(Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 high-entropy ceramic with low thermal conductivity, tunable thermal expansion coefficient, and excellent resistance to CMAS corrosion

Low thermal conductivity, compatible thermal expansion coefficient, and good calcium—magnesium—aluminosilicate (CMAS) corrosion resistance are critical requirements of environmental barrier coatings for silicon-based ceramics. Rare earth silicates have been recognized as one of the most promising environmental barrier coating candidates for good water vapor corrosion resistance. However, the relatively high thermal conductivity and high thermal expansion coefficient limit the practical application. Inspired by the high entropy effect, a novel rare earth monosilicate solid solution (Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 was designed to improve the overall performance. The as-synthesized (Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 shows very low thermal conductivity (1.07 W·m−1·K−1 at 600 °C). Point defects including mass mismatch and oxygen vacancies mainly contribute to the good thermal insulation properties. The thermal expansion coefficient of (Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 can be decreased to (4.0–5.9)×10−6 K−1 due to severe lattice distortion and chemical bonding variation, which matches well with that of SiC ((4.5–5.5)×10−6 K−1). In addition, (Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 presents good resistance to CMAS corrosion. The improved performance of (Ho0.25Lu0.25Yb0.25Eu0.25)2SiO5 highlights it as a promising environmental barrier coating candidate.

, and SiO 2 were mixed at a molar ratio of 1 : 1 : 1 : 1 : 4. Then, the mixture was ball-milled for 12 h by using ethyl alcohol as the medium. The obtained slurry was dried at 80 ℃ for 12 h, followed by passing through a 60-mesh sieve to get fine powder. The fine powder was sintered at 1650 ℃ for 8 h to get pure (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 powder. The as-prepared powder was ball-milled, dried, and sieved again. Then, it was made into a disc green body by uniaxially pressing at 5 MPa and cold isostatically pressing at 200 MPa for 15 min. Dense bulk (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 ceramic was fabricated by sintering the green body at 1550 ℃ for 12 h.

2 Phase composition and microstructure
X-ray diffractometer (XRD, PANalytical Empyrean, Almero, the Netherlands) was applied to identify the phase composition. The Rietveld method in the General Structure Analysis System (GSAS) software was used for crystal structure refinement [26]. The scanning electron microscope (SEM, Hitachi, SU8230, Japan) equipped with an energy dispersive spectrometer (EDS) was used for microstructure observation and element distribution analysis. The stoichiometric ratio of reaction www.springer.com/journal/40145 products was identified by an electron probe microanalyzer (EPMA, JEOL, JXA-8530F Plus, Japan).
ImageJ software (open source) was used to analyze the grain size distribution, and at least 300 grains were counted. X-ray photoelectron spectrometer (XPS, Thermo Fisher, Nexsa, USA) was applied to analyze the chemical states of the elements of the specimen.

3 Thermal and mechanical properties
The thermal diffusivity was measured by a laser flash analyzer (NETZSCH, LFA 427, Germany) from room temperature to 1000 ℃ . The dimension of the specimen is 12.7 mm × 1 mm. Before the test, a graphite coating was applied to both sides of the specimen to reduce the effect of thermal radiation. The thermal conductivity ( )  was obtained from Eq. (1) [27]: where  represents the density and c p denotes the heat capacity. The heat capacity was calculated by the Neumann-Kopp law [28]. The thermal conductivity of a fully dense specimen ( 0  ) is calculated by [29]: where  is the porosity.
The minimum thermal conductivity min ( )  was calculated by [30]: where B  represents the Boltzmann constant, A N denotes the Avogadro's constant, n is the number of atoms in the primitive cell,  is the density, E is the Young's modulus, and M is the molecular weight. TEC was measured by an optical thermal expansion meter (ODHT, Modena, Italy) with a specimen dimension of 3 mm × 4 mm × 12 mm.
The reduced modulus and hardness characterization were performed by a nanoindenter (Bruker, Hysitron TI980, Germany). 400 points were taken in the range of 40 μm × 40 μm for measurement.

4 CMAS corrosion
The composition of CMAS melt used in this work was 33CaO-9MgO-13AlO 1.5 -45SiO 2 , and the element proportion was expressed as molar ratios of single cationic oxides [31]. CaO, MgO, Al 2 O 3 , and SiO 2 were mixed according to the stoichiometric ratio of CMAS and a homogeneous mixture was obtained by wet ball milling for 12 h. The mixture was annealed at 1200 ℃ for 24 h, and then ball-milled, dried, and sieved again to obtain fine CMAS powder. Figure 1 shows a schematic diagram of the CMAS corrosion test procedure. The CMAS powder firstly was mixed with alcohol, and then they were uniformly coated on the sample surface. After several repeated coatings, the CMAS loading was kept at about 35 mg/cm 2 . The CMAS-coated RE 2 SiO 5 ceramic was heated at 1300 ℃ for 20 h. The heat-treated ceramic was cut along the midline for microstructure characterization.

