Preparation and properties of CMAS resistant bixbyite structured high-entropy oxides RE2O3 (RE = Sm, Eu, Er, Lu, Y, and Yb): Promising environmental barrier coating materials for Al2O3f/Al2O3 composites

Y2O3 is regarded as one of the potential environmental barrier coating (EBC) materials for Al2O3f/Al2O3 ceramic matrix composites owing to its high melting point and close thermal expansion coefficient to Al2O3. However, the relatively high thermal conductivity and unsatisfactory calcium-magnesium-aluminosilicate (CMAS) resistance are the main obstacles for the practical application of Y2O3. In order to reduce the thermal conductivity and increase the CMAS resistance, four cubic bixbyite structured high-entropy oxides RE2O3, including (Eu0.2Er0.2Lu0.2Y0.2Yb0.2)2O3, (Sm0.2Er0.2Lu0.2Y0.2Yb0.2)2O3, (Sm0.2Eu0.2Er0.2Y0.2Yb0.2)2O3, and (Sm0.2Eu0.2Lu0.2Y0.2Yb0.2)2O3 were designed and synthesized, among which (Eu0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 and (Sm0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 bulks were prepared by spark plasma sintering (SPS) to investigate their mechanical and thermal properties as well as CMAS resistance. The mechanical properties of (Eu0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 and (Sm0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 are close to those of Y2O3 but become more brittle than Y2O3. The thermal conductivities of (Eu0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 and (Sm0.2Er0.2Lu0.2Y0.2Yb0.2)2O3 (5.1 and 4.6 W·m−1·K−1) are only 23.8% and 21.5% respectively of that of Y2O3 (21.4 W·m−1·K−1), while their thermal expansion coefficients are close to those of Y2O3 and Al2O3. Most importantly, HE RE2O3 ceramics exhibit good CMAS resistance. After being attacked by CMAS at 1350 °C for 4 h, the HE RE2O3 ceramics maintain their original morphologies without forming pores or cracks, making them promising as EBC materials for Al2O3f/Al2O3 composites.

When choosing the compositions, crystal structures and atomic differences were taken into account as the main criteria. Firstly, the constituting oxides are expected to crystallize in similar crystal structures. Secondly, the chosen five kinds of rare earth elements are supposed to have small ionic radius difference but high atomic mass difference. Thus, (Eu 0.2 Er 0. 2  The mechanisms underlying the low thermal conductivity of HECs are attributed to atomic mass difference and lattice distortion. For the electrical insulating HECs, the thermal conductivities are typically determined by a combination of phonon-phonon scattering and defect scattering [38]. The phonon relaxation time  can be described as where U  and PD  refer to Umklapp phonon-phonon scattering and point defect scattering, respectively. In detail, M is the average mass, g  is the phonon group velocity, p  is the phonon phase velocity, V is the volume per atom,  is the Grüneisen parameter,  is the phonon frequency, i f is the fraction of atoms with mass i m and radius i r on the site with average mass m and radius r . Based on Eq. (1) and Eq. (2), it is reasonable to expect that the thermal conductivity of HE RE 2 O 3 will be reduced compared to Y 2 O 3 owing to big atomic mass difference and lattice distortion in HE RE 2 O 3 .
Aiming at reducing the thermal conductivity and improving the CMAS resistance of Y 2 O 3 , four cubic bixbyite structured high-entropy rare earth oxides, i.e., (Eu 0.2 Er 0. 2 3 were designed, which have big atomic mass difference and ionic radius difference. These high-entropy rare earth oxides were synthesized using Sm 2 O 3 , Eu 2 O 3 , Er 2 O 3 , Lu 2 O 3 , Y 2 O 3 , and Yb 2 O 3 as starting materials, and then the mechanical and thermal properties as well as CMAS resistance were explored to assure their qualification as promising EBC materials for Al 2 O 3f /Al 2 O 3 composites.

