Improvement strategy on thermophysical properties of A₂B₂O₇-type rare earth zirconates for thermal barrier coatings applications: A review

1.   Introduction

The employment of gas turbine engines is prevalent in the fields of power generation, aviation, and astronautics [1–2]. With the growing demand for gas turbine efficiency, high-performance nickel-based superalloys have been developed rapidly by adding rare metallic elements and exploiting single-crystal manufacturing technology. Despite advancing to its fifth generation, the superalloy is still faced with inherent limitations such as reduced strength and inadequate corrosion resistance at elevated temperature, rendering it susceptible to failure when exposed to temperature exceeding 1473 K for extended periods. In the 1990s, researchers began to focus on developing and manufacturing ceramic thermal barrier coatings (TBCs) because traditional turbine materials had attained their maximum temperature capabilities. The deposition of TBCs is a common practice in high-temperature components of gas turbines and other propulsion systems, aimed at protecting the underlying superalloy substrates and enabling engines to achieve enhanced efficiency even in elevated temperature [1–5].

The use of advanced TBCs enhanced gas temperature and reduced substrate temperature through the heat transfer facilitated by the flow of cooling air, thereby optimizing engine efficiency. To achieve the above objective, TBC materials can be selected on the basis of the following criteria: (1) possessing a high melting point, (2) exhibiting low thermal conductivity, (3) exhibiting chemical inertness, (4) displaying high thermal expansion to match the superalloy substrate, (5) maintaining high phase stability between room temperature and the operating temperature, and (6) providing good sintering resistance. The standard TBC system comprises four stages of coating such as ceramic topcoat (TC), thermally grown oxide layer (TGO), bond coat (BC), superalloy base material (BM), and substrate (SUB) [6–7]. The topcoat TBC materials with 250 μm in thickness can reduce surface temperature by ~150°C and are generally deposited through various techniques, such as atmospheric plasma spraying (APS) and electron beam–physical vapor deposition (EB-PVD) [2,8].

The commonly used ceramic material for TBCs is typically composed of 7wt%–8wt% yttria-stabilized zirconia (YSZ), which exhibits relatively low thermal conductivity and unique comprehensive mechanical properties [1,5–7]. However, a higher gas temperature in advanced engines has recently been in demand. The combustion chamber temperature of a gas engine must be elevated to 1300–1700°C to achieve an enhanced thrust–weight ratio. Under these conditions of service, YSZ is restricted to future applications above 1200°C because of a series of problems, such as TGO thickening, nonequilibrium phase transformation, and hot corrosion from silicate melts generally known as CMAS [4,9]. The A₂B₂O₇-type compounds of pyrochlore-type and fluorite-type rare earth zirconates have been considered as promising candidates for next-generation gas turbine TBCs due to their lower sintering rate, better phase stability within the temperature range from room temperature to the melting point, and lower thermal conductivity than YSZ. These characteristics are crucial for ensuring the optimal performance of gas turbine components under high-temperature operating conditions. However, the limitations on the thermal expansion coefficient (TEC) and inadequate damage tolerance remain the primary obstacles to further application of rare earth zirconates [9–12]. The mechanical and thermophysical properties of typical ceramics suitable for use in TBC systems are summarized in Table 1.

Table  1.  Mechanical and thermophysical properties of typical TBC materials

Materials	Young’s modulus, E / GPa	Poisson’s number, ν	Thermal conductivity, λ / (W·m−1·K−1)	Thermal expansion coefficient, α / (10−6 K−1)	Heat capacity, Cp / (J·g−1·K−1)	Refs.
La2Zr2O7	175 (293 K)	—	1.15 (1723 K)	9.1 (1273 K)	0.49 (1273 K)	[10,13–14]
Sm2Zr2O7	—	—	1.21 (1473 K)	11.3 (1473 K)	—	[15]
BaZrO3	181 (293 K)	—	3.42 (1273 K)	8.1 (1273 K)	0.45 (1273 K)	[10]
Al2O3	30 (293 K)	0.26 (293 K)	5.8 (1400 K)	9.6 (1273 K)	—	[9,13]
Garnet (Y3Al5O12)	—	—	3.0 (1273 K)	9.1 (1273 K)	—	[16]
Lanthanum aluminate (LaMgAl11O19)	—	—	1.7 (1273 K)	10.1 (1473 K)	0.86 (1273 K)	[17–18]
ErTaO4	128 (293 K)	0.33 (293 K)	1.6 (1173 K)	10.7 (1473 K)	—	[19]
Eu3TaO7	245 (293 K)	0.27 (293 K)	1.54 (1173 K)	9.8 (1473 K)	0.42 (1173 K)	[20]
Dy3NbO7	235 (293K)	—	—	10.6 (1273K)	—	[21]
Gd3NbO7	211 (293K)	—	1.4 (1273 K)	10.4 (1673K)	—	[22]
LaPO4	133 (293 K)	0.28 (293 K)	1.8 (973 K)	10.5 (1273 K)	—	[23]
8YSZ coating	40 (293 K)	0.22 (293 K)	—	10.7 (1273 K)	—	[24]
NiCoCrAlY (bond coat of TBC)	86 (293 K)	0.3 (293 K)	—	17.5 (1273 K)	—	[24]
IN738 superalloy	197 (293 K)	0.3 (293 K)	—	16 (1273 K)	—	[24]

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The application of density functional theory (DFT) based on the first principles calculation method has gained considerable attention in the field of materials science. DFT relies on solving the Kohn–Sham equation to accurately determine the structural properties of materials and, subsequently, the thermophysical properties. Much effort has been directed at rare earth zirconates for nearly 20 years, focusing on thermal conductivity and TEC from the theoretical foundation to high-entropy design [12,25–30]. This paper presents solid-state heat transfer mechanisms and thermophysical performance enhancement strategies based on defect engineering and the material compositing approach. In addition, recent progress on the intrinsic thermophysical properties of rare earth zirconate TBC materials has been reviewed, and future considerations on the materials design of rare earth zirconates are highlighted.

2.   Heat transfer mechanism in rare earth zirconates

The dominant mechanism of heat conduction in rare earth zirconates is generally considered the propagation of phonons [31]. According to the Debye model, the thermal conductivity ($\kappa$) of ceramic materials can be depicted as follows [32]:

where C_V represents the specific heat, v_s denotes the average sound velocity, ω signifies the phonon frequency, and l corresponds to the phonon mean free path. Notably, regulating the phonon mean free path emerges as a feasible approach.

In solid materials, the presence of defects, boundaries, and other phonon scattering effects in a lattice structure restricts the mean free path of phonons and the overall thermal conductivity [33]. On the basis of the assumption that all phonon scattering processes can be effectively represented by relaxation times (τ_C), Callaway formulated an expression for thermal conductivity as [24]

where x = ћω/(k_BT), k_B denotes the Boltzmann constant, ћ represents the reduced Planck constant, T is the temperature, and θ_D signifies the Debye temperature. Then, the combined relaxation time τ_C is defined as [34]

where τ_P, τ_D, and τ_B are denoted as the relaxation time of phonon–phonon scattering, phonon–defect scattering, and phonon–boundary scattering, respectively.

Ιn practical materials, phonon–boundary scattering can be neglected throughout the temperature range. For phonon–point defect scattering, point defects contribute to the inverse relaxation time, Klemens [35] proposed the following expressions:

If point defects scatter mainly in virtue of their mass difference, the coefficient A of the above formula (4) can be expressed as

where ω corresponds to the phonon frequency, Ω is the average volume per atom, and Γ represents the phonon scattering coefficient.

Furthermore, phonon–phonon scattering (Umklapp scattering) can be presented in terms of its relaxation time, illustrated as

When T > θ_D, B ∝ T, and C represents the proportionality constant:

Therefore, the thermal conductivity of materials can be transformed from Eq. (1) as [36]

The thermal conductivity can be deduced from Eq. (8), indicating that phonon–phonon scattering results in a temperature-dependent inverse relationship with thermal conductivity. In addition, the thermal conductivity of materials with defects is inversely proportional to the square root of the coefficient for phonon scattering.

