1 Introduction
The pursuit of advanced thermal barrier coating (TBC) materials with ultra-low thermal conductivity has been a persistent endeavor in the field of high-temperature energy management, particularly for applications in gas turbines, aero engines, and nuclear reactors where enhanced energy efficiency and robust environmental protection are critically demanded [1-4]. Thermal conductivity (k) serves as a pivotal parameter governing the heat insulation capability of TBCs, and a lower k effectively reduces the heat flux penetrating the coated components, thereby enabling higher operating temperatures and prolonged service life of the underlying superalloys or ceramic matrix composites [5-8].
To achieve a reduction in thermal conductivity, two primary strategies have been extensively explored over the past decades: defect engineering and the enhancement of compositional complexity [9-11]. Specifically, defect engineering is devoted to introduce micro defects (such as oxygen vacancies, dislocation, or grain boundaries) into host materials to enhance phonon scattering, thereby suppressing lattice thermal conduction. The classical case is yttria-stabilized zirconia (YSZ), where oxygen vacancies introduced by Y2O3 doping effectively reduce thermal conductivity [12]. Similarly, a large number of candidate materials for TBCs, such as RE2Zr2O7, RE2Ce2O7, RE3TaO7, leverage intrinsic oxygen vacancies to achieve low thermal conductivity [13-17]. On the other hand, low thermal conductivity materials can also be obtained by the enhancing the compositional complexity. Typically, high-entropy engineering relies on compositional complexity to create severe lattice distortion and mass fluctuation, which intensifies phonon scattering [18-21]. For instance, high-entropy ceramics (La0.2Ce0.2Nd0.2Sm0.2Eu0.2)2Zr2O7 have demonstrated an ultralow thermal conductivity of 0.76 W·m-1·K-1 [22], and high-entropy rare-earth oxides with more components have shown further reductions in thermal conductivity [23,24]. While these approaches have proven effective in lowering thermal conductivity, they inevitably introduce a critical yet often overlooked challenge: the degradation of oxygen barrier capability.
Oxygen-ion conductivity is an essential parameter governing the oxidation resistance of TBCs. During high-temperature service, oxygen ions (O²⁻) and hydroxide anions (OH⁻) can penetrate the ceramic top coat via lattice diffusion and grain boundary migration, reaching the underlying bond coat and promoting the formation of a thermally grown oxide (TGO) layer [25-27]. Excessive TGO growth induces thermal expansion mismatch stresses, leading to cracking, delamination, and eventual failure of the coating system. Materials with high oxygen-ion conductivity, such as 8YSZ, facilitate rapid oxygen transport, and thereby accelerating TGO formation and undermining the durability of the TBC system [28,29]. Unfortunately, although the strategies such as increasing compositional complexity or introducing microstructural defects effectively reduce thermal conductivity, they often simultaneously enhance oxygen-ion mobility by creating additional diffusion pathways or increasing carrier concentration [30,31]. For example, high-entropy oxides with abundant oxygen vacancies exhibit improved phonon scattering but also provide numerous channels for oxygen-ion conduction [32,33]. Consequently, the conventional wisdom of reducing thermal conductivity through compositional and structural complexity poses an inherent trade-off between thermal insulation and oxygen barrier performance—a dilemma that remains unresolved. Hence, identifying TBC candidate materials that simultaneously exhibit low thermal conductivity and superior oxygen barrier capability is of paramount importance. Such materials would not only provide effective thermal protection but also suppress TGO growth, thereby extending the operational lifetime of TBC systems. Ideally, these materials should achieve low k without relying heavily on oxygen vacancies or extreme compositional complexity, thereby preserving their oxygen resistance. This necessitates a fundamental shift in phonon engineering strategies, i.e. from defect or entropy dominated scattering toward intrinsic lattice anharmonicity and bond heterogeneity as the primary mechanism for thermal transport suppression.
Herein, we propose a new TBC candidate material, strontium tantalate (SrTa2O6), which uniquely combines amorphous-like low thermal conductivity with ultra-low oxygen-ion conductivity. Unlike conventional low-k materials that depend on high concentrations of oxygen vacancies or multi-component high-entropy design, SrTa2O6 achieves strong phonon scattering through the large disparity in interatomic bonding strength between Sr-O and Ta-O bonds, as well as the presence of a minimal concentration of oxygen vacancies (4.26%) arising from Ta2O5 volatilization during synthesis. This bonding inhomogeneity induces strong intrinsic phonon-phonon scattering, effectively suppressing heat transport while maintaining a low density of mobile oxygen vacancies. The mechanism, which relies on the bonding inhomogeneity to enhance phonon scattering and thereby reduce thermal conductivity, has been proven in various material systems, such as RETaO4 and RE3NbO7 [34,35]. As a result, SrTa2O6 exhibits an amorphous-like thermal conductivity of 1.69-2.12 W·m-1·K-1 over 25-900 °C, which is lower than most state-of-the-art TBC materials. While its oxygen-ion conductivity at 900 °C (2.07 ×10-5 S·cm-1) is three orders of magnitude lower than that of 8YSZ. This work not only introduces SrTa2O6 as a promising candidate for next-generation TBCs, but also establishes a new paradigm for synergistically optimizing thermal and oxygen transport properties through bond engineering rather than defect or entropy proliferation.
