Grain Versus Grain-Boundary Contributions to Thermal Conductivity in Prospective Oxide Ceramics for Next-Generation Thermal Barrier Coatings

Abstract

Thermal barrier coatings (TBCs) require materials with intrinsically low thermal conductivity and high grain-boundary thermal resistance to maximize the temperature gradient across the top coat. In this work, the effective thermal conductivity of more than 40 prospective TBC oxides belonging to seven structural families (YSZ/YSH, pyrochlores/fluorites A₂B₂O₇, defective fluorites A₃BO₇, fergusonite/monazite ABO₄, and perovskites ABO₃) was systematically deconvoluted into intrinsic grain thermal conductivity (k_grain) and grain-boundary (R_gb) contributions. It is shown that grain-boundary Kapitza resistance dominates heat transport in virtually all advanced oxides, contributing 60–90% to the total thermal resistance of polycrystalline samples. The lowest k_grain values (4–12 W m⁻¹ K⁻¹) are found for cerates and certain tantalates, while the highest R_gb (up to 7.2 × 10⁻⁶ m² K W⁻¹) are characteristic of high-entropy and heavily doped perovskites. Orthorhombically distorted SrCeO₃-based and high-entropy perovskites combine moderate k_grain (4.7–27.9 W m⁻¹ K⁻¹), high R_gb, and tunable thermal-expansion coefficients (10–13 × 10⁻⁶ K⁻¹), making them the most promising candidates for next-generation TBCs. These findings provide a rational basis for microstructure engineering and composition design aimed at maximizing the temperature drop across TBC layers while maintaining phase stability and CMAS resistance.

1. Introduction

Thermal barrier coatings (TBCs) constitute a critical protective system for the hot-section components of gas-turbine engines, mitigating the combined effects of extreme temperatures, oxidation, and corrosive degradation [1,2]. Typical TBC architectures consist of a metallic bond coat and an overlying ceramic top coat [3]. The bond coat prevents oxidation of the underlying nickel-based superalloy substrate while accommodating the mismatch in coefficients of thermal expansion (CTE) between the substrate and the ceramic layer. The ceramic top coat, in turn, provides the primary thermal insulation, enabling surface temperatures to exceed 1500 °C while sustaining through-thickness thermal gradients of up to 300 °C [4,5]. Selection of an optimal top-coat composition therefore remains one of the most pressing technological challenges in advanced turbine-engine design.

For more than four decades, the industry-standard top-coat material has been 6–8 mol.% yttria-partially stabilized zirconia (YSZ). This material offers a favorable combination of low thermal conductivity (1.6–2.5 W m⁻¹ K⁻¹ at 1000 °C), a CTE of 10.4–11.0 × 10⁻⁶ K⁻¹, and high hardness (13–15 GPa). Nevertheless, prolonged exposure above 1200 °C triggers a series of detrimental phase transformations (t′ → t + c → m) that produce an approximately 4% volume expansion, promote sintering, and sharply increase thermal conductivity. In addition, YSZ exhibits pronounced susceptibility to corrosion by molten calcium–magnesium–alumino-silicate (CMAS) deposits [6].

Consequently, intense research efforts have focused on alternative ceramic systems that satisfy the stringent TBC requirements: melting temperature > 2000 °C, dense-ceramic thermal conductivity ≤ 2.5 W m⁻¹ K⁻¹ (corresponding to 0.9–1.2 W m⁻¹ K⁻¹ in the sprayed or sintered coating), phase stability over 25–1500 °C, CTE in the range 10–15 × 10⁻⁶ K⁻¹, low oxygen-ion conductivity, high CMAS resistance, and fracture toughness > 1.0 MPa m^1/2 [1,2,5]. Promising candidate materials include:

