Thermo-Physical Properties of Hexavalent Tungsten W⁶⁺-Doped Ta-Based Ceramics for Thermal/Environmental Barrier Coating Materials

Abstract

The CaTa_0.8WO₆ ceramic was fabricated by a solid-state reaction for thermal/environmental barrier coating (Thermal and Environmental Barrier Coating) applications, and the microstructures, mechanical and thermal properties were investigated. The result showed CaTa_0.8WO₆ has a lower thermal conductivity (1.05 W·m⁻¹·K⁻¹ at 900 °C) than 8 wt.% yttria-stabilized zirconia and the doped Ta-based ceramics with Mg²⁺, Yb³⁺, Zr⁴⁺ and Nb⁵⁺, indicating that hexavalent tungsten element W⁶⁺ doping effectively reduces thermal conductivity and improves thermal insulation performance of Ta-based ceramics. The thermal expansion rates curve without inflection points resulting from phase transition indicates that CaTa_0.8WO₆ has excellent high-temperature phase stability. Since the Young’s modulus and Pugh’s ratio of CaTa_0.8WO₆ ceramics were lower than those of various valence states doping Ta-based ceramics, which means that CaTa_0.8WO₆ has better damage tolerance.

1. Introduction

A Thermal/Environmental Barrier Coating (T/EBC) has the advantages of preventing high-temperature corrosion of the substrate, prolonging the service life of hot-end components, increasing engine power, high hardness, good chemical stability, and reducing fuel consumption [1,2,3]. Moreover, the main interest in a thermal barrier coating is its ability to ensure a strong thermal gradient within it and then prevent the overheating of the substrate. The primary criteria for screening materials for T/EBCs are as follows [4,5,6]: (1) high melting point (>2000 K); (2) low thermal conductivity; (3) high-temperature phase stability; (4) matching the thermal expansion coefficient to the substrate; (5) excellent mechanical properties; and (6) excellent high-temperature corrosion resistance. Currently, 8 wt.% yttria-stabilized zirconia (8YSZ) ceramic, utilized as thermal barrier coatings material (TBCs), exhibits excellent thermal insulation and thermal shock resistance, making them suitable for application on metal substrates in high-temperature environments [7,8]. However, the reversible phase transfer from monoclinic zirconia (m-ZrO₂) to tetragonal zirconia (t-ZrO₂) occurs at around 1170 °C; the results may induce a volume fluctuation between 3–5%, leading to high thermal stresses and severe coating destruction [9,10]. Exploring alternate materials for high-temperature performance above 1200 °C has thus been an ongoing and unrelenting endeavor. Potential TBC materials have recently undergone evaluation, including RETaO₄ [11], RE₂Zr₂O₇ [12,13], RE₂Ce₂O₇ [14], RE₂Si₂O₇ [5,15], REPO₄ [16], RENbO₄ [17] (RE = La~Gd), ABO₃ (A = Ba, Sr, Ca and La, B = Zr and Ti) [18,19], etc.

Although most ceramics have high thermal insulation properties, there is an urgent need to improve the thermophysical properties of ceramics or find new candidate materials due to low thermal expansion coefficient, poor high-temperature stability and low fracture toughness for those ceramics. Although most ceramics have high thermal insulating properties due to the low thermal expansion coefficient, poor high-temperature stability, and low fracture toughness, these properties either improve the thermophysical properties of ceramics or indicate a new candidate material is urgently needed [20].

