High-entropy (Nd0.2Sm0.2Eu0.2Y0.2Yb0.2)4Al2O9 with good high temperature stability, low thermal conductivity, and anisotropic thermal expansivity

Abstract: The critical requirements for the environmental barrier coating (EBC) materials of silicon-based ceramic matrix composites (CMCs) include good tolerance to harsh environments, thermal expansion matches with the interlayer mullite, good high-temperature phase stability, and low thermal conductivity. Cuspidine-structured rare-earth aluminates RE₄Al₂O₉ have been considered as candidates of EBCs for their superior mechanical and thermal properties, but the phase transition at high temperatures is a notable drawback of these materials. To suppress the phase transition and improve the phase stability, a novel cuspidine-structured rare-earth aluminate solid solution (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was designed and successfully synthesized inspired by entropy stabilization effect of high-entropy ceramics (HECs). The as-synthesized HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ exhibits a close thermal expansion coefficient (6.96×10^-6 K^-1 at 300–1473 K) to that of mullite, good phase stability from 300 to 1473 K, and low thermal conductivity (1.50 W·^m–1·K^–1 at room temperature). In addition, strong anisotropic thermal expansion has been observed compared to Y₄Al₂O₉ and Yb₄Al₂O₉. The mechanism for low thermal conductivity is attributed to the lattice distortion and mass difference of the constituent atoms, and the anisotropic thermal expansion is due to the anisotropic chemical bonding enhanced by the large size rare-earth cations.

Keywords: (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉; high-entropy ceramics (HECs); environmental barrier coatings; phase stability; thermal properties

1 Introduction

Silicon-based ceramics such as Si₃N₄ and SiC_f/SiC ceramic matrix composites (CMCs) have been considered as candidates to replace superalloys to manufacture the hot section structural components in gas turbine engines due to their superior high-temperature mechanical properties, good durability, and excellent creep- and oxidation-resistance ^[1–6]. However, a key barrier to realizing silicon-based turbine hot section structural components is the lack of environmental durability in combustion environments because the protective silica scale on the surface of silicon-based ceramics can be corroded by high-temperature water vapor and yields volatile products, such as Si(OH)₄, which will result in the rapid recession ^[7–11]. Thus, environmental barrier coatings (EBCs) are necessary for silicon-based ceramics, which can protect the hot section structural components from the corrosion of high-temperature water vapor ^[12,13]. 

Generally, the current prime EBC system of Si₃N₄ and SiC_f/SiC CMCs consists of a multiple-layer silicon/mullite/refractory oxide coating structure and each layer is under a specific purpose. Silicon as the adhesive layer bonds the substrate and the upper coatings, mullite as the interlayer reduces the thermal stress between the substrate and the upper coatings, and the refractory oxide as the top layer protects the underlayer coatings and the substrate from the corrosion of harsh environments ^[12–14]. The key requirements for selecting the top refractory oxides include good tolerance to harsh environments, thermal expansion match with the interlayer and the substrate materials, good phase stability at high temperatures, and low thermal conductivities. ^[12,15–17]. Particularly, cuspidine-type rare-earth aluminates RE₄Al₂O₉ are a class of ceramics that have been considered as potential materials for EBCs of silicon-based ceramics owing to their high melting point, low Young’s modulus, good damage tolerance, close thermal expansion coefficients to that of mullite, low thermal conductivity, and good resistance to the hot gas atmosphere ^[15,18–21]. However, one major weakness of RE₄Al₂O₉ compounds for EBC application is the high-temperature phase transition with a sudden change in volume, which can lead to cracking of the coatings in thermal cycling ^[22–25]. Therefore, the suppression of phase transformation of RE₄Al₂O₉ compounds is of great significance for their high-temperature applications. 