Above 600°C, rare earth zirconates exhibit infrared transparency. High-temperature gas produces intense infrared radiation, which can penetrate the material and transfer heat directly to the substrate, finally leading to a reduction in the thermal barrier effect of rare earth zirconates at gas turbine operation temperature. Consequently, the high-emissivity design of rare earth zirconates appears particularly important. According to Kirchhoff’s law, the emissivity of a body at equilibrium at a given wavelength λ and temperature T is equal to its absorption coefficient. The emissivity, denoted as ε, is defined as the ratio of energy radiated by a material to that radiated by a black body (a body that absorbs all incident radiation and emits all absorbed energy with the same spectrum ε = 1), which is described by Eq. (9) [37]:

where E(T) represents the radiant heat of gray body to its surroundings at temperature T, and E_b(T) corresponds to the radiant heat of a black body to its surroundings at temperature T. The closer the emissivity value is to 1, the stronger the ability of an object to radiate electromagnetic waves [38]. Therefore, the higher the emissivity of an object in the infrared band, the more heat it radiates to outer space, the higher the heat dissipation power, and the faster the cooling [39].

The infrared radiation of a material is mainly affected by its internal structure, which mainly includes two mechanisms: electronic transitions and lattice vibrations [40–41]. Depending on the activation energy required, an electron transition corresponds to infrared absorption in the short band of 0.76–8 μm, while a lattice vibration corresponds to infrared absorption in the long band of 8–25 μm [42]. The material radiates infrared electromagnetic waves because the electrons of internal atomic, molecular, and ionic systems transition between energy levels and the dipole moment change induced by molecular bond vibrations [43].

3.   Strategy for improving thermophysical performance

3.1   Defect engineering

3.1.1   Pure phase single rare earth zirconates

Ln₂Zr₂O₇ (Ln = lanthanide series rare-earth elements) with a pyrochlore or fluorite structure contains approximately 12.5% (1/8) intrinsic oxygen vacancies, which generates a low thermal conductivity. Pyrochlore-type Ln₂Zr₂O₇ with an ordered structure can be regarded as A₂B₂O₆O', whose crystalline sites 16c, 16d, 48f, 8a, and 8b are occupied by the A, B, O, O' ions and oxygen vacancies, respectively. In contrast, fluorite-type Ln₂Zr₂O₇ has totally disordered cations, for which it can be regarded as AO₂ with one-eighth intrinsic oxygen vacancies [44]. Fig. 1 shows the simulated models of the pyrochlore and defective fluorite structures of rare earth zirconates.

Fig. 1.  Simulated models of crystal structures of rare earth zirconates: (a) pyrochlore; (b) defective fluorite.

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The thermophysical properties of Ln₂Zr₂O₇ rare earth zirconates synthesized by various methods have been extensively investigated by numerous scholars. The current consensus is that an emphasis should be placed on investigating the thermal conductivity (Fig. 2) and TEC (Fig. 3) of Ln₂Zr₂O₇ at high temperature (the maximum test temperature varies across different sources of references) as the service temperature increases. The thermophysical characteristics of identical ceramics can vary substantially, which can be attributed to the differences in the experimental design and particle size of raw materials. Nonetheless, the thermal conductivity of Ln₂Zr₂O₇ is considerably lower than that of YSZ; however, more efforts are needed to enhance the TEC to improve the thermal cycling life.

Fig. 2.  Thermal conductivity of Ln₂Zr₂O₇ at the maximum test temperature varies across different sources of references.

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Fig. 3.  Thermal expansion coefficient of Ln₂Zr₂O₇ at the maximum test temperature varies across different sources of references.

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(1) Ln₂Zr₂O₇ bulk materials.

Wu et al. [57] measured the thermal conductivities of hot-pressed Ln₂Zr₂O₇ (Ln = Gd, Sm, and Nd) ceramics compared with pressureless-sintered 7wt% yttria-stabilized zirconia (7YSZ). The measured thermal conductivities of all rare earth zirconates were nearly identical, exhibiting a 30% decrease compared to that of 7YSZ at 25–700°C. Dy₂Zr₂O₇ with a defective fluorite structure was prepared by Xu et al. [58] through a solid-state reaction at 1600°C for 10 h. The TEC of the Dy₂Zr₂O₇ ceramic (11.3 × 10⁻⁶ °C⁻¹, at 1300°C) was slightly higher than that of conventional 8wt% Y₂O₃−ZrO₂ (8YSZ), while its thermal conductivity (1.32 W/(m·K), at 800°C) was distinctly lower than that of 8YSZ. Defective fluorite-type Ln₂Zr₂O₇ (Ln = Dy, Er, and Yb) with similar oxygen vacancy concentrations, approximately 12.5% (1/8), have considerably lower thermal conductivities of approximately 1.3–1.9 W/(m∙K) than the referenced pyrochlore-type Ln₂Zr₂O₇ ceramics at 20–800°C [59].

Furthermore, a combination of first-principles calculations and the quasi-harmonic (QH) approximation is adopted by Feng et al. [60] to predict the thermal conductivities of rare earth zirconates with a pyrochlore structure. The thermal conductivities are estimated under Slack’s model, which agrees with experimental results. Another consideration for the first-principles calculations is DFT with a plane-wave pseudopotential total energy scheme method by Yang et al. [61], a new approach to studying the electronic structure and mechanical and thermal properties of La₂B₂O₇ (B = Zr, Sn, Hf, and Ge) pyrochlore (Fig. 4). In addition, the first-principles with QH phonon calculations can also be applied to predict the coefficient of thermal expansion. Lan et al. [62] proposed a QH approximation approach based on stable phonon modes and further clarified that the QH Debye model overestimated the observed TECs of RE₂Zr₂O₇ pyrochlores. However, a more reliable method is still urgently needed to characterize the thermal expansion property. A model proposed by Wang et al. [63] integrated Grüneisen’s equation and the Debye heat capacity model to establish an efficient coupled model of α_∞, which characterizes the coefficient of thermal expansion at extremely high temperatures. The α_∞ values of cubic ZrO₂, cubic HfO₂, La₂Zr₂O₇, Pr₂Zr₂O₇, Gd₂Zr₂O₇, and Dy₂Zr₂O₇ were calculated, which exhibited a similar trend to the measured experimental results. Chen et al. [64] studied the influence of the concentration of cation vacancies on TEC by constructing nonstoichiometric gadolinium zirconate using first-principles calculations. Excessive Gd³⁺ increases the TEC of ceramics from 11.108 × 10⁻⁶ to 11.593 × 10⁻⁶ K⁻¹. Therefore, a high TEC of Gd₂Zr₂O₇ ceramics can be achieved by introducing excessive Gd³⁺ because of the increased disorder in Gd–O bonds, enhanced thermal diffusivity, and reduced solid solubility.

Fig. 4.  Thermal conductivity of La₂B₂O₇ (B = Zr, Sn, Hf, and Ge) pyrochlore vs. temperature according to Cahill’s model. Reprinted from J. Alloys Compd., 663, J. Yang, M. Shahid, M. Zhao, J. Feng, C. Wan, and W. Pan, Physical properties of La₂B₂O₇ (B = Zr, Sn, Hf, and Ge) pyrochlore: First-principles calculations, 834, Copyright 2016, with permission from Elsevier.

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In addition to the solid-state reaction and chemical coprecipitation methods, soft chemical processes using alkoxide and citrate synthesis can be performed at a relatively low temperature to synthesize rare earth zirconates (RE₂Zr₂O₇, RE = La and Gd) [65]. Xu et al. [14] proposed a co-ions complexation method (CCM) to synthesize pyrochlore lanthanum zirconate at 1300°C. The grain size of La₂Zr₂O₇ is approximately 300 nm, which may lead to a lower thermal conductivity of 1.15 W/(m·K) (at 1450°C) compared to 1.99 W/(m·K) by the solid-state method. A schematic of the complexation and crystallization in CCM is shown in Fig. 5.

Fig. 5.  Schematic of the complexation and crystallization in CCM. Reprinted from J. Eur. Ceram. Soc., 37, C. Xu, H. Jin, Q. Zhang, et al., A novel Co-ions complexation method to synthesize pyrochlore La₂Zr₂O₇, 2871, Copyright 2017, with permission from Elsevier (LZ represents La₂Zr₂O₇).

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Kaliyaperumal et al. [66] studied phase transformation from pyrochlore to fluorite in nanocrystalline Nd₂Zr₂O₇, which is accomplished at 1300°C (Fig. 6). Despite the same concentration of oxygen vacancies, the structural transition from pyrochlore to fluorite occurring in rare earth zirconate remains an important factor affecting TBC applications.