2 Experiments
2.1 Specimen preparation
The SrTa2O6 powders were synthesized by solid-state reaction method. Firstly, the raw materials including SrCO3 and Ta2O5 powders (99.99% purity, Aladdin Biochemical Technology Co., Ltd, Shanghai, China) were weighted according to the stoichiometric ratio and milled in anhydrous alcohol medium with zirconia grinding balls for 24 h under a speed of 350 rpm. The mixture after ball milling was dried at 80 °C in a drying oven for 12 h. After being fully dried, the resulting powders were sieved through a 300-mesh screen to obtain homogeneous particles. Bulk SrTa2O6 was sintered by a vacuum hot press furnace 1450 ℃ for 2 h under a pressure of 70 MPa, with both the heating and cooling rates being 10℃/min. Finally, the bulk SrTa2O6 was annealed at 1350 ℃ for 2 h in atmospheric environment to remove carburization on the surface of the sample. The heating rate was 5℃/min below 1200℃ and 2℃/min above 1200℃. To ensure the reproducibility of the results, we synthesized three independent batches of SrTa2O6 powder and bulk materials.
2.2 Phase composition and microstructure
X-ray diffractometer (XRD, Rigaku, MiniFlex600, Japan) using a Cu Kα radiation (λ = 1.5406 Å) was used to determine the phase composition of the synthesized samples. The lattice parameters were obtained by Rietveld refinement method based on the obtained XRD patterns [36]. The chemical composition and valence state of the oxygen and cationic species in SrTa2O6 were analyzed using an X-ray photoelectron spectrometer (XPS, PHI5000 Versa probe II, ULVAC-PHI, Japan). Using the magnetic resonance spectrometer (EMXplus-6/1 model from Bruker, Germany), the possibility of oxygen vacancies was detected. First, the powder sample was placed in a quartz tube, and then it was placed in the resonance cavity of the instrument, ensuring that the sample was at the center of the resonance cavity. A scanning test was conducted with the scanning range of 3460-3560 G. A field emission scanning electron microscope (SEM, Nova-Nano450, FEI, USA), equipped with an energy dispersive spectroscopy detector, was employed to examine the morphology and elemental composition of polished and annealed samples. High-resolution transmission electron microscopy (HRTEM, Tecnai F30, FEI, USA) was used to further determine the crystal structure of the samples. The density (ρ) of the sintered compacts was measured by the Archimedes method, and the relative density (ρr) was calculated by the following equation:
${\rho }_{r}=\frac{\rho }{{\rho }_{0}}\times 100\% $
where ρ0 is the theoretical density of the samples, which is calculated based on the refined crystal structure parameters.
2.3 Mechanical properties
Elastic properties were determined by an ultrasonic reflection method using an ultrasonic reflection device (UMS-100, Teclab, France). Based on the measured longitudinal (VL) and transverse (VT) acoustic velocity, the mean acoustic velocity (VM), Young’s modulus (E) and Poisson’s ratio (υ) were calculated as [37]:
${V}_{M}={\left[\frac{1}{3}\left(\frac{1}{{V}_{L}^{3}}+\frac{2}{{V}_{T}^{3}}\right)\right]}^{-\frac{1}{3}}$
Each sample was tested three times and the results were averaged. Bulk modulus (B) and shear modulus (G) were calculated according to the following formula:
$G=\frac{E}{2\left(1+\upsilon \right)}$
In order to reduce the influence of porosity on the elastic modulus, the elastic modulus of the dense sample (E0) is obtained by the following formula [38]：
where the Φ is the porosity of the sintered specimen, and E is the experimental elastic modulus.
Vickers hardness (Hv) and fracture toughness (KIC) were measured by using a Vickers indentation instrument (HMV-G-FA, Shimadzu, Japan). The load applied on the polished sample was 0.49, 0.98, 1.96, 2.94, 4.90, and 9.80 N respectively, and the dwell time was 10 s. Each sample was tested three times and the results were averaged. Hv and KIC were calculated by indentation method according to the following equations [39,40]:
${H}_{v}=\frac{0.464F}{{d}^{2}}$
where F, d, c, E represent the indentation load, half of the indentation length, half of the crack length, and Young’s modulus, respectively.
The Young’s modulus (E) and Vickers hardness (Hv) at the nanoscale were measured by a nano-hardness tester (Nanomechanisc, Inc iMicro, USA). A 30 × 30 indentation lattice was performed to characterize the changes in Young's modulus and Vickers hardness on the surface of the sample.
2.4 Thermal properties
The thermal expansion characteristics were measured using a thermal dilatometer (DIL 402, Netzsch, Germany) within a temperature range of 25-1200 °C. The sample was cut into rectangular strips with dimensions of 10 mm× 2 mm× 1 mm, and polished to a smooth surface. The CTE (α) at various temperatures (T) was calculated as:
$\alpha =\frac{\mathrm{\Delta }L}{\left(T-{T}_{0}\right)L}$
where L and ΔL represents the length of the sample at room temperature (T0), and the change in length, respectively.
The thermal diffusivities (Dth) were measured with a laser flash analyzer (Netzsch LFA457, Germany). Prior to testing, a uniform carbon coating was applied to the surface of the ceramic samples, and measurements were conducted under an argon atmosphere. Heat capacity (Cp) was estimated by the Neumann-Kopp rule based on the data of its constituent oxides [41,42]. The thermal conductivity of fully dense ceramic (κ) was extrapolated using Kelemen’s formula [43]:
$\kappa ={D}_{th}\bullet {C}_{\mathfrak{p}}\bullet \rho /(1-\frac{4}{3}\mathrm{\Phi })$
where ρ is the density measured by the Archimedes method and $\mathrm{\Phi }$ is the porosity.