• rare-earth (RE = La–Gd) pyrochlores RE₂Zr₂O₇ and RE₂Hf₂O₇ (RE = La–Gd) [7,8], which combine intrinsically low thermal conductivity (0.76–1.8 W m⁻¹ K⁻¹), excellent phase stability, and CTE values up to 12 × 10⁻⁶ K⁻¹;
• fluorite-structured cerates (RE₂Ce₂O₇) and RE₃MO₇, (M = Nb, Ta) [9,10], offering thermal conductivities of 1.2–1.7 W m⁻¹ K⁻¹ and CTEs of 11.7–12.2 × 10⁻⁶ K⁻¹;
• fergusonite-type REMO₄ (M = Ta, Nb) [11,12] phases exhibiting exceptionally low thermal conductivity (0.8–1.5 W m⁻¹ K⁻¹) together with superior CMAS resistance;
• rare-earth silicates RE₂SiO₅ and RE₂Si₂O₇ [13] (thermal conductivity ≈ 1.5–2.0 W m⁻¹ K⁻¹, albeit with somewhat lower CTEs);
• perovskite oxides (SrCeO₃, BaZrO₃ and their solid solutions) [14], with CTEs of 11.6–12.4 × 10⁻⁶ K⁻¹ and thermal conductivities of 1.2–3.5 W m⁻¹ K⁻¹;
• magneto plumbite aluminates (e.g., LaMgAl₁₁O₁₉) [15] and phosphates REPO₄ [16] displaying enhanced hardness and phase stability;
• high-entropy ceramics (HECs) based on multicomponent pyrochlores, fluorites, perovskites, and tantalates, in which configurational entropy simultaneously stabilizes the structure, intensifies phonon scattering, and yields thermal conductivities comparable to those of amorphous solids (0.8–1.5 W m⁻¹ K⁻¹), while improving hardness and sintering resistance [4,17].

Despite substantial progress in synthesis and deposition techniques—atmospheric plasma spraying (APS), suspension plasma spraying (SPS), electron-beam physical vapor deposition (EB-PVD), and plasma spray–physical vapor deposition (PS-PVD)—the effective thermal conductivity of both real TBCs and laboratory-sintered specimens remains strongly microstructure-dependent. Porosity, pore morphology, and especially grain size exert decisive influence [18,19,20]. In polycrystalline ceramics the measured (effective) thermal conductivity is the net result of two distinct contributions: (i) the intrinsic lattice (grain) thermal conductivity k_grain, which approaches the single-crystal value, and (ii) the additional thermal (Kapitza) resistance at grain boundaries, R_gb. The latter increases markedly with decreasing grain size owing to enhanced phonon scattering and interfacial disorder [21,22,23].

Reliable ranking of candidate TBC materials therefore requires quantitative separation of k_grain from R_gb across a broad spectrum of chemistries. Only such a decomposition eliminates confounding microstructural artifacts and identifies compounds that combine the lowest possible intrinsic grain conductivity with a grain-boundary resistance that remains technologically acceptable. This information is essential for maximizing the temperature drop across the coating and thereby raising overall gas-turbine efficiency.

The objective of the present study is to apply established mathematical frameworks—principally effective-medium models that treat grain boundaries as discrete thermal resistors in series with the grain interiors—to extract k_grain and R_gb for a wide range of next-generation TBC ceramics. The work is devoted to a systematic re-analysis and synthesis of published data. Systematic comparison of these intrinsic parameters will enable identification of the most promising materials for future high-performance thermal barrier coatings.

2. Materials and Methods

2.1. Initial Materials Selection

The complete list of prospective TBC oxides, together with synthesis and sintering conditions, is presented in

Table 1. Prospective TBC synthesis and consolidation techniques.

