Dual-site cationic disorder engineering for ultralow amorphous-like thermal conductivity in thermal barrier coatings

Abstract

Developing thermal barrier coatings (TBCs) with ultralow thermal conductivity and substrate-matched thermal expansion remains a long-standing challenge for enhancing aero-engine efficiency and durability. In this study, we report a single-cation dual-site occupation strategy in a high-entropy pyrochlore (A₂B₂O₇) oxide, formulated as (La_1−xY_x)₂(Zr_0.25Sn_0.125Ce_0.125Nb_0.250Y_0.250)₂O₇ (denoted as La_1−xY_x-HE), in which Y³⁺ simultaneously occupies both A and B lattice sites. Remarkably, Y³⁺ serves as the smallest cation suitable for the A site while also being the largest cation suitable for the B site, creating an extreme cation size mismatch-induced lattice disorder. This dual-site disorder effectively enhances phonon scattering, leading to excellent thermal insulation performance, together with a well-matched thermal expansion coefficient. Notably, La_0.500Y_0.500-HE exhibits an ultralow amorphous-like thermal conductivity of 1.06 W m⁻¹ K⁻¹, approximately half that of conventional/commercial YSZ, while maintaining a compatible thermal expansion coefficient of 10.01 × 10⁻⁶ K⁻¹, which aligns well with that of the substrate. Meanwhile, it exhibits excellent mechanical properties, including a Vickers hardness of 9.86 GPa and a Young's modulus of 133.4 GPa. The dual-site disorder strategy provides an effective pathway for designing next-generation TBCs with superior thermal insulation performance.

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1. Introduction

To enhance the operational efficiency and thrust-to-weight ratio of aero-engines, it is necessary to increase the turbine inlet temperature, which has now exceeded 1800 K.¹ This imposes more stringent demands on the thermal protection of critical components, such as Ni-based superalloy blades.² Depositing thermal barrier coatings (TBCs) on the blade surface can effectively reduce the operating temperature of the substrate.³ However, the commercially available TBC material, yttria-stabilized zirconia (YSZ), is limited to applications below 1500 K owing to phase transition and rapid sintering at higher temperatures.⁴ Consequently, it is critical to develop new TBC materials to replace YSZ. Due to their excellent phase stability and low thermal conductivity, pyrochlore oxides (A₂B₂O₇) have emerged as promising alternatives.⁵ To further optimize the performance of pyrochlore-based TBCs, introducing oxygen vacancies and atomic disorder has been widely adopted as an effective strategy for enhancing phonon scattering and reducing thermal conductivity.⁶ However, introducing additional oxygen vacancies often leads to an undesirable increase in oxygen ion migration rates at high temperatures, which accelerates the oxidation of the substrate and degrades the coating reliability.⁷ Therefore, enhancing the intrinsic lattice disorder is a more rational approach.

High-entropy modification has been demonstrated as an efficient strategy to enhance the intrinsic lattice disorder, which originates from the simultaneous incorporation of multiple principal cations at equivalent lattice positions.⁸ Some studies have effectively reduced thermal conductivity via A-site high-entropy doping while simultaneously improving the thermal expansion coefficient and mechanical properties. Wang et al.⁹ synthesized (La_0.2Nd_0.2Gd_0.2Yb_0.2Y_0.2)₂Zr₂O₇via a solid–state reaction and obtained a low-temperature thermal conductivity of 1.91 W m⁻¹ K⁻¹, markedly lower than 2.99 W m⁻¹ K⁻¹ for La₂Zr₂O₇. Ren et al.¹⁰ prepared (Sm_0.2Eu_0.2Tb_0.2Dy_0.2Lu_0.2)₂-Zr₂O₇ using a co-precipitation method, achieving a lower thermal conductivity of 1.44 W m⁻¹ K⁻¹ along with a thermal expansion coefficient of 10.42 × 10⁻⁶ K⁻¹. Wang et al.¹¹ synthesized a series of pyrochlore oxides with varying configurational entropies, (3Re_0.33)₂Zr₂O₇, (4Re_0.25)₂Zr₂O₇, and (5Re_0.2)₂Zr₂O₇, where Re represents the rare earth elements. The results indicated that with increasing entropy, the grain size gradually decreased, leading to enhanced mechanical properties. Although A-site high-entropy doping has achieved notable optimization of thermal and mechanical properties, the lattice distortion in current pyrochlore oxides remains insufficiently pronounced due to the similar cationic radius and mass of the lanthanide elements doped at the A site.¹²

