Extreme-mixing-boosted CMAS corrosion resistance and thermophysical properties in high-entropy rare-earth disilicates

Abstract

Superior calcium–magnesium–alumino–silicate (CMAS) corrosion resistance, along with favorable thermophysical properties, is crucial for high-entropy rare-earth disilicates (HEREDSs) to be used as environmental barrier coatings. To achieve this goal, we expand the composition space of HEREDSs and develop 9- to 16-cation HEREDSs using a laser-driven synthesis technique. Specifically, the intensified sluggish diffusion effect induced by extreme elemental mixing and the superior stability of the F-type phase in HEREDSs is beneficial for reducing the dissolution rate of the formed multicomponent apatite in the CMAS melt, while the inclusion of more elements with great atomic weight differences can induce phase separation, leading to deteriorated corrosion behavior. As a result, the synthesized (Lu, Yb, Tm, Er, Ho, Dy, Gd, Sm, Nd, Pr, Ce, La, Eu, Tb)₂Si₂O₇ (14HEREDS) is found to demonstrate superior CMAS corrosion resistance with a low corrosion rate of 6.7 μm h⁻¹ at 1400 °C for 48 h. Moreover, remarkable thermophysical properties, including superior phase stability over 1600 °C, extremely low room temperature thermal conductivity (1.05 W m⁻¹ K⁻¹), and excellent match of coefficient of thermal expansion (5.4 × 10⁻⁶ K⁻¹) with SiC_f/SiC composites (4.5–5.5 × 10⁻⁶ K⁻¹), are observed in the synthesized 14HEREDS. Our work develops a novel material with remarkable CMAS corrosion resistance and thermophysical properties, showing great promise for environmental barrier coating applications.

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New concepts

Exploiting high-entropy rare-earth disilicates (HEREDs) with significantly enhanced calcium–magnesium–aluminum–silicate (CMAS) corrosion resistance, along with exceptional thermophysical properties, is vital for potential applications as environmental barrier coatings (EBCs) on SiC_f/SiC composites. However, this goal has not been achieved yet.

In this work, we achieve the profound enhancement of CMAS corrosion resistance in a novel 14-cation HERED (14HERED) through extreme elemental mixing using a laser-driven synthesis technique. The superior CMAS corrosion resistance is attributed to the aggravated sluggish diffusion effect induced by extreme elemental mixing and the superior stability of the F-type phase, which markedly reduces the dissolution rate of the formed apatite in the CMAS melt. Additionally, the as-developed 14HERED also demonstrates remarkable thermophysical properties, including superior phase stability over 1600 °C, extremely low thermal conductivity, and excellent match of coefficient of thermal expansion with SiC_f/SiC composites. These impressive and comprehensive properties have surpassed those of previously reported EBC materials, positioning our material as a promising candidate for next-generation EBC applications.

1. Introduction

Since their discovery in 2015, high-entropy ceramics, as a class of innovative high-entropy inorganic materials, have garnered significant attention owing to their vast composition space and widely tunable properties.^1–4 This growing interest has led to the rapid development of high-entropy ceramics, branching into various categories, such as high-entropy carbides,^5–10 high-entropy borides,^11–19 high-entropy nitrides,^20–22 and high-entropy oxides.^23–29 In particular, as a distinguished class of high-entropy oxides, high-entropy rare-earth disilicates (HEREDSs) stand out for their remarkable calcium–magnesium–aluminum silicate (CMAS) corrosion resistance, excellent high-temperature stability, reduced thermal conductivity, and well-matched coefficients of thermal expansion (CTEs) with SiC_f/SiC composites.^30–34 Benefiting from these exceptional properties, HEREDSs have become the leading candidates for environmental barrier coating (EBC) materials.

