.

2.3.2. Thermoelectric Properties

The electrical conductivity of the WO_x samples strongly correlates with the O/W-ratio x. When the oxygen concentration is increased to x ≥ 2.90, there is a continuous decrease of σ(T) with minor temperature dependence similar to that of WO_2.90 (Figure 8a). According to PXRD (Figure 4), next to W₂₀O₅₈ the nearly insulating phases δ- and γ-WO₃ occur in this composition range. Thus, the charge carrier concentration and σ(T) mainly depend on the W₂₀O₅₈ content, which decreases with increasing x. The influence of one further phase, possibly W₂₀O₇₃ (x = 2.92), is not known as of yet.

For decreasing O/W-ratio x < 2.90, a metallic behaviour is promoted continuously (Figure 8a). The σ(T) approaches that of x = 2.72 with the increasing W₁₈O₄₉ (x = 2.72) phase content (Figure 4). No discontinuity of σ(T) is found for x = 2.82 where the highest amount of “WO_2.82” is observed. Thus, this phase is electrically conducting. Altogether, the composition x = 2.90 is the limit between metallic and nonmetallic behaviour (Figure 8b).

A similar trend is observed for the Seebeck coefficient (Figure 9a). Strong non-monotonic behaviour for the composition x = 2.98 results from the large amounts of WO₃ in the material (Figure 4) and its therefore near-insulating character during the TE property measurements. The specific influence of the “WO_2.82”and W₂₅O₇₃ (x = 2.92) phases cannot be considered yet due the lack of the TE properties of the phase-pure material.

The continuous property change of WO_x materials for 2.80 ≤ x ≤ 3 also appears in the thermal conductivity κ_tot (Figure 10a). With respect to the uncertainty of the Wiedemann–Franz approximation of κ_el (Equations (4) and (5)), κ_lat is very similar for all samples x < 2.98 (Figure 10b). In the composition range 2.90 ≤ x ≤ 2.95 where CS plane phases are found (Table 2), the lattice contribution κ_lat appears almost temperature-independent. For T > 550 K these samples show no significant reduction of κ_lat regarding the WO₃ reference sample with respect to the occuring errors. The exceptionally low value for x = 2.98 might be the result of porosity also found by microstructure analysis. However, in the three-phase region (2.82 ≤ x ≤ 2.88) of the system (Table 2), a significantly reduced κ_lat is found for x = 2.84 up to T ≤ 700 K. This tendency is also noticable from a plot of κ_lat vs. the O/W-ratio x (Figure 10b inset). It indicates that at high temperatures, the lowest κ_lat is achieved for WO_x materials with multiple phases due to enhanced phonon scattering at the interfaces.

The resulting ZT for the WO_x compositions are very similar to that of WO_2.90 (Figure 9b). For x = 2.92, the highest ZT = 0.072 is reached at 963 K. An exceptional low ZT is reached for x = 2.82 and x = 2.98 due to the high ${\kappa }_{tot}$ and low σ(T) respectively. However, none of the compositions shows a ZT maximum in the measured temperature range as of yet.

3. Materials and Methods

3.1. Materials

The purchased powders of starting materials WO₃ (Alfa Aesar, 99.998 wt %, 10–20 µm), WO₂ (Sigma-Aldrich, 99.99 wt %, <150 μm) and elemental W (Chempur, 99.9 wt %, 8–9 µm) were analyzed regarding crystalline contaminations with PXRD. For the preparation of WO_x samples (2.50 ≤ x ≤ 2.98), WO₃ was manually mixed for 15 min under argon atmosphere with appropriate amounts of W.

3.2. Spark Plasma Sintering

For spark plasma sintering (SPS), graphite dies with diameters of 8 mm or 10 mm (Figure 2b) and a graphite lining were filled with ca. 1 g of starting mixture under argon atmosphere, and processed with a SPS-515 ET Sinter Lab apparatus (Fuji Electronic Industrial Co. Ltd., Tsurugashima, Japan).

3.3. Powder X-ray Diffraction

The starting materials and SPS-processed samples were examined with powder X-ray diffraction (PXRD) on the Guinier camera G670 (HUBER Diffraktionstechnik GmbH & Co., KG, Rimsting, Germany) with Cu-K_α1 radiation (λ = 1.540598 Å, graphite monochromator, 5° ≤ 2θ ≤ 100°, ∆2θ = 0.005°). All PXRD data was compared to the theoretical patterns of known phases (Table 1). A LaB₆ standard was added to single-phase materials for a subsequent cell parameter determination using the least-square method in the WinCSD software package [38].

3.4. High-Resolution Transmission Electron Microscopy

For high-resolution transmission electron microscopy (HR-TEM), a sample was ground to fine powder and dispersed in methanol. The suspension was loaded on a 100-mesh hexagonal copper grid Quantifoil S7/2 (Quantifoil Micro Tools GmbH, Jena, Germany), which was covered beforehand with a carbon film (2 nm). After a complete drying, HR-TEM imaging was performed on a Tecnai F30 (FEI Technologies Inc., Hillsboro, OR, USA) with a field-emission gun at an acceleration voltage of 300 kV. The point resolution amounted to 1.9 Å, and the information limit amounted to ca. 1.2 Å. The microscope was equipped with a wide-angle slow-scan CCD camera (MultiScan, 2 k × 2 k pixels; Gatan Inc., Pleasanton, CA, USA). TEM images were analyzed with the DigitalMicrograph software (Gatan Inc., Pleasanton, CA, USA).