In recent years, a new type of ceramics consisting of multi-principal component elements in equal molar or near equal molar fractions but form single phase solid solutions have triggered much attention, which are referred to as high-entropy ceramics (HECs) ^[26–28]. These materials exhibit many intriguing properties, such as higher hardness, sluggish grain growth rate, lower thermal conductivity, strong microwave absorption capability, and better water-vapor resistance, etc. ^[29–34]. More importantly, our previous work indicates that HECs usually possess better high-temperature phase stability than the single-component ceramics owing to the entropy stabilization effect of HECs ^[35,36], which may provide a new way to improve the phase stability of RE₄Al₂O₉ at high temperatures, i.e., through forming HE solid solutions. Consequently, to suppress high-temperature phase transformation and reduce the thermal conductivity of RE₄Al₂O₉ compounds, a novel HE cuspidine-structured rare-earth aluminate solid solution (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was designed and successfully synthesized in this study. The phase composition, microstructure, phase stability, average linear thermal expansion coefficient, anisotropy of thermal expansion coefficient, and thermal conductivity of this new type of HE rare-earth aluminate were investigated synthetically. These fundamental data are of great importance to evaluate the prospect of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ for EBC application. In addition, the mechanisms for low thermal conductivity and anisotropic thermal expansion will be presented. 

2 Experimental 

2. 1 Synthesis of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders

The starting materials used for synthesizing (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders are as follows: RE(NO₃)₃·6H₂O (RE = Nd, Sm, Eu, Y, and Yb) powders (99.9% purity, Aladdin Biochemical Technology Co., Ltd., Shanghai, China), Al(NO₃)₃·9H₂O powders (99.9% purity, Aladdin Biochemical Technology Co., Ltd., Shanghai, China), and ammonia (NH₃·H₂O, pH = 12.5, Beihua Fine Chem. Co., Ltd., Beijing, China). 

A co-precipitation method was performed to synthesize (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders. Firstly, RE(NO₃)₃·6H₂O (RE = Nd, Sm, Eu, Y, and Yb) powders were weighted in equal molar ratio and mixed, then dissolved in distilled water to form a clear solution with a concentration of 0.3 mol/L. Separately, Al(NO₃)₃·9H₂O powders were also dissolved in distilled water to form a clear solution with the same molar concentration and then added into the mixed RENO₃ solution with stirring. The molar ratio of total RE elements and Al is RE_total:Al = 2:1. After mixing thoroughly, excess aqueous ammonia was added slowly into the mixed solution with vigorously stirring to obtain gel-like precipitants. The precipitants were then filtered and washed with distilled water for several times to ensure impurity ions (NH₄⁺ and NO₃^–) eliminated before being dried in an oven at 383 K for 12 h. Finally, the (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders were synthesized by calcining the precursors at 1873 K for 1 h in a muffle furnace. The calcined products were ball-milled with agate balls for 20 h by a planetary ball mill (XQM-2, NEWRICE Technology Co., Ltd.). The ball to powder weight ratio was controlled to be 6:1 and the speed of ball milling was 400 rpm. Then the mixed slurry was dried in a vacuum oven at room temperature. Fine-particle powders were obtained by screening the calcined products in a 300 mesh sieve. 

2. 2 Preparation of bulk (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉

Bulk (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was prepared using a spark plasma sintering apparatus (SPS-20T6-IV, Shanghai Chenhua Science and Technology Co., Ltd., China) at 1923 K for 4 min under a pressure of 30 MPa. Details of the preparation process were reported in our previous studies ^[31,32,36]. After sintering, the surface of the bulk sample was ground by silicon carbide sandpapers to remove the carburized layer. 

2. 3 Characterization of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders and the sintered compacts 

The phase compositions of the as-synthesized powders and the sintered compacts were determined by an X-ray diffractometer (XRD, D8 Advanced, Bruker, Germany) using Cu Kα radiation (λ = 1.5406 Å) with a step size of 0.02°. The scanning rate was 2 (°)/min. The lattice parameters of as-synthesized (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ were refined by the Rietveld method (TOPAS, Bruker Corp., Karlsruhe, Germany). 

The density of the sintered compacts was measured by Archimedes’ method. The investigation of the microstructure and the element distributions of the sintered compacts were performed by using a scanning electron microscope (SEM, Apollo300, CamScan, Cambridge, UK) equipped with energy dispersive X-ray spectroscopic system (EDS, Inca X-Max 80T, Oxford, UK). Before the SEM observation, the samples were polished by silicon carbide sandpapers and then thermally etched at 1673 K for 2 h to ensure the grain boundary is clear. 