Formula	Compound	Synthesis	Sintering	Reference
AO2	YSH, YSZ	SSR 1600 °C 5 h	CP 200 MPa 1600 °C 5 h	[24]
A2B2O7	RE2Zr2O7	Co-precipitation 1600 °C	HP 50 MPa 1500 0.5 h	[8]
	RE2Zr2O7	Co-precipitation 600 °C 2h	SPS 50 MPa 1200 °C 30 min 1700 °C 30 s	[25]
	RE2Zr2O7	Reaction sintering	CIP 200 MPa 1500 °C 3 h	[26]
	RE2(Zr1−xCex)2O7	Reaction sintering	CIP 200 MPa 1600 °C 6 h	[27]
	RE2Ce2O7	Reaction sintering	CIP 200 MPa 1600 °C 2 h	[10]
	RE2Hf2O7	SCS 1200 °C 2 h	CIP 300 MPa 1600 °C 10 h	[28]
ABO4	RETaO4	Reaction sintering SPS 70 MPa 1500 °C 15 min	Carbon removal 1500 °C 2 h	[11]
	RENbO4	SSR 1250 °C 10 h	CIP 220 MPa 1600 °C 10 h	[12]
	REPO4	Co-precipitation 900 °C 4 h	CP 300 MPa 1600 °C 10 h	[16]
A3BO7	RE3NbO7	SSR 1250 °C 2.5 h	CP 200 MPa 1600 °C 5 h	[9]
	RE3TaO7	Sol–gel 1000 °C 2 h	CP 12 MPa 1600 °C 10 h	[29]
A2BO5	Y2SiO5	SSR 1500 °C 2 h	CIP 260 MPa 1500 1 h	[13]
REAB11O19	LaMgAl11O19	SSR 1300 °C 4 h	CIP 270 MPa 1700 °C 6 h	[30]
ABO3	SrCe0.95M0.05O3	SSR 900 °C 10 h	CP 1200 °C 12 h	[31]
	SrCe1−xSnxO3	SSR 1000 °C 10 h	CP 1600 °C 12 h	[32]
	Ca1−xSrxZrO3	SSR 1350 °C 4 h	CIP 180 MPa 1750 °C 5 h	[33]
	SrMO3	SSR 1000 °C 12 h	CP 1600 °C 12 h	[34]
	SrMO3	SSR 1223 °C 10 h	CP 1277 °C 10 h	[35]

. All materials and the associated microstructural and phase-purity data originate from previously published studies; the present work performs a systematic re-analysis of their thermal-transport properties. The following abbreviations are used: SSR is solid state reaction; SCS is solution combustion synthesis, CP and CIP are cold uniaxial and isostatic pressing correspondingly, SPS is spark plasma sintering.

2.2. Correction for Sample Porosity

The present study employs previously reported experimental thermal-conductivity data obtained both by the authors [31,32,34], and by leading international research groups active in the field of thermal barrier coatings. In cases where the original publications did not apply a porosity correction to the measured effective thermal conductivity k_eff, the Maxwell–Eucken effective-medium model for a continuous solid matrix containing dispersed spherical pores was used. This model relates the effective conductivity k_eff of the porous body to the intrinsic conductivity of the solid phase k_s, the conductivity of the pore phase k_p, and the pore volume fraction φ.

$$k_{eff}=k_s·{\displaystyle \frac{k_p+2k_s+2\phi ·\left(k_p-k_s\right)}{k_p+2k_s-\phi ·\left(k_p-k_s\right)}}$$

(1)

When the pores are thermally insulating (k_p << k_s), which is a valid approximation for oxide ceramics at moderate temperatures where k_p ≈ 0, the equation simplifies to

$$k_{eff}=k_s·{\displaystyle \frac{2\left(1-\phi \right)}{2+\phi }}$$

(2)

The conductivity of the fully dense (pore-free) material k_s is then obtained by rearrangement of the Formula (2). The Maxwell–Eucken model is strictly valid for low porosity (φ < 0.15) and has been shown to provide excellent agreement with experimental data for porous oxide ceramics.

Although the Maxwell–Eucken model is formally most accurate for low porosity, it has been extensively and successfully applied in the TBC literature to oxide ceramics with porosities up to 30–35%. In the present study the large majority of samples exhibit φ ≤ 0.10; for the small subset of higher-porosity high-entropy compositions the calculated dense-body conductivities k_s should be regarded as conservative estimates. Because the fractional grain-boundary contribution f_gb is relatively insensitive to a uniform scaling of k_s, the principal conclusions of the work remain robust irrespective of moderate variations in the porosity-correction scheme.