1 Phase composition and microstructure
The reaction path of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 was investigated by heating the mixed powder at different temperatures. Figure 2 presents the XRD patterns of the reaction products. RE 2 O 3 does not react with SiO 2 until 1200 ℃. RE 2 SiO 5 gradually appears with the increase of temperature, and a pure    Fig. 3. The X-ray diffraction peaks of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 powder match well with the standard card of Lu 2 SiO 5 , indicating that the multiple RE elements have been successfully incorporated into the RE 2 SiO 5 crystal lattice. Figures 3(b) and 3(c) display the enlarged XRD patterns in the diffraction angle ranges of 21°-24° and 27°-29°, respectively. The diffraction peaks of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 shift to a lower angle compared to that of Lu 2 SiO 5 , since the radii of Ho 3+ , Yb 3+ , and Eu 3+ are all larger than that of Lu 3+ . For the mixed powder, it splits into four diffraction peaks which indicates that it is a mixture of four kinds of RE 2 SiO 5 ceramics. Figure 4 exhibits the XRD pattern Rietveld refinement of X-ray diffraction data of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 powder is shown in Fig.  5(a). The R wp is 5.862%, and the goodness of fit (GOF) is 1.27, indicating that the refinement results are considered to be reliable. The lattice parameters of (Ho 0. 25 [32]. The lattice constant of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is between those of Ho 2 SiO 5 and Yb 2 SiO 5 . Though Eu 2 SiO 5 belongs to the X1-RE 2 SiO 5 phase and crystalizes in the P2 1 /c space group, when combined with other RE elements to form a high-entropy ceramic, Eu atoms will occupy the RE lattice sites in X2-RE 2 SiO 5 . The theoretical density of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 was calculated to be 6.83 g/cm 3 , and the as-prepared specimen was measured with a porosity of 5%. The atomic occupation information is shown in Table 2. There are two independent RE sites (RE1 and RE2) in the X2-RE 2 SiO 5 crystal structure ( Fig. 5(b)). Small RE elements (Yb and Lu) tend to occupy the RE2 lattice position with a coordination number of 6, while large RE elements (Ho and Eu) prefer to occupy the RE1 lattice position with a coordination number of 7.    is relatively dense. The four RE elements are distributed homogeneously, while some areas are rich in silicon.
The point analysis of each region is summarized in Table 3. In the silicon enriched area (point 2), the ratio of RE to Si is about 1 : 1, which proves to be RE 2 Si 2 O 7 impurities.