In contrast, doping at the B-site of pyrochlore oxides is expected to induce a substantially greater disorder. This is because the BO₆ octahedra, which are corner-shared and form the crystal framework, are highly sensitive to variations in the size and mass.¹³ Notably, several studies have confirmed that specific B-site dopants effectively enhance thermal-protective performance. For example, the addition of Ce⁴⁺ expands the lattice due to its larger cationic radius, softening the crystal structure and reducing the high-temperature plateau thermal conductivity.¹⁴ Meanwhile, Sn⁴⁺ doping effectively suppresses radiative heat transfer at elevated temperatures by impeding photon transport.¹⁵ However, there are few studies on B-site high-entropy pyrochlores. This is because only a limited number of cations are suitable for the B-site, and the significant lattice disorder often induces phase segregation.¹⁶ For instance, Xu et al.¹³ synthesized a B-site high-entropy pyrochlore, Sm₂(Nb_0.2Sn_0.2Ti_0.2Y_0.2Zr_0.2)₂O₇, which exhibited an ultralow thermal conductivity of 1.35 W m⁻¹ K⁻¹ and a thermal expansion coefficient of 10.20 × 10⁻⁶ K⁻¹. Similarly, Jin et al.¹⁷ reported Eu₂(Y_0.2Ce_0.2Zr_0.2Hf_0.2Ta_0.2)₂O₇, another B-site high-entropy pyrochlore, which achieved a thermal conductivity of 1.41 W m⁻¹ K⁻¹ and a thermal expansion coefficient of 9.8 × 10⁻⁶ K⁻¹. However, high-entropy doping at the B-site remains a significant challenge and is rarely reported, primarily due to the cationic radius limitation and the tendency for phase segregation. Consequently, research on synergistically enhancing disorder through simultaneous A-site and B-site co-doping is even more scarce. Notably, Y³⁺ possesses a cationic radius larger than that of conventional tetravalent transition metals at the B site but smaller than that of typical trivalent rare-earth cations at the A site, along with a relatively low atomic mass. Therefore, the simultaneous incorporation of Y³⁺ into both A and B sites is expected to introduce significant lattice disorder at both crystallographic positions.

To achieve pronounced dual-site disorder, this study synthesized a series of B-site high-entropy pyrochlore oxides with graded A-site Y³⁺ doping, formulated as (La_1−xY_x)₂-(Zr_0.25Sn_0.125Ce_0.125Nb_0.25Y_0.25)₂O₇, abbreviated as La_1−xY_x-HE (x = 0–0.75). Y³⁺ simultaneously occupied both A and B sites, serving as the smallest cation suitable for the A site and the largest cation suitable for the B site. Thus, a pronounced size disorder at dual sites was achieved, which is associated with enhanced phonon scattering. By varying the Y³⁺ content at the A-site, this study aims to precisely regulate the lattice parameters and disorder and to establish clear correlations between these factors and the resulting crystalline phase, thermal conductivity, thermal expansion coefficient, and mechanical performance. Furthermore, a phonon point-defect scattering model was developed to describe the thermal transport behavior. In conclusion, dual-site disorder engineering provides an effective strategy for designing next-generation TBCs with superior thermal insulation performance.

2 Experimental

2.1 Materials synthesis

The high-entropy pyrochlore oxides with the formula (La_1−xY_x)₂(Zr_0.25Sn_0.125Ce_0.125Nb_0.25Y_0.25)₂O₇ (x = 0, 0.125, 0.25, 0.375, 0.5, 0.625, and 0.75) and La₂Zr₂O₇ were synthesized via a solid–state reaction method. The material design principle is to maintain a fixed high-entropy configuration at the B-site while gradually increasing the proportion of smaller Y³⁺ substituting for La³⁺ at the A site. The minimum doping molar ratio in this chemical formula is set to 0.125, representing the doping of two cations within a single pyrochlore unit cell.

Prior to the synthesis, high-purity raw powders, including La₂O₃, Y₂O₃, ZrO₂, SnO₂, CeO₂, and Nb₂O₅, were pre-dried at 390 K for 12 hours to remove adsorbed moisture. All chemicals (purity >99.9%) were purchased from Shanghai Aladdin Bio-Chem Technology Co., Ltd, China. The starting powders were accurately weighed according to the stoichiometric molar ratios of the target compositions. Subsequently, the mixtures were ball-milled with ethanol for 24 hours using zirconia balls and then dried at 350 K for 12 hours. After drying, the resulting powders were uniaxially pressed into green pellets under a pressure of 200 MPa for 5 minutes. To enhance the phase purity, the green pellets were sintered in a high-temperature tube furnace at 1923 K for 24 hours, followed by furnace cooling to room temperature to obtain the final samples.

2.2 Characterization

The phase composition of the synthesized samples was analyzed by X-ray diffraction (XRD, PANalytical X'Pert). The microstructure and elemental distribution of the sintered pellets were examined by field-emission scanning electron microscopy (FE-SEM, Hitachi SU5000) equipped with energy-dispersive X-ray spectroscopy (EDS, Oxford Ultim Max). The chemical states of oxygen and dopant cations were investigated by X-ray photoelectron spectroscopy (XPS, Thermo Fisher K-Alpha). The thermal diffusivity (λ) was measured from 300 K to 1300 K using a laser flash analyzer (NETZSCH LFA 467), and the specific heat capacity (C_p) was estimated based on the Neumann–Kopp rule. Finally, the thermal conductivity (κ) was calculated according to κ = λρC_p, where the bulk density (ρ) was determined by the Archimedes method. The thermal insulation performance of the samples was further evaluated through a numerical simulation. The thermal expansion behavior was also evaluated from 300 K to 1300 K using a dilatometer (NETZSCH DIL 402). The acoustic velocity and mechanical properties were determined by the ultrasonic pulse-echo method. Vickers hardness (H_V) and fracture toughness (K_IC) were measured using a Vickers hardness tester (HRS-150, Shangcai). Additional characterization details are provided in the SI.