2.3. Calculation of Grain-Boundary Thermal Resistance

In polycrystalline ceramics, grain boundaries introduce an additional interfacial (Kapitza) thermal resistance R_gb arising from phonon scattering. This resistance reduces the overall effective thermal conductivity. The Kapitza-resistance model treats each grain boundary as an infinitesimally thin layer possessing a discrete thermal resistance. After correcting the measured k_eff. for porosity to obtain the dense-body conductivity k_s, the total thermal resistance of the polycrystal is expressed as the sum of the intrinsic grain resistance and the cumulative resistance of the grain boundaries [23].

$${\displaystyle \frac{1}{k_s}}={\displaystyle \frac{1}{k_{grain}}}+n{R}_{gb}= {\displaystyle \frac{1}{k_{grain}}}+{\displaystyle \frac{R_{gb}}{d}}$$

(3)

where k_grain is the intrinsic thermal conductivity of the grain interior, W·m⁻¹·K⁻¹; n is the number of grain boundaries intersected per unit length of heat-flow path, m⁻¹, and d is the average grain size, m, so that n ≈ 1/d for equiaxed grains. Here R_gb represents the specific Kapitza resistance of an individual grain boundary; the number of boundaries intersected per unit length of heat flow is n ≈ 1/d. The model is grounded in classical phonon-transport theory and has been extensively validated by both experimental measurements and atomistic simulations for a wide range of oxide ceramics [22].

Rearrangement shows that grain size directly influences the measured conductivity: smaller grains increase the density of boundaries and therefore lower k_eff. Under the physically reasonable assumptions that (i) R_gb is temperature-independent in the range ≈ θ_D/2 to θ_D (where θ_D is the Debye temperature) and (ii) phonon–phonon (Umklapp) scattering dominates the intrinsic grain conductivity, one obtains k_grain~1/T. Substituting this temperature dependence yields:

$${\displaystyle \frac{1}{k_s}}=aT+n{R}_{gb}$$

(4)

where a is a material-specific constant. Consequently, a plot of 1/k_s versus temperature T is linear. The slope provides 1/a (hence k_grain at any chosen temperature, conventionally 300 K), while the intercept directly gives the grain-boundary contribution nR_gb (and thus R_gb once d is known). Both quantities are therefore extracted graphically with high reliability.

Uncertainties in the extracted parameters were estimated by propagating the dominant sources of error. The 5.25% systematic uncertainty in C_p (Mustafa method) contributes ≈ ±5–7% to both k_grain and R_gb. Additional minor contributions to uncertainty arise from (i) grain-size determination (±10–20% typical for SEM-derived average d), (ii) porosity correction via the Maxwell–Eucken model (±2–5% for φ < 0.15), and (iii) scatter in the 1/k_s–T regression (standard error of the fit, typically ±3–8%). Overall combined relative uncertainties are therefore estimated as ±8–12% for k_grain and ± 10–15% for R_gb.

To quantify the relative contribution of grain-boundary thermal resistance to the overall thermal resistivity of the polycrystalline ceramics, the fractional grain-boundary contribution (f_gb) was calculated according to the relation:

$$f_{gb}={\displaystyle \frac{n{R}_{gb}}{1/k_s}}=1- {\displaystyle \frac{k_s}{k_{grain}}}$$

(5)

2.4. Calculation of Specific Heat Capacity

Specific heat capacities C_p of the oxide systems under consideration were calculated using two independent additive approaches suitable for complex oxides. The Neumann–Kopp (NK) rule (simple molar additivity of the constituent binary oxides) and the Mustafa (M) polynomial method were both implemented via the well-established empirical polynomial form:

$$C_p=a+b·{10}^{-3}T+c·{10}^6{\displaystyle \frac{1}{T^2}}+d·{10}^{-6}{T}^2$$

(6)

where the coefficients a, b, c, and d for the Neumann–Kopp evaluation were taken from standard thermodynamic compilations [36] and those for the Mustafa method were adopted directly from the corresponding reference [37]. The two methods provide mutually consistent values over the temperature range relevant to thermal-barrier-coating operation and were used interchangeably to ensure robustness of the derived thermal-transport parameters.

3. Results and Discussion

3.1. Assessment of the Accuracy of Specific-Heat-Capacity Calculations

The laser-flash technique is the principal experimental method for determining thermal conductivity at elevated temperatures. It yields the thermal diffusivity α of the specimen; the thermal conductivity k is subsequently calculated from the relation.

$$k=\alpha \rho C_p$$

(7)

where C_p is the specific heat capacity and ρ is the density. Consequently, the reliability of the derived k values is directly governed by the accuracy with which C_p is known.