2.5 Oxygen ion conductivity
The AC impedance of ceramic samples was measured using an AC impedance spectrometer (SP-300, BioLogic, France). Silver paste was applied to both sides of each sample, and Ag wires were attached to form electrodes. The measurement was conducted under the following conditions: voltage range of ±10 V, frequency range of 1 Hz to 2 MHz, and temperature range of 600-900 °C at 50 °C intervals.
Based on the obtained impedance value (R), along with sample thickness (H) and electrode surface area (S), the oxygen ion conductivity (σ) was calculated as [44]:
$\sigma =\frac{H}{R\cdot S}$
$\sigma =({\sigma }_{0}/T)\mathrm{e}\mathrm{x}\mathrm{p}(-{E}_{\alpha }/{k}_{\mathrm{B}}\bullet T)$
where σ0 is the pre-exponential factor, Eα is the activation energy, kB is Boltzmann constant and T is absolute temperature.
3 Results and discussion
3.1 Phase composition and structural characterization
Fig. 1(a) shows the XRD pattern of the prepared SrTa2O6 ceramic together with its Rietveld refinement result. The fitting factors Rwp value is 9.10% and goodness of fitting (GOF) is 1.39, indicating that the refined result is reliable. The prepared SrTa2O6 ceramic belongs to the orthorhombic system with the space group of Pbam, and its crystal structure model is shown in Fig. 1(b). There is no extra diffraction peaks detected, implying that the SrTa2O6 ceramic is phase-pure. The refined lattice parameters are a= 12.36 Å, b= 12.43 Å, and c= 3.86 Å, which agree well with that reported by Lee and Kim et al. [47,48]. Based on the refined lattice parameters, the theoretical density of SrTa2O6 ceramic is calculated as 7.07 g/cm3.
Fig. 1 Rietveld refinement results of SrTa2O6 ceramic: (a) refinement XRD pattern; (b) crystal structure model. |
Microstructure morphology of SrTa2O6 ceramic is shown in Fig. 2. Fig. 2(a)-(b) display the SEM image of the SrTa2O6 ceramic after annealed at 1350 ℃ for 2 h, where neither micropores nor microcracks are visible within the field of observation, implying that the SrTa2O6 ceramic is near fully dense. The density measured by the Archimedes method is 6.93 g/cm3, which is 98% of the theoretical density. Fig. 2(c) shows the gain size distribution collected from Fig. 2(a)-(b) using the Image J software. The grains are small and uniform with a narrow size distribution, the average grain size is statistically determined to be 1.84 μm. Fig. 2(d) shows a low magnification SEM image of the SrTa2O6 ceramic together with the corresponding EDS mappings of substitutional elements, which indicates that the distribution of each element in SrTa2O6 is uniform. EDS energy spectrum obtained by point scanning mode is shown in Fig. 2(e). The atom ratio of O, Sr and Ta is 65%, 17.8%, and 17.2% respectively, which deviates from the stoichiometric ratio of SrTa2O6 (the atom ratio of O, Sr and Ta is 66.7%, 11.1%, and 22.2% respectively). Specifically, relative to the theoretical stoichiometric ratio of SrTa2O6, the experimental value for Sr is substantially higher, while that for Ta is substantially lower. The reason for the deviation in the content of the cations may be attributed to the higher saturation vapor pressure and lower melting point (1800 ℃) of Ta2O5 relative to SrO (melting point: 2430 ℃) [49]. The higher saturation vapor pressure of Ta2O5 renders it prone to volatilization during the synthesis process of SrTa2O6, leading to a deviation from the target stoichiometry. This non-molar ratio caused by the volatilization of Ta2O5 is an inherent phenomenon in the synthesis process, not an accidental error. It is precisely this deviation that leads to the formation of oxygen vacancies, and, under the same synthesis conditions, this deviation is repeatable.
Fig. 2 Microstructure morphology of SrTa2O6 ceramic: (a)-(b) Surface grain morphology observed by SEM; (c) Grain size statistics; (d) EDS elemental mappings; (e) EDS energy spectrum obtained by point scanning mode. |
The crystal structure of SrTa2O6 was further determined by high-resolution TEM analysis. Fig. 3(a)-(c) shows the HRTEM images of SrTa2O6 ceramic and corresponding fast Fourier transform (FFT) patterns along different zone axis: [-2, -3, 0], [-5,8], and [-9,4,7], respectively. The atomic arrangement d-spacing is 0.193 nm, 0.279 nm, and 0.264 nm, which is consistent with the interplanar spacing of the (3, -2, -2), (5,1,0), and (3, -3, -1) planes, further proving the accuracy of the fitted crystal structure of SrTa2O6 in Fig. 1.