3 Results and discussion

3.1 Phase composition

Based on the crystallographic distinction between the pyrochlore structure (Fig. 1(a)) and defective fluorite (Fig. 1(b)),¹⁸ we investigated the phase composition of the synthesized samples. XRD patterns (Fig. 1(c)) reveal that the synthetic La_1−xY_x-HE oxides exhibit a structural transition from an ordered pyrochlore to a disordered defect-fluorite phase with increasing x. For compositions with x ≤ 0.5, pyrochlore superlattice diffraction peaks are clearly observed at approximately 36° and 44°, corresponding to the (331) and (511) crystal planes, respectively.¹⁷ These superlattice diffraction peaks arise from the ordered arrangement of cations and oxygen vacancies. At x > 0.5, the superlattice diffraction peaks disappear, indicating a transition to the defect-fluorite phase. The phase transition is primarily determined by the cation radius ratio of the A-site to B-site cations (r_A/r_B), with the pyrochlore structure typically requiring r_A/r_B to be between 1.46 and 1.78.¹⁹

Fig. 1 Structures of (a) pyrochlore and (b) defective fluorite. (c) XRD patterns of the La_1−xY_x-HE samples and LZO with an enlarged view in the range of 30–38°.

Fig. 2 displays the Rietveld-refined XRD patterns of representative La_1−xY_x-HE compositions and LZO. Due to the large number of Y³⁺ doping levels, additional XRD patterns are included in SI Fig. S1. The refinement fitting factors, R_wp, for all samples are below 5%, indicating that the structural models are reliable. The variation in lattice parameters provides compelling evidence for the specific site occupancy of Y³⁺ in the La_1−xY_x-HE series. Initially, compared to LZO, La_1.000Y_0.000-HE exhibits a significant lattice expansion (increasing from 10.81 Å to 10.87 Å). Because the ionic radius of the multi-component dopants (Ce⁴⁺, Sn⁴⁺, Nb⁵⁺, and Y³⁺) is smaller than that of the La³⁺ cation, this expansion confirms that these elements preferentially occupy the B site rather than substituting at the A site. However, as the Y³⁺ content (x) increases, the lattice parameter gradually decreases, reaching 10.69 Å for La_0.500Y_0.500-HE. Because the ionic radius of Y³⁺ is larger than the average cationic radius of the B site (0.76 Å), the observed lattice shrinkage indicates that the additional Y³⁺ cations begin to substitute for the larger La³⁺ cations at the A site. Further quantitative evidence supporting the dual-site occupancy of Y³⁺, derived from Rietveld refinement and formation energy calculations, is provided in Section 2 of the SI. When the Y³⁺ content exceeds 0.5, the structure transforms into the defect fluorite phase with a lattice parameter of 5.31 Å, roughly half that of the pyrochlore cell. This systematic evolution of lattice parameters aligns with our occupancy design and follows Vegard's law,²⁰ confirming the formation of a high-quality solid solution.

Fig. 2 Rietveld refinement of the XRD patterns of (a) LZO and (b–d) La_1−xY_x-HE with x = 0.000, 0.500, and 0.625, respectively.

3.2 Microstructure

Fig. 3 presents the FE-SEM images and corresponding EDS elemental mapping images of La_1−xY_x-HE (represented by La_0.500Y_0.500-HE) and LZO after polishing and thermal etching at 1500 K for 1 hour. Both samples exhibit dense and uniform microstructures with clear grain boundaries, indicating excellent sintering quality and phase stability, consistent with their measured relative density exceeding 95%. The average grain size of LZO is 8.23 µm, while that of La_0.500Y_0.500-HE is significantly reduced to 3.76 µm, demonstrating that the co-doping of multiple cations effectively suppresses grain growth during high-temperature sintering. This phenomenon is commonly attributed to the sluggish diffusion effect induced by the high-entropy configuration, which impedes grain boundary migration and promotes grain refinement.²¹ The resulting finer grains lead to a higher density of grain boundaries, which are known to strongly scatter phonons. EDS elemental mapping further confirms the uniform distribution of all constituent elements within grains and at grain boundaries in both LZO and La_0.500Y_0.500-HE without secondary phase precipitation. The nominal atomic compositions are in good agreement with the EDS-measured values for LZO and La_0.500Y_0.500-HE (Table S1), with slight deviations attributed to the varying sensitivity of EDS toward different elements.

Fig. 3 FESEM and elemental mapping images of (a) LZO and (b) La_0.500Y_0.500-HE samples with (c and d) their corresponding grain size distributions.