Tantalate-based ceramics, with their low thermal and ionic conductivities, matrix-matched thermal expansion coefficients, excellent ferroelastic toughness, and high phase transition temperatures, are another novel candidate for T/EBCs [21,22,23]. The thermal conductivity of RETaO₄, RE₃TaO₇, and RETa₃O₉ ceramics were 1.43~2.25 W·m⁻¹·K⁻¹ [24,25,26], respectively. However, the thermal conductivity of Ta-based ceramics still needs to be reduced to improve their thermal barrier properties. An added dopant can either enhance or suppress the thermophysical properties. Defects are being introduced into materials by the process of doping with metal ions, which is becoming an increasingly popular method for improving the properties of materials [27]. To improve the thermophysical properties of Ta-based ceramics by doping, defects are introduced by utilizing dopants with varying valence states including 2⁺, 3⁺, 4⁺, and 5⁺ elements, such as Y_1−xMg_xTaO_4−x/2 [28], (Y_1−xDy_x)TaO₄ [29], (Y_1−xYb_x)TaO₄ [30], Dy_1−xTa_1−xZr_2xO₄ [31], and Yb(Ta_xNb_1−x)O₄ [32]. These materials exhibit good thermo-physical properties, but the decrease in thermal conductivity was still limited. Herein, a new Ta-based oxide ceramic CaTa_0.8WO₆ with a large cation radius and cation mass variation was designed and successfully synthesized using a solid-state reaction method. The microstructure and thermal and mechanical properties of CaTa_0.8WO₆ were investigated. The results indicate that CaTa_0.8WO₆ has relatively low thermal conductivity, Young’s modulus and Pugh’s ratio, thereby indicating the possibilities of CaTa_0.8WO₆ for environmental/thermal barrier coatings.

2. Experimental Procedure

2.1. Materials and Synthesis

The CaTa_0.8WO₆ ceramic was fabricated using a solid-state reaction method. The raw materials include calcium oxide (CaO), tungsten oxide (WO₃), tantalum pentoxide (Ta₂O₅) (≥99.99% purity, Aladdin-China), and anhydrous ethanol. The raw materials weighted in stoichiometric ratios were well-mixed with anhydrous ethanol using ball milling under 300 rpm for 24 h in an air atmosphere; the solution was dried at 80 °C for 36 h and then passed through a 100-mesh sieve. The substance was prepared into discs with a diameter of 6 cm and a thickness of 1.13 cm by cold isostatic pressing, then sintered in a box furnace at 1550 °C for 5 h to obtain CaTa_0.8WO₆ ceramic discs. The reaction equation is described as follows:

$${5\mathrm{CaO}+5\mathrm{WO}}_3{+2\mathrm{Ta}}_2{\mathrm{O}}_5{=5\mathrm{CaTa}}_{0.8}{\mathrm{WO}}_6$$

(1)

2.2. Microstructure Characterization

The phase structures of CaTa_0.8WO₆ are tested by employing X-ray diffraction (XRD, Cu/Kα, Bruker D8, Karlsruhe, Germany) and are identified with reference to the PDF#39-1430 of CaTa₂O₆. The microstructure was characterized using Scanning Electron Microscopy (SEM, VEGA3 SBH, Brno, Czech Republic) and Energy Dispersive Spectroscopy (EDS, Oxford, UK).

The ultrasonic pulser ultrasonic pulser receiver instrument (UMS-100; RITEClab, RITEClab, Chelles, France) was employed to detect the transverse acoustic velocity (υ_t, parallel to the sample surface) and longitudinal acoustic velocity (υ_l, vertical to the sample surface) of the sample with a diameter of 6 cm and a thickness of 1.13 cm. Additionally, the following formula is used to determine the average acoustic velocity (υ_m), Poisson ratio (v), Young’s modulus (E), shear modulus (G), bulk modulus (B), and Debye temperature (θ_D) [33,34]:

$${\upsilon }_m={\left[{\displaystyle \frac{1}{3}}({\displaystyle \frac{1}{{\upsilon }_l^3}}+{\displaystyle \frac{2}{{\upsilon }_t^3}})\right]}^{-{\displaystyle \frac{1}{3}}}$$

(2)

$$v={\displaystyle \frac{1-2{({\upsilon }_t/{\upsilon }_l)}^2}{2-2{({\upsilon }_t/{\upsilon }_l)}^2}}$$

(3)

$$E={\displaystyle \frac{\rho {\upsilon }_t^2(3{\upsilon }_l^2-4{\upsilon }_t^2)}{({\upsilon }_l^2-{\upsilon }_t^2)}}$$