Fig. 3 HRTEM images of SrTa2O6 ceramic and corresponding diffraction patterns along different zone axis: (a) [-2, -3, 0]; (b) [-5,8]; (c)[-9, 4, 7]. |
3.2 Mechanical properties
Elastic/mechanical and thermal properties are key indicators for evaluating thermal barrier coating materials, but these parameters of SrTa2O6 are still unknown. Thus, a comprehensive investigation on the elastic/mechanical and thermal properties of SrTa2O6was carried out. Table 1 exhibits the acoustic velocity, elastic modulus, Poisson's ratio, and Vickers hardness of SrTa2O6 as well as those of other ceramic materials, such as Al2O3, YSZ, SiC, CrTaO4, CrNbO4, and YTaO4 [50-53]. The Young's modulus (E), shear modulus (G) and bulk modulus (B) of SrTa2O6 is 207, 86, and 115 GPa respectively, which is similar to those of yttria-stabilized zirconia (YSZ) [51]. On the other hand, Pugh's ratio (G/B) and Poisson's ratio are commonly used to distinguish ductile from brittle materials. Typically, a material with low Pugh's ratio (below 0.571) and high Poisson's ratio (above 0.25) indicates ductility, while high Pugh's ratio and low Poisson's ratio are indication of brittleness. SrTa2O6 has a G/B ratio of 0.75 and a Poisson's ratio of 0.201, implying that SrTa2O6 is more brittle than YSZ, Al2O3, CrTaO4, CrNbO4, and YTaO4 but SiC.
Table 1 Acoustic velocity (vl,vt and vm), Young's modulus (E), Bulk modulus (B), Shear modulus (G), Poisson's ratio (ε), Vickers hardness (Hv) of SrTa2O6 and those of other ceramic materials, such as Al2O3, 8YSZ, SiC, CrTaO4, CrNbO4, and YTaO4. |
| Compounds | vl (m/s) | vt (m/s) | vm (m/s) | ε | B (GPa) | E (GPa) | G (GPa) | G/B | Hv (GPa) |
|---|---|---|---|---|---|---|---|---|---|
| SrTa2O6 | 5760 | 3523 | 3890 | 0.201 | 115 | 207 | 86 | 0.75 | 8.9 |
| Al2O3 | / | / | / | 0.220 | 251 | 370 | 163 | 0.65 | 15.0 |
| 8YSZ | / | / | / | 0.300 | 176 | 210 | 81 | 0.46 | 14.0 |
| SiC | / | / | / | 0.16 | 225 | 415 | 192 | 0.85 | 32 |
| CrTaO4 | 6640 | 3814 | 4211 | 0.254 | 181 | 268 | 107 | 0.59 | 12.2 |
| CrNbO4 | / | / | / | 0.266 | 180 | 253 | 100 | 0.56 | 10.2 |
| YTaO4 | 6127 | 2971 | 3338 | 0.35 | 184 | 170 | 63 | 0.34 | 4.5 |
Hardness is usually considered to evaluate the resistance of materials to permanent local deformation. The Vickers hardness of SrTa2O6 ceramic was investigated and Fig. 4(a)-(b) shows Vickers hardness indentation under the load of 2.94 and 4.90 N. The indentation is in a regular diamond shape with no collapse at the edge, indicating that the measured value is reliable. The relationship between Vickers hardness and indentation load is shown in Fig. 4(c). Hardness increases from 4.1 GPa to 9.1 GPa with increasing load and stabilizes at high loads. The hardness measured under a 9.80 N load is 8.9 ± 0.1 GPa, which is lower than that of YSZ (14 GPa), CrTaO4 (12.2 GPa) and CrNbO4, (10.2 GPa) [51,52], but higher than that of YTaO4 (4.5 GPa) [53]. Based on the length of indentation and crack, the average fracture toughness from eight measurements is 1.146 ± 0.071 MPa·m¹ /², as shown in Fig. 4(d). Fig. 5(a)-(b) exhibit 3D mappings of elastic modulus and Vickers hardness of SrTa2O6 ceramic obtained by Nanoindentation array. The average elastic modulus and Vickers hardness of SrTa2O6 ceramic on a two-dimensional plane is 219 GPa and 10.86 GPa, which is slightly higher values and minor fluctuations compared to ultrasonic and Vickers measurements (207 GPa and 8.9 GPa), attributed to grain boundary and microscopic pores in the sample.
Fig. 4 Measurement of Vickers hardness and fracture toughness of SrTa2O6 ceramic: (a) Vickers hardness indentation under the load of 2.94 N; (b) Vickers hardness indentation under the load of 4.90 N; (c) Vickers hardness under different loads; (d) Fracture toughness results obtained by indentation method. |
Fig. 5 3D mappings of elastic modulus and Vickers hardness of SrTa2O6 ceramic obtained by Nanoindentation array: (a) Vickers hardness; (b) Elastic modulus. |
3.3 Thermal properties
The coefficient of thermal expansion (CTE) is critical for TBC applications, as the thermal expansion mismatch between the substrate and the coating can lead to cracking and spallation during thermal cycling. The thermal expansion rate of SrTa2O6 ceramic at 200-1200 ℃ is shown in Fig. 6(a). It can be seen that SrTa2O6 ceramic exhibit a linear expansion characteristic with the temperature increases from 200 to 900 °C, and the rising rate slows down above 900 ℃, which may be attributed to the escape of oxygen ions from the lattice at high temperatures, increasing the concentration of oxygen vacancies and causing local lattice relaxation, and thereby leading to a slowdown in thermal expansion. However, there is no abrupt volume change throughout the entire temperature range, indicating that SrTa2O6 ceramic is stable at high temperature. Fig. 6(b) shows the temperature dependent CTE of SrTa2O6 ceramic. The CTE of SrTa2O6 ceramic is 10.8 × 10-6/K at 1200 ℃, comparable to that of 8YSZ (10.2-10.8 × 10⁻⁶ /K) [54].