As the demand for future practical EBC applications increasingly grows, further enhanced CMAS corrosion resistance, coupled with outstanding thermophysical properties, is highly needed. To meet these stringent requirements, considerable efforts have been devoted to the development of HEREDSs, and notable advancements in improving CMAS corrosion resistance and thermophysical properties have been achieved. For example, Sun et al.³⁵ reported a novel (Gd_1/6Tb_1/6Dy_1/6Tm_1/6Yb_1/6Lu_1/6)₂Si₂O₇ HEREDS with a γ-type phase that exhibited excellent thermal stability at 1900 °C. Meanwhile, Chen et al.³³ demonstrated that (Yb_0.2Y_0.2Lu_0.2Ho_0.2Er_0.2)₂Si₂O₇ performed better in CMAS corrosion resistance than individual Yb₂Si₂O₇ and Lu₂Si₂O₇. In addition, Kavak et al.³⁶ developed a novel (Y_0.25Er_0.25Tm_0.25Yb_0.25)₂Si₂O₇ HEREDS with outstanding CMAS corrosion resistance (a corrosion depth of 176.73 μm at 1300 °C for 24 h), low room-temperature (RT) thermal conductivity (2.86 W m⁻¹ K⁻¹), close CTE (2.4–4.8 × 10⁻⁶ K⁻¹) to SiC_f/SiC composites, and high thermal stability (1300 °C). Recently, we successfully prepared a series of 3- to 8-cation HEREDSs (3–8HEREDSs) and found that 7HEREDS exhibited outstanding CMAS corrosion resistance, due to their low chemical activity and relatively high configuration entropy.²⁶ Considering the huge composition space of HEREDSs, it is promising to exploit HEREDSs with further improved CMAS corrosion resistance and comprehensive thermophysical properties. However, the limited accessible composition space in previous research studies has severely hindered the advancement of HEREDSs as next-generation EBC materials.

In this work, we greatly expand the composition space of HEREDSs and successfully synthesized 9- to 16-cation HEREDSs (9–16HEREDSs, see Table S1 for specific compositions) using a laser-driven synthesis technology. Particularly, the desired superior CMAS corrosion resistance and thermophysical properties, including high thermal stability, ultralow thermal conductivity, and good CTE match with SiC_f/SiC composites, are achieved in the synthesized 14HEREDS. Further experimental and theoretical studies show that the impressive CMAS corrosion resistance of 14HEREDS is attributed to the significantly reduced diffusion rate of the formed multicomponent apatite in the CMAS melt, which is induced by the inherent superior stability of the F-type structure and the intensified sluggish diffusion effect from the markedly enhanced configurational entropy. The developed 14HEREDS with remarkable CMAS corrosion resistance and comprehensive thermophysical properties are promising for future EBC applications.

2. Results and discussion

Leveraging the profound expansion of accessible compositional space of HEREDSs due to ultrahigh temperatures up to ∼3600 °C within milliseconds (Fig. S1), which facilitates the full solid-solution reactions, concurrent with the formation of cavitation bubbles to prevent the evaporation of volatile raw oxides,³⁷ we synthesized 9–16HEREDSs using the newly developed laser-driven synthesis technique. Fig. 1a illustrates the X-ray diffraction (XRD) patterns of the as-fabricated 9–16HEREDS samples, revealing the presence of two distinct phases among these HEREDSs: the E-type phase (space group Pnma) and the F-type phase (space group P1̄). Particularly, only a single E-type phase or F-type phase can be found in the as-fabricated 9–10HEREDS and 12–14HEREDS samples, respectively (Fig. S2 and Table S2), while both E- and F-type phases can be observed in the as-fabricated 11HEREDS, 15HEREDS, and 16HEREDS samples. Such a phase separation in HEREDSs may result from the variations in average RE³⁺ ionic radius (r̅), lattice size difference (δ_r), or atomic weight difference (δ_g). Previous studies have identified r̅ as a key factor in determining the phase types of REDSs.³⁸ Fig. 1b displays the polymorphic formation diagram, where 9–16HEREDSs are all predicted to be the E-type phase. However, given the discrepancy between the theoretical and practical r̅, the threshold for the polymorphic transition may shift (dashed line). Consequently, 11HEREDS, which has a median r̅ among all 9–16HEREDSs, shows a dual-phase structure. Additionally, δ_r and δ_g may also influence the phase of HEREDSs, which can be calculated as follows:where n is the number of RE species, n_i is the molar fraction of the ith RE, a_i, b_i, and c_i are the corresponding lattice parameters of individual RE₂Si₂O₇. g_i and g̅ are the atomic weight of individual RE₂Si₂O₇ and the average atomic weight of all individual RE₂Si₂O₇, respectively. a̅, b̅, and c̅ are the average lattice parameters of HEREDSs. As shown in Fig. 1c, the δ_r values of different components with the same phase do not vary significantly, signifying that δ_r is not the fundamental factor for the phase separation in the synthesized 15HEREDS and 16HEREDS samples. Intriguingly, with the same elements, δ_r of the F-type phase is lower than that of the E-type phase (red circle), suggesting that the F-type phase may be more stable. To clarify the reason for the phase separation of 15HEREDS and 16HEREDS samples, we further evaluated δ_g. Obviously, larger δ_g can be found in 15HEREDS and 16HEREDS, reaching 13.5% and 23.2%, respectively. During the synthesis, atoms with smaller (larger) masses are expected to diffuse faster (slower), leading to elemental inhomogeneity.³⁹ Consequently, mixing elements with substantial δ_g results in the phase separation of HEREDSs. Combined with back-scattered electron (BSE) images (see Fig. 1d) and energy dispersive spectroscopy (EDS) analyses (Fig. 1e and Table S3), the as-fabricated 9HEREDS and 14HEREDS samples can be confirmed to have uniform elemental distributions. Notably, the 15HEREDS sample exhibits distinct grey and black phases, whereas 11HEREDS shows no morphological differences. Given the phase separation found in both samples, such a difference may come from the inhomogeneous distributions of elements with significant δ_g, namely, the heavier the atoms, the brighter the phases. Additionally, all the samples are fully dense, with densities ranging from 92.9% to 94.1% (see Table S4), indicating the successful fabrication of HEREDS with high density.