To further investigate the chemical composition of La_1−xY_x-HE, XPS was performed on the representative La_0.500Y_0.500-HE sample. Fig. 4 shows the high-resolution XPS spectra of the substituted cations and oxygens, calibrated relative to the C 1s peak at 284.8 eV. As shown in Fig. 4(a–f), the substituted cations (Zr⁴⁺, Sn⁴⁺, Ce⁴⁺, Nb⁵⁺, and Y³⁺) in La_0.500Y_0.500-HE all exhibit their expected oxidation states. Due to the 1 : 1 ratio of Nb⁵⁺ and Y³⁺ at the B site, no additional oxygen vacancies are generated within the anionic lattice. The O 1s spectrum in Fig. 4(g) reveals three distinct chemical states of oxygen: lattice oxygen (O_lat), oxygen vacancy (O_vac), and adsorbed oxygen (O_ads). Their binding energies are 529.06 eV, 530.98 eV, and 531.51 eV, respectively, which align well with the peak positions reported by Zhao et al.²² The area ratio of the oxygen vacancy peak to the lattice oxygen peak (O_vac/O_lat) for the La_0.500Y_0.500-HE sample is calculated to be 0.12. This value is consistent with the inherent 1/8 oxygen vacancy concentration of pyrochlore.

Fig. 4 High-resolution XPS spectra of (a) La 3d, (b) Zr 3d, (c) Ce 3d, (d) Sn 3d, (e) Nb 3d, (f) Y 3d, and (g) O 1s regions for La_0.500Y_0.500-HE.

3.3 Thermal conductivity

The thermophysical properties of La_1−xY_x-HE high-entropy oxides were systematically investigated as a function of the temperature, as shown in Fig. 5. The heat capacity of all samples rises with temperature (Fig. 5(a)), ultimately nearing the Dulong–Petit limit of 3R (R is the ideal gas constant) per mole, which signifies the complete excitation of lattice vibrations at high temperatures. As displayed in Fig. 5(b), the thermal diffusivity of all samples decreases monotonically with increasing temperature, consistent with the intrinsic phonon scattering process. The porosity-corrected thermal conductivity is presented in Fig. 5(c) (enlarged in Fig. 5(d)). The traditional La₂Z₂rO₇ exhibits a distinct temperature-dependent thermal conductivity, following a 1/T trend due to dominant phonon–phonon Umklapp scattering. In contrast, the La_1−xY_x-HE samples show amorphous-like thermal transport behavior, manifesting as temperature-independent thermal conductivity from 300 to 1300 K.²³

Fig. 5 Thermal properties of La_1−xY_x-HE: (a) heat capacity, (b) thermal diffusivity, (c) thermal conductivity, (d) magnified view of (c), (e) thermal conductivity and r_A/r_B as a function of the Y³⁺ content, and (f) experimental phonon mean free path estimated using Λ_exp = 3κ/(C_vV_M).

Furthermore, Fig. 5(e) illustrates the relationship between the thermal conductivity and Y³⁺ content and the relationship between the r_A/r_B value and Y³⁺ content. High-entropy doping at the B-site of LZO reduces the thermal conductivity from 1.87 W m⁻¹ K⁻¹ to 1.24 W m⁻¹ K⁻¹, corresponding to a decrease of 33.69%. This reduction is attributed to the strong B⁴⁺–O²⁻ bonds and the severe B-site cationic disorder. In addition, the introduction of Y³⁺ at the A-site, which has a smaller cation radius than La³⁺, induces localized lattice vibrations, known as the “rattler” effect.²⁴ These vibrations act as additional phonon-scattering centers, consequently leading to a further reduction in thermal conductivity. Specifically, La_0.500Y_0.500-HE exhibits a thermal conductivity of 1.06 W m⁻¹ K⁻¹, which is only 49.55% of that of the commercial TBCs yttria-stabilized zirconia (YSZ, ∼2.4 W m⁻¹ K⁻¹).²⁵ However, as the r_A/r_B ratio decreases to 1.41, a slight increase in thermal conductivity is observed. This is because the crystal structure transforms from pyrochlore to defect fluorite, accompanied by the disappearance of the “rattler” effect.