Fig. 6 Thermal expansion properties of SrTa2O6 ceramic: (a) thermal expansion rate; (b) the coefficients of thermal expansion (CTE). |
Besides thermal expansion properties, the thermal transport properties are also critical parameters for selecting thermal barrier coating (TBC) materials. A low thermal conductivity is essential to effectively reduce heat flux and maintain excellent thermal insulation performance at elevated temperatures. of SrTa2O6 ceramic were also investigated. Fig. 7(a) shows the temperature dependent thermal diffusivity of SrTa2O6 ceramic. The thermal diffusivity can be fitted by the following polynomial equation:
${D}_{th}=0.711-3.955\times {10}^{-4}T+8.880\times {10}^{-7}{T}^{2}-9.265\times {10}^{-10}{T}^{3}+3.738\times {10}^{-13}{T}^{4}$
Fig. 7 Thermal properties of SrTa2O6 ceramic: (a) temperature dependent thermal diffusivity (α); (b) temperature dependent heat capacity (Cp); (c) temperature dependent thermal conductivity (k) together with those of other TBC materials, such as 8YSZ, 7YSZ, RETaO4 (RE= Y, Yb, Er, Nd, Tm, and Ho). |
The reliability (R2) of the fitted result is 0.997. The thermal diffusivity of SrTa2O6 ceramic at 25 ℃ is 0.70 mm2·s-1. With temperature increases to 700 ℃, the thermal diffusivity decreases gradually and approaches a limit (0.64 mm2·s-1) due to the phonon mean free path decreases to the average atomic distance. As the temperature exceeds 700 ℃, the thermal diffusivity slightly increases due to the enhancement of thermal radiation effect. Fig. 7(b) exhibits the temperature dependent heat capacity (Cp) of SrTa2O6 ceramic, which increases and gradually tends towards its asymptotic value of Cp→3NkB + R per mole as predicted by the Dulong-Petit law. The temperature dependent thermal conductivity of the SrTa2O6 ceramic was subsequently calculated using Eq. (11), with the results presented in Fig. 7(c), and those of other TBC materials, such as 8YSZ, 7YSZ, RETaO4 (RE= Y, Yb, Er, Nd, Tm, and Ho) were also exhibited for comparison [[55,56]. The thermal conductivity of SrTa2O6 ceramic at 1.69 W·m-1·K-1, which is almost half that of 7YSZ (3.10 W·m-1·K-1) and 8YSZ (3.48 W·m-1·K-1). As the temperature increases, the thermal conductivity of SrTa2O6 ceramic increases slowly and reaches the highest value at 900 °C (2.12 W·m-1·K-1), which is also lower than that of 7YSZ (2.32 W·m-1·K-1), 8YSZ (2.41 W·m-1·K-1) and RETaO4 (RE= Yb, Er, Nd, Tm, and Ho, those k900°C = 2.14-2.62 W·m-1·K-1), but slight higher than that of YTaO4 (2.06 W·m-1·K-1). Therefore, it can be concluded that SrTa2O6 ceramic exhibits lower thermal conductivity than most TBC materials throughout the entire temperature range, which is beneficial for its application of TBC material.
It is worth noting that most oxide materials (such as YSZ and RETaO4) exhibit typical crystalline thermal conductivity characteristics, where thermal conductivity decreases with increasing temperature, as shown in Fig. 7(c). In contrast, thermal conductivity of SrTa2O6 ceramic increases with increment of the temperature, which is amorphous-like thermal conductivity characteristics. According to the Cahill-Waston-Pohl (CWP) model [57], the thermal conductivity of amorphous materials can be predicted by the following equation:
${k}_{\mathrm{m}\mathrm{i}\mathrm{n}}={\left(\frac{\mathrm{\pi }}{6}\right)}^{\frac{1}{3}}{k}_{B}{n}^{\frac{2}{3}}{{\sum }_{i}{v}_{i}\left(\frac{T}{\theta }\right)}^{2}{\int }_{0}^{\frac{{\theta }_{i}}{T}}\frac{{x}^{3}{\mathrm{e}}^{x}}{{\left({\mathrm{e}}^{x}-1\right)}^{2}}\mathrm{d}x$
Where the sum is taken over the three sound modes (two transverse modes and one longitudinal mode) with speeds of sound vi (i represents the sound mode). θi is the Debye temperature for each polarization, which is calculated by [58]:
${\theta }_{i}=\frac{h}{{k}_{B}}{\left[\frac{3n}{4\mathrm{\pi }}\left(\frac{{N}_{A}d}{M}\right)\right]}^{\frac{1}{3}}{v}_{i}$
Where h is Planck constant, kB is Boltzmann constant, n is the number of atoms in the molecular formula, NA is Avogadro’s number, d is the density, and M is the molecular weight. The transverse and longitudinal velocities of SrTa2O6 ceramic is 3523 and 5760 m s-1 respectively, as shown in Table 1. Based on the Eq. (17), the Debye temperature for transverse and longitudinal velocities is calculated to be 462 and 756 K, respectively. Fig. 8(a) shows the comparison of experimental thermal conductivity of SrTa2O6 ceramic, amorphous κmin calculated by CWP model and κmin calculated by Clarke model, which assumes that the phonon means free path equals to the inter-atomic distance [59]:
${k}_{\mathrm{m}\mathrm{i}\mathrm{n}}=0.87{k}_{B}{\left(\frac{md{N}_{A}}{M}\right)}^{\frac{2}{3}}{\left(\frac{E}{d}\right)}^{\frac{1}{2}}$