Fig. 1 Phase, microstructural, and elemental analyses of 9–16HEREDS samples. (a) XRD patterns. (b) Polymorphic formation diagram. (c) Calculated lattice size difference δ_r and atomic weight difference δ_g (d) BSE images of 9HEREDS, 11HEREDS, 14HEREDS, and 15HEREDS samples. (e) EDS mappings of the 14HEREDS sample.

Next, the CMAS corrosion resistance of the 9–16HEREDS samples at 1400 °C for 48 h was evaluated. As summarized in Fig. 2a, the corrosion depths of samples exhibit a downward trend with an increasing number of elements and reach a minimum of 324 ± 5.8 μm at 14HEREDS before slightly increasing. The initial linear relationship in 9–14HEREDSs indicates that configurational entropy is key to the CMAS corrosion resistance of HEREDSs. Given the significant phase separation in 15HEREDS and 16HEREDS (see Fig. 1a), it can be inferred that the phase structure also strongly affects their corrosion performance, leading to an increasing trend in these samples. To reveal the corrosion resistance mechanisms of 9–16HEREDSs against CMAS, we conducted characterization of the morphology and phase structure of post-corrosion samples. Fig. 2b–d display the BSE images of 9HEREDS, 14HEREDS, and 15HEREDS samples, respectively (others can be seen in Fig. S3). All HEREDS samples can be divided into three distinct regions based on morphology: (i) CMAS layer, (ii) reaction layer, and (iii) HEREDS substrate. Specifically, the reaction layer features a mixture of the CMAS melt and the corrosion product apatite (with increased circularity (C) as configurational entropy increases; see Fig. S4), as confirmed by XRD (Fig. 2e–g) and EDS analyses (Fig. S5, S6 and Table S5). According to previous work,^26,29,40 the volume fraction of the reaction layer plays a crucial role in resisting CMAS penetration. However, the volume fractions of reaction layers shown in Fig. 3a fluctuate within a small range, signifying their marginal impact on the differences in the corrosion resistance of 9–16HEREDSs. Note that only the F-type phase is detected on the surfaces of 9–11HEREDS samples, with no evidence of the E-type phase. This suggests that the E-type phase is unstable in the CMAS melt, and there exists a phase transformation from E- to F-type phases in 9–11HEREDSs during CMAS corrosion. To further confirm the preference of phase transition from E to F types, density functional theory (DFT) simulations were conducted. As shown in Fig. 3b, the Gibbs free energy (ΔG) for this phase transition is negative, showing that the F-type phase is more energetically preferable than the E-type phase in the CMAS melt. Thereby, 15HEREDS and 16HEREDS, with the combination of F- and E-type phases, demonstrate decreased CMAS corrosion resistance compared to pure F-type 12–14HEREDSs.

Fig. 2 CMAS corrosion tests of 9–16HEREDSs at 1400 °C for 48 h. (a) CMAS corrosion depths. Cross-section BSE images of the as-fabricated (b) 9HEREDS, (c) 14HEREDS, and (d) 15HEREDS samples. XRD patterns of the as-fabricated (e) 9–11HEREDSs, (f) 12–14HEREDSs, and (g) 15–16HEREDSs.