(4)

$$G={\displaystyle \frac{E}{2(2+v)}}$$

(5)

$$B=\rho ({{\upsilon }_l}^2-{\displaystyle \frac{4}{3}}{{\upsilon }_t}^2)$$

(6)

$$\gamma ={\displaystyle \frac{3}{2}}({\displaystyle \frac{1+v}{2-3v}})$$

(7)

$${\theta }_D={\displaystyle \frac{h}{k_B}}{({\displaystyle \frac{3N}{4\pi V}})}^{{\displaystyle \frac{1}{3}}}\times {\upsilon }_m$$

(8)

where Plank’s constant h = 6.6260693 × 10⁻³⁴ J·s, Boltzmann constant k_B = 1.380649 × 10⁻²³ J·K⁻¹, γ is the Grüneisen parameter, and N and V are the number of atoms and the volume in unit cell, respectively. The reduced Young’s modulus and hardness values of CaTa_0.8WO₆ at the nanoscale were examined using NanoBlitz 3D (Nanomechanisc, Inc. iMicro, Oak Ridge, TN, USA) with a load of 40 mN, a holding time of 10 s, an indentation depth of 5078.68 nm and a Poisson ratio (v = 0.32) measured by UMS. The Vickers hardness (Hv) was determined by employing the Vickers indentation technique (Buehler, Omnimet MHT, Lake Bluff, IL, USA) with loads ranging from 0.98 N to 9.8 N and a holding time of 15 s. To remove the effect of porosity on the test hardness, the samples are polished with a polishing machine to flatten the sample surface prior to testing. Meanwhile, to obtain the average value and standard deviation, the hardness values under the same conditions were repeated 10 times.

The thermal diffusivity (α) of CaTa_0.8WO₆ ceramics was measured using NETZSCH’s LFA-427 laser thermal conductivity meter (NETZSCH, Bobingen, Germany). The principle of the test is as follows: The lower surface of the specimen is heated by a 0.2 to 1.2 ms laser pulse generated by an Nd:GGG laser and the heat diffuses through the specimen, raising the temperature on the upper surface. The temperature on the back of the sample is monitored using an InSb infrared detector to determine the sample’s thermal diffusivity. The sample size is φ6 mm × 1.13 mm, and the test circumstances are three tests at each temperature point at 25 °C, 100 °C, 200 °C, 300 °C, 400 °C, 500 °C, 600 °C, 700 °C, 800 °C, and 900 °C. The test gas is Ar₂, the laser voltage is 650 V, and the pulse width is 0.5 ms. After collecting the density, specific heat, and thermal diffusion coefficient of the sample, the thermal conductivity κ can be calculated using the following equation:

$$\kappa =\alpha C_P\rho$$

(9)

where bulk density $\rho$ was determined using the Archimedes method, and heat capacity C_p was calculated by the Kopp–Neumann rule. The thermal expansion coefficients (TECs) of the CaTa_0.8WO₆ ceramic from room temperature to 1100 °C were determined via a thermo-mechanical analyzer (NETZSCH TMA 402 F3, Selb, Germany).

3. Results and Discussion

3.1. Microstructure

Figure 1a displays the experimental XRD patterns of the CaTa_0.8WO₆, where the main peaks are in agreement with the PDF card (39-1430) of the orthorhombic structured CaTa₂O₆. However, there are peaks corresponding to Ta₈W₉O₄₇ (PDF#50-0091) at 2θ = 14.4° and 16.5°, which could be the result of the preferential orientation that occurs during the sintering process. Therefore, it can be supposed that after the CaO-Ta₂O₅ reaction, which yields CaTa₂O₆, WO₃ interacts with CaTa₂O₆ to produce CaTa_0.8WO₆. The closer the ions are to each other, the easier it is to form a solid solution, and the type of solid solution is determined according to Hume-Rothery [35]:

$$\delta ={\displaystyle \frac{r_1-r_2}{r_1}}$$

(10)

