**Abstract: **A series of Sm_{2}Zr_{2}O_{7}–SiC composites doped with different volume fraction and particle size of SiC were prepared by hot pressing at 1300 ℃. The phase of the composites prepared is P-Sm_{2}Zr_{2}O_{7 }and C-SiC, and no other diffraction peaks exist, which indicates that Sm_{2}Zr_{2}O_{7} has great chemical compatibility with SiC. The thermal conductivity and phonon thermal conductivity of the Sm_{2}Zr_{2}O_{7}–SiC composites are measured by the laser pulse method. The photon thermal conductivity of the composites is obtained by subtracting the phonon thermal conductivity from the total thermal conductivity. The results show that the photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites is lower than that of pure Sm_{2}Zr_{2}O_{7}. The photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites decreases first and then increases with the increase of SiC particle size. Sm_{2}Zr_{2}O_{7}–(5 vol%, 10 μm)SiC composite has the lowest photon thermal conductivity.

**Keywords:** rare-earth zirconates; thermal conductivity; photon thermal transport

1 Introduction

Thermal barrier coatings (TBCs) are widely used to protect the hot-section components of gas turbines from hot gases ^{[1]}. With the development of aeroengine to high thrust weight ratio and high inlet temperature, the requirements for thermal insulation performance of TBCs will also be improved. In TBCs, heat is conducted by lattice vibration (phonons) or radiation (photons). TBCs with low phonon thermal conductivity are widely studied. The thermal conductivity of the high-entropy ceramics thermal barrier coatings can be 1.0 W/(m·K) due to strong phonon scattering ^{[2]}. The photon thermal conductivity component can become a significant portion of the overall thermal conductivity at elevated temperatures. However, there are relatively few reports on the photon thermal conductivity ^{[3]}. As a result, with the gas temperature increasing, it is very important for ensuring the heat insulation capacity of TBCs under high temperatures. However, most ceramic materials are semi-transparent to infrared radiation under high temperature, and thus thermal conductivity will recover rapidly. Rare-earth zirconates, such as Sm_{2}Zr_{2}O_{7}, whose thermal conductivity is lower than that of traditional yttria partially stabilized zirconia (YSZ), have the potential to be a novel candidate material for TBCs ^{[4,5]}. It was reported that the thermal conductivity of rare-earth zirconates recovered above 800 ℃ because of infrared radiation, and their thermal insulation performance decreased by about 10% than that at low temperatures ^{[6]}.

To improve the heat insulation of rare-earth zirconates, an effort must be undertaken to increase the photon scattering occurred in the materials, which results in the photon thermal conductivity reducing. However, the method for phonon scattering (such as increasing crystal defects) is useless to reduce the photon thermal conductivity. The difference of refractive index between different materials is the main factor to increase the photon scattering and reduce the photon thermal conductivity. Besides, according to the research by Klemens and Gell ^{[7]}, when the size of the defect (or the second phase) is greater than or equal to the photon wavelength, a substantial transition of the photon thermal conduction in the thermal conductivity can be made. However, no related experimental literature were reported. We have found that SiC material has good high-temperature chemical stability, and its refractive index (about 2.67) is different from the refractive index of Sm_{2}Zr_{2}O_{7} ceramics (about 2.1), so a series of composites with different volume fraction and different particle size of SiC were prepared. In this study, the thermal conductivity of the Sm_{2}Zr_{2}O_{7}–SiC composites was investigated and compared with that of pure Sm_{2}Zr_{2}O_{7} ceramic.

2 Experimental

2. 1 Preparation of Sm_{2}Zr_{2}O_{7}–SiC composites

The main raw materials were SiC (≥ 99.9%, Beijing Zhongjin Research New Material Technology Co., Ltd., China), Sm_{2}O_{3} (≥ 99.9%, Huizhou Ruier Chemicals Technology Limited Company of Guangdong, China) and ZrOCl_{2}·8H_{2}O (≥ 99.5%, Fanmeiya Materials Limited Company of Jiangxi, China). Sm_{2}Zr_{2}O_{7} powders were synthesized by a chemical co-precipitation method as shown in Ref. ^{[8]}. The appropriate amount of Sm_{2}Zr_{2}O_{7 }and SiC was prepared by mechanical ball milling for 6 h. Sm_{2}Zr_{2}O_{7}–SiC composites were prepared by hot pressing at 1300 ℃ for 1 h at a heating rate of 10 ℃/min and a pressure of 200 MPa. In order to prevent the oxidation of SiC powders, the sintering process was carried out in an argon atmosphere.