The investigation of linear thermal expansion of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at 300–1473 K was performed by an optical dilatometer (Misura ODHT 1600-50, Expert System Solutions, Italy). The asmeasured sample is a polished rectangular bar with a size of 3 mm × 4 mm × 15 mm. A 45° chamfer was cut at one end of the sample. The anisotropic thermal expansion coefficient of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was investigated by a powder X-ray diffractometer equipped with an isothermal sample heating system (XRD, X’Pert MPD Pro Panalytical Holland). (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders were heated from 300 to 1473 K at a heating rate of 5 K/min and held for 5 min to achieve temperature equilibration at 100 K intervals, and then the XRD patterns of the sample at the desired temperatures were recorded with a scanning rate of 1 (°)/min. The lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at different temperatures were refined by the Rietveld method. The volumetric thermal expansion coefficient (α_v) and the linear thermal expansion coefficients along principal axes (α_a, α_b, and α_c) were obtained by fitting the lattice parameters versus temperature curves of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉. 

Thermal diffusivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was investigated by the laser flash method. The as-measured sample is a disk with a size of ϕ 10 mm × 2 mm. Before measurement, the surface of the sample was sprayed a layer of graphite to prevent heat radiation from penetrating through it. The heat capacity at constant pressure was calculated by Neumann–Kopp rule using the data of its constituent oxides (Nd₂O₃, Sm₂O₃, Eu₂O₃, Y₂O₃, Yb₂O₃, and Al₂O₃) ^[37,38]. Thermal conductivity (κ) was calculated by the following equation ^[39]:

κ = D_th · C_p · d  (1) 

where κ is thermal conductivity, D_th is thermal diffusivity, C_p is heat capacity at constant pressure, and d is bulk density of the sample.

3 Results and discussion 

3. 1 Phase composition and microstructure

The first step for synthesizing HE rare-earth aluminate is choosing the compatible rare-earth elements that warrant the easy formation of phase-pure solid solution. Generally, there are two criteria for selecting the compatible components of HE materials ^[36]. Firstly, the difference in the ion radius of the selecting elements is small. Secondly, the single-component phases containing the selected elements possess the same or similar crystal structures. Herein, the cation radius and radius difference of the selecting rare-earth elements for the design of HE rare-earth aluminate together with the space group of the single-component phases containing these rare-earth elements are listed in Table 1 ^[25]. It can be seen that the radius difference of the selected rare-earth elements is less than 13% and that all the single-component of RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) possesses the same crystal structure, which warrants the easy formation of the phase-pure HE rare-earth aluminate. Figure 1 exhibits the crystal structure of rare-earth aluminate. The HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ has the same crystal structure with those of the single-component RE₄Al₂O₉, which crystallizes in a monoclinic structure with a space group of P2₁/c and five component elements (Nd, Sm, Eu, Y, and Yb) occupy the RE sites evenly and randomly ^[40]. 

Table 1 Space group, cation radius, and radius difference of RE₄Al₂O₉ for design of HE rare-earth aluminates (the data are obtained from the database of Materials Studio program, © Accelrys Inc., San Diego, USA, 2014) 

Fig. 1 Crystal structure of rare-earth aluminate. 

Figure 2 shows the XRD pattern of as-synthesized (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders, and the data of single-component RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) obtained from ICDD/JCPDS cards are also exhibited for comparison. The as-synthesized powders are phase-pure and only a monoclinic phase was detected, indicating that a solid solution (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is formed. Rietveld refinement was performed by using TOPAS software to obtain information about the lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉. The results are presented in Table 2 and compared with the data of the single-component RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) obtained from ICDD/JCPDS cards. It can be seen that the refined lattice parameters (a, b, and c) of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ are larger than those of Y₄Al₂O₉ and Yb₄Al₂O₉ but smaller than those of Nd₄Al₂O₉, Sm₄Al₂O₉, and Eu₄Al₂O₉. Based on the refined lattice parameters, the theoretical density of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is calculated to be 6.06 g/cm², which is between the data of five single-component phases. 

Fig. 2 XRD patterns of the as-synthesized (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders together with the data of single-component RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) obtained from ICDD/JCPDS cards. 

Table 2 Refined lattice parameters, relative change of lattice parameters compared to Yb₄Al₂O₉, and theoretical density of HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ together with those of the single-component RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) obtained from ICDD/JCPDS cards

Figure 3 illustrates the XRD pattern of the as-sintered (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ compact. The phase composition of the as-sintered compact is unchanged compared with that of the as-synthesized powders. Figure 4 displays the SEM image of the as-sintered (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ compact after thermally etched at 1673 K for 2 h and the corresponding EDS mappings of rare-earth elements (Nd, Sm, Eu, Y, and Yb). No pores and cracks can be found from the observed region, indicating that the as-sintered compact has a high relative density. The experimental density of the as-sintered compact measured by the Archimedes’ method is 6.02 g/cm² and the corresponding relative density is 99%. It also can be found that the containing rare-earth elements are uniformly distributed in the grains, which further indicate that (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is a single-phase solid solution.