1 Preparation and characterization of HE RE 2 O 3 powders and bulks
Powders of (Eu 0.2 Er 0. 2  The mixtures were cold pressed into pallets and then calcined at 1600 for 4 h in air. After cooling, these ℃ pallets were smashed and ball milled for 4 h to obtain fine powders. Phase identification was performed by an X-ray diffractometer (XRD, D8 advanced, Bruker, Germany) using Cu Kα (λ =1.54178 Å) radiation at a scanning speed of 2 (°)/min. To prove that the as-prepared powders exhibit the cubic bixbyite structure, Rietveld refinement was conducted using TOPAS software (TOPAS, Bruker Corp., Karlsruhe, Germany). In Rietveld refinement, R factor is the sum of weighted and squared differences between observed and calculated intensities at each point in an XRD pattern which is minimized by least squares refinement as [39]: where S is a phase-specific scale factor, k p is the multiplicity factor, k L is the Lorentz and polarization factor for the kth Bragg reflection, k F is the structure factor for an individual reflection of a particular phase, is the reflection profile function, Δ ik  is the Bragg angle for the kth reflection, k P is the preferred orientation function, and (bkg) i y is the refined background. In this way, reliability factors R p [39] and R wp [40] wherein lower values indicate higher degree of agreements. The particle size distribution of HE RE 2 O 3 powders was observed in a scanning electron microscope (SEM, Apollo300, CamScan, Cambrige, UK) and analyzed using ImageJ software (Open resource) [41] with at least 300 particles were counted. Bulk HE RE 2 O 3 ceramics were prepared by a spark plasma sintering apparatus (SPS-20T-6-IV, Shanghai Chenhua Science and Technology Co., Ltd., China) at 1500 for 10 min under a pressure of 30 MPa. The ℃ bulk density was measured by the Achimede's method. After being polished and thermally etched at 1500 ℃ for 1 h, microstructures and element distribution of HE RE 2 O 3 ceramics were observed by a scanning electron microscope (SEM, Apollo300, CamScan, Cambridge, UK) equipped with energy dispersive X-ray spectroscopic system (EDS, Inca X-Max 80 T, Oxford, UK). The grain size distribution was analyzed using ImageJ software (open resource) [41] based on the microstructures of the thermally etched surface and at least 300 grains were counted.

2 Mechanical properties of bulk HE RE 2 O 3
Good mechanical properties and damage tolerance are basic requirements for EBC materials. To evaluate the suitability of HE RE 2 O 3 as EBC materials, their mechanical properties were measured. For flexural strength and fracture toughness, at least five samples were tested using a universal testing machine (MTS-Criterio C45.105, USA). The flexural strength of HE RE 2 O 3 was measured through a three-point bending test method with the sample dimension of 3 mm × 4 mm × 36 mm. Fracture toughness K IC was determined using single-edge notched beam (SENB) specimens with the dimension of 3 mm × 6 mm × 36 mm. The elastic modulus and Poisson's ratio of the specimen, while E i and v i are the elastic modulus and Poisson's ratio of the indenter, respectively.

3 Thermal properties of bulk HE RE 2 O 3
Thermal conductivity is one of the most important properties for HE RE 2 O 3 that needs to make a breakthrough in this work. Thermal conductivity (  ) of HE RE 2 O 3 can be calculated from thermal diffusivity (D th ), heat capacity (c p ), and bulk density (d) using: where c p was calculated from the data of the constituent oxides ( ( 3 Ia space group) [44], while Sm 2 O 3 is in monoclinic structure (C2/m space group) [44,45].  Figure 2(c) shows the schematic crystal structure of high-entropy RE 2 O 3 , which was built based on a 2 × 2 × 2 supercell of Y 2 O 3 . In Y 2 O 3 , Y atoms are located at 8a (1/4, 1/4, 1/4) and 24d (x, 0, 1/4) sites, while O atoms occupy the 48e (x, y, z) site. In HE RE 2 O 3 , five kinds of RE atoms occupy the 8a and 24d sites randomly. Using the structure model of HE RE 2 O 3 in Fig. 2(c), a simulated XRD pattern is obtained as shown in Fig.  2(d). This XRD pattern is very similar to those of cubic bixbyite oxides but with tiny peaks at low angle due to the supercell.
It has come to light that the stable crystal structure of the RE 2 O 3 at room temperature varies with the atomic number of RE [46].  [46][47][48][49][50][51][52] are listed in Table 1. 1153 [46] 2170 [46] 2369 [46] 2526 [46] 1173-1273 [47] 2143 [48] 2403 [50] 2523 [50] 1153 [49] 2173 [50] 2343 [48] 2498 [48] Eu 2 O 3 1348 [46] 2323 [46] 2413 [46] 2526 [46] 1348 [47] 2323 [50] 2413 [50] 2523 [50] 1323 [51] 2323 [52] 2413 [52] 2498 [48] According to has been dissolved into the cubic bixbyite structure. Since Sm 2 O 3 has a different crystal structure, it demonstrates that materials with different crystal structures can be integrated into a homogeneous solid solution through entropy stabilization. In addition, cubic bixbyite structured Eu 2 O 3 is supposed to transfer to a monoclinic structure after being heated at 1600 ℃ for 4 h. However, it remains in a cubic bixbyite structure in HE RE 2 O 3 . These facts demonstrate that the structural constraint of high-entropy oxides is effective in restraining phase transition and sustaining the phase stability [55].   Table 2. The average lattice parameter a av and density d av of five constituting oxides are also included for comparison. Primarily, the R p and R wp values are less than 10, which indicate good reliability of the refinement. Analyzing of the data in the table, one can find that the refined lattice parameters a are somewhat smaller than the average lattice parameters a av . And the theoretical densities d t of HE RE 2 O 3 are lower than the average densities of the constituting oxides d av , from which the deviations are around 2%. From the above results, a conclusion can be drawn that for the HE RE 2 O 3 , the lattice parameters are not just the average of those the constituting components but are the results of energetic optimization of the structure after they reach thermodynamic equilibrium.
Interestingly, it should be pointed out that during the synthesis procedure, the solubility of (Sm 0. 2 Table 3 Atomic and ionic radii, relative atomic mass, and the relative ionic radius differences of the selected rare earth elements