2 Thermal properties
Thermal properties are important parameters for EBC. Figure 7(a) compares the thermal diffusivities of (Ho 0. 25  In thermal insulation materials, the propagation of phonons determines thermal conductivity [33]. According to the Debye model, the thermal diffusivity is defined as [34]: where m v denotes the average sound velocity,  represents the mean free path of phonon, and  can be expressed as [35]: phonon defect boundary In crystalline materials, the mean free path of phonon is defined as [35]: where 0  represents the pre-exponential factor, the constant b is approximately equal to 2, D  denotes the Debye temperature, and n represents the number of atoms in the unit cell. In the high-temperature stage, 1   can be estimated as [33]: Equation (7)  is almost independent of temperature, and thus there is also a linear relationship between thermal diffusivity and temperature [33]: The temperature-dependent part of Eq. (8) is the slope which is determined by phonon-phonon scattering, and the temperature-independent part is the intercept which is determined by external factors such as defects [37].
The relationship of the inverse thermal diffusivity 1   versus temperature T is shown in Fig. 7 For materials with defects, the thermal conductivity is inversely proportional to the square root of the phonon scattering coefficient. According to the elastic continuum medium model, Wan et al. [38] defined a method of quantifying the phonon scattering coefficient based on the effective elastic properties of the matrix and the effective ionic radius of the defect: where the subscript i denotes a certain lattice defect, f i denotes the concentration of this defect,  represent the atomic mass and the ionic radius of the specific defect, respectively, γ is the Grüneisen parameter, which represents the anharmonic vibrations within the whole lattice, and v is the Poisson ratio. Based on Eq. (9), it is known that, the mismatch of atomic masses and ionic radii of several RE elements in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 leads to an increase in the phonon scattering coefficient and thus a decrease in the thermal conductivity. In addition, because the outer electron structure of the Eu is 4f 7 6s 2 , when it loses two electrons, the outer electron structure is 4f 7 . 4f 7 is half-filled, which is also a stable state according to Hundt's rule. Therefore, Eu 2+ may exist in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 , thereby promoting the generation of oxygen vacancies which can dramatically decrease the thermal conductivity.
XPS analysis was used to further investigate the valence state of the elements in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 . Figure 8(a) is the XPS spectrum of Ho 4d. Three peaks are located at 160.97, 163.13, and 167.06 eV. They correspond to the Ho 3+ 4d 5/2 , Ho 3+ 4d 3/2 , and Ho 3+ 4d 5/2 , respectively. In Fig. 8(b), two peaks are determined at 196.73 and 206.46 eV, which belong to Lu 3+ 4d 5/2 and Lu 3+ 4d 3/2 , respectively. Figure 8(c) exhibits the XPS spectrum of Yb 4d, and there are two weak peaks located at 185.64 and 189.21 eV, which correspond to Yb 3+ 4d 5/2 and Yb 3+ 4d 3/2 , respectively. Figure 8( SiO 5 , which can enhance the scattering of phonons, resulting in a decrease in thermal conductivity. Typically speaking, the oxygen vacancies may lead to the high oxygen ion conductivity of the TBC or EBC, resulting in the accelerated oxidation of the bond coat. It has been found that, two main factors dominate the oxygen ionic conductivity of oxide ceramics: the oxygen vacancies and the activation energy of oxygen migration [39]. As shown in Fig. 8(d), the content of Eu 2+ is not high; therefore, the number of oxygen vacancies originating from the Eu element is not large. The activation energy of oxygen migration in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is controlled mainly by the strength of RE-O bonds. It suggests that a smaller radius of RE 3+ presents higher activation energy of oxygen ion migration. In (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 , the ionic radii of Ho, Yb, and Lu are small, and the oxygen diffusion rate should not be high. In addition, Matsudaira et al. [40] evaluated the oxygen diffusion in Yb 2 SiO 5 . The results confirm that oxide ion diffuses more preferentially along the grain boundary than the interior of the grain. Therefore, oxygen vacancies introduced by Eu 2+ in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 should not lead to a significant effect on the oxidation of the bond coat. As EBC materials, the TEC is required to match with the substrate to release the thermal stress between the coating and the substrate during thermal cycling [6]. The TEC of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 was measured and compared with RE 2 SiO 5 (RE = Ho, Lu, Yb, and Eu), some high-entropy RE 2 SiO 5 , and SiC ( Fig. 9)  is in the range of (4.0-5.9)×10 −6 K −1 which is close to that of SiC ((4.5-5.5)× 10 −6 K −1 ) [41]. Although there is a very small amount of RE 2 Si 2 O 7 in the specimen, Nasiri et al. [42] suggested that RE 2 Si 2 O 7 impurities have little contribution to thermal expansion. They prepared RE 2 SiO 5 (RE = Gd, Yb, Lu) ceramics containing RE 2 Si 2 O 7 impurities. But the TECs of Gd 2 SiO 5 , Yb 2 SiO 5 , and Lu 2 SiO 5 are (10.3± 0.4)×10 −6 K −1 , (7.2±0.5)×10 −6 K −1 , and (6.7±0.6)×10 −6 K −1 , respectively, which not show a significant decrease in TEC. Therefore, RE 2 Si 2 O 7 impurities do not contribute much to thermal expansion.
It has been found that, there are two species of phonons with different signs of Grüneisen constant in X2-RE 2 SiO 5 . One type of phonon has a positive Grüneisen constant and contributes to positive thermal expansion, and the other has a negative Grüneisen constant and contributes to negative thermal expansion [43]. According to the crystal structure, (Ho 0. 25 where d  is the degree of lattice distortion, (L O) d  represents the bond length between the RE or Si atom and the nth O atom, and (L O) d  represents the average bond length between them. In Table 5, we can see that (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 shows the  [23]. Therefore, the TEC of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is lower than those of RE 2 SiO 5 (RE = Ho, Lu, Yb, and Eu).