Fig. 5(f) presents the phonon mean free path (Λ_exp) of the samples, which is estimated by the relation Λ_exp = 3κ/(C_vV_M), where C_v is the heat capacity per unit volume. Compared with LZO, the La_1−xY_x-HE system exhibits a significantly reduced phonon mean free path. Specifically, the value decreases from approximately 10 Å to 3–4 Å at room temperature. In order to make a direct comparison between the experimentally obtained phonon mean free path (Λ_exp) in La_1−xY_x-HE and the theoretical phonon mean free path (Λ_th) corresponding to atomic-scale phonon scattering, the following quantitative analysis was conducted. Generally, the phonon mean free path is dominated by grain boundary scattering, oxygen vacancies, and lattice atomic vibrations. In our work, the synthesized samples exhibit an average grain size of 3.78 µm, which is much larger than the phonon mean free path, as shown in Fig. 3. Therefore, it is justifiable to disregard the contributions of grain boundaries. Regarding oxygen vacancies, the pyrochlore oxide contains an inherent 1/8 oxygen vacancy concentration, which lacks atoms and interatomic bonds. Thus, it can be assumed that phonons are annihilated upon encountering the oxygen vacancy.²⁶ Therefore, the phonon mean free path contributed by oxygen vacancies (Λ_vac) is taken as the distance between neighboring oxygen vacancies, which is estimated as N^−1/3, where N is the number density. To demonstrate that phonon scattering has reached the atomic scale, the interatomic distance is considered as the phonon mean free path contributed by lattice vibrations (Λ_atoms), and it is used to calculate the theoretical phonon mean free path via the following equation:²⁷.

For La_0.500Y_0.500-HE, the calculated phonon mean free paths contributed by lattice atoms and oxygen vacancies are 4.81 Å and 10.69 Å, respectively. Accordingly, the theoretical phonon mean free path of La_0.500Y_0.500-HE is 3.32 Å, which closely matches the experimental values shown in Fig. 5(f). These results confirm that high-entropy doping in La_1−xY_x-HE induces lattice distortions that scatter phonons at the atomic scale.

Notably, at elevated temperatures, a slight increase in thermal conductivity is observed (Fig. 5(d)), deviating from the expected plateau of amorphous-like behavior. This abnormal behavior is primarily attributed to the semi-transparency of the TBC ceramic and the consequent radiative transfer through the sample at high temperatures.²⁸ The increase in thermal conductivity caused by radiative transfer has already drawn attention, for example, in YSZ²⁹ and Gd₂Zr₂O₇.³⁰ For better understanding, Fig. 6(a) illustrates the thermal diffusivity measurement process of a semi-transparent sample via a laser flash analyzer. A laser pulse irradiates the graphite layer on the top surface of the sample, which rapidly absorbs the optical energy and heats up, forming a localized high-temperature source. Subsequently, heat is transferred into the sample through three primary mechanisms: phonon thermal conduction, direct transmission of photons with mean free paths longer than the sample thickness, and absorption and re-emission of photons with mean free paths comparable to the sample thickness.

Fig. 6 (a) Schematic of the heat transfer process in the laser flash analyzer and (b) rear-surface temperature rise curves of the La_1.000Y_0.000-HE and La_0.500Y_0.500-HE samples, along with the fitting results using the Cape–Lehmann and Mehling models.

Fig. 6(b) presents the time-dependent temperature rise signal recorded by the InSb detector at the rear surface. A distinct abrupt rise appears just after the laser irradiates, directly reflecting the contribution of radiative transmission, with a greater rise indicating a higher transmittance. Notably, La_0.500Y_0.500-HE exhibits a significantly smaller rise compared to La_1.000Y_0.000-HE, indicating lower radiative transmittance. The Cape–Lehmann model fails to accurately characterize the thermal diffusion behavior of semi-transparent materials because it neglects radiative effects. In contrast, the Mehling model effectively eliminates the contribution from long mean free path photons (i.e., those that transmit directly across the sample), but it still accounts for the absorption and re-emission of photons, thereby increasing the thermal conductivity at high temperatures. However, this increase is insignificant for La_0.500Y_0.500-HE (Fig. 5(d)), indicating that it more effectively suppresses internal radiative transport. This stems from the fact that La_0.500Y_0.500-HE lies near the compositional boundary between pyrochlore and defect-fluorite phases, resulting in a crystal structure with a higher disorder and a greater defect concentration. These features strongly enhance the scattering of thermal radiation, thereby effectively inhibiting radiative heat transfer. As a result, La_0.500Y_0.500-HE demonstrates superior thermal barrier performance under high-temperature operating conditions.

3.4 Influence of the cationic size disorder on thermal conductivity

The reduced thermal conductivity and phonon mean free path in La_1−xY_x-HE are mainly caused by size and mass mismatches among doping ions at A- and B-sites. The corresponding size disorder (δ_r) and mass disorder (δ_m) parameters are calculated as follows:where c_i, r_i and m_i are the concentration, cation radius, and atomic mass of the i-th cation, respectively, with r̄ and m̄ being the corresponding averages. Fig. 7(a) shows the cationic disorder in La_0.500Y_0.500-HE and three other recently reported A-site high-entropy pyrochlore materials: (La_0.3Sm_0.35Gd_0.15Er_0.1Lu_0.1)₂Zr₂O₇ (HE-Zr-1),¹⁹ (La_0.2Ce_0.2Gd_0.2Er_0.2Sm_0.2)₂Zr₂O₇ (HE-Zr-2),³¹ and (La_0.2Gd_0.2Sm_0.2Er_0.2Yb_0.2)₂Zr₂O₇ (HE-Zr-3).³² It can be observed that the size and mass disorder at the B-site are generally larger than those at the A-site. This can be attributed to the smaller cation radius of B-site cations and shorter bonding distances with coordinating oxygen ions. Consequently, the B-site is more sensitive to local variations in the cation size and mass. Moreover, introducing the transition element Y³⁺ at the A-site significantly increases the A-site disorder. Correspondingly, Fig. 7(b) demonstrates that the thermal conductivity of La_1.000Y_0.000-HE is lower than that of the A-site high-entropy pyrochlore samples. In addition, the introduction of Y³⁺ at the A-site in La_0.500Y_0.500-HE further reduces the thermal conductivity due to dual-site disorder.