Fig. 3 XRD pattern of the as-sintered (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ compact. 

Fig. 4 SEM image of the as-sintered (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ compact after thermally etched at 1673 K for 2 h and the corresponding EDS mappings of rare-earth elements (Nd, Sm, Eu, Y, and Yb). 

3. 2 Phase stability and thermal expansion behavior

The linear thermal expansion curve of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ measured at 300–1473 K is illustrated in Fig. 5. It is evident that the expansion of bulk (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ increases linearly with the increase of temperature and no abrupt volume change was found, which indicates that (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ has good phase stability at the measured temperature range. Note that the single-component Sm₄Al₂O₉ and Eu₄Al₂O₉ exhibit reversible phase transition with abrupt volume changes at 1317 and 1387 K, respectively ^[25]. This phase transition is harmful to the materials applied in the high-temperature environment due to that the sudden change in volume will reduce the thermal shock resistance of the materials and cause the cracking of coatings in thermal cycling. Thus, good phase stability of high-entropy (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ renders it more suitable for high-temperature applications. 

Fig. 5 Linear thermal expansion curve of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ measured at 300–1473 K. 

In addition, the thermal expansion versus temperature curve in Fig. 5 can be fitted using a linear function: ΔL/L₀ × 100% = 6.96×10^-6T(K) – 0.25, with a reliability value of R² = 0.999. The linear thermal expansion coefficient of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is determined in terms of the slope of the curve and calculated to be 6.96×10^-6 K^-1 at 300–1473 K, which is in between those of Y₄Al₂O₉ (7.37×10^-6 K^-1) ^[19] and Yb₄Al₂O₉ (6.27×10^-6 K^-1) ^[16], and close to that of the interlayer phase of EBC system, mullite (5×10^-6 – 7×10^-6 K^-1) ^[41]. 

To investigate the anisotropy of the thermal expansion of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉, the XRD patterns of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders at different temperatures were recorded and are exhibited in Fig. 6. It can be seen that there is no phase transformation detected when the temperature increases from 300 to 1473 K, further proving that (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ has good phase stability at high temperatures. The diffraction peaks of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ gradually shift to the lower angle direction with the increase of temperature, which indicates that the lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ change when the temperature increases. The lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at different temperatures were obtained by fitting the XRD patterns in Fig. 6 according to the Rietveld refinement method. 

Fig. 6 XRD patterns of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ powders at different temperatures. 

Figure 7 shows the normalized lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at 300–1473 K. The lattice parameters a, b, c, and the unit cell volume V monotonously increase as the temperature increases from 300 to 1473 K. The αv, namely, the relative change in volume when the temperature rises by 1 K, is defined by the following equations ^[42]:

where α_v(T) is the temperature-dependent volumetric thermal expansion coefficient, V₀ is the volume of a unit cell at 300 K. α_v(T) tends to be a constant at high temperatures and thus Eq. (2) can be simplified as 

ln(V/V₀) =  α_v( T-T₀)  (3) 

Based on Eq. (3), the αv of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ can be obtained by fitting the data in Fig. 7. Moreover, the linear thermal expansion coefficients along three crystallographic directions (α_a, α_b, and α_c) were also calculated in the same way. Table 3 shows the anisotropic thermal expansion coefficients (α_a, α_b, and α_c) and αv of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ together with those of Y₄Al₂O₉ ^[19]. The α_v of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ (24.40×10^-6 K^-1) is slightly higher than that of Y₄Al₂O₉ (23.37×10^-6 K^-1), and the anisotropy of thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is much stronger than that of Y₄Al₂O₉. 

Fig. 7 Normalized lattice parameters of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at 300–1473 K. 