3 Mechanical properties
In addition to the TEC, the elastic modulus and hardness are also critical parameters of EBC [25].  Table 6. The reduced modulus of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is lower than those of Lu 2 SiO 5 and Yb 2 SiO 5 but higher than the reduced moduli of Ho 2 SiO 5 and Eu 2 SiO 5 . Also, the hardness of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is comparable with those of RE 2 SiO 5 (RE = Ho, Lu, Yb, and Eu). Young's modulus of ceramic is related to the bond strengths which can be represented by the cation field strength (CFS) [46]. CFS can be calculated by using the equation: CFS = Z c /r c 2 , where Z c is the cationic charge, and r c is the cationic radius. Therefore, Eu 3+ and Ho 3+ with larger radii contribute to the relatively low reduced modulus of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 . Also, the synergistic effect of the four RE elements leads to the reduced modulus of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 lower than the average value of the four RE 2 SiO 5 (Fig. 15).

4 CMAS corrosion
The turbine blade in the gas turbine engines usually suffers from severe hot corrosion by debris (such as dust, sand, and ash), which is generically known as CMAS corrosion [5]. A high-temperature CMAS corrosion test was performed to evaluate the resistance of corrosion. Figure 11(a) displays the surface morphology of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 after the CMAS corrosion at 1300 ℃ for 20 h. Some reaction products can be observed to be immersed in the CMAS melt. Figure 11( and garnet-type phase are the main reaction products [12]. Figure 12(a) exhibits the microstructure of the cross-section of the specimen. The infiltration depth is determined to be 125.4 ± 8.7 μm. Figure 12(b) displays the cross-section image at higher magnification, and Figs. 12(c)-12(h) presents the EDS element mappings. The cross-section can be divided into three layers. The top layer which is rich in Ca and Si elements and less in RE elements is the residual CMAS melt. The middle layer with a large number of rod-like grains is the reaction zone. Besides the rod-like grains, there are also large gray regions where Ca and Si contents are relatively low, with a certain amount of RE elements (Fig. 13). The bottom is (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 high-entropy ceramic. The compositions of reaction products analyzed by EPMA are summarized in Table 7. The top layer with a low content of RE elements is residual CMAS melt (point A). The ratio of Ca to RE elements of the rod-like grains is about 1 : 4, which can be identified The interaction between CMAS and RE 2 SiO 5 (RE = Ho, Lu, Yb, and Eu) has been performed, and their CMAS infiltration depths are 166.5±23.6 μm, 40.2 ± 3.2 μm, 75.1±2.0 μm, and 248.6±14.3 μm, respectively (Fig. 14). The CMAS infiltration depth of (Ho 0. 25 [50]. Hence, Lu, Yb, Ho, and Eu ions present a gradient velocity in the precipitation of Ca 2 RE 8 (SiO 4 ) 6 O 2 [51]. Yb and Lu with small ionic radii will slow down the formation of reaction product Ca 2 RE 8 (SiO 4 ) 6 O 2 which is comprised of Lu, Yb, Ho, and Eu elements ( Table 7). Our previous work has revealed that the resistance to CMAS corrosion of RE 2 SiO 5 (RE = Tb, Dy, Ho, Er, Y, Tm, Yb, and Lu) at 1300 ℃ increases with the reduction of the radius of RE 3+ [12]. Consequently, Lu and Yb in (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 effectively mitigate CMAS corrosion. The thermal conductivity, thermal expansion coefficient, reduced modulus, and CMAS corrosion resistance of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 were compared with the average value of Ho 2 SiO 5 , Lu 2 SiO 5 , Yb 2 SiO 5 , and Eu 2 SiO 5 , as shown in Fig. 15. The high-entropy (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 ceramic exhibits excellent thermal insulation properties, tunable TEC, low reduced modulus, and good resistance to CMAS corrosion. The above results demonstrate that (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is a promising EBC candidate.

Conclusions
In this study, a novel high-entropy RE silicate ceramic (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 was designed and successfully fabricated. (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 shows very low thermal conductivity, exhibiting excellent thermal insulation properties. Oxygen vacancies and severe lattice distortion mainly contribute to the low thermal conductivity. The TEC of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 from room temperature to 1200 ℃ is (4.0 -5.9) × 10 −6 K −1 , which is close to that of SiC. The reduced modulus of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 is 149.0± 16.5 GPa which is lower than those of Lu 2 SiO 5 , Yb 2 SiO 5 , and the average of RE 2 SiO 5 (RE = Ho, Lu, Yb, and Eu). In addition, (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 presents good CMAS corrosion resistance. Ca 2 RE 8 (SiO 4 ) 6 O 2 and garnettype phase (Ca x RE 3−x )(Mg y Al z Si 5−y−z )O 12 are the main reaction products. Excellent thermal insulation properties, suitable TEC, low reduced modulus, and good CMAS corrosion resistance of (Ho 0.25 Lu 0.25 Yb 0.25 Eu 0.25 ) 2 SiO 5 make it a potential EBC material candidate.