Fig. 3 (a) Volume fractions of apatite in the reaction layers of 9–16HEREDSs. (b) ΔG from E- to F-type phases. (c) SEM image of the 14HEREDS sample after annealing at 1400 °C for 10 h. (d) Grain size histograms of the 14HEREDS sample measured from (c). (e) Average grain sizes of 12–14HEREDSs before and after annealing at 1400 °C for 10 h. (f) Grain growth velocities of 12–14HEREDSs at 1400 °C. (g) D of the elements in 12HEREDS and 14HEREDS samples. (h) Average (abbreviated as Avg) D of all elements in 12HEREDS and 14HEREDS samples.

It is noteworthy that, unlike previously reported HEREDSs with 4–7 cations,²⁶ the infiltration region, characterized by the infiltration of the CMAS melt along HEREDS boundaries, is not observed in our 9–16 HEREDS series. Therefore, it is reasonable to hypothesize that increasing configurational entropy can effectively enhance the stability of HEREDS in the CMAS melt through the sluggish diffusion effect, thereby inhibiting the infiltration of the CMAS melt along grain boundaries. To validate the positive role of configurational entropy in enhancing the CMAS corrosion resistance of HEREDSs, we then established the relationship among configurational entropy, the sluggish diffusion effect, and CMAS corrosion resistance by studying the grain growth rates of 12–14 HEREDS samples before and after annealing at 1400 °C. Fig. 3c displays the scanning electron microscopy (SEM) image of the representative 14HEREDS sample after annealing at 1400 °C for 10 h (others can be seen in Fig. S7), where grains and grain boundaries can be clearly observed. Based on these SEM images, the grain sizes of these HEREDS samples were also quantified. Taking 14HEREDS as an example, its average grain size (μ_g) can be fitted at 1.1 ± 0.05 μm using Gaussian function fitting (Fig. 3d). Fig. 3e exhibits the μ_g of 12–14 HEREDSs before and after annealing, revealing that grain sizes increase more slowly during 1400 °C annealing with increasing configurational entropy. Moreover, Fig. 3f shows the calculated growth rates, which decrease from 1.16 nm h⁻¹ to 1.03 nm h⁻¹ for 12–14 HEREDSs, indicating intensified sluggish diffusion due to the incorporation of more elements.

Meanwhile, a comparative study between 12HEREDS and 14HEREDS using ab initio molecular dynamics (AIMD) simulations was conducted to further confirm the sluggish diffusion effect. Fig. 3g and h clearly demonstrate that the average D of all elements in 14HEREDS is markedly lower than that in 12HEREDS (1.63 × 10⁻⁶ cm² s⁻¹ vs. 4.37 × 10⁻⁶ cm² s⁻¹), coupled with the increased range (R) of diffusion coefficients from 1.28 × 10⁻⁶ cm² s⁻¹ to 1.55 × 10⁻⁶ cm² s⁻¹ as the δ_g increases from 7.68% to 8.22%. These simulation results, together with experimental observations, offer robust evidence that the increased configurational entropy in HEREDSs can enhance their stability in the CMAS melt due to amplified sluggish diffusion, and eventually, lead to the enhanced CMAS corrosion resistance of HEREDSs.

To further investigate the CMAS corrosion behavior of the optimal 14HEREDS over a wider temperature range, corrosion kinetics were performed from 1300 °C to 1500 °C. As depicted by the kinetic curves in Fig. 4a, the corrosion depths of 14HEREDS samples at different temperatures exhibit a parabolic increase as the corrosion time increases. Specifically, after 48 h of exposure, the measured corrosion depths are 160 ± 6.7 μm, 324 ± 5.8 μm, and 453 ± 27.5 μm at 1300 °C, 1400 °C, and 1500 °C, respectively. Fig. 4b demonstrates that the corrosion depth increased linearly according to the square root of the corrosion time, where the parabolical parameter k increases from 23 to 51 as the corrosion temperature rises from 1300 °C to 1500 °C. The adherence to the parabolical law indicates that the CMAS corrosion process of 14HEREDS is controlled by the infiltration of the CMAS melt, showcasing superior CMAS corrosion resistance across a broad temperature range. Fig. 4c displays the XRD patterns of post-corrosion samples, validating their identical corrosion products across 1300–1500 °C. Fig. 4d and e show the cross-sectional BSE images of 14HEREDS samples after CMAS corrosion at 1300 °C and 1500 °C for 48 h, respectively (others can be seen in Fig. S8). Beyond the distinct reaction layer composed of slender particles, no infiltration regions can be observed in 14HEREDS samples at each temperature. EDS analysis also provided more substantial confirmation that all the corrosion products are apatite phases (see Fig. 4f and Table S6), further verifying the benefit of the sluggish diffusion effect in hindering the elemental diffusion of HEREDSs due to the increased configurational entropy. Eventually, we benchmarked 14HEREDS against other reported EBC materials using the same CMAS melt. As shown in Fig. 4g, our as-developed 14HEREDS exhibits significantly lower corrosion rates across 1300–1500 °C, surpassing previously reported rare-earth monosilicates (REMSs),⁴¹ REDSs,^42–44 HEREDSs,^26,29,45,46 and partial high-entropy rare-earth monosilicates (HEREMSs).^47–49