where r₁ and r₂ represent the solvent or solute ion radii, respectively. Here, the ionic radius of W⁶⁺ (62 pm) is closer to that of Ta⁵⁺ (69 pm), the δ = 10.15% based on Equation (10), which is less than 15%, implying that it forms a continuous solid solution. Thus, W⁶⁺ and Ta⁵⁺ occupy the same lattice site in the CaTa₂O₆ lattice to form CaTa_0.8WO₆ ceramics. Figure 1b,c show the microstructure of the CaTa_0.8WO₆ sample sintered at 1550 °C for 5 h. The grain boundary was obvious; small grains are attached to the surface of large grains, and the grain size of the samples was approximately 1–15 μm. No pores and cracks are observed at the surface of the sample, revealing that the sample has a high relative density. The density of CaTa_0.8WO₆ determined by Archimedes method is 5.3 g/cm³. Figure 1d–g are the EDS mappings of CaTa_0.8WO₆, which indicates no obvious element segregation, and the distribution of all elements was homogeneous at the micrometer scales.

3.2. Mechanical Properties

The mechanical properties are an essential criterion for the application of T/EBCs materials.

Table 1. The transverse acoustic velocity (υ_t), longitudinal acoustic velocity (υ_l), mean acoustic velocity (v_m), Bulk modulus (B), Young’s modulus (E), Shear modulus (G), Poisson’s ratio (v), Grüneisen parameter (γ), and Debye temperature (θ_D) of oxide ceramics of Mg²⁺, Yb³⁺, Zr⁴⁺, Nb⁵⁺, and W⁶⁺-doped Ta-based ceramics.

Samples	vt (m·s−1)	vl (m·s−1)	vm (m·s−1)	E (GPa)	B (GPa)	G (GPa)	γ	v	θD (K)	Refs.
CaTa0.8WO6	2618	5132	2934	96.2	91.2	36.33	1.93	0.32	236	This work
YTaO4	2702	5286	2742	138	156	51	2.13	0.35	354	[36]
Y0.8Mg0.2TaO3.9	2369	5067	2771	94.9	86.11	36.1	1.84	0.31	341	[28]
Y2/6Yb4/6TaO4	2249	4236	2516	106	78.5	41.2	1.6	0.28	325	[30]
Dy0.97Ta0.97Zr0.06O4	-	-	-	130	98	51	-	0.28	-	[31]
Yb(Ta2/6Nb4/6)O4	2430	4943	3376	120.41	126.64	44.88	2.06	0.34	438.92	[32]

shows that CaTa_0.8WO₆ has a lower Young’s modulus (96.2 GPa) than YTaO₄ [36], Y_2/6Yb_4/6TaO₄ [30], Dy_0.97Ta_0.97Zr_0.06O₄ [31], Yb(Ta_2/6Nb_4/6)O₄ [32], and YSZ (210~250 GPa) [37]. The Young’s modulus of oxide ceramics is indicative of the bonding strength of the chemical interactions within the material. The ductile–brittle distinction is frequently achieved by utilizing Pugh’s ratio (G/B). Ductility or damage tolerance is indicated by a low Pugh’s ratio (G/B < 0.57) [38]. The Pugh’s ratio (G/B) of CaTa_0.8WO₆ is calculated based on the data in Table 1 to be 0.40, which is lower than that of Y_0.8Mg_0.2TaO_3.9 (0.42), Y_2/6Yb_4/6TaO₄ (0.52), and Dy_0.97Ta_0.97Zr_0.06O₄ (0.52). A low Pugh’s ratio implies that CaTa_0.8WO₆ is expected to be a damage-tolerant ceramic.

Hardness is an important descriptor of the resistance of thermal barrier coating materials to permanent localized deformation [23]. Indentation is the primary way of assessing hardness in the Vickers hardness test. First and foremost, before beginning the experiment, the sample must be ground and polished to ensure the stability of the testing surface. Various loads are used to apply pressure to the sample and are held for a set amount of time to form an indentation. Figure 2 illustrates that the Vickers hardness rises with increasing load, exhibiting a gentler rise when the force exceeds 4.9 N. On the one hand, at low loads, the size of the indentation is relatively small, and the micro-uniformity of the material surface has a greater effect on the hardness measurement. As the load increases and the indentation size increases—the measurement results are more reflective of the overall properties of the material, resulting in an increase in the hardness value [39]. On the other hand, low loads may be more affected by the surface state of the material (e.g., oxide layer, roughness, etc.). High loads can penetrate the surface layer to a certain extent, reducing the interference of surface effects and allowing hardness measurements to more accurately reflect the internal properties of the material [40]. Therefore, the corresponding hardness value of 9.4 GPa, when the load is large (P = 9.8 N), reflects the actual mechanical properties of CaTa_0.8WO₆.