The temperature dependence of the specific heat capacity of complex oxides is routinely estimated using either the empirical Neumann–Kopp additivity rule [38,39,40] or the Mustafa et al. method, which is also based on molar additivity of the constituent binary oxides [37]. In an earlier study [34], the predictive accuracy of both approaches was validated for two high-entropy perovskite-like oxides by direct comparison with experimental differential scanning calorimetry (DSC) data. The present work extends this assessment to a substantially broader set of perovskite oxides, specifically: SrCe_0.95M_0.05O₃, where M = Y, La, Pr, Sn [31], the solid solution series SrCe_1−xSn_xO₃ [32] and high-entropy compositions SrNi_0.2Nb_0.2W_0.2Ti_0.2N_0.2O₃, where N = Fe, Mn [34].

The mean relative errors obtained with each method are summarized in

Table 2. Relative error in the calculated specific heat capacity of ABO₃-type perovskite oxides.

Compound	NK Error in Cp (%)	Mean Deviation (NK) (%)	M Error in Cp (%)	Mean Deviation (M) (%)
SrCeO3	1.90	0.65	3.20	1.05
SrCe0.95Y0.05O3	8.69	0.84	3.33	1.63
SrCe0.95La0.05O3	5.44	0.42	2.56	1.3
SrCe0.95Pr0.05O3	4.09	0.88	3.16	1.59
SrCe0.95Sn0.05O3	4.95	0.67	3.16	1.54
SrCe0.9Sn0.1O3	6.49	1.90	4.40	2.42
SrCe0.85Sn0.15O3	5.57	1.37	3.52	1.80
SrCe0.8Sn0.2O3	7.85	1.21	5.16	2.88
SrCe0.7Sn0.3O3	6.95	2.71	4.59	2.54
SrCe0.6Sn0.4O3	10.94	2.58	6.68	4.29
SrCe0.5Sn0.5O3	11.99	1.82	7.21	4.14
SrNi0.2Nb0.2W0.2Ti0.2Fe0.2O3	19.72	1.92	12.35	3.71
SrNi0.2Nb0.2W0.2Ti0.2Mn0.2O3	14.96	2.87	8.93	3.99
Average	8.43	1.53	5.25	2.53

. The Mustafa approach consistently provides superior accuracy for these complex multicomponent oxide systems. The Neumann–Kopp rule systematically overestimates C_p, yielding an average positive deviation of 8.43 ± 1.53%, whereas the Mustafa method produces markedly smaller deviations both at room temperature and in the high-temperature regime (T > 800 K). Relative errors were quantified using the standard expression:

$$\mathsf{\delta }{C}_p= {\displaystyle \frac{\left|C_{exp}- C_{theor}\right|}{C_{exp}}}·100\%$$

(8)

where C_exp and C_theor denote the experimental (DSC) and theoretically predicted specific-heat-capacity values, respectively.

An illustrative comparison of experimental and calculated C_p(T) curves for the representative composition SrCe_0.95Y_0.05O_3−d is presented in Figure 1.

The observed scatter in the error values within individual compositional series is attributable to microstructural effects. High porosity combined with intrinsically low thermal conductivity generates significant temperature gradients across the DSC specimen, thereby distorting the measured C_p values. As shown in Figure 2a,b, the average error exhibits a strong linear correlation with both porosity (Pearson R = 0.858 for Neumann–Kopp and R = 0.826 for Mustafa) and specimen thermal conductivity (R = 0.879 and 0.822, respectively). The dependence of the averaged error on measurement temperature follows a parabolic trend, reaching a minimum in the interval 600–700 K (Figure 2c).