Table 3 Anisotropic thermal expansion coefficients (α_a, α_b, and α_c) and α_v of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ together with those of Y₄Al₂O₉

To obtain an intuitive and complete representation of the anisotropic thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉, the variation of thermal expansion coefficients as a function of crystal orientation is necessary. Figure 8 exhibits the surface contour of the thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ and the planar projections of the thermal expansion coefficients on (001), (010), and (100) crystallographic planes. It can be seen that the anisotropy of thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is clearly illustrated and the anisotropy of thermal expansion coefficients on (010) plane is stronger than those on (001) and (100) planes. The maximum and minimum values of thermal expansion coefficients are 10.60×10^-6 K^-1 (α₁₁) and 4.87×10^-6 K^-1 (α₃₃), respectively. The strong anisotropy of thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ can be explained by the crystal structure feature of RE₄Al₂O₉. Figure 9 exhibits the planar projections of the crystal structure of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ on (001), (010), and (100) crystallographic planes. It can be seen that the arrangement of RE atoms along a- and b-axis is much denser than that along the c-axis. Thus, the fluctuation of the lattice parameters a and b is much stronger than that of the lattice parameter c when the RE³⁺ radius changes, which is demonstrated by the relative change regularity of the lattice parameters of RE₄Al₂O₉ compounds. Figure 10 shows the relative change of the lattice parameters of RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) as a function of RE³⁺ radius, and the data were obtained from ICDD/JCPDS cards and are listed in Table 2. As the RE³⁺ radius increases, the relative change of the lattice parameters a and b are much larger than that of the lattice parameter c, which will result in the anisotropy of bonding strength, i.e., the bonds along a- and b-axis are weaker than that along the c-axis. 

Fig. 8 Surface contour of the thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ and planar projections of the thermal expansion coefficients on (001), (010), and (100) crystallographic planes. 

Quantitative description of this bonding anisotropy is accessible by estimating the bond energy of HE RE₄Al₂O₉ and Y₄Al₂O₉ using a simple theory called chemical bonding theory (CBT). Due to the similarity in the crystal structure, the calculation procedure for parameters of all chemical bonds in HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is the same as that in Y₄Al₂O₉, and for detail description, one may refer to Ref. ^[18]. The chemical parameters for each bond of two materials are listed in Table 4 (worth noting that the listed bond energies for HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ are the average ones since the bond length (l^μ) around different rare-earth atoms is different. For both materials, the covalency (f_c^μ) and bond energies (U^μ) of Al–O bonds are significantly larger than those of RE–O bonds, demonstrating stronger bonding nature of Al–O tetrahedron. Large bond energy also leads to less contribution of AlO₄ tetrahedron to total thermal expansion, and the chemical environments around RE atoms determine the expansion behavior of HE (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉. With different RE atoms incorporating in the structure, the bond strength of all RE–O bonds varies accordingly. However, the energy changing for different RE–O bonds is quite anisotropic, e.g., the response of RE1–O3, RE1–O7, RE1–O2, and RE1–O1 is more evident than the rest RE1–O bonds. The spatial configuration of RE1–O polyhedra is shown in Fig. 11(a). The bonds with large energy degradation are almost parallel with ab-plane, leading to an increase of anisotropy in bonding strength between the ab-plane and c-direction. For the other three RE sites listed in Table 4, the same situation is observed, and the RE–O bonds along the ab-plane are disturbed notably than that along the c-direction. Since the thermal expansion of RE₄Al₂O₉ is determined by RE–O bonds, the increase of anisotropy of RE–O bonds along different directions will eventually result in the increase of anisotropy in thermal expansion. In addition, the same variety trend was also found from Young’s modulus of RE₄Al₂O₉ compounds. The anisotropy of Young’s modulus of Yb₄Al₂O₉ is weaker than that of Y₄Al₂O₉ due to that Yb³⁺ has a smaller radius than Y³⁺, which also proves that RE₄Al₂O₉ with large RE³⁺ radius exhibits the strong anisotropy of bonding strength ^[16,18].

Fig. 9 Planar projections of the crystal structure of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ on (001), (010), and (100) crystallographic planes. 

Fig. 10 Relative change of the lattice parameters of RE₄Al₂O₉ (RE = Nd, Sm, Eu, Y, and Yb) as a function of RE³⁺ radius. 

Table 4 Chemical parameters of each bond for (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ and Y₄Al₂O₉ by chemical bond theory

Fig. 11 Spatial configuration of RE–O polyhedra for (a) RE1, (b) RE2, (c) RE3, and (d) RE4 sites, respectively.