3.5. Thermoelectric Properties

TE properties were measured for the reference samples x = {2, 2.72, 2.90, 3} and the WO_x samples in the range 2.82 ≤ x ≤ 2.98. Samples previously powdered for PXRD were compacted with SPS-1320 K/10 min and a heating rate of 75 K·min⁻¹. Subsequently, the mass density ρ was determined with Archimedean method (Table S1).

The thermal diffusivity D(T) was measured by laser flash analysis (LFA) on a LFA 457 MicroFlash (NETZSCH GmbH & Co. Holding KG, Selb, Germany) in vacuum between room temperature and 963 K in steps of 25 K. Subsequent polishing removed a subtle yellow stain from the pellet surface which occurred during the LFA. Differential scanning calorimetry (DSC) measurements of the specific heat capacity c_p (T) yielded values that for all WO_x samples were identical to WO₃ with respect to the measurement error (Figure S4). Thus, for the calculation of the total thermal conductivity

κ_tot(T) = ρc_p(T)D(T)

(3)

(T—absolute temperature) of WO_x and WO₂ there were used theoretic $c_p\left(T\right)$ curves for WO₃ and WO₂, respectively [39,40]. After an Archimedian density determination, the microstructure was analyzed with polarized light microscopy (LM), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). Tetragonal bars with the dimensions a ≈ 1.5 mm and b ≈ 6–8 mm were cut from the pellets using a wire saw (Figure 2c). The measurements of the electrical conductivity σ(T) and Seebeck coefficient α(T) were performed perpendicular to the SPS pressure direction along the b-edge on a ZEM-3 (ULVAC-RIKO, Munich, Germany) under low pressure helium from RT to 863 K or 963 K in steps of 25 K. The samples were polished before every measurement. The electronic contribution ${\kappa }_{\mathsf{e}\mathsf{l}}$ to the total thermal conductivity and consequently the lattice contribution κ_lat = κ_tot − κ_el were calculated with the Wiedemann–Franz equation

κ_el(T) = L(T)σ(T)T

(4)

Since for semiconductors the Lorenz number L(T) can strongly deviate from the constant value L = 2.4453 × 10⁻⁸ WΩ·K⁻² the approximation

L(T) = 1.5 + exp [−|α(T)|/116]

(5)

was used, which is based on the single parabolic band model with acoustic phonon scattering [41]. Comparative results obtained with constant L show only minor deviations and all trends remain the same. For a comparison with other TE materials, the figure-of-merit ZT was calculated according to

ZT = [α²(T)σ(T)T]/κ_tot(T).

(6)

4. Conclusions

According to powder X-ray diffraction (PXRD), a new phase termed as “WO_2.82” is observed in the composition range 2.72 ≤ x ≤ 2.90 in addition to the expected pentagonal column (PC) phase W₁₈O₄₉ (x = 2.72) and crystallographic shear (CS) plane phase W₂₀O₅₈ (x = 2.90). The reflection positions of “WO_2.82” in the synchrotron pattern of a two-phase W₁₈O₄₉/“WO_2.82” sample somewhat fit the PC phase W₁₂O₃₄ (x = 2.83) with slightly changed lattice parameters. The synthesis as single-phase material and structure refinement still failed, which indicates that the phase is metastable and its structure needs to be further analyzed.

Single-phase WO_2.90 material is directly obtained from SPS-1420 K/10 min. Both powder X-ray diffraction (PXRD) and high-resolution transmission electron microscopy (HR-TEM) show disorder of the CS planes. Single-phase WO_2.70 material is obtained from SPS-1420 K/35 min followed by grinding and SPS-1420 K/5 min.

Electronic transport properties of WO_x materials (2.80 ≤ x ≤ 2.98) from the routine SPS-1420 K/10 min reveal a continuous tunability, practically independent from the phases present in the samples. Both the electrical conductivity σ(T) and the thermal conductivity κ_tot(T) indicate an increase of the charge carrier concentration with increasing oxygen deficiency. Here, the composition WO_2.90 is the limit between metallic (x < 2.90) and nonmetallic behaviour (x ≥ 2.90).

The multi-phase character of these samples found by PXRD is crucial for the thermal conductivity. Significant reduction of κ_lat regarding WO₃ is found up to 700 K for the three-phase material WO_2.84. Thus, for x < 2.90 the introduction of multiple phases is a way for reducing the thermal conductivity due to increased phonon scattering at the phase interfaces. The formation of the PC phases in this composition range might have additional influence. In contrast, for 2.90 ≤ x ≤ 3, which is the typical range for the formation of CS plane phases, a reduction of κ_lat is observed only below 550 K. For high-temperature applications, CS planes might be less appropriate phonon scattering centers.