Fig. 4 CMAS corrosion resistance of the 14HEREDS sample at different temperatures for 48 h. (a) Corrosion depth as a function of corrosion time. (b) Corrosion depth as a function of the square root of corrosion time. (c) XRD patterns of samples after CMAS corrosion at 1300 and 1500 °C. Cross-section BSE images of samples post-corroded at (d) 1300 °C and (e) 1500 °C for 48 h. (f) EDS spot analyses of (d) and (e). (g) CMAS corrosion rates of the 14HEREDS and other reported EBC materials.^{26,29,41–49}

Besides CMAS corrosion resistance, other crucial parameters for the potential application of 14HEREDS as EBC materials, including melting point, high-temperature stability, thermal conductivity, and CTE, were also evaluated. We directly measured the melting point of 14HEREDS using a laser-assisted method.⁵⁰ Experimentally, the 14HEREDS sample was rapidly heated to approximately 2500 °C by the laser, followed by its deactivation to induce rapid cooling. Theoretically, upon reaching the solidification point, the release of latent heat generated a thermal arrest, manifesting as the emergence of a melting plateau in the cooling curve. As clearly shown in Fig. 5a, a melting plateau is observed at around 1630 °C, which is therefore determined to be the melting point of 14HEREDS. Fig. 5b demonstrates that the melting point of 14HEREDS is lower than the prediction from the rule of mixtures based on its individual components. This phenomenon may be attributed to the deviation of melting points between different phase types (see Table S7). Subsequently, we subjected 14HEREDS samples to isothermal and thermal cycling conditions to evaluate their high-temperature stability. After isothermal treatment at 1600 °C for 10 h in a furnace or thermal cycling at 1600 °C for 4 cycles using the laser platform,⁵¹ no phase changes were observed, indicating exceptional high-temperature phase stability of 14HEREDS (see Fig. 5c). Fig. 5d illustrates the thermal conductivity of the 14HEREDS sample, which was measured to slightly increase from 1.05 W m⁻¹ K⁻¹ to 1.52 W m⁻¹ K⁻¹ with increasing temperature from RT to 1200 °C. Such an ultralow thermal conductivity regime primarily originates from severe lattice distortion that causes strong strain-field fluctuations and intense phonon scattering.⁵² Ultimately, the CTE of 14HEREDS was tested. As evidenced in Fig. 5e, the values exhibit a monotonic increase from 4.8 × 10⁻⁶ K⁻¹ to 5.5 × 10⁻⁶ K⁻¹ as the temperature rises from 200 °C to 1300 °C, demonstrating exceptional CTE match with SiC_f/SiC composites (4.5–5.5 × 10⁻⁶ K⁻¹) across a wide temperature range. It is evident that 14HEREDS displays the lowest thermal conductivity while aligning its CTE match with SiC_f/SiC composites (see Fig. 5f).^{29,36,49,53–58} Integrating these remarkable thermophysical properties, the as-developed 14HEREDS is a promising candidate for next-generation EBC applications.