Fig. 6.  TEM images and SAED patterns of Nd₂Zr₂O₇ heat treated at (a, b) 800°C, (c, d), 1000°C, and (e, f) 1300°C. Reprinted from Mater. Lett., 228, C. Kaliyaperumal, A. Sankarakumar, J. Palanisamy, and T. Paramasivam, Fluorite to pyrochlore phase transformation in nanocrystalline Nd₂Zr₂O₇, 493, Copyright 2018, with permission from Elsevier.

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(2) Ln₂Zr₂O₇ coating materials.

In addition to bulk materials, rare earth zirconates with intrinsic oxygen vacancies as the ceramic topcoat have attracted considerable attention. Zhao et al. [67] investigated Sm₂Zr₂O₇ coatings using electron beam evaporation and directed vapor deposition (EB-DVD, Fig. 7). Because of the vapor-phase disparities of the constituent oxides, the cation ordering necessary for pyrochlore structure formation is impeded by kinetic constraints, ultimately resulting in an equilibrium pyrochlore structure in the as-deposited Sm₂Zr₂O₇ with thermal conductivity of (0.5 ± 0.1) W/(m·K) at 1100°C. Yu et al. [68] compared the plasma-sprayed Sm₂Zr₂O₇ coatings with plasma-sprayed 8YSZ, as shown in Fig. 8. Sm₂Zr₂O₇ coatings exhibited a lower thermal conductivity than 8YSZ because of thin individual splats. Because of rapid cooling, the defective fluorite phase in the as-sprayed Sm₂Zr₂O₇ coating can transform into the pyrochlore structure during heat treatment above 1200°C. Zhao et al. [69] deposited Sm₂Zr₂O₇ and Sm₂Zr₂O₇/YSZ double-layer ceramic coatings on a polished NiCoCrAlY bond coat using the electron beam–physical vapor deposition method. The YSZ layer in the double-layer coatings serves as a diffusion barrier, resulting in a reduced TGO growth rate and extended lifespan. In addition, a new solution combustion process for synthesizing plasma sprayable La₂Zr₂O₇ powders after granulation was reported by Aruna et al. [70]. Plasma-sprayed La₂Zr₂O₇ coatings exhibited a thermal conductivity of 1.08 W/(m·K) at 900°C. Furthermore, a double-layer Gd₂Zr₂O₇/YSZ TBC topcoat was deposited via a solution precursor plasma spray process (SPPS) by Jiang et al. [71]. The double-layer Gd₂Zr₂O₇/YSZ coatings had thermal cyclic durability comparable to single-layer SPPS YSZ coating, which stabilized the phase/microstructure under the integrated gasification combined thermal cycling (IGCC) environment up to 300 h. Moreover, Mahade et al. [72] studied a multilayered Gd₂Zr₂O₇/YSZ TBC approach via suspension plasma spraying, which exhibited a low thermal conductivity and improved thermal cyclic lifespan; the SEM micrographs of multilayered Gd₂Zr₂O₇/YSZ TBCs are shown in Fig. 9.

Fig. 7.  Schematic of the directed vapor deposition (DVD) apparatus used to deposit Sm₂Zr₂O₇ coatings. Reprinted from Surf. Coat. Technol., 203, H. Zhao, C. G. Levi, and H.N.G. Wadley, Vapor deposited samarium zirconate thermal barrier coatings, 3157, Copyright 2009, with permission from Elsevier.

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Fig. 8.  SEM micrographs of the fracture surface of (a) Sm₂Zr₂O₇ and (b) 8YSZ coatings. Reprinted from J. Eur. Ceram. Soc., 30, J. Yu, H. Zhao, S. Tao, X. Zhou, and C. Ding, Thermal conductivity of plasma-sprayed Sm₂Zr₂O₇ coatings, 799, Copyright 2010, with permission from Elsevier.

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Fig. 9.  SEM micrographs of the as-sprayed double-layer Gd₂Zr₂O₇/YSZ TBC: (a) cross section and (b) top surface morphology. Reprinted from Surf. Coat. Technol., 283, S. Mahade, N. Curry, S. Björklund, N. Markocsan, and P. Nylén, Thermal conductivity and thermal cyclic fatigue of multilayered Gd₂Zr₂O₇/YSZ thermal barrier coatings processed by suspension plasma spray, 329, Copyright 2015, with permission from Elsevier.

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In summary, doping with rare earth oxides into zirconia or A₂B₂O₇-type zirconates is used to tailor the concentration of oxygen vacancies and the ordering degree of rare earth zirconates, which is directly correlated with thermal conductivity and thermal expansion property. Although the adjustment in the concentration of oxygen vacancies is specifically tough [11], the abovementioned literature laid the foundation of defect engineering for rare earth zirconates.

3.1.2   Substitutions

Rare earth zirconates are characterized by a high concentration of intrinsic oxygen vacancies, which are difficult to enhance and even facilitate the diffusion of oxygen, thereby promoting the growth of TGO [73]. The substitution method is an alternative approach to reducing the phonon mean free path while maintaining the intrinsic concentration of vacancies unchanged. Equivalent substitutions of trivalent rare-earth elements at the A site or tetravalent cations at the Zr site represent great chemical and structural compatibility and flexibility, with even infinite solution concentration compared to the fixed concentration of the intrinsic concentration of vacancies. In addition, substitutions of elements with different cationic radii can easily lead to lattice distortions in the pyrochlore or fluorite structure, which can be effectively used to reduce thermal conductivity. According to these characteristics, various doped rare earth zirconates have been developed over the decades.

(1) A-site doping.

A site doping is endowed with a wealth of options due to the diverse range of rare earth elements available. Since the onset of the 21st century, extensive research has been conducted on A site doping in rare earth zirconates. Lehmann et al. [74] investigated the thermal conductivities and TECs of lanthanum zirconates doped with and without partial or complete substitutions (Fig. 10). The thermal conductivities of the modified lanthanum zirconates are lower than that of pure lanthanum zirconate, and complete substitution of the lanthanum by neodymium, europium, and gadolinium causes an evident increase in TECs. Liu et al. [75] investigated the thermophysical properties of Nd_xZr_1−xO_2−x/2 (x = 0.1, 0.2, 0.3, 0.4, 0.5) ceramics synthesized using chemical coprecipitation and the calcination method. A low thermal conductivity of 1.50–2.01 W/(m·K) was obtained from room temperature to 1400°C. Furthermore, Liu et al. [45] prepared (Nd_xGd_1−x)₂Zr₂O₇ (x = 0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0) ceramics to investigate the thermal conductivity and thermal expansion property. The thermal conductivity decreases from room temperature to approximately 800°C and then increases because of the influence of high-temperature infrared radiation. The reduction of TEC is attributed to an increase in Nd content.

Fig. 10.  Thermal expansion coefficients versus the temperature of completely substituted and pure lanthanum zirconates. H. Lehmann, D. Pitzer, G. Pracht, R. Vassen, and D. Stöver, J. Am. Ceram. Soc., 86, 1338(2004) [74]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

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The structural evolution and thermophysical properties of (Sm_xGd_1−x)₂Zr₂O₇ (0 ≤ x ≤ 1.0) were reported by Liu et al. [46] via a chemical coprecipitation and calcination method. The measured thermal conductivities are 1.20–1.99 W/(m·K), with a slight increase above 800°C. A similar tendency was observed in (Yb_xSm_1−x)₂Zr₂O₇ (0 ≤ x ≤ 1.0) ceramics and (Yb_xGd_1−x)₂Zr₂O₇ (0 ≤ x ≤ 1.0) ceramics by Liu et al. [47–48]. Additionally, a glass-like thermal conductivity in (La_1−xYb_x)₂Zr₂O₇ (1/6 ≤ x ≤ 1/3), as shown in Fig. 11, and the large atomic displacement parameter of the Yb³⁺ impurity was observed by Wan et al. [49], which illustrates that resonant scattering by the rattling Yb³⁺ is mainly responsible for the glass-like thermal conductivity. Wan et al. [50] investigated the order–disorder transition in (Sm_1−xYb_x)₂Zr₂O₇ ceramics as a function of composition parameter x. A discontinuous phase transition from an ordered pyrochlore phase to a disordered defective fluorite phase is found within the compositional range of x = 1/6 to x = 1/3, in which a minimum thermal conductivity is located at a transition composition of (Sm_2/3Yb_1/3)₂Zr₂O₇.