Element
Atomic radius (Å) [56] Ionic radius RE 3+ (Å) [56] Coordination number  Figure 7 shows the SEM  Figure 8 shows the surface microstructures and grain size distributions of bulk (Eu 0.2 Er 0. 2 [60], which still warrant their resistance to damage. Figure 10 compares the fracture surfaces of (Eu 0.2 Er 0. 2   after fracture toughness test. It can be seen that both of the fracture surfaces exhibit a combination of intragranular fracture (blue arrows indicate region) and intergranular fracture (red arrows indicate region). In Fig. 10(a), intact grain boundaries can clearly be seen, which signify that intergranular fracture occurs primarily in (Eu 0.2 Er 0.2 Lu 0.2 Y 0.2 Yb 0.2 ) 2 O 3 . On the contrary, cleavage steps caused by crack penetration inside the grains exist mainly in Fig. 10(b), which promotes the dissipation of fracture energy. The difference between fracture surfaces of (Eu 0.2 Er 0. 2 Fig. 11. Distinctly, the expansion of samples increases linearly with temperature without excessive fluctuation caused by phase transition or decomposition, which also  [58,61]. Table 5 compares the thermal expansion coefficients (TECs) of the selected cubic bixbyite structured rare earth oxides [53]. In general, the TECs of HE RE 2 O 3 are slightly smaller than those of single component rare earth oxides, which distribute in a range of (8.2-8.9)×10 -6 K -1 . This fact implies that the TECs of HE RE 2 O 3 stem from complex synergism of the component rare earth oxides instead of the average of them. Basically, thermal expansion of materials originates from anharmonic vibration of lattice at finite temperatures, which is closely related to the bond strength of chemical bond. Since the TECs of HE Table 5 Thermal expansion coefficients of the selected cubic bixbyite structured rare earth oxides in different temperature ranges [ Figure 12 shows the thermal diffusivities measured from room temperature to 1173 K. Curve fitting of the scatters of (Eu 0.2 Er 0. 2 (15) with R 2 equals to 0.973 and 0.973, respectively. As shown in Fig. 14 (1) and (2). According to the ionic radii of rare earth elements and relative atomic mass that are listed in Table 3 [22], YSZ [22,62], REPO 4 (RE = Nd, Sm, Gd) [62], Ba 2 REAlO 5 (RE = Yb, Er, Dy) [63], and high-entropy RE 2 Si 2 O 7 [64].  [62] and Ba 2 REAlO 5 (RE = Yb, Er, Dy) [63] (with a concentration of about 15 mg/cm 2 ). After being corroded at 1250 for 1 h, ℃ MOCVD YSZ coating possessed a 5 μm-thick reaction layer while YSZ pellet infiltrated by CMAS for 4 h has a reaction layer with a depth of 50 μm. substrates largely, leaving Si behind them, while Ca remains mostly in the CMAS layer. As for rare earth elements, Y seems to be eagerly to climb upward while the other four elements are similar and remain mostly in the substrates of HE RE 2 O 3 . To figure out the reaction mechanism, samples half-coated by CMAS were designed as shown in Fig. 17(a). In Figs. 17(b) and 17(c), a step appears at the transition zone of each sample, revealing that the reaction mechanism is characterized by the diffusion from CMAS to HE RE 2 O 3 . Figure 18 (2) and (3) are similar despite a new strong peak at 2θ ≈ 37° appears in curve (3), which also exists in curve (4). However, most of the peaks still remain unknown, demonstrating that the phase compositions of the surface of (Sm 0.2 Er 0. 2 [65,66] are identified. However, XRD patterns of these three phases cannot match any of the unknown peaks in Fig. 18. The mismatch between XRD patterns in Fig. 18 and Fig. 19 might be related to reaction methods. The XRD patterns shown in Fig. 19 are from the reaction of (Eu 0.2 Er 0. 2

Conclusions
In this study, four cubic bixbyite structured high-entropy rare earth oxides, including (Eu 0.2 Er 0. 2