where m, d, NA, M, and E is the number of atoms in the molecule, density, Avogadro’s number, molecular weight and Young’s modulus, respectively. As shown in Fig. 8(a), the variation trend of experimental thermal conductivity of SrTa2O6 ceramic with temperature is quite similar to that of amorphous state. The minimum thermal conductivity of SrTa2O6 ceramic obtained by the Clarke model is 1.11 W m-1 K-1, which is lower than the experimental value. Fig. 8(b) shows the ratio of elastic constant to thermal conductivity (E/k) of SrTa2O6 ceramic and other TBC materials. As shown in Fig. 8(b), SrTa2O6 ceramic exhibits an extremely large E/k value (122 GPa·m·K·W-1) at room temperature, which surpass that of other TBC materials, such as La2Zr2O7 (94 GPa·m·K·W-1), 8YSZ (60 GPa·m·K·W-1), LaPO4 (37 GPa·m·K·W-1), YTaO4 (40 GPa·m·K·W-1), and BaZrO3 (38 GPa·m·K·W-1 f) [60]. Generally, the ratio of elastic constant to thermal conductivity (E/k) measures the extent to which the bonding strength of a dielectric material is effectively converted into long-range efficient phonon transport [61,62]. A high E/k ratio implies that, despite strong atomic bonding (high E), the efficiency of heat transfer is low (low κ) due to strong phonon scattering mechanisms, which typically points to strong lattice anharmonicity or complex microstructures. Thus, the high E/k ratio of SrTa2O6 suggests the presence of strong intrinsic phonon-phonon scattering, which may be attributed to the lattice defect scattering (such as oxygen vacancies) in the crystal structure. To verify this hypothesis, the oxygen vacancies concentration of SrTa2O6 was investigated by XPS, and the results were shown in Fig. 9. All the XPS spectra were calibrated according to the reference C1s at 284.8 eV. Fig. 9(a) shows the survey spectra of SrTa2O6, all the containing elements (Ta, Sr and O) were detected. Fig. 9(b) exhibits the High-resolution XPS spectrum and Gaussian fitted curves of O1s. The high-resolution O1s spectrum was deconvoluted into three distinct peaks, corresponding to different oxygen species: Ta-O bonding (OⅠ) at 529.98 eV, Sr-O bonding (OⅡ) at 531.82 eV, and oxygen vacancies (Vo) at 533.02 eV. Based on the quantitative analysis of the integrated peaks areas, the oxygen vacancy concentration on the O site of SrTa2O6 was calculated to be 4.26%. Based on the EPR test results (as shown in Fig. 9(c)), the sample curve presents a Lorentz shape, and an EPR oxygen vacancy signal is observed at g = 2.003, further confirming the certainty of the existence of oxygen vacancies. The season for the formation of oxygen vacancy is the deviation of the stoichiometric ratio of SrTa2O6 caused by the volatilization of Ta2O5, as shown in Fig. 2(e). Due to the partial loss of Ta⁵⁺ ions, excess Sr²⁺ ions partially occupy the original lattice sites of Ta⁵⁺. Consequently, oxygen vacancies are formed to maintain charge balance. The reaction of oxygen vacancies generation can be represented by the Kröger-Vink notation [63]:
$SrO\stackrel{Sr{Ta}_{2}{O}_{6}}{\to }+{Sr}_{Ta}^{\text{'}\text{'}\text{'}}+{O}_{O}^{\times }+1.5{V}_{O}^{\bullet \bullet }$
where ${Sr}_{Ta}^{\text{'}\text{'}\text{'}}$ represents Sr2+ occupying Ta5+ site (trebly negative charge), ${O}_{O}^{\times }$ is the oxygen on the oxygen site, ${V}_{O}^{\bullet \bullet }$ is an oxygen vacancy (doubly positive charge).
Fig. 8 (a) Comparison of the experimental thermal conductivity of SrTa2O6 ceramic, amorphous κmin calculated by CWP model and κmin calculated by Clarke model; (b) The ratio of elastic constant to thermal conductivity (E/k) of SrTa2O6 ceramic and other TBC materials. |
Fig. 9 XPS profiles of SrTa2O6 ceramic: (a) Survey spectra; (b) High-resolution XPS spectrum and Gaussian fitted curves of O1s; (c) The EPR test spectrum of oxygen vacancies in SrTa2O6. |
Besides of oxygen vacancies, another reason for the strong intrinsic phonon-phonon scattering of SrTa2O6 is the rattling effect of Sr2+ cations arising from the large difference in the interatomic bonding between Sr-O and Ta-O. The atomic radii contrast between the tantalum ions (0.64 Å) strontium ions (1.18 Å) and is higher than those in the rare-earth ions (Y3+: 0.90 Å, Yb3+: 0.87 Å, Er3+: 0.89 Å, Nd3+: 0.98 Å, Tm3+: 0.88 Å, Ho3+: 0.90 Å). Accordingly, the difference of bonding length between Ta-O and Sr-O in the SrTa2O6 is higher than the corresponding difference in the RETaO4 (Ta-O vs RE-O). Moreover, the charge difference between Sr2+ and Ta5+ in SrTa2O6 is also larger than that in the RETaO4 (RE3+ vs Ta5+). Thus, the difference of Coulomb force between Ta-O and Sr-O is higher than that in the RETaO4. Both of these two factors can lead to much stronger ionic bonding of Ta-O compared with Sr-O in the SrTa2O6, thereby diversifying the strength of chemical bonding in the crystal [[64]. In brief, the bonding inhomogeneity between Ta-O and Sr-O in the SrTa2O6 maximize scattering of the vibrational modes, and thus suppress the thermal conductivity by reducing the energy transfer rate of acoustic vibration modes.