Fig. 11.  Glass-like thermal conductivities of (La_1−xYb_x)₂Zr₂O₇ (x = 0, 1/6, 1/3, 1/2, 2/3, 5/6, 1). Reprinted from Acta Mater., 58, C. Wan, W. Zhang, Y. Wang, et al., Glass-like thermal conductivity in ytterbium-doped lanthanum zirconate pyrochlore, 6166, Copyright 2010, with permission from Elsevier.

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Furthermore, Ren et al. [51] achieved a quasi-eutectoid mixture comprising a La₂Zr₂O₇-rich pyrochlore phase and a Yb₂Zr₂O₇-rich fluorite phase by introducing La³⁺ and Yb³⁺ ions with considerably disparate atomic radii at the A site. The grain size decreases to 0.8–1 μm, and a considerably low thermal conductivity is attributed to the rattling effect and strong heat-carrying phonon scattering. With a similar phase transition, Wu et al. [52] used a solid-state reaction at 1600°C for 10 h to prepare a sequence of (Nd_1−xYb_x)₂Zr₂O₇ (x = 0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics. A pyrochlore–fluorite transformation of (Nd_1−xYb_x)₂Zr₂O₇ ceramics was observed when increasing the doping concentration of Yb. Additionally, Guo et al. [76] prepared Yb₂O₃ and Sc₂O₃ co-doped Gd₂Zr₂O₇ ceramics by chemical coprecipitation. The co-doping of Yb₂O₃ and Sc₂O₃ facilitates the order–disorder transition from the pyrochlore structure to the fluorite structure. Moreover, Sc₂O₃ doping helped enhance fracture toughness in comparison with undoped Gd₂Zr₂O₇.

The influence of the rattler effect on thermal conductivity was investigated by Yang et al. [77] by synthesizing a sequence of multicomponent ceramics, namely, (La_1/3Eu_1/3Gd_1/3)_2−2xYb_2xZr₂O₇ (x = 0, 0.25, 0.5, 0.75, and 1). A schematic representation of the rattler effect is shown in Fig. 12. The phase transition from the pyrochlore structure to the fluorite structure was observed with increasing Yb³⁺ content. Dual-phase (La_1/3Eu_1/3Gd_1/3)_1.5Yb_0.5Zr₂O₇ ceramics has a high coefficient of thermal expansion of 11.2 × 10⁻⁶ K⁻¹. Li et al. [78] prepared 6 types of (Nd_1/2Sm_1/2Eu_1/2Gd_1/2)_1−xDy_2xZr₂O₇ rare-earth zirconates using a solid-state reaction. The augmentation of Dy³⁺ incorporation leads to a phase transition from an ordered pyrochlore to a disordered fluorite occurring with increasing Dy³⁺, thereby providing a descriptor for predicting the formation of a single- or dual-phase system.

Fig. 12.  Schematic of the crystal structure of multicomponent RE₂Zr₂O₇ ceramics doped by the rattler effect. Reprinted from Ceram. Int., 48, R. Yang, J. Xu, M. Wei, et al., Rattler effect on the properties of multicomponent rare-earth zirconate ceramics, 28586, Copyright 2022, with permission from Elsevier.

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Fan et al. [55] used molecular dynamics to calculate the TECs of a sequence of rare earth zirconates. The Zr–O bond is considered the primary determinant of overall TECs, while the A–O bond plays a secondary role and O–O has minimal impact on TECs based on potential functions and equilibrium-location deviations between atoms. Using DFT, Zhao et al. [79] investigated the mechanical properties, Debye temperatures, thermal conductivities, and electronic structures of Gd_2−xTh_xZr₂O₇ and Gd₂Zr_2−xTh_xO₇ pyrochlores. The Young’s modulus, Debye temperature, and thermal conductivity of Gd₂Zr_2−xTh_xO₇ exhibit generally lower values compared to Gd_2−xTh_xZr₂O₇, as predicted by Clarke’s model. Furthermore, a reduction of thermal conductivity by doping was predicted through a comprehensive computational route proposed by Lan et al. [80], which is based on first-principles calculations. Thermodynamic modeling was combined with the first-principles calculations, with clarified defects from doping.

(2) B-site doping.

The introduction of B-site doping in rare earth zirconates, which exhibits excellent chemical and structural compatibility, can also effectively enhance lattice distortion and reduce the phonon mean free path. The selection of B-site elements is limited because of their high coordination and small ionic radius, in contrast to the wider range of choices available for A-site elements. However, the doping of B-site elements enhances the flexibility in tailoring the TEC. According to Liu et al. [81], the TEC decreases with increasing Ti content at a given temperature level, which may attributed to the pyrochlore phase of Ti doping ranging from 25mol% to 100mol%. However, the doping of Ti did not increase the TEC as expected. Zhang et al. [53] prepared the Sm₂(Zr_0.6Ce_0.4)₂O₇ ceramic with a fluorite structure using a solid-state reaction at 1600°C for 10 h. The thermal conductivity of Sm₂(Zr_0.6Ce_0.4)₂O₇ is lower than that of YSZ but higher than that of Sm₂Zr₂O₇, which can be attributed to the phase transition from pyrochlore to fluorite. The nano-sized La₂(Zr_0.7Ce_0.3)₂O₇ ceramic as a novel TBC material was synthesized by Wang et al. [82] using the sol–gel process. La₂(Zr_0.7Ce_0.3)₂O₇ maintains a pyrochlore-type structure at 1000–1500°C and exhibits exceptional thermal stability through prolonged annealing at 1400°C.

La₂(Zr_1−xCe_x)₂O_7−δ was synthesized by a soft chemistry method [53]. The fluorite-type structure is stable until 1400°C in air and then evolves into pyrochlore- and fluorite-type structures. Wang et al. [83] studied the determining factors of substitutional defects on thermal conductivity (k) by doping Hf⁴⁺ (which is 96% heavier than Zr⁴⁺ but has a similar ionic radius) and Ce⁴⁺ (50% heavier and 21% larger), as replacements for Zr⁴⁺ on the B site of La₂Zr₂O₇ pyrochlores (Fig. 13). They found that the size values of the dopants determine k_min, which may provide guidelines for low-k material design and selection. Ma et al. [84] synthesized the La₂(Zr_1−xCe_x)₂O₇ (x = 0, 0.3, 0.5, 1.0) ceramics by the coprecipitation–calcination method and then investigated the mechanical and thermophysical properties of La₂(Zr_1−xCe_x)₂O₇. La₂(Zr_0.7Ce_0.3)₂O₇ effectively mitigates the abrupt decrease in thermal expansion observed in La₂Ce₂O₇ and exhibits a low sintering rate of 1.13 × 10⁻⁷ s⁻¹ at 1400°C. Cerium was introduced as a substitution for zirconium by Yang et al. [54] to enhance the TEC of rare earth zirconates. A sequence of Yb₂(Zr_1−xCe_x)₂O₇ was prepared using a solid-state reaction. The increase in TEC with the volume fraction of Ce substitution is ascribed to the lattice relaxation and the conversion of Ce⁴⁺ to Ce³⁺ at elevated temperature. The thermal conductivity of doped Yb₂(Zr_1−xCe_x)₂O₇ is lower than that of pure Yb₂Zr₂O₇.

Fig. 13.  Plots of (a) thermal diffusivity and (b) thermal conductivity of Hf/Ce-doped La₂Zr₂O₇ with the single pyrochlore phase vs. the dopant content x. Reprinted from Acta Mater., 68, Y. Wang, F. Yang, and P. Xiao, Role and determining factor of substitutional defects on thermal conductivity: A study of La₂(Zr_1−xB_x)₂O₇ (B = Hf and Ce, 0 ≤ x ≤ 0.5) pyrochlore solid solutions, 106, Copyright 2014, with permission from Elsevier.

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(3) Co-doping at A site and B site.