Fig. 7 (a) Lattice size and mass disorder for La_0.500Y_0.500-HE, HE-Zr-1,¹⁹ HE-Zr-2,³¹ and HE-Zr-3 ³² and (b) thermal conductivity of the corresponding samples.

The influence of disorder on thermal conductivity was quantitatively studied using the phonon point-defect scattering model proposed by Abeles and Slack. Based on this model, the phonon scattering parameter, Γ, is expressed as a function of atomic mass and cationic size:

where Г_m and Г_s are the phonon scattering parameters arising from mass and size disorder, respectively, and ε is the strain field factor, which can be expressed by the following:where ν is Poisson's ratio, and γ denotes the Grüneisen parameter derived from the thermal expansion coefficient (α), B, C_p, and density (ρ) as follows:

The lattice thermal conductivity of a material with point defects (k_cal) is related to that of the unmodified material (k_p) by the following expression:

where θ, V̄, h, κ_B, n, and N_A represent the Debye temperature, average volume per atom, Planck constant, Boltzmann constant, the number of atoms in the molecular formula, and Avogadro's number, respectively. The mean acoustic velocity is calculated as shown in Table S2. Using LZO as the unmodified material, the calculated thermal conductivities for La_1.000Y_0.000-HE and La_0.500Y_0.500-HE are 1.31 W m⁻¹ K⁻¹ and 1.12 W m⁻¹ K⁻¹, respectively, along with other related parameters, as summarized in Table 1. These calculated values are in close agreement with the corresponding experimental results (1.26 W m⁻¹ K⁻¹ and 1.06 W m⁻¹ K⁻¹, respectively).

Table 1 Strain field factor, Grüneisen parameter, Debye temperature, phonon scattering coefficient, and κ_cal of La_1−xY_x-HE at room temperature

Sample	ε	γ	θ (K)	Г	κ cal (W m^−1 K^−1)
La1.000Y0.000-HE	30.55	1.41	467.6	0.38	1.31
La0.500Y0.500-HE	62.32	1.01	418.0	0.52	1.12

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To further evaluate the thermal insulation performance of the La_0.500Y_0.500-HE coating in practical application environments, we conducted finite element simulations on the thermal response of TBCs under high-temperature service conditions, following the method detailed in (ref. 33 and 34).

As shown in Fig. S4, the simulation model comprises a multilayer system consisting of a Ni-based superalloy substrate, a bond coating, a thermally grown oxide layer, and a top TBC layer. The simulation results demonstrate that under identical boundary conditions (top surface at 1773 K and bottom surface at 873 K), the steady-state temperature at the bottom of the La_0.500Y_0.500-HE coating is calculated to be only 1106.0 K, significantly lower than that of the LZO (1173.6 K) and conventional YSZ (1234.2 K) systems. More importantly, the temperature at the interface of the Ni-based superalloy substrate is minimized to 1075.8 K, representing a substantial reduction compared to the corresponding values for LZO (1135.2 K) and YSZ (1187.8 K). This superior thermal insulation performance directly stems from the ultralow thermal conductivity of the La_0.500Y_0.500-HE material. This suggests that the application of such advanced TBCs in gas turbines could enable higher turbine inlet temperatures and significantly extend the blade service life by reducing the thermal load on the metallic substrate.

3.5 Thermal expansion

The mismatch in thermal expansion coefficients between TBCs and the alloy substrate can cause interfacial crack growth and coating spallation. Therefore, it is crucial to increase the thermal expansion coefficient of TBCs to approach that of the alloy substrate. As shown in Fig. 8(a), the thermal expansion ratio of La_1−xY_x-HE increases linearly with temperature. There is no abrupt volume change, suggesting good phase stability in these materials.

Fig. 8 Thermal expansion behavior of La_1−xY_x-HE: (a) thermal expansion ratio (dL/L₀), (b) thermal expansion coefficient, and (c) thermal expansion coefficient and lattice constant as a function of the Y³⁺ content.