3.4 Oxygen-ion conductivity
Oxygen-ion conductivity is an easily overlooked but critical performance parameter for thermal barrier coatings (TBCs). When TBCs are subjected to high-temperature oxidizing environments, external oxygen and water vapor can infiltrate the coating through multiple pathways, such as grain boundaries, microcracks, pores, and lattice diffusion, ultimately reaching the underlying bonding coat. This leads to the oxidation of the bonding coat and the formation of a thermally grown oxide (TGO) layer at the interface. Overgrowth of the TGO layer will induce thermal expansion mismatch within the coating system, which ultimately results in cracking and failure of the coating [25-27]. Although reducing internal defects in the TBCs can suppress the oxygen permeability, the oxygen-ion conduction through the lattice of the ceramic layer remains non-negligible. Accordingly, oxygen-ion conductivity serves as a key parameter for evaluating the oxygen-ion transport rate in TBCs. A low oxygen-ion conductivity can suppress the inward penetration of oxygen ions, thereby mitigating TGO growth and extending the service life of the coating. Fig. 10 shows the oxygen-ion conductivity of SrTa2O6 ceramic. By continuously varying the angular frequency ω, the corresponding frequency response functions of the system were obtained and used to construct the electrochemical impedance spectra, as shown in Fig. 10(a) and Fig. 10(b). The impedance response was modeled using an equivalent circuit consisting of two parallel resistor-capacitor (RC) elements. The circular arc corresponding to the high-frequency region represents the electrical response within the crystal grains, while the circular arc in the low-frequency region represents the hindrance effect of crystal boundaries on charge transmission. The diameter of the semicircular arc in the impedance spectrum is inversely related to the resistance of the corresponding component. It can be observed that the resistance of the material decreases progressively with increasing temperature, suggesting enhanced oxygen ion mobility at elevated temperatures. Fig. 10(c) and Fig. 10(d) illustrate the temperature-dependent oxygen-ion conductivity of SrTa₂O₆ together with other TBC materials, such as 8YSZ, HoTaO4, and TmTaO4 [65,66]. The oxygen-ion conductivities (σ) of all the selecting materials increase steadily with rising temperature, indicating that thermal activation facilitates the migration of oxygen ions within the lattice, thereby reducing the overall resistance. This behavior is consistent with the thermally enhanced ionic conduction mechanism. For dielectric materials, the Fermi level lies within the bandgap, and thus the contribution of thermally excited carriers must be taken into account. As the temperature increases, more electrons are excited from the valence band to the conduction band, and atoms undergo greater deviation from their equilibrium positions. This enhances the formation of oxygen vacancies, thereby increasing the concentration of charge carriers available for conduction. As a result, the electrical resistivity decreases and the oxygen-ion conductivity improves. Significantly, SrTa2O6 exhibits lower oxygen-ion conductivity compared with those of 8YSZ, HoTaO4, and TmTaO4 throughout the entire measured temperature range. The oxygen-ion conductivity of SrTa2O6 at 900 ℃ is 2.07 × 10-5 S·cm-1, which is lower than that of HoTaO4 (4.08 ×10-5 S·cm-1) [66], and TmTaO4 (2.65 ×10-5 S·cm-1) [66], and even three orders of magnitude lower than that of the state of art TBC material 8YSZ (3.47 ×10-2 S·cm-1) [65]. Fig. 10(e) shows the Arrhenius plots of SrTa2O6, 8YSZ, HoTaO4, and TmTaO4. It can be found that there is a linear relation between the logarithm of the oxygen-ion conductivity (lnσT) and the reciprocal of the absolute temperature (1/T), which can be expressed as [44]:
$\mathrm{l}\mathrm{n}\left(\sigma T\right)=C-{E}_{\alpha }/\left({k}_{B}T\right)$
Where C is a physical quantity related to crystal structure, Eα is activation energy of carrier transport, kB = 8.617 × 10-2 eV/K, respectively. This formula is equivalent to Eq. (13), meaning that the result can be obtained by taking the logarithm on both sides of Eq. (13) and then simplifying. Based on the Eq. (19), the Arrhenius plots of SrTa2O6, 8YSZ, HoTaO4, and TmTaO4 can be fitted by linear equations, and the fitting results were exhibited as following:
$8\mathrm{Y}\mathrm{S}\mathrm{Z}:\mathrm{l}\mathrm{n}\left(\sigma T\right)=5.882-\frac{10.878}{T},{R}^{2}=0.999$
Fig. 10 Oxygen-ion conductivity of SrTa2O6 ceramic: (a) AC impedance spectra measured over the temperature range of 600-900 °C; (b) Partial enlarged view of Fig. 10(a); (c) Temperature dependent oxygen-ion conductivity of SrTa2O6, HoTaO4, and TmTaO4; (d) Temperature dependent oxygen-ion conductivity of 8YSZ; (e) Arrhenius plots of SrTa2O6, 8YSZ, HoTaO4, and TmTaO4; (f) Activation energy of SrTa2O6, 8YSZ, HoTaO4, and TmTaO4. |
Based on the Eqs. (20)-(23), the activation energies of SrTa2O6, 8YSZ, HoTaO4, and TmTaO4 can be calculated, as shown in Fig. 10(f). It is shown that SrTa2O6 have a larger activation energy (1.43 eV) than that of other TBCs, as the differences of atomic radii and charge between the Sr2+ and Ta5+ cations in SrTa2O6 is larger than that in YSZ and RETaO4, rendering a larger energy barrier for oxygen diffusion. However, the major reason for the ultra-low oxygen-ion conductivity of SrTa2O6 is due to be the remarkable reduction of the mobile oxygen vacancy in the crystal structure. Different from TBC materials containing a large number of intrinsic oxygen vacancies, such as 8YSZ and RE2Zr2O7, the oxygen vacancy concentration of SrTa2O6 is much lower than that of the above materials, thus reducing the channels for external oxygen ions to transfer inward through oxygen vacancies [60]. Therefore, the ultra-low oxygen-ion conductivity of SrTa2O6 suggests that it have the potential to slow down the oxidation of metallic component and the growth of TGO, and thereby prolong the TBC lifetime.