In addition, the Young’s modulus and hardness of CaTa_0.8WO₆ on the nanoscale were tested with NanoBlitz 3D. The test area measures 300 μm × 300 μm with a lateral step of 10 µm, comprising 900 indentation points; a high density of test points can significantly minimize testing errors. Figure 3a illustrates that the hardness of CaTa_0.8WO₆ ceramics ranges from 2 to 12 GPa, and the average value of the hardness is around 6.8 GPa, which is inferior to that of YSZ (10 GPa) [37,41,42]. The Young’s modulus is significantly lower than that of YSZ (250 GPa) [37], as shown in Figure 3b, which spans from 70 to 180 GPa, and the average value of the Young’s modulus is around 146 GPa. The scatter plot of Young’s modulus against the hardness of CaTa_0.8WO₆ ceramics is shown in Figure 3c. The fitting results show a clear positive link between the Young’s modulus and hardness, and this relationship can be fitted as follows: E = 104.6 + 6.2H. It is worth noting that hardness values below 4 GPa and a Young’s modulus below 110 GPa are more dispersed from the total number of data points, which may be the result caused by the contact of the indenter with the hole. Thus, these dispersed data have been removed from Figure 3c.

The comparison of Young’s modulus and hardness was measured using two methods; the Young’s modulus tested by the ultrasonic pulse method is lower than that of NanoBlitz 3D. This is because there are voids in the bulk sample, and phonon scattering exists, which reduces the transverse and longitudinal acoustic velocity. On the other hand, the diamond indenter for nanoindentation equipment is relatively small, and the test area is also relatively small, so it is difficult to encounter holes. Thus, the reduced Young’s modulus tested by nanoindentation better reflects the true mechanical properties of the material. Here, the hardness values tested by indentation and nanoindentation are closer to each other.

3.3. Thermal Properties

The thermal diffusion coefficient was obtained using a laser thermal conductivity meter, and the thermal conductivity of CaTa_0.8WO₆ was calculated by Equation (9). Figure 4 depicts the thermal properties of Mg²⁺, Yb³⁺, Zr⁴⁺, Nb⁵⁺, and W⁶⁺-doped Ta-based ceramics. The heat capacity C_p was calculated by the Kopp-Neumann rule, thermal diffusivity (α) of were conducted using a thermal analyzer, the thermal conductivities were determined using equation (9) for CaTa_0.8WO₆ ceramics, and the thermal properties of CaTa_0.8WO₆ and reported Y_0.8Mg_0.2TaO_3.9 [28], (Y_2/6Yb_4/6)TaO₄ [30], Dy_0.97Ta_0.97Zr_0.06O₄ [31], and Yb(Ta_2/6Nb_4/6)O₄ [32] were compared. Figure 4a shows the specific heat capacity (C_p) rises with the temperature increase results from volumetric expansion and phonon excitation [21]; the specific heat capacity (C_p) of CaTa_0.8WO₆ is higher than that of Y_0.8Mg_0.2TaO_3.9 [28], Y_2/6Yb_4/6TaO₄ [30], and Yb(Ta_2/6Nb_4/6)O₄ [32]. As shown in Figure 4b, the experimental thermal diffusivity (${\alpha }_{exp}$) rises with increasing temperature due to enhanced thermal radiation at elevated temperatures as a result of the competition of photon scattering over phonon scattering [43,44,45]. To eliminate the thermal conductivity associated with photon scattering, the thermal conductivity intrinsic thermal conductivity (${\kappa }_{Int}$) of CaTa_0.8WO₆ resulting from phonon scattering can be calculated using the following equation [46]:

$${\displaystyle \frac{1}{\alpha }}~{\displaystyle \frac{1}{l(w,T)}}~({\displaystyle \frac{b{n}^{1/3}C}{{\theta }_D}})T+(D-{\displaystyle \frac{C}{2}})$$