This conclusion is further supported by the thermogravimetric-differential scanning calorimetry (TG-DSC) curves and in situ XRD patterns of La_0.500Y_0.500-HE, as shown in Fig. S5. Fig. 8(b) displays the thermal expansion coefficient of La_1−xY_x-HE. The thermal expansion coefficient below 400 K can be ignored because of strain release between the sample and fixture, which causes anomalous behavior in the measured data. Above 400 K, the thermal expansion coefficient of all samples increases monotonically with temperature. The thermal expansion coefficient of the material is inversely correlated with its lattice energy (U), as described by the following equation:

where M, z, e, r₀, and n represent Madelung's constant, the ionic charge, the electron charge, the interionic distance, and Born's constant, respectively. Therefore, increasing the temperature results in an increase in the interionic distance and bond lengths, which elevates the thermal expansion coefficient. To better analyze the influence of A-site and B-site doping on the thermal expansion coefficient, the thermal expansion coefficients of the samples are shown in Fig. 8(c), along with the evolution of the lattice constant as a function of the A-site Y doping content.

The introduction of cations such as Ce⁴⁺, Sn⁴⁺, Nb⁵⁺, and Y³⁺ at the B-site of LZO leads to an increase in the lattice parameter. Specifically, Rietveld refinement reveals that the B⁴⁺–O²⁻ bond length increases from 2.105 Å to 2.119 Å, resulting in a rise in the thermal expansion coefficient from 9.25 × 10⁻⁶ K⁻¹ to 10.01 × 10⁻⁶ K⁻¹. When the small-radius ion Y³⁺ is introduced at the A-site, the lattice parameter and the A³⁺–O²⁻ bond length decrease. However, the thermal expansion coefficient shows no significant reduction. This can be explained by the fact that B⁴⁺–O²⁻ bonds are shorter than the A³⁺–O²⁻ bonds, and B-site cations constitute the crystal framework, making them more responsive to variations in the dopant cation radius. La_0.500Y_0.500-HE exhibits a thermal expansion coefficient of 10.01 × 10⁻⁶ K⁻¹, equivalent to 91.82% of YSZ. As the Y-doping content exceeds 0.5, the samples exhibit a defective fluorite phase, accompanied by a slight increase in the thermal expansion coefficient. This is because the A-site and B-site ions are randomly distributed among the 4a Wyckoff positions, and the cation radius of the subsequently doped Y is larger than the average cation radius at the 4a sites. Consequently, a promising strategy for enhancing the thermal expansion coefficient is to incorporate larger-radius ions at the B-site of the pyrochlore crystal.

Fig. 9 presents a comparison of the thermal resistivity (1/κ, m K W⁻¹) and thermal expansion coefficient of the La_0.500Y_0.500-HE synthesized in this work and other candidate TBC materials reported in the literature.^6,35–43 An ideal TBC should exhibit high thermal resistivity for effective thermal insulation and a high thermal expansion coefficient to ensure compatibility with Ni-based superalloy substrates. The results show that La_0.500Y_0.500-HE exhibits the highest thermal resistivity while maintaining a thermal expansion coefficient comparable to that of commercial YSZ. To quantitatively evaluate the balance between the thermal insulation capability and thermal expansion compatibility, we introduce the ratio of α/κ as an indicator of merit for TBC performance. La_0.500Y_0.500-HE exhibits an α/κ value of 9.42, which is significantly better than those of commercial YSZ (4.17) and LZO (4.95), indicating its superior synergy between thermal insulation and thermal expansion matching with the metallic substrate.

Fig. 9 Comparison of the thermal resistivity versus thermal expansion coefficient of La_0.500Y_0.500-HE and other typical TBC materials.^6,35–43

3.6 Mechanical properties

Fig. 10 and Table S3 show the mechanical properties of the samples. The Vickers hardness of LZO is 6.32 GPa, consistent with the results reported by Li et al.⁴⁴ In comparison, the hardness of La_1−xY_x-HE has been significantly enhanced, with values exceeding 9.50 GPa. This can be primarily attributed to the refined grain size, as shown in Fig. 3. Furthermore, the hardness gradually increases with a higher Y-doping content at the A-site. La_0.500Y_0.500-HE achieves a hardness of 9.86 GPa, which corresponds to 75.85% of YSZ.⁴⁵ This trend is likely due to the doping of smaller Y³⁺ cations strengthening the A³⁺–O²⁻ bond. In addition, the refined grain increases crack deflection, leading to additional fracture energy dissipation. Consequently, the fracture toughness of La_0.500Y_0.500-HE increases from 1.98 MPa m^1/2 to 2.46 MPa m^1/2, approximately 84.83% of YSZ.⁴⁵ High hardness and fracture toughness are beneficial for TBCs to resist erosion and suppress crack propagation. The elastic modulus is another crucial mechanical property. Notably, a lower Young's modulus is desirable for TBCs because it improves strain tolerance and mitigates interfacial stresses during thermal cycling. La_0.500Y_0.500-HE exhibits a Young's modulus of 133.4 GPa, decreased from 187.7 GPa for LZO, which corresponds to 65.07% of YSZ.⁴⁵ This reduction stems from its highly disordered crystal structure, which significantly weakens the effective elastic response. This reduced modulus effectively mitigates stresses arising from thermal expansion mismatch in TBCs.

Fig. 10 Vickers hardness and Young's modulus as a function of the Y³⁺-doping content in La_1−xY_x-HE.