4 Conclusions
A tantalate SrTa2O6 with amorphous-like thermal conductivity and ultra-low oxygen-ion conductivity have been successfully synthesized by solid reaction method, and its phase composition, microstructure, mechanical and thermal properties, and oxygen barrier capability were investigated and summarized as following:
(1) The phase composition and microstructure investigation demonstrates that SrTa2O6 exhibits an orthorhombic structure with the space group of Pbam. EDS result indicates that the content of Sr2+ and Ta5+ deviates from the stoichiometric ratio of SrTa2O6 due to the volatilization of Ta2O5 and excess Sr²⁺ ions partially occupy the original lattice sites of Ta⁵⁺during the synthesis process. This provides the possibility for the formation of oxygen vacancies, and XPS provides quantitative confirmation, with the concentration of oxygen vacancies being 4.26%.
(2) The Young's modulus, shear modulus and bulk modulus of SrTa2O6 measured by ultrasonic reflection method is 207, 86, and 115 GPa respectively. While the Vickers hardness and fracture toughness measured by Vickers indentation method is 8.9 ± 0.1 GPa and 1.15 ± 0.07 MPa·m¹/² respectively. The average elastic modulus and Vickers hardness of SrTa2O6 ceramic determined by nanoindentation is 219 GPa and 10.86 GPa respectively.
(3) SrTa2O6 possess excellent thermal stability from room temperature to 1200 ℃, and its CTE is 10.8 × 10−6/K at 1200 ℃, which is close to that of YSZ. The thermal conductivity of SrTa2O6 ranges from 1.69 to 2.12 W·m-1·K-1 at 25-900 ℃ and exhibits amorphous-like thermal conductivity characteristics with the increment of temperature. This is attributed to the strong intrinsic phonon-phonon scattering arising from two aspects: One is the oxygen vacancy originates from the deviation of the stoichiometric ratio of SrTa2O6 caused by the volatilization of Ta2O5. Another is the large difference in the interatomic bonding between Sr-O and Ta-O in SrTa2O6.
(4) The oxygen-ion conductivity of SrTa2O6 at 900 ℃ is as low as 2.07 × 10−5 S·cm−1, which is three orders of magnitude lower than that of the state of art TBC material 8YSZ (3.47 ×10−2 S·cm−1). The ultra-low oxygen-ion conductivity of SrTa2O6 is attributed to a higher activation energy barrier for oxygen diffusion, thereby inhibiting the growth of the thermally grown oxide (TGO) layer and extending the service life of the coating.
(5) The main innovations of this work are twofold. Firstly, regarding material innovation, SrTa2O6 is proposed and validated as a promising thermal barrier coating (TBC) candidate that concurrently exhibits glass-like ultralow thermal conductivity and ultralow oxygen-ion conductivity. Secondly, in terms of mechanistic innovation, this work reveals a novel paradigm distinct from conventional strategies. Unlike traditional approaches that rely on defect engineering or high-entropy engineering—which often achieve reduced thermal conductivity at the expense of oxygen-blocking capability—the present approach utilizes bonding heterogeneity engineering to synergistically suppress both phonon transport and oxygen-ion migration. This provides a new material system for developing TBCs that integrate high thermal insulation with exceptional oxidation resistance.
Although its intrinsic brittleness may challenge the coating's thermal shock resistance, this issue can be mitigated through microstructural design, such as fabricating a columnar structure or constructing a double-layer/graded system with YSZ. Concurrently, the extremely low oxygen-ion mobility of SrTa2O6 is expected to significantly extend the coating service life by fundamentally suppressing the growth of the thermally grown oxide (TGO). Future work should focus on the coating deposition of this material, the control of its phase stability, and the evaluation of its thermal cycling performance to advance it toward practical application.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article. Zifan Zhao is a member of Editorial Board of this journal and he was not involved in the editorial review or the decision to publish this article.
CRediT authorship contribution statement
Yang Yang: Supervision, Formal analysis. Kaiye Xiao: Visualization, Methodology. Jing Feng: Writing - review & editing. Zifan Zhao: Writing - review & editing. Xingshun Teng: Writing - original draft, Visualization, Investigation. Enjin Liu: Methodology, Investigation. Yiwang Bao: Writing - review & editing. Jianyu Li: Supervision, Investigation. Peng Wu: Software, Methodology. Xiaoli Shi: Visualization, Supervision.