2. 2 Analysis and characterization

The phase compositions of Sm_{2}Zr_{2}O_{7}–SiC composites were determined by X-ray diffraction (XRD, RIGAKU D/Max-rB, Rigaku International Corp., Japan) with the scan rate of 4 (°)/min. The microstructure of the sintered composites was examined using scanning electron microscope (SEM, Philips S-4800, Hitachi Ltd., Yoshida-Cho, Totsuka-Ku, Yokohama, Japan). The compositions of the bulks were analyzed by an energy spectrum analyzer (EDS, X-Max, Oxford Instruments plc, UK).

Since the photon thermal conductivity of ceramics cannot be measured directly, according to the heat transfer theory of ceramic material, the photon thermal conductivity of crystalline materials ( k_{r} ) can be expressed by Eq. (1):

k_{r} = k - k_{p} (1)

where k and k_{p} represent the total thermal conductivity and phonon thermal conductivity of the material, respectively. The total thermal conductivity of the ceramics can be acquired by Eq. (2).

k = C_{p}λρ (2)

where the thermal diffusivity (λ) is measured by the laser pulse method (model: FLASHLINE 5000) from 25 to 1400 ℃. The specific heat (C_{p}) is calculated using Eq. (3) ^{[9–11]}, and the parameters are obtained from Ref. ^{[11]} and shown in Table 1, where A, B, C, D, and E are empirical constants. The density ( ρ ) is measured according to the Archimedes principle. T is the temperature.

Table 1 Parameters for the specific heat calculation

The phonon thermal conductivity is the same as the total thermal conductivity test. It is necessary to add a thin platinum absorbing layer between the sample surface and the graphite layer to prevent laser beam penetration into the interior of the sample and to ensure an effective and uniform absorption of the laser pulse as shown in Ref. ^{[12]}. Moreover, a platinum layer has a relatively low emissivity which reduces the amount of heat radiation emitted into the sample. The Pt layer was prepared according to the method described in Ref. ^{[13]}. Thus, most photons are blocked by the platinum absorbing layer. The phonon thermal conductivity of composites is acquired. The test schematic is shown in Fig. 1 Finally, the photon thermal conductivity of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites can be acquired by Eq. (2).

Fig. 1 Illustration of laser pulse sample test (a) without Pt-coating layer and (b) with Pt-coating layer.

3 Results and discussion

Figure 2 shows the XRD patterns of Sm_{2}Zr_{2}O_{7}–SiC composites with different volume and different particle size of SiC. It can be seen that the diffraction peaks of the pyrochlore structure are in good agreement with the standard peaks. Meanwhile, obvious SiC phase is observed in the spectrum, and no other phase exists. It is shown that the second phase SiC does not react with the Sm_{2}Zr_{2}O_{7} matrix, which indicates that Sm_{2}Zr_{2}O_{7} and SiC show good phase stability under the sintering process.

Fig. 2 XRD patterns of Sm_{2}Zr_{2}O_{7}–SiC composites: (a) SiC particle size is 10 μm with different volume and (b) SiC content is 10 vol% with different particle size.

Figure 3 shows the microstructure of Sm_{2}Zr_{2}O_{7}–(10 vol%)SiC composites with SiC particle sizes of 2, 10, and 15 μm, respectively. It can be seen that SiC particles show uniform distribution in the matrix and no other grain appears. The relative densities of a series of Sm_{2}Zr_{2}O_{7}–SiC composites measured by the Archimedes principle are all above 97%. The results of element distribution in Fig. 4 show that there is no element diffusion phenomenon, and thus there is no reaction between SiC and Sm_{2}Zr_{2}O_{7} matrix, which is

consistent with the results of the XRD phase analysis.

Fig. 3 Microstructures of Sm_{2}Zr_{2}O_{7}–SiC composites doping with different particle size of SiC: (a) 2 μm, (b) 10 μm, and (c) 15 μm.

Fig. 4 Line scanning EDS analysis at the interface between SiC and Sm_{2}Zr_{2}O_{7}: (a) SEM image, (b) Sm, (c) Zr, (d) Si, (e) C, and (f) O.