(11)

where l(w,T) corresponds to phonon mean free path; b, C, and D represent constants; and n refers to the number of atoms in the primitive cell. As shown in Figure 4c, the reciprocal intrinsic thermal diffusion (${\alpha }_{Int}^{-1}$) of CaTa_0.8WO₆ ceramic was linearly fitted using the experimental thermal diffusivity (${\alpha }_{exp}$) from 100 to 500 °C, and the linear fitting formula is ${\alpha }_{Int}^{-1}=0.00113T+1.33576$. Therefore, the intrinsic thermal diffusion (${\alpha }_{Int}$) from 100 to 900 °C was determined based on the above fitting formula, and the intrinsic thermal conductivity ${\kappa }_{Int}$ is determined using Equation (9). The intrinsic thermal diffusivity of CaTa_0.8WO₆ in Figure 4b is lower than that of Yb(Ta_2/6Nb_4/6)O₄ [32] and 7YSZ [7], close to that of YTaO₄ [36], Y_0.8Mg_0.2TaO_3.9 [28], Y_2/6Yb_4/6TaO₄ [30], and Dy_0.97Ta_0.97Zr_0.06O₄ [31].

Figure 4d illustrates the dependence of the thermal conductivity of CaTa_0.8WO₆ on the temperature. Thermal conductivities dropped from 1.374 to 1.215 W·m⁻¹·K⁻¹ when temperatures rose from 100 to 500 °C, then slightly rose from 600 to 900 °C due to the competition of photon scattering over phonon scattering. The intrinsic thermal conductivity (1.05 W·m⁻¹·K⁻¹ at 900 °C) of CaTa_0.8WO₆ is much lower than YTaO₄ [36], Y_0.8Mg_0.2TaO_3.9 [28], Y_2/6Yb_4/6TaO₄ [30], Dy_0.97Ta_0.97Zr_0.06O₄ [31], Yb(Ta_2/6Nb_4/6)O₄ [32], and 7-8YSZ [7,8], which indicates that CaTa_0.8WO₆ has excellent thermal barrier properties, which could be related with the following factors. Firstly, the heat capacity and thermal diffusion of CaWTa₂O₉ are similar to those of YTaO₄, Y_0.8Mg_0.2TaO_3.9, Y_2/6Yb_4/6TaO₄, Dy_0.97Ta_0.97Zr_0.06O₄, and Yb(Ta_2/6Nb_4/6)O₄, but the density of CaWTa₂O₉ (5.3 g/cm³) is lower than that of the above TBCs, thus the thermal conductivity of CaWTa₂O₉ is lower. Meanwhile, the low Young’s modulus means the material has a higher lattice vibration anharmonicity and a lower intrinsic heat conductivity [47]. The Young’s modulus of CaTa_0.8WO₆ ceramics is 96.2Gpa which is lower than that of YTaO₄ (138 GPa), Y_2/6Yb_4/6TaO₄ (106 GPa), Dy_0.97Ta_0.97Zr_0.06O₄ (130 GPa), Yb(Ta_2/6Nb_4/6)O₄ (120.41 GPa), and 7-8YSZ (210 and 250 GPa). Thirdly, since the Ta and W ions have a similar ionic radius and different valence, their non-equivalent substitution leads to electron exchange between Ta⁵⁺ and W⁶⁺ ions, and the electrical structure becomes complicated. This, in turn, causes lattice distortion and extra multi-mode vibrations, thus decreasing the thermal conductivity of Ta-based ceramics; similar results were reported by Wang et al. [44], which is a broadband high emissivity Ca²⁺-doped YbCrO₃ ceramic. Inequivalent doping induces electron exchange between chromate ceramic ions, which complicates the electronic structure (producing lattice distortion and extra multi-mode vibrations) and reduces the band gap width, thus boosting the emissivity in the mid-infrared band. Thus, it is reasonable that the thermal conductivity of CaTa_0.8WO₆ ceramics is lower than that of 7-8YSZ and YTaO₄, Y_0.8Mg_0.2TaO_3.9, Y_2/6Yb_4/6TaO₄, Dy_0.97Ta_0.97Zr_0.06O₄, and Yb(Ta_2/6Nb_4/6)O₄. In addition, the magnitude of change of thermal conductivity over the entire temperature range of CaTa_0.8WO₆ is much lower than YTaO₄, Y_0.8Mg_0.2TaO_3.9, Y_2/6Yb_4/6TaO₄, Dy_0.97Ta_0.97Zr_0.06O₄, Yb(Ta_2/6Nb_4/6)O₄, and 7-8YSZ, indicating that CaTa_0.8WO₆ ceramics have better thermal stability. The Clarke model was used to calculate the limiting thermal conductivity of CaTa_0.8WO₆ [48]:

$$k_{\mathrm{c}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}}=0.87k_{\mathrm{B}}{N}_A^{2/3}{\displaystyle \frac{n^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\mathsf{\rho }}^{1/6}{E}^{1/2}}{{\mathrm{M}}^{2/3}}}$$

(12)

where Avogadro constant N_A = 6.02 × 10²³, n (here n = 9) is the number of atoms in the unit cell, and m (here m = 0.46467) is the atomic mass in a unit cell. The ultimate thermal conductivity calculated based on Equation (12) is 0.99 W·m⁻¹·K⁻¹, which is very close to that of CaTa_0.8WO₆ in the range from 100 to 900 °C.

A mismatch of thermal expansion coefficients between the substrate and the T/EBCs results in large volume differences and thermal stresses, which ultimately lead to coating failure. The TECs of CaTa_0.8WO₆ and Mg²⁺, Yb³⁺, Zr⁴⁺, Nb⁵⁺, and W⁶⁺-doped Ta-based ceramics are shown in Figure 5a, the TECs of CaTa_0.8WO₆ rise steadily as the temperature increases, peaking at 8.6 × 10⁻⁶ K⁻¹ at 1100 °C, surpassing the value of Y_0.8Mg_0.2TaO_3.9 [28] and Y_2/6Yb_4/6TaO₄ [30], and lower than that of Dy_0.97Ta_0.97Zr_0.06O₄ [31] and Yb(Ta_2/6Nb_4/6)O₄ [32]. The slope of the curve in Figure 5b showing the thermal expansion rates (dL/L₀) of the CaTa_0.8WO₆ is constant, which means that there is no phase transition between 100 and 1100 °C.

4. Conclusions

The CaTa_0.8WO₆ ceramics were fabricated using a solid-state method. CaTa_0.8WO₆ exhibits a lower intrinsic thermal conductivity (1.05 W·m⁻¹·K⁻¹ at 900 °C) than 8YSZ and the doped Ta-based ceramics with Mg²⁺, Yb³⁺, Zr⁴⁺, and Nb⁵⁺, indicating that hexavalent tungsten element W⁶⁺ doping effectively reduces thermal conductivity and improves thermal insulation performance of Ta-ceramics. The Young’s modulus (96.2 GPa) and Pugh’s ratio (G/B = 0.40) of CaTa_0.8WO₆ ceramics were lower than those of doped Ta-based ceramics with Mg²⁺, Yb³⁺, Zr⁴⁺, and Nb⁵⁺, suggesting that CaTa_0.8WO₆ has better damage tolerance, and the average hardness at a nanoscale of CaTa_0.8WO₆ is 6.8 GPa. CaTa_0.8WO₆ has a higher thermal expansion coefficient (8.6 × 10⁻⁶ K⁻¹ at 1100 °C) compared to divalent and trivalent doped Ta-based ceramics. These results demonstrate that CaTa_0.8WO₆ has low thermal conductivity, Young’s modulus, moderate coefficient of thermal expansion and hardness, indicating that CaTa_0.8WO₆ has potential as a promising TBC.