Fig. 5 Thermophysical properties of the 14HEREDS sample. (a) Temperature vs. time curve during measurement. (b) Melting point comparison of the 14HEREDS sample with individual components. (c) XRD patterns of the samples after isothermal (1600 °C for 10 h) and thermal cycling (1400 °C for 4 cycles) tests. (d) Thermal conductivity across RT–1200 °C. (e) Average CTE across 200–1200 °C. (f) Thermal conductivity vs. average CTE at RT of the 14HEREDS sample compared to other reported REM, RED, HEREM, and HEREDS materials.^{29,36,49,53–58}

3. Conclusion

In summary, we have successfully expanded the composition space of HEREDSs and developed a new 14HEREDS with exceptional CMAS corrosion resistance and thermophysical properties through extreme elemental mixing. Specifically, we show that the F-type 14HEREDS with extreme elemental mixing is thermodynamically more stable in the CMAS melt due to the sluggish diffusion effect, resulting in superior CMAS corrosion resistance compared to HEREDSs with fewer elements. Meanwhile, more elemental incorporation, e.g., up to 16 principal elements, may induce phase separation owing to aggravated atomic differences, leading to inferior CMAS corrosion resistance. In addition to CMAS corrosion resistance, the 14HEREDS also demonstrates impressive thermophysical properties, including superior phase stability up to 1600 °C, extremely low thermal conductivity of 1.05 W m⁻¹ K⁻¹ at RT, and the remarkable CTE match (5.4 × 10⁻⁶ K⁻¹) with SiC_f/SiC composites. This study presents a new HEREDS that shows promise for EBC applications.

4. Experimental

4.1. Sample preparation

9–16HEREDS samples were fabricated through a two-step procedure. As listed in Table S8, raw materials consist of commercially available SiO₂ and RE oxide powders. A continuous-wave fiber laser operating at 1080 nm (RFL-C3000S, Raycus Fiber Laser Technology Co., Ltd, Beijing, China) served as the heating source. First, raw materials were weighed according to stoichiometric proportions and homogenized via planetary ball milling for 6 h. After drying, the mixtures were placed into graphite crucibles and uniformly compacted. The synthesis of HEREDSs was then carried out using a custom-built laser-driven synthesis platform, equipped with an infrared pyrometer (GmbH M313, SensorTherm, Bavaria, Germany) and operated at 1500 W. The temperature versus time curves during laser-driven synthesis are shown in Fig. S1. The resulting powders were subsequently heat-treated at 1200 °C for 10 h in air to eliminate laser-induced oxygen vacancies. Second, the treated powders were ball-milled for 12 h, followed by 3 min uniaxial pressing at a pressure of 10 MPa to form green pellets (∅ 16 mm × 6 mm). These pellets were then densified by cold isostatic pressing at a pressure of 250 MPa for 3 min. Dense bulk samples were eventually obtained by sintering the pellets in air at 1600 °C for 12 h. It should be noted that the variation in initial grain size across the HEREDS series is primarily due to the differing particle sizes of HEREDS powders. The laser particle size analysis (Fig. S9) revealed that the average particle sizes of the treated powders for the 12HEREDS sample are significantly smaller than those for the 14HEREDS sample (e.g., D_v90 values of 2.61 and 4.92 μm, respectively), resulting in a relatively large initial grain size of the 14HEREDS sample.

4.2. CMAS corrosion tests

To evaluate CMAS corrosion resistance, a standard CMAS composition (33CaO–9MgO–13Al₂O₃–45SiO₂) was used. The CMAS powders, whose preparation has been detailed in our previous work,^26,40,59 were pressed at 5 MPa for 3 min into pellets (∅ 6 mm × 2 mm). Each pellet, with a loading of 30 mg cm⁻², was placed at the center of the synthesized 9–16HEREDS samples. Finally, the CMAS corrosion resistance of the samples was evaluated by heating them to the desired temperatures. The corrosion depth, defined as the distance from the original surface to the reaction front, and the volume fraction of reaction products were measured from three samples using Image J software to ensure statistical reliability. The circularity C of 9- to 16HEREDS samples based on SEM images was calculated using the following formula:where S is the area and P is the perimeter. Statistical data on C values are calculated through Gaussian fitting based on at least 50 individual apatite particles.

4.3. Thermophysical properties

Melting points of 14HEREDS samples were determined using the laser heating platform. Measurements were conducted at a laser power of 400 W, with a uniform laser beam (∅ 3 mm) focused on the center of the samples. The emissivity for the infrared temperature measurement was set to 0.9. Subsequently, the laser was deactivated immediately upon full melting of the samples. To ensure accuracy, three samples were tested for each condition, and at least five random areas were measured for each sample.