The excellent structural and chemical stability of A₂B₂O₇-type rare earth zirconates makes it feasible to consider co-doping of the A site and B site. Liu et al. [85] used the solid-state reaction method to synthesize single phase (La_0.4Sm_0.5Yb_0.1)₂(Zr_0.7Ce_0.4)₂O_7.4 and (Sr_0.1La_0.3Sm_0.5Yb_0.1)₂(Zr_0.7Ce_0.4)₂O_7.3 with a pyrochlore structure. The lower thermal conductivity and slightly higher TEC of (Sr_0.1La_0.3Sm_0.5Yb_0.1)₂(Zr_0.7Ce_0.4)₂O_7.3 can be attributed to the difference in atomic weight of the substitutional cation and the increased concentration of oxygen vacancies in this material. Furthermore, Zhang et al. [15] synthesized rare earth zirconates (Sm_0.5La_0.5)₂Zr₂O₇ and (Sm_0.5La_0.5)₂(Zr_0.8Ce_0.2)₂O₇ ceramics with a pyrochlore structure via a solid-state reaction method at 1600°C for 10 h. Because of phonon scattering resulting from doping of La₂O₃ and CeO₂, the (Sm_0.5La_0.5)₂(Zr_0.8Ce_0.2)₂O₇ ceramic exhibits low thermal conductivity and high TEC above 400°C, as shown in Fig. 14. Zhou et al. [56] investigated the effect of rare earth doping on the thermophysical properties of La₂Zr₂O₇ synthesized via the coprecipitation–calcination method. La₂(Zr_1.8Ce_0.2)₂O₇ and La_1.7(DyNd)_0.15(Zr_0.8Ce_0.2)₂O₇ with pyrochlore structure have higher TECs than La₂Zr₂O₇ and La_1.7Dy_0.3Zr₂O₇. All the doped ceramics have lower thermal conductivity than undoped La₂Zr₂O₇.

Fig. 14.  Linear thermal expansion of Sm₂Zr₂O₇, (Sm_0.5La_0.5)₂Zr₂O₇, (Sm_0.5La_0.5)₂(Zr_0.8Ce_0.2)₂O₇, and 8YSZ. Reprinted from J. Alloys Compd., 475, H.S. Zhang, Q. Xu, F.C. Wang, L. Liu, Y. Wei, and X.G. Chen, Preparation and thermophysical properties of (Sm_0.5La_0.5)₂Zr₂O₇ and (Sm_0.5La_0.5)₂(Zr_0.8Ce_0.2)₂O₇ ceramics for thermal barrier coatings, 624, Copyright 2009, with permission from Elsevier.

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Liu et al. [86] prepared single-phase pyrochlore (Mg_xLa_0.5−xSm_0.5)₂(Zr_0.7Ce_0.3)₂O_7−x (x = 0, 0.1, 0.2, 0.3) using the coprecipitation–calcination method. When doping up to x = 0.2, thermal conductivity has a minimum value near 1.57 W/(m·K), and the TEC reaches a peak of 11.3 × 10⁻⁶ K⁻¹. Additionally, Zhao et al. [87] prepared dense monoliths with dual-phase rare-earth zirconate–stannate structures of Yb₂Zr₂O₇ + Ln₂Sn₂O₇ (Ln = Nd and Sm) using a solid-state reaction. Dual-phase structures of Yb₂Zr₂O₇-rich fluorite and Nd₂Sn₂O₇-rich pyrochlore were observed in the specimens of (1−x)Yb₂Zr₂O₇ + xNd₂Sn₂O₇ (x = 0.4 and 0.5); however, a complete solid solution of (Yb_1−xSm_x)₂(Zr_1−xSn_x)₂O₇ was finally formed in the case of sintering the (1–x)Yb₂Zr₂O₇ + xSm₂Sn₂O₇ series. In both series, low thermal conductivities with a positive temperature dependence are realized, as shown in Fig. 15. Xue et al. [88] prepared a sequence of Y₂O₃ and Ta₂O₅ co-doped Gd₂Zr₂O₇, designated as (Gd_1−xY_x)₂(Zr_1−xTa_x)₂O_7+x (x = 0, 0.1, 0.2, 0.3, and 0.4), using a solid-state reaction. The measured thermal conductivity of doped Gd₂Zr₂O₇ has a minimum of 1.41 W/(m·K) at 800°C and x = 0.3. The phase stability of (Gd_0.7Y_0.3)₂(Zr_0.7Ta_0.3)₂O_7.3 is illustrated in Fig. 16.

Fig. 15.  Thermal conductivity of the specimens: (a) (1−x)Yb₂Zr₂O₇ + xNd₂Sn₂O₇ series; (b) (1−x)Yb₂Zr₂O₇ + xSm₂Sn₂O₇ series. M. Zhao, X.R. Ren, J. Yang, and W. Pan, J. Am. Ceram. Soc., 99, 293(2016) [87]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission (YZ10—Yb₂Zr₂O₇; YZ8NS2—(Yb₂Zr₂O₇)_0.8(Nd₂Sn₂O₇)_0.2; YZ6NS4—(Yb₂Zr₂O₇)_0.6(Nd₂Sn₂O₇)_0.4; YZ5NS5—(Yb₂Zr₂O₇)_0.5(Nd₂Sn₂O₇)_0.5; YZ4NS6—(Yb₂Zr₂O₇)_0.4(Nd₂Sn₂O₇)_0.6; YZ2NS8—(Yb₂Zr₂O₇)_0.2(Nd₂Sn₂O₇)_0.8; NS10—Nd₂Sn₂O₇; YZ8SS2—(Yb₂Zr₂O₇)_0.8(Sm₂Sn₂O₇)_0.2; YZ6SS4—(Yb₂Zr₂O₇)_0.6(Sm₂Sn₂O₇)_0.4; YZ5SS5—(Yb₂Zr₂O₇)_0.5(Sm₂Sn₂O₇)_0.5; YZ4SS6—(Yb₂Zr₂O₇)_0.4(Sm₂Sn₂O₇)_0.6; YZ2SS8—(Yb₂Zr₂O₇)_0.2(Sm₂Sn₂O₇)_0.8; SS10—Sm₂Sn₂O₇).

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Fig. 16.  Thermal diffusivities (a) and thermal conductivities (b) of (Gd_1−xY_x)₂(Zr_1−xTa_x)₂O_7+x series ceramics as a function of Y or Ta doping concentration. Reprinted by permission from Springer Nature: J. Mater. Eng. Perform., Influence of Y₂O₃ and Ta₂O₅ co-doping on microstructure and thermal conductivity of Gd₂Zr₂O₇ ceramics, Z.L. Xue, S.Q. Wu, L.H. Qian, E. Byon, and S.H. Zhang, Copyright 2020.

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(4) Cationic substitutions in rare earth zirconate ceramic coatings.

Even if numerous voids present in the coating, rare earth zirconate ceramic topcoat can be improved by cationic doping. Guo et al. [89] prepared (Gd_0.9Yb_0.1)₂Zr₂O₇/YSZ double-layer ceramic TBCs using EB-PVD. The coatings showed more than 3700 thermal cycle lifespan at approximately 1350°C during flame shock test and the lowest thermal conductivity, as shown in Fig. 17. Zhou et al. [90] fabricated the La₂(Zr_0.75Ce_0.25)₂O₇ coatings by APS using nanostructured feedstocks. These nanostructured La₂(Zr_0.75Ce_0.25)₂O₇ coatings exhibit a favorable wear resistance. Gd₂Zr₂O₇ coatings doped with Ti⁴⁺ or Mg²⁺ were fabricated by Wang et al. [91]. The incorporation of Ti⁴⁺ into Gd₂Zr₂O₇ can enhance the infrared absorption/emittance within a specific wavenumber range (0.75–2.5 μm), which is due to the augmentation of electronic transitions induced by the impurity energy levels associated with the widening of the conduction band. Shen et al. [92] deposited the (Gd_0.9Er_0.1)₂Zr₂O₇/YSZ double-layer TBCs by EB-PVD, which exhibits a measured thermal conductivity of 0.95 W/(m·K) at 1000°C and 1.02 W/(m·K) at 1200°C. Additionally, Jiang et al. [93] fabricated Y-doped La₂Zr₂O₇ coatings with a Y to La molar ratio of 1:1 via the APS method. The fluorite phase begins to precipitate after prolonged annealing, increasing thermal conductivity. The presence of a robust phonon scattering source, in conjunction with the suppression of radiative thermal conduction, constitutes the underlying mechanism for low thermal conductivity.