3. 3 Thermal conductivity

Table 5 Thermal diffusivity (D_th), heat capacity (C_p), bulk density (d), and thermal conductivity (κ) of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ measured at room temperature

Table 5 shows the thermal diffusivity, heat capacity, bulk density, and thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ measured at room temperature. The thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at room temperature is as low as 1.50 W·m–1·K–1, which is 55% lower than that of Y₄Al₂O₉ (3.31 W·m^–1·K^–1). This value is also much lower than those of other candidate EBC materials, such as Y₂SiO₅ (1.86 W·m^–1·K^–1) ^[43], Yb₂SiO₅ (2.3 W·m^–1·K^–1) ^[44], γ-Y₂Si₂O₇ (4.91 W·m^–1·K^–1) ^[43], and β-Yb₂Si₂O₇ (4.31 W·m^–1·K^–1) ^[45]. The low thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is likely attributed to the HE effect ^[28]. For opaque dielectric materials, the major process that leads to a finite thermal conductivity is phonon scattering and the extent of phonon scattering depends on the anharmonicity of the lattice vibrations ^[46]. Based on the Umklapp phonon–phonon scattering mechanism ^[47,48]: 

where κ_a is the thermal conductivity of acoustic contribution, M is average mass, v_s is average speed of sound, T is temperature, V_a is the volume per atom, γ is Grüneisen parameter, and N is atom per primitive cell. For (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉, five rareearth atoms with different atomic mass and bonding strengths share RE-site in the crystal structure, resulting in increased structural complexity. Correspondingly, the number of N of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ increases and its thermal conductivity decreases. Point defect scattering is also a dominant process that giving rise to the low thermal conductivity of HE materials. Based on the point defect scattering mechanism ^[49,50]:

where κ_L is lattice thermal conductivity, C_s(ω) is spectral heat capacity, τ is phonon relaxation time, ω is phonon frequency, v_p is phonon phase velocity, v_g is phonon group velocity, f_i is the fraction of atoms with mass m_i and radius r_i that reside on a site with average mass and radius ( m▔ and r▔ ), respectively. It can be found from Eqs. (5) and (6) that scattering by point defect arises from the fluctuations of mass and strain within the lattice. For (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉, the severe lattice distortion caused by the HE effect will result in the increase of the fluctuations of mass and strain within the lattice ^[51]. This can lead to the intensification of phonon scattering and decrease of the thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉. 

For a desirable EBC material, possessing good phase stability from room temperature to the service temperature is essential. Meanwhile, thermal expansion matches those of the substrate and the interlayer is also required to minimize the thermal stress and ensure that the coating does not crack in thermal cycling. The investigation on the thermal properties of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ in this study ascertains that (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ exhibits good phase stability at high temperatures, close thermal expansion coefficient to that of the interlayer mullite, and extremely low thermal conductivity. These results indicate that (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is a promising candidate EBC material of silicon-based structural ceramics.

4 Conclusions

In this study, a novel HE cuspidine-structured rare-earth aluminate ceramic (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ was designed and successfully synthesized. The investigation of the phase composition and the micro structure proves that the synthesized (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is a phase-pure solid solution with uniform component distribution. (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ exhibits good high-temperature phase stability and no phase transition is detected from 300 to 1473 K. The linear thermal expansion coefficient of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at 300–1473 K is 6.96×10^–6 K^-1, which is close to that of the interlayer mullite of EBC system. The anisotropy of thermal expansion coefficient of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ is stronger than that of Y₄Al₂O₉ due to the anisotropy of bonding strength of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉. The volumetric thermal expansion coefficient and the anisotropic thermal expansion coefficients of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ are: α_v = 24.40×10^–6 K^-1, α_a = 10.59×10^–6 K^-1, α_b = 8.93×10^–6 K^-1, and α_c = 5.66×10^–6 K^-1. (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ exhibits low thermal conductivity owing to the intensification of phonon scattering caused by HE effect. The thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ at room temperature is 1.50 W·m^-1·K^-1, which is 55% lower than that of Y₄Al₂O₉. Good high-temperature phase stability, close thermal expansion coefficient to that of the interlayer mullite, and extremely low thermal conductivity of (Nd_0.2Sm_0.2Eu_0.2Y_0.2Yb_0.2)₄Al₂O₉ make this material promising as a candidate EBC material of silicon-based structural ceramics. 

Reference: Omitted