The high-temperature stability of the 14HEREDS sample was assessed via isothermal and thermal cycling tests, using a conventional furnace and a laser heating platform, respectively. For the isothermal test, the 14HEREDS sample was heated to 1600 °C at a heating rate of 5 °C min⁻¹ in air, held at that temperature for 10 h, and naturally cooled to RT (see Fig. S10a). For the thermal cycling test, the 14HEREDS sample underwent four cycles, each comprising rapid heating to approximately 1600 °C and a five-minute hold at that temperature, followed by naturally cooling (see Fig. S10b).

The CTE of the synthesized 14HEREDS sample was investigated using the thermal expansion instrument (DIL 402 Expedis Supreme, Netzsch, Germany) from 200 °C to 1300 °C at a heating rate of 10 °C min⁻¹ in air. The thermal conductivity (κ_T) of the as-fabricated 14HEREDS sample was tested by the laser flash analysis (LFA467, Netzsch, Germany) from RT to 1000 °C at a heating rate of 5 °C min⁻¹ in air. Then, the real thermal conductivity (κ_t) was measured using the following formulas:

where the experimental density (ρ) of the samples was calculated according to the Archimedes drainage method, and the theoretical density (ρ_t) can be calculated according to the following formula:where N represents the number of molecules in the unit cell, M is the molar mass of the crystalline substance, N_A is the Avogadro's constant, and V is the volume of the unit cell, which can be calculated as follows:
where a, b, c, α, β, and γ are the unit parameters obtained from the XRD Rietveld refinements.

4.4. Phase structure and morphology characterization

Phase compositions of 9–16HEREDSs and corresponding corrosion products were determined by XRD (X'pert PRO, PANalytical, Almelo, Netherlands) using Cu-Kα radiation (λ = 1.54 Å). The Rietveld refinement of XRD patterns was performed using the general structural analysis system software (GSAS-II).⁶⁰ An SEM (Supra-55, Zeiss, Oberkochen, Germany) with EDS was utilized to characterize the morphology and elemental distributions of samples.

4.5. Computational details

10HEREDS, 12HEREDS, and 14HEREDS models were built based on 1 × 1 × 5, 3 × 1 × 1, and 7 × 1 × 1 supercells of the Sm₂Si₂O₇ conventional cell, respectively, and the generalized special quasirandom structure method (gSQS), as implemented in the Universal Structure Predictor: Evolutionary Xtallography (USPEX), was employed.^61,62 DFT calculations were carried out using the Vienna Ab-initio Simulation Package (VASP).⁶³ The electronic exchange–correlation functional was approximated using the generalized gradient approximation (GGA) as formulated by the Perdew, Burke, and Ernzerhof (PBE) functional.^64,65 Interactions between electrons and ions were described via projector-augmented wave (PAW) pseudopotentials.⁶⁶ A plane-wave cutoff energy of 400 eV was applied, and the Γ-centered method with a density of approximately 0.5 Å⁻¹ was used to sample the Brillouin zone.⁶⁷ The energy convergence criterion for electronic self-consistency cycles was set as 10⁻⁵ eV. AIMD simulations were conducted under the NPT ensemble with a time step of 1 fs and a total simulation time of 5 ps. The system temperature was maintained at 1673 K using the Nosé–Hoover thermostat.⁶⁸ The data from the final 2 ps of the simulation, which have been confirmed to have converged (Fig. S11), were used to evaluate the diffusion behaviors. The diffusion coefficient (D) was calculated based on the Einstein relation:⁶⁹where 〈|r(t) − r(0)|²〉 is the ensemble-averaged mean square displacement (MSD) as a function of time t.

The R of diffusion coefficients with different δ_g was calculated using the following equation:

R = D_max − D_min (9)

where D_max and D_min represent the maximum and minimum diffusion coefficients of specific elements.

Author contributions

Y. C. conceived and designed this work. Y. L. performed the experiments. Y. L. and H. Y. performed the calculations. Y. L., Y. C., L. Z., and H. Y. analyzed the data and wrote the manuscript. All authors commented on the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5mh02012c.

Acknowledgements

We acknowledge the financial support from the National Key Research and Development Program of China (2022YFB3708600), the National Natural Science Foundation of China (No. 52572072 and 52472072), the Guangzhou Basic and Applied Basic Research Foundation (No. SL2024A04J01220), the Research Foundation of the Science and Technology on Thermostructural Composite Materials Laboratory (No. JCKYS20250106-01), and the Foundation of Laboratory for High Energy Density Beam Processing Technology (No. KZ571801).

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