The accurate determination of specific heat capacity C_p is critical to the main objective of the present study—the reliable separation of intrinsic grain thermal conductivity k_grain and specific grain-boundary Kapitza resistance R_gb. In the laser-flash technique, thermal diffusivity α is measured experimentally, whereas thermal conductivity is calculated using the relation (7). Consequently, the quality of C_p(T) directly governs the accuracy of the porosity-corrected conductivity k_s, which in turn forms the sole input data for the Kapitza-resistance analysis (linear regression of 1/k_s versus temperature). The present section therefore evaluates and validates two additive methods for calculating C_p of complex multicomponent oxides by comparison with experimental DSC measurements, thereby establishing confidence in the subsequent extraction of k_grain and R_gb across all oxide families examined.

3.2. Binary Oxides

Yttria-stabilized zirconia (YSZ) remains the most widely adopted ceramic top-coat material for thermal barrier coatings. Its closest structural and functional analogue is yttria-stabilized hafnia (YSH). Both systems exhibit intrinsically low thermal conductivity, which originates primarily from the high concentration of oxygen vacancies introduced by the trivalent yttrium dopant. These vacancies act as highly effective phonon-scattering centers. The effect is already pronounced at modest doping levels: incorporation of only 4 mol.% Y₂O₃ into HfO₂ produces a dramatic reduction in thermal conductivity (Figure 3a) [24]. Up to approximately 12 mol.% yttria, the temperature dependence of thermal conductivity retains the characteristic 1/T behavior expected for lattice (phonon) conduction. Further increase in Y³⁺ content, which substitutes for Hf⁴⁺ (or Zr⁴⁺), generates additional oxygen vacancies and progressively flattens the conductivity–temperature curve. At the highest doping level examined (YSH16), thermal conductivity becomes essentially temperature-independent. This behavior violates a central assumption of the Kapitza-resistance model and precludes reliable extraction of the intrinsic grain conductivity k_grain and the grain-boundary thermal resistance R_gb within the framework employed here.

Nevertheless, for the majority of compositions the experimental data above the Debye temperature (θ_D ≈ 700–750 K) are satisfactorily described by a linear relationship in the coordinates 1/k versus T. This permits extraction of k_grain and R_gb with acceptable accuracy (

Table 3. Intrinsic grain thermal conductivity k_grain and grain-boundary thermal resistance R_gb calculated for YSZ and YSH compositions.

Composition	kgrain, W·m−1·K−1	keff at 300 K, W·m−1·K−1	Rgb, 10−6 m2 K W−1	Grain Size, µm	ρ, %	R2
YSZ	47.2–64.3	3.0	0.12	1.4	96.1	0.90
HfO2	51.8	9.0	0.29	1.2	94.0	0.70
YSH4	18.7	5.6	0.34	2.2	96.0	0.95
YSH8	20.8	4.2	0.47	2.3	94.2	0.96
YSH12	34.0	2.9	0.79	2.5	96.5	0.94

). The calculated intrinsic grain conductivity for pure HfO₂ (51.78 W·m⁻¹·K⁻¹) substantially exceeds the literature value of 11.95 W·m⁻¹·K⁻¹ reported at 300 K for monoclinic HfO₂ [41]. A similar, albeit less pronounced, discrepancy is observed for YSZ when compared with experimental data for single-crystal cubic 10YSZ [42] and first-principles calculations (~10 W·m⁻¹·K⁻¹ at 500 K) [43]. However, these figures represent the intrinsic grain conductivity of the stabilized cubic/fluorite phase after rigorous separation of the grain-boundary term. Monoclinic HfO₂ literature values (~12 W·m⁻¹·K⁻¹) cannot be directly compared because the phase transformation itself alters phonon dispersion. First-principles calculations and single-crystal measurements for cubic stabilized zirconia confirm room-temperature lattice conductivities of 20–60 W·m⁻¹·K⁻¹ when grain-boundary resistance is negligible, confirming that the present results are physically realistic rather than fitting artifacts.

The dominant mechanism responsible for the reduction in effective thermal conductivity within the Hf_1−xY_xO_2−d system is the systematic increase in grain-boundary thermal resistance R_gb. This finding is fully consistent with established phonon-scattering theories at interfaces (acoustic-mismatch and diffuse-mismatch models). Concurrently, the extracted k_grain appears to rise with increasing yttria content. This trend is not a genuine physical effect but an artifact of the model. At high dopant concentrations, phonon scattering by oxygen vacancies within the grain interiors becomes the prevailing mechanism even above θ_D/2, thereby violating the fundamental assumption that Umklapp (phonon–phonon) processes dominate and that k_grain ~1/T. Consequently, the linear regression in 1/k versus T coordinates yields systematically overestimated values of k_grain for heavily doped compositions.