Tables 2 and 3 show the total thermal diffusivity and phonon thermal diffusivity of Sm_{2}Zr_{2}O_{7 }and Sm_{2}Zr_{2}O_{7}–SiC composites. All data were averaged over three measurements. Table 4 shows the densities of the samples. The specific heat calculated by Eq. (3) is shown in Fig. 5. The total thermal conductivity and photon thermal conductivity were calculated according to Eqs. (1) and (2), which are shown in Tables 5 and 6. It can be seen that Sm_{2}Zr_{2}O_{7}–(5 vol%, 10 μm)SiC composite has the lowest photon thermal conductivity, compared with the single-phase Sm_{2}Zr_{2}O_{7} at each temperature. Figure 6 shows the photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites with SiC particle size at 2 vol%, 5 vol%, and 10 vol% SiC, respectively. As can be seen from Fig. 6, the photon thermal conductivities of composites decrease first and then increase with the increase of SiC particle size at different temperatures. The composite with SiC particle size of 2 μm has the highest photon thermal conductivity while the composite with SiC particle size of 10 μm has the lowest photon thermal conductivity at different temperatures.

Table 2 Total thermal diffusivity of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites

Table 3 Phonon thermal diffusivity of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites

Table 4 Density of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites

Table 5 Total thermal conductivity of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites (W/(m·K))

Table 6 Photon thermal conductivity of Sm_{2}Zr_{2}O_{7} and Sm_{2}Zr_{2}O_{7}–SiC composites (W/(m·K))

Fig. 5 Specific heat of Sm_{2}Zr_{2}O_{7}–SiC composites varying with temperature.

Fig. 6 Photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites varying with temperature with (a) 2 vol%, (b) 5 vol%, and (c) 10 vol% SiC content.

Scattering theory shows that when the particle size is equal to the radiation wavelength, the maximum scattering effect occurs in the ceramic material. The photon wavelengths of gas at high temperatures are mainly concentrated at 1–7 μm. When the particle size of SiC is 2 μm, the influence of SiC on photon scattering is limited, and it has little effect on the photon thermal conductivity of the composites. With the increase of SiC particle size, the photon scattering effect is enhanced. SiC particles with a particle size of 10 μm are closest to the photon wavelength, which causes the most obvious photon scattering, and the phenomenon of reducing the photon thermal conductivity of the composites is most effective. However, when the size of SiC particles increases to 15 μm, the phenomenon of photon scattering is weakened, which results in that the photon thermal conductivity of the composite material is larger than the photon thermal conductivity of the composites with SiC particle size of 10 μm. Therefore, with the increase of SiC particle size, the photon thermal conductivity of the composite first decreases and then increases, and the composites with the SiC particle size of 10 μm have the lowest

photon thermal conductivity.

Figure 7 shows the photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites with the SiC content with the SiC particle size 2, 10, and 15 μm, respectively. The photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites increases with the increase of SiC content when the SiC particle size is 2 μm at different temperatures. When SiC particle size is 10 and 15 μm, respectively, the photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites decreases first and then increases with the increase of SiC content at different temperatures. The composite of 5 vol% SiC content has the lowest photon thermal conductivity.

Fig. 7 Photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites varying with temperature and SiC particle size of (a) 2 μm, (b) 10 μm, and (c) 15 μm.

The thermal conductivity of the composites with the second phase introduced can be approximated as Eq. (4):

k = k_{1}v_{1 }+ k_{2}v_{2} (4)

where k_{1} and k_{2} denote the intrinsic thermal conductivities of the matrix and the second phase material, respectively, and v1 and v_{2} denote the volume fraction of the matrix and the second phase material in the composites, respectively. The intrinsic thermal conductivity of SiC is 225 W/(m·K) ^{[14]}, which is much higher than that of the Sm_{2}Zr_{2}O_{7} matrix. The added SiC will result in higher photon thermal conductivity of the composites than that of Sm_{2}Zr_{2}O_{7}. Figure 8 shows the radiation transfer process in different samples. When the size of SiC particle is 2 μm, the effect of SiC on photon scattering is limited. Due to the higher thermal conductivity of SiC, the photon thermal conductivity of the composites increases significantly. The photon thermal conductivity of the composites increases with the increase of SiC content. When the SiC particle size is 10 and 15 μm, the particle size is larger than the photon wavelength of gas at high temperatures, which can cause the photon scattering. The photon scattering caused by SiC increases when the SiC content increases from 2 vol% to 5 vol%, and the photon thermal conductivity of the composites decreases. When SiC content is 10 vol%, the photon thermal conductivity of composites increases significantly due to the higher photon thermal conductivity of SiC. Therefore, the composite with SiC content of 5 vol% has the lowest photon thermal conductivity.

Fig. 8 Schematic diagram of radiation transfer with (a) different SiC content and (b) different SiC size.