Fig. 17.  Thermal conductivity of (Gd_1−xYb_x)₂Zr₂O₇ (x = 0, 0.1, 0.3, 0.5, and 0.7) ceramics. Reprinted from J. Eur. Ceram. Soc., 34, L. Guo, H.B. Guo, H. Peng, and S.K. Gong, Thermophysical properties of Yb₂O₃-doped Gd₂Zr₂O₇ and thermal cycling durability of (Gd_0.9Yb_0.1)₂Zr₂O₇/YSZ thermal barrier coatings, 1255, Copyright 2014, with permission from Elsevier.

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3.1.3   Design on high-entropy rare earth zirconate ceramics

Since high-entropy alloys (HEAs) were proposed in 2004, the concept of high entropy has attracted increasing attention [94–95]. Ceramic scientists have extended the concept of high entropy into different advanced ceramic materials, including oxides, carbides, borides, nitrides, silicides, carbonitrides, and even composites [25–26]. The term high-entropy ceramics refers to a single-phase system where almost equimolar multicomponent elements not less than five cations occupy the same lattice site, resulting in a considerably large configurational entropy (S_conf ≥ 1.5R, with R representing the ideal gas constant) [25].

Depending on the demand for high-entropy ceramics on a single phase, the formation ability of a single phase becomes an important issue that must be studied [28]. A size disorder parameter has been expanded to high-entropy zirconates to tailor the thermal conductivity [96] and the single-phase formation ability [97]. Yang et al. [98] synthesized a five-component equimolar high-entropy ceramic of (La_0.2Eu_0.2Gd_0.2Y_0.2Yb_0.2)₂Zr₂O₇ with a dual-phase of pyrochlore and fluorite structures. They claimed that the single-phase forming ability is determined by the difference in cationic radius rather than the entropy, with a critical threshold value of 5.2%. Subsequently, Wang et al. [97] prepared a sequence of five-principal equimolar rare earth zirconates via a solid-state reaction method. The single-phase formation ability was mainly controlled by the size disorder parameter (δ*); meanwhile, the average cation radius ratio (r_A/r_B) is the threshold value for the formation of a pyrochlore- or defective fluorite-type structure. When δ* is less than 5%, multicomponent zirconate ceramics tend to form a single phase; otherwise, a dual-phase ceramic with pyrochlore and defective fluorite structures occurs, as shown in Fig. 18. They also concluded that the threshold value of the average cation radius ratio is tailored accurately to be 1.467 for a phase transition of pyrochlore to defective fluorite when δ* is less than 5%.

Fig. 18.  (a) 3D schematic of the correlation of phase structure with the average ionic radius ratio (r_A/r_B), configuration entropy (S_conf), and size disorder (δ*) of the synthesized zirconate ceramics; (b) 2D projection of (a), phase zone distribution dependence on δ* and S_conf . Reprinted from J. Alloys Compd., 918, Y.H. Wang, Y.J. Jin, T. Wei, et al., Size disorder: A descriptor for predicting single- or dual-phase formation in multicomponent rare earth zirconates, 165636, Copyright 2022, with permission from Elsevier.

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(1) High-entropy single-phase zirconates.

In a strict sense, the term “high-entropy ceramics” should be reserved exclusively for single-phase ceramics. Consequently, many researchers have investigated rare earth composition adjustments to explore single-phase high-entropy rare earth zirconates. Li et al. [99] prepared high-entropy pyrochlore-type structures based on rare earth zirconates (5RE_1/5)₂Zr₂O₇ (RE = La, Nd, Sm, Eu, Gd, and Y) via a solid-state reaction method. The measured thermal conductivities of (5RE_1/5)₂Zr₂O₇ high-entropy ceramics are below 1 W/(m·K). Zhao et al. [29] synthesized a high-entropy rare-earth zirconate of (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)₂Zr₂O₇. With a sluggish grain growth rate, the thermal conductivity of (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)₂Zr₂O₇ is only 0.76 W/(m·K) at room temperature. Furthermore, Ren et al. [100] prepared (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Zr₂O₇ and (Sm_1/3Eu_1/3Dy_1/3)₂Zr₂O₇ by spark plasma sintering. The high-entropy ceramics exhibited an enhanced Young’s modulus, and the fracture toughness of the (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Zr₂O₇ bulk ceramic was measured to be approximately 2.24 MPa·m^1/2, higher than those of single-component Sm₂Zr₂O₇ and Lu₂Zr₂O₇. The (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Zr₂O₇ ceramic exhibited a low thermal conductivity of 0.86 W/(m·K) and a high TEC of approximately 11 × 10⁻⁶ K⁻¹ at 1000°C. In addition, multicomponent rare-earth cerate (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Ce₂O₇ and zirconocerate (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂ZrCeO₇ ceramics synthesized by Ren et al. [101] had a homogeneous composition distribution of rare-earth elements and exhibited pure fluorite structure up to 1400°C. The (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Ce₂O₇ ceramic has an improved TEC of 12.60 × 10⁻⁶ K⁻¹ at 1200°C and a reduced thermal conductivity. However, (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂ZrCeO₇ zirconocerate exhibited a better sintering resistance than (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂Ce₂O₇ cerate.

He et al. [102] prepared a sequence of high-entropy ceramics with RE₂(Ce_0.2Zr_0.2Hf_0.2Sn_0.2Ti_0.2)₂O₇ (RE₂HE₂O₇, RE = Y, Ho, Er, and Yb) compositions using a solid-state reaction. RE₂HE₂O₇ ceramics exhibit exceptional phase stability at high temperatures, along with considerably high TECs of 10.3 × 10⁻⁶–11.7 × 10⁻⁶ K⁻¹ at 1200°C and low thermal conductivities of 1.10–1.37 W/(m·K) at 25°C, all of which are attributed to the single-phase defective fluorite structure. Subsequently, a (Y,Yb)₂(Ti,Zr,Hf)₂O₇ high-entropy ceramic prepared by Song et al. [103] has a low glass-like thermal conductivity of 1.27 W/(m·K) at 25°C and a TEC of 10.08 × 10⁻⁶ K⁻¹ at 1000°C, which is attributed to its highly disordered crystal structure and substantial mass disorder among the multiple cations. Zhang et al. [104] investigated the structures and thermophysical properties of (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1–xTi_x)₂O₇ (x = 0 to 0.5) high-entropy ceramics synthesized using a solid-state reaction method. (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂Zr₂O₇ zirconate shows a defective fluorite structure, and others demonstrate a pure pyrochlore phase. The average coefficients of thermal expansion for (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1−xTi_x)₂O₇ ceramics range from 10.65 × 10⁻⁶ to 10.84 × 10⁻⁶ K⁻¹, while the substitution of Ti⁴⁺ leads to a reduction in thermal conductivity from 1.66 to 1.20 W/(m·K).

In addition, single-phase high-entropy rare-earth zirconate of (Yb_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇ fabricated by Luo et al. [105] has a TEC value of 10.52 × 10⁻⁶ K⁻¹ at RT–1500°C and a thermal conductivity of 1.003 W/(m·K). Furthermore, its thermophysical properties are tunable by introducing a high-entropy design to form single-phase rare-earth zirconates utilizing spark plasma sintering [106]. Compared with lanthanum zirconate, the HECs have outstanding high-temperature phase stability, a large TEC of 10.20 × 10⁻⁶–10.39 × 10⁻⁶ K⁻¹ at RT–1500°C, low thermal conductivity of 1.17–1.37 W/(m·K) at 1500°C, and fracture toughness of 1.61–1.69 MPa·m^1/2. Yan et al. [107] synthesized a high-entropy (Gd_0.2Y_0.2Er_0.2Tm_0.2Yb_0.2)₂Zr₂O₇ zirconate ceramic with a fluorite structure via a solid-state reaction. (Gd_0.2Y_0.2Er_0.2Tm_0.2Yb_0.2)₂Zr₂O₇ ceramic has an ultra-low thermal conductivity of 0.82 W/(m·K), a high TEC of 10.61 × 10⁻⁶ K⁻¹, and a fracture toughness of 1.54 MPa·m^1/2, which is attributed to the synergistic effects resulting from implementing a high-entropy strategy. Zhang et al. [108] investigated the underlying mechanism of unusual thermal conductivity in high-entropy ceramics by synthesizing pure defective fluorite phase (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1−xCe_x)₂O₇ (x = 0–0.5) high-entropy ceramics using a solid-state reaction method. With increasing CeO₂ content, the effect of electronic thermal conductivity decreases thermal diffusivities and thermal conductivities. Moreover, high-entropy rare earth zirconate powders were deposited as a double-layer ceramic TBC by Zhou et al. [109] via APS. The (La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇ coating exhibited a thermal cycling lifetime of 53 cycles, compared to a lifetime of 10 cycles for the La₂Zr₂O₇ system.