To provide a comprehensive evaluation of La_0.500Y_0.500-HE, we conducted a comparative analysis of its thermomechanical properties against other high-entropy pyrochlores, as well as commercial YSZ and LZO, using the radar charts shown in Fig. 11 and S6. Compared to other La_1−xY_x-HE compositions, La_0.500Y_0.500-HE exhibits a significantly larger coverage area in the radar chart, indicating superior synergistic optimization in terms of the density, thermal conductivity, thermal expansion coefficient, Vickers hardness, and Young's modulus. Although La_0.500Y_0.500-HE shows a slightly lower Vickers hardness and thermal expansion coefficient than conventional YSZ, this minor trade-off is more than compensated for by its significantly lower thermal conductivity, lower density, and reduced Young's modulus (which is highly beneficial for improving the strain tolerance of the coating). Overall, the maximized coverage area of the radar chart for La_0.500Y_0.500-HE visually and quantitatively confirms that it represents the optimal compromise between extreme thermal insulation performance and mechanical reliability.

Fig. 11 Radar charts of the comprehensive properties of La_1−xY_x-HE.

4 Conclusion

In the present work, a series of dual-site disorder high-entropy oxides, La_1−xY_x-HE, were successfully synthesized via a solid–state reaction, and their phase composition, thermophysical properties, and mechanical properties were systematically evaluated. The results are summarized as follows:

(i) With increasing A-site Y³⁺ content, La_1−xY_x-HE undergoes a structural transition from pyrochlore to defect-fluorite, with the pyrochlore phase retained for x ≤ 0.5. The systematic variation of the lattice parameters, following Vegard's law, confirms the simultaneous incorporation of Y³⁺ into both A and B sites. Moreover, the sluggish diffusion effect leads to a significant reduction in the grain size of La_0.500Y_0.500-HE to 3.76 µm, with all elements uniformly distributed and maintaining the expected valence state.

(ii) La_1−xY_x-HE exhibit amorphous-like ultralow thermal conductivity, which markedly deviates from the 1/T behavior in La₂Zr₂O₇. The thermal conductivity of La_0.500Y_0.500-HE decreases from 1.87 W m⁻¹ K⁻¹ in LZO to 1.06 W m⁻¹ K⁻¹, representing only 49.6% of commercial YSZ. The significant suppression of thermal transport is attributed to pronounced dual-site disorder, caused by Y³⁺ occupation at multiple sites and the high configurational entropy at the B site.

(iii) The thermal expansion coefficient of La_1−xY_x-HE monotonically increases with temperature within the range of 400–1300 K, exhibiting no phase transition or volume change. B-site high-entropy doping effectively increases the B⁴⁺–O²⁻ bond length from 2.105 Å to 2.119 Å, thereby raising the thermal expansion coefficient from 9.25 × 10⁻⁶ K⁻¹ to 10.01 × 10⁻⁶ K⁻¹, which is comparable to that of YSZ and demonstrates favorable thermal expansion compatibility.

(iv) La_0.500Y_0.500-HE exhibits a Vickers hardness of 9.86 GPa (75.85% of YSZ) and an increased fracture toughness of 2.46 MPa m^1/2 (84.83% of YSZ). Concurrently, its Young's modulus is reduced to 133.4 GPa (65.07% of YSZ). This combination of higher hardness and toughness, together with a lower modulus, contributes to the enhancement of erosion resistance, suppression of crack propagation, and improvement of strain tolerance.

In summary, La_0.500Y_0.500-HE exhibits excellent phase composition, thermophysical properties, and mechanical properties. Furthermore, the dual-site disorder engineering provides an effective strategy for designing next-generation TBCs with superior thermal insulation performance.

Author contributions

Zide Wu: conceptualization, methodology, validation, and writing – original draft. Yuning Cao: formal analysis, methodology, and validation. Jiaxin Xue: methodology and validation. Tianyixiao Yang: methodology and validation. Zhiyuan Ma: investigation. Mu Li: conceptualization, supervision, resources, and writing – review and editing. Dawei Tang: supervision and resources.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting the findings of this study, including phase composition analysis, microstructural characterization, thermophysical property measurements, and mechanical property evaluations, are available within the article and its supplementary information (SI). Supplementary information: detailed experimental methods (XRD, SEM, XPS, LFA, thermal dilatometer, ultrasonic reflection, Vickers hardness); Rietveld refinement of XRD patterns; finite element simulation results of thermal response in TBC systems; TG-DSC and in situ XRD analysis for high-temperature phase stability; tables providing nominal/measured elemental compositions, acoustic velocities, and mechanical properties (Young's modulus, shear modulus, bulk modulus, Poisson's ratio, Vickers hardness, fracture toughness) of the synthesized samples. See DOI: https://doi.org/10.1039/d6ta01569g.

Acknowledgements

This research was funded by the National Natural Science Foundation of China (Grant No. 52306210) and the Liaoning Revitalization Talents Program (Grant No. XLYC2403080) and partially supported by the National Natural Science Foundation of China (No. 52175496).

Notes and references

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