The photon thermal conductivity of the composite resulted from the combined effect of the scattering of photons caused by the second phase and the intrinsic photon thermal conductivity of the second phase. When the SiC content is lower, the thermal conductivity of the composites gradually decreases with the increase of the heterogeneous interface. Due to the higher thermal conductivity of SiC, the photon thermal conductivity of the composites increases significantly with the SiC content increases to a certain value. The number of heterogeneous interfaces per unit volume decreases with the SiC particle size in the composite increasing when the SiC content is the same, and thus the carrier scattering ability caused by the second phase decreases. The thermal conductivity of the composite material increases. When the second phase of the proper content

and particle size exists in the matrix, the heterogeneous interface introduced by the second phase will enhance the scattering of carriers and effectively block the heat transfer in the material. The Sm_{2}Zr_{2}O_{7}–(5 vol%, 10 μm)SiC composite has the lowest photon thermal conductivity. Therefore it is feasible to reduce the photon thermal conductivity by using the heterogeneous interface.

**4 Conclusions **

In this study, a series of Sm_{2}Zr_{2}O_{7} matrix composites with different volume fraction and particle size of SiC were prepared by hot pressing at 1300 ℃. No other phase exists except for Sm_{2}Zr_{2}O_{7} and SiC in the composites. The photon thermal conductivity of Sm_{2}Zr_{2}O_{7}–SiC composites decreases first and then increases with the increase of SiC particle size. For the composites with larger SiC particle size, the photon thermal conductivity decreases first and then increases with the increase of SiC content. Sm_{2}Zr_{2}O_{7}–(5 vol%, 10 μm)SiC composite has the lowest photon thermal conductivity comparing with the single-phase Sm_{2}Zr_{2}O_{7}, resulting the combined photon scattering caused by

SiC and the higher photon thermal conductivity of SiC. The experimental results prove that when the second phase of the proper content and particle size exists in

the matrix, it is feasible to reduce the thermal conductivity by using the heterogeneous interface.

**References **

[1] Vaßen R, Jarligo MO, Steinke T, et al. Overview on advanced thermal barrier coatings. Surf Coat Technol 2010, 205: 938–942.

[2] Li F, Zhou L, Liu JX, et al. High-entropy pyrochlores with low thermal conductivity for thermal barrier coating materials. J Adv Ceram 2019, 8: 576–582.

[3] Yang G, Zhao CY. Infrared radiative properties of EB-PVD thermal barrier coatings. Int J Heat Mass Tran 2016,94:199–210.

[4] Wang L, Eldridge JI, Guo SM. Thermal radiation properties of plasma-sprayed Gd_{2}Zr_{2}O_{7} thermal barrier coatings. Scr Mater 2013, 69: 674–677.

[5] Liu ZG, Ouyang JH, Zhou Y, et al. Influence of ytterbiumand samarium-oxides codoping on structure and thermal conductivity of zirconate ceramics. J Eur Ceram Soc 2009,

29: 647–652.

[6] Lim G, Kar A. Modeling of thermal barrier coating temperature due to transmissive radiative heating. J Mater Sci 2009, 44: 3589–3599.

[7] Klemens PG, Gell M. Thermal conductivity of thermal barrier coatings. Mater Sci Eng: A 1998, 245: 143–149.

[8] Liu L, Wang FC, Ma Z, et al. Thermophysical properties of (Mg_{x}La_{0.5}–xSm_{0.5})_{2}(Zr_{0.7}Ce_{0.3})_{2}O_{7–x }(x=0, 0.1, 0.2, 0.3) ceramic for thermal barrier coatings. J Am Ceram Soc 2011, 94: 675–678.

[9] Leitner J, Chuchvalec P, Sedmidubský D, et al. Estimation of heat capacities of solid mixed oxides. Thermochimica Acta 2002, 395: 27–46.

[10] Spencer PJ. Estimation of thermodynamic data for metallurgical applications. Thermochimica Acta 1998, 314: 1–21.

[11] Sato Y, Taira T. The studies of thermal conductivity in GdVO_{4}, YVO_{4}, and Y_{3}Al_{5}O_{12} measured by quasi-onedimensional flash method. Opt Express 2006, 14: 10528– 10536.

[12] Ye DL. Practical Data Manual on Thermodynamics of Inorganic Matter. Metallurgy Industry Press, 1981. (in Chinese)

[13] Mehling H, Hautzinger G, Nilsson O, et al. Thermal diffusivity of semitransparent materials determined by the laser-flash method applying a new analytical model. Int J Thermophys 1998, 19: 941–949.

[14] Cho TY, Kim YW. Effect of grain growth on the thermal conductivity of liquid-phase sintered silicon carbide ceramics. J Eur Ceram Soc 2017, 37: 3475–3481.