(2) High-entropy dual-phase zirconates.

The formation of single-phase ceramics is essential for high-entropy ceramics; however, excessive distortion from the high-entropy strategy often leads to the occurrence of dual-phase ceramics. Zhu et al. [110] synthesized a sequence of high-entropy rare earth zirconates with single- and dual-phase structures (Fig. 19). (La_0.2Nd_0.2Y_0.2Er_0.2Yb_0.2)₂Zr₂O₇ (LNYEY) with “rattling” ions exhibited a low glass-like thermal conductivity of 1.62–1.59 W/(m·K) at 100–600°C and an enhanced TEC of 10.45 × 10⁻⁶ K⁻¹ at 1000°C. Fan et al. [111] prepared a sequence of dual-phase medium- and high-entropy rare earth zirconates by tailoring the principal elements. Dual-phase pyrochlore–fluorite structure formed under the circumstance of an average ionic radius ratio of 1.4 to 1.5 and more than 5% size disorder. Liu et al. [112] fabricated high-entropy Y₂(Ti_0.2Zr_0.2Hf_0.2Nb_0.2Ta_0.2)₂O₇ and Y₂(Ti_0.25Zr_0.25Hf_0.25Ta_0.25)₂O₇ ceramics via a solid-state reaction, aiming to assess the influence of B-site cations on thermal conductivity. The Y₂(Ti_0.2Zr_0.2Hf_0.2Nb_0.2Ta_0.2)₂O₇ ceramic has a thermal conductivity of 1.8 W/(m·K), which is lower than that of Y₂(Ti_0.25Zr_0.25Hf_0.25Ta_0.25)₂O₇ ceramics (1.8 to 2.5 W/(m·K)) at 25 to 1400°C. Wang et al. [113] synthesized novel non-equimolar (Nd_0.58Gd_0.05Y_0.05Er_0.05Yb_0.27)₂Zr₂O₇ composed of coexisting defect fluorite and pyrochlore phases and (Nd_0.2Gd_0.2Y_0.2Er_0.2Yb_0.2)₂Zr₂O₇ by a solid-state reaction. (Nd_0.58Gd_0.05Y_0.05Er_0.05Yb_0.27)₂Zr₂O₇ and (Nd_0.2Gd_0.2Y_0.2Er_0.2Yb_0.2)₂Zr₂O₇ possess higher TECs and lower thermal conductivities than Nd₂Zr₂O₇ (Fig. 20).

Fig. 19.  (a) Thermal diffusivity and (b) thermal conductivity of different RE₂Zr₂O₇ ceramics. Reprinted from J. Eur. Ceram. Soc., 41, J.T. Zhu, X.Y. Meng, P. Zhang, et al., Dual-phase rare earth zirconate high-entropy ceramics with glass-like thermal conductivity, 2861, Copyright 2021, with permission from Elsevier (LNSEG—(La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇; LNSGY—(La_0.2Nd_0.2Sm_0.2Gd_0.2Yb_0.2)₂Zr₂O₇; LNYEY—(La_0.2Nd_0.2Y_0.2Er_0.2Yb_0.2)₂Zr₂O₇; DYHEY—(Dy_0.2Y_0.2Ho_0.2Er_0.2Yb_0.2)₂Zr₂O₇; single rare earth RE₂Zr₂O₇ (RE = La, Yb)).

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Fig. 20.  Relationship between temperature and (a) dL/L₀ and (b) TECs of 1Nd, 0.58Nd, and 0.2Nd samples. Reprinted from J. Alloys Compd., 938, Y.L. Wang, G.Q. Lin, L.X. Yang, et al., Preparation and thermophysical properties of novel dual-phase and single-phase rare earth zirconate high-entropy ceramics, 168551, Copyright 2023, with permission from Elsevier.

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(3) Other preparation methods and simulation calculations.

In addition, new theories and techniques have been applied to high-entropy ceramics. Using an innovative high-speed positive grinding strategy combined with a solid-state reaction, Liu et al. [114] fabricated high-entropy rare-earth zirconate (La_0.2Nd_0.2Sm_0.2Gd_0.2Yb_0.2)₂Zr₂O₇ with a defective fluorite structure, which possesses not only a low thermal conductivity of 0.9–1.72 W/(m·K) at 200–1000°C and a high TEC of 10.9 × 10⁻⁶ K⁻¹ at 1000°C but also excellent mechanical properties, including a high Young’s modulus of 186–257 GPa and fracture toughness of 2.7 MPa·m^1/2. Ultrafast high-throughput sintering was used to synthesize five lanthanide group rare earth zirconates of Ln₂Zr₂O₇ (Ln = La, Nd, Sm, Eu, and Gd) by Zhao et al. [115], as shown in Fig. 21. With an increase in the number of rare earth components, the average grain size of Ln₂Zr₂O₇ decreases; however, the hardness and Young’s modulus increase, because of the sluggish diffusion and lattice distortion effects caused by an increase in entropy. Using a combustion synthesized nano powder, Zhang et al. [116] fabricated a high-entropy ceramic of (La_0.2Nd_0.2Sm_0.2Gd_0.2Yb_0.2)₂Zr₂O₇ with a dual-phase of pyrochlore and defective fluorite. The in-line transmittance of the (La_0.2Nd_0.2Sm_0.2Gd_0.2Yb_0.2)₂Zr₂O₇ ceramic is 69.06% at a wavelength of 2108 nm. Deng et al. [117] synthesized a single-phase high-entropy (Y_0.2Gd_0.2Er_0.2Yb_0.2Lu_0.2)₂Zr₂O₇ ceramic by spark plasma sintering, which has a suitable TEC of 10.2 × 10⁻⁶ K⁻¹ and an extremely low thermal conductivity of less than 0.6 W/(m·K) at 25–1000°C. Furthermore, Zhang et al. [118] fabricated the high-entropy zirconate of (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1–xTi_x)₂O₇ to evaluate thermal conductivity at high temperature. For x = 0.1–0.5 compositions, an increased thermal conductivity above 600°C is attributed to the improved photon thermal conductivity.

Fig. 21.  Schematic of the ultrafast, high-temperature, high-throughput sintering apparatus. Reprinted from J. Eur. Ceram. Soc., 41, Z.T. Zhao, R.F. Guo, H.R. Mao, and P. Shen, Effect of components on the microstructures and properties of rare earth zirconate ceramics prepared by ultrafast high-throughput sintering, 5768, Copyright 2021, with permission from Elsevier.

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A first-principles calculation effectively elucidates the effect of ionic bonding and a structural polyhedron on the properties of high-entropy ceramics. Using first-principles calculations, Li et al. [119] investigated the influence of chemical disorder on mechanical and thermal properties by producing a pyrochlore-type rare earth zirconate with and without chemical disorder (nRE_1/n)₂Zr₂O₇ (n = 1, 2, and 4, RE = La, Nb, Sm, Eu, and Gd). The lattice parameters of all pyrochlores exhibit a linear increase in RE—O1, RE—O2, and Zr—O2 bonds. Additionally, multicomponent pyrochlores have relatively high elastic constants and moduli. (LaSmEuGd)₂Zr₂O₇ has the lowest thermal conductivity. A molecular dynamics simulation is another highly effective computational method. Using molecular dynamics simulations, Fan et al. [120] prepared multicomponent rare-earth zirconates (4RE_1/4)₂Zr₂O₇ (RE = La, Nd, Sm, Eu, and Gd) and the corresponding single-component compounds to investigate the temperature-dependent structural and mechanical/thermal property evolution in pyrochlore. With an increase in temperature, the bond lengths increase, and the deformation of (ZrO₆) polyhedra tends to be obvious, which decreases the phonon mean free path and enhances scattering, resulting in lower thermal conductivity.