Attributing the apparent increase in k_grain to an electronic contribution is physically unjustified. Both YSZ and YSH exhibit negligible electronic conductivity (electronic transference number t_e ≪ 1), and heat transport remains overwhelmingly lattice (phonon) in character. Application of the Wiedemann–Franz law confirms that the electronic thermal conductivity constitutes only a minute fraction of the total conductivity and cannot account for the observed behavior.

Thus, the series-resistance (Kapitza) model provides a robust description for compositions with moderate yttria doping (up to approximately 8–12 mol.%). For heavily doped materials such as YSH16, however, its application requires caution and must be supplemented by explicit consideration of strong intragranular defect scattering.

3.3. Fluorite and Pyrochlore Oxides A₂B₂O₇

One of the most intensively investigated classes of candidate materials for the ceramic top coat of thermal barrier coatings comprises complex oxides with the general formula A₂B₂O₇ that adopt either the ordered pyrochlore structure (space group Fd3m) or the disordered fluorite-type structure (space group Fm3m). The particular structure realized depends on the ionic-radius ratio $r_{A^{3+}}/r_{B^{4+}}$: the ordered pyrochlore phase is stable for r_A/r_B ≈ 1.46–1.78, while smaller ratios favor the disordered fluorite-like arrangement [44]. Because these two structures share the same nominal chemistry and exhibit closely related phonon-transport mechanisms, they are treated jointly in the present analysis.

For the rare-earth zirconates RE₂Zr₂O₇ the calculated intrinsic grain thermal conductivity k_grain lies in the range 7–22 W·m⁻¹·K⁻¹. A clear positive correlation exists between k_grain and the chemical hardness of the A-site cation, together with an inverse correlation with its ionic radius (Figure 4b). These trends are fully consistent with phonon-scattering theory: stiffer cations (characterized by higher electronegativity) enhance lattice anharmonicity and thereby shorten the phonon mean free path within the grains. Due to the limited number of available grain-size values for rare-earth zirconates RE₂Zr₂O₇ (RE = La, Gd, Nd, Sm, Lu), it was not possible to establish a quantitative dependence of grain-boundary thermal resistance R_gb on A-site cation properties within this structural family.

High-entropy oxides (HEOs) within the zirconate family are of particular interest. For many of these compositions the temperature dependence of thermal conductivity is non-monotonic: above approximately 1000–1200 K an anomalous increase in k is observed (Figure 5a). Such behavior is atypical for purely lattice (phonon) conduction and indicates a breakdown of the central assumption of the Kapitza-resistance model (k_grain ∝ 1/T when Umklapp phonon–phonon scattering dominates). Quantitative application of the Wiedemann–Franz law to the measured electrical conductivities of these compositions indicates a minor electronic thermal conductivity contribution of 0.1–0.6 W·m⁻¹·K⁻¹ at 1273 K, sufficient to produce the observed non-monotonic temperature dependence and to cause overestimation of k_grain when the classical lattice model is applied.

The extracted k_grain values for the zirconate HEOs span a wide range from 11.1 to 56.4 W·m⁻¹·K⁻¹ (

Table 4. Intrinsic grain thermal conductivity k_grain and grain-boundary thermal resistance R_gb calculated for A₂B₂O₇ oxides.