3.2   Material compositing strategy

To meet the demand for high-temperature infrared radiation resistance and improved mechanical properties, the material compositing strategy has been introduced into TBCs. Li et al. [121] investigated the thermal properties of rare earth zirconate composites containing various contents of NiCr₂O₄ at elevated temperature. A better general thermal conductivity was achieved with NiCr₂O₄ content of 15vol%. The radiative thermal conductivity in La₂Zr₂O₇/LaPO₄ composites was investigated by Yang et al. [122] using a solid-state reaction in air atmosphere. The addition of more than 20wt% LaPO₄ was observed to effectively impede radiation thermal conductivity, thereby enhancing fracture toughness. Moreover, Qayyum et al. [123] employed DFT to investigate the comprehensive optoelectronic properties of rare-earth zirconates Nd₂Zr₂O₇, encompassing spin-up and spin-down states. They proposed that the calculated optical properties showed a considerable spin-dependent effect. Zhang et al. [118] studied the thermal conductivity of the (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1–xTi_x)₂O₇ high-entropy system. The increase in high-temperature thermal conductivity can be attributed to the effects of improved photon thermal conductivity on actual thermal conductivity. Although the rare earth zirconate exhibits higher transmittance at elevated temperature, it is still better than YSZ TBCs, which was verified by the results of Wang et al. [124]. Compared to YSZ, Gd₂Zr₂O₇ exhibits enhanced reflectance and reduced transmittance within the wavelength range of 0.8–2.7 μm. Wang et al. [125] investigated the heat insulating capacity of multilayer coatings containing a pure Sm₂Zr₂O₇ (SZO) layer and a Sm₂Zr₂O₇−15vol%NiCr₂O₄ (SZO–15%NCO) layer, which exhibited the same insulating capacity (Fig. 22) as the Sm₂Zr₂O₇−NiCr₂O₄ (SZO–NCO) bulk materials.

Fig. 22.  Schematic for heat conversion in single-, double-, and triple-layer coatings. Reprinted from Ceram. Int., 43, D.Y. Wang, L. Liu, Y.B. Liu, T. Li, Z. Ma, and H.X. Wu, Heat insulating capacity of Sm₂Zr₂O₇ coating added with high absorptivity solids, 2884, Copyright 2017, with permission from Elsevier.

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Composite ceramics can easily adjust mechanical properties by incorporating different reinforcements. Wang et al. [126] added 3mol% Y₂O₃-tetragonal zirconia polycrystals (3Y-TZP) to improve the fracture toughness of La₂Zr₂O₇ ceramics. The t-3YSZ/La₂Zr₂O₇ composites exhibit a primary toughening mechanism resulting from the phase transformation occurring in dispersive 3YSZ second phases. Zhong et al. [127] fabricated Gd₂Zr₂O₇ toughened by nanostructured 3mol% yttria-partially stabilized zirconia (YSZ). The Gd₂Zr₂O₇–10mol%YSZ composite exhibits a substantial increase in fracture toughness of approximately 60% compared to monolithic Gd₂Zr₂O₇. Schmitt et al. [128] combined rare earth zirconate Gd₂Zr₂O₇ with a thermochemically compatible and phase-stable GdAlO₃ aluminate to develop a new strategy. The mechanical properties, particularly fracture toughness, are distinctly enhanced by GdAlO₃, and the erosion rate is even reduced by over 61%.

In addition, Luo et al. [129] prepared various dual-phase composites x(5RE)AlO₃/(1−x)(5RE)₂Zr₂O₇ (x = 0.1–0.5, RE = La, Sm, Eu, Gd, and Yb) using the reverse coprecipitation method. x(5RE)AlO₃/(1−x)(5RE)₂Zr₂O₇ have a superior fracture toughness of 2.77 MPa·m^1/2 at x = 0.3, surpassing Ho₂Zr₂O₇ by 64% and La₂Zr₂O₇ by 101%. Using the reverse coprecipitation method, Yu et al. [130] prepared rare earth zirconate/aluminate composites containing Y or Y/Gd, which exhibit a low sintering rate, in contrast to pure fluorite at 1400°C. The rare earth zirconate/aluminate composite containing equimolar Y/Gd exhibits the lowest densification rate at 1500°C. Carpioa et al. [131] fabricated multilayered and functionally graded coatings of YSZ/Gd₂Zr₂O₇. The multilayered YSZ/Gd₂Zr₂O₇ coating exhibited a better thermal fatigue resistance, while the functionally graded YSZ/Gd₂Zr₂O₇ coating exhibited an excellent resistance to thermal fatigue. Rai et al. [132] prepared a two-phase toughened composite coating containing 30wt% Gd₂Zr₂O₇ and 70wt% low-k t'-ZrO₂–2Y₂O₃–1Gd₂O₃–1Yb₂O₃. It is found that erosion performance is improved to address long-term service. Reinforcements of YSZ fibers and multi-walled carbon nanotubes (MWCNTs) were employed by Jin et al. [133] to enhance a double-layer YSZ/La₂Zr₂O₇ TBC. In contrast to MWCNT-reinforced La₂Zr₂O₇ coating, YSZ fibers exhibit the exceptional reinforcement capability of fibers, resulting in considerably reduced thermal conductivity and enhanced bonding strength. In contrast, the La₂Zr₂O₇ coating modified with MWCNTs exhibited high fracture toughness and superior thermal cycling stability.

In addition to conventional methods for materials design and research, recent advancements in artificial intelligence have led to the emergence of data-driven scientific approaches that rely on extensive datasets derived from numerous previous experiments and simulations. The use of artificial intelligence (AI), machine learning (ML), deep learning (DL) and big data (BD) techniques has emerged as a crucial driving force in the realm of materials science, facilitating accelerated advancements in materials design and development. The performance of new TBCs can be enhanced from intrinsic and technological perspectives by these future design methods.

To improve the performance of TBCs and promote the development of new TBCs for various industrial applications, the ML and DL models were trained by Liu et al. [134] using a substantial amount of YSZ TBC experimental data, revealing that thermal conductivity is considerably influenced by five key factors. Various ML models and algorithms, namely, support vector regression (SVR), Gaussian process regression (GPR), and convolution neural network (CNN) regression algorithms, can considerably enhance the predictive performance of machine learning in estimating thermal conductivity. The effective use of various algorithms and models is observed in the prediction of microstructure features. A support vector machine method optimized by the cuckoo search algorithm (CS-SVM) can filter out the optimal parameters of the spray powder size, spray distance, and spray power during APS processing, by which the prediction accuracy has surpassed 95% [135]. In the same pursuit of optimizing the preparation process parameters, Zhu et al. [136] employed a typical back propagation (BP) model and extreme machine learning machine (ELM) model combined with the flower pollination algorithm (FPA) optimization algorithm to analyze and train the complex preparation model, which reached 94% accuracy.

4.   Conclusions and outlook

In summary, rare earth zirconates have become the most important candidate for applications as TBC materials during the last several decades. Defect engineering, the high-entropy strategy, and compositing approaches have been promising and effective methods for improving the thermophysical properties of rare earth zirconates.

(1) Because of the unique crystal structure of rare earth zirconates, doping emerges as an effective strategy for reducing thermal conductivity and enhancing mechanical properties instead of using vacancies. The impact of lanthanide rare earth ion doping on the basic thermophysical and mechanical properties of zirconate has been extensively investigated through materials design and calculation, with a particular emphasis on the electronic structure of rare earth lanthanides.

(2) Despite the occurrence of component evaporation during coating deposition, high-entropy engineering has garnered considerable attention. Various descriptors have been introduced to characterize phase transitions and the emergence of complex phases resulting from high-entropy designs. A range of computational tools have been employed to explore the mechanism behind the enhancement of properties induced by high-entropy ceramics, which will catalyze future design development in high-entropy strategic materials. However, further investigation is required to explore the impact trends and mechanisms of entropy increase on material properties.

(3) Thermal radiation absorption has gradually become another key point for improving the performance of TBCs, particularly at elevated temperature. The current research in this area is relatively limited, with all studies focusing on incorporating reinforcement phases to create composite materials. Meanwhile, composite strategies are frequently employed to enhance the mechanical properties of rare earth zirconates to achieve a matching thermal expansion with a bond coat.

Doping, high-entropy engineering, and compositing approaches will undoubtedly continue to serve as effective strategies for developing next-generation rare earth zirconate TBC materials characterized by low thermal conductivity, a high thermal expansion match, and superior comprehensive mechanical properties. The heat transfer mechanisms and thermo-optical responses of rare earth zirconates modified with doping, high-entropy engineering, and compositing approaches need in-depth investigation for applications as hot-section components in the advanced turbine engine of the future.