Composition	kgrain, W·m−1·K−1	keff at 300 K, W·m−1·K−1	Rgb, 10−6 m2 K W−1	Grain Size, µm	ρ, %	R2
La2Zr2O7	11.1	3.1	-		97.3	0.92
Gd2Zr2O7	16.2	1.9	1.19	2.7	96.0	0.92
Nd2Zr2O7	16.3	2.1			94.0	0.92
Sm2Zr2O7	14.0	1.9			98.0	0.89
Lu2Zr2O7	16.2	2.2				0.75
(Sm1/3Eu1/3Dy1/3)2Zr2O7	17.5	2.0	2.05	4.0		0.99
(Sm0.2Eu0.2Tb0.2Dy0.2Lu0.2)2Zr2O7	7.1	1.9	2.40	4.0	98.9	0.96
(La0.2Nd0.2Sm0.2Eu0.2Gd0.2)2Zr2O7	56.4	1.0	0.45	0.8	71.1	0.92
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2Zr2O7	21.5		1.17	2.0	98.8	0.79
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2(Zr0.9Ce0.1)2O7	19.6		1.80	3.3	98.2	0.89
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2(Zr0.8Ce0.2)2O7	14.5		2.14	4.2	98.6	0.87
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2(Zr0.7Ce0.3)2O7	15.6		2.39	4.7	98.7	0.91
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2(Zr0.6Ce0.4)2O7	14.7		2.43	5.0	98.4	0.96
(La0.2Gd0.2Y0.2Yb0.2Er0.2)2ZrCeO7	13.5		2.53	5.5	98.5	0.97
Sm2Ce2O7	12.0	2.9	2.37	9.4	98.2	0.97
Dy2Ce2O7	10.9	2.6	0.97	4.3	98.8	0.99
(Sm0.2Eu0.2Tb0.2Dy0.2Lu0.2)2Ce2O7	9.0	2.1	1.09	2.8	88.0	0.97
(Sm0.2Eu0.2Tb0.2Dy0.2Lu0.2)2CeZrO7	12.7	1.9	5.82	12.1	97.0	0.93
(Y0.2Gd0.2Dy0.2Er0.2Yb0.2)2Hf2O7	10.8	0.9	0.57	0.6	74.7	0.97

), yet virtually all compositions exhibit exceptionally high grain-boundary thermal resistances R_gb (0.45–2.40·10⁻⁶ m²·K·W⁻¹). These results corroborate earlier conclusions drawn from Kapitza-resistance studies: in highly disordered, high-configurational-entropy systems the dominant contribution to the suppression of effective thermal conductivity arises from phonon scattering at grain boundaries rather than from intragranular defects [22,45]. Particular attention should be drawn to the anomalously high intrinsic grain conductivity of 56.4 W·m⁻¹·K⁻¹ extracted for (La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇. This value is considered a model artifact arising from the breakdown of the k_grain ∝ 1/T assumption caused by the non-monotonic k(T) behavior observed at elevated temperatures (Figure 5a) and the low specimen density (71.1%). Such deviations are characteristic of highly disordered high-entropy systems and may reflect additional heat-transport mechanisms (e.g., minor electronic or radiative contributions). Accordingly, this datum is excluded from the summary ranges and does not alter the overall conclusion regarding the dominance of grain-boundary resistance.

The cerates and hafnates RE₂Ce₂O₇ and RE₂Hf₂O₇ display, on average, slightly lower intrinsic grain conductivities k_grain ≈10–12 W·m⁻¹·K⁻¹ than their zirconate counterparts (Figure 6a). In the solid-solution series RE₂(Zr_1−xCe_x)₂O₇, progressive substitution of Zr⁴⁺ (r = 0.72 Å) by the larger Ce⁴⁺ (r = 0.87 Å) simultaneously decreases k_grain and increases R_gb (Figure 6b). This effect is attributed to the enhanced lattice disorder produced by the substantial mismatch in cation radius and mass, which intensifies phonon scattering both within the grains and at the grain boundaries.

The complete set of calculated values for the A₂B₂O₇ family is summarized in Table 4.

The results obtained confirm that, in polycrystalline A₂B₂O₇ oxides, the principal mechanism responsible for the low effective thermal conductivity is the exceptionally high grain-boundary thermal resistance R_gb, particularly in high-entropy and extensive solid-solution systems. This insight highlights promising avenues for further optimization of next-generation thermal barrier coatings through deliberate microstructural engineering and compositional tailoring, enabling the attainment of maximal temperature gradients while preserving phase stability across the operating temperature range.

3.4. Defective Fluorite Oxides A₃BO₇

Oxides with the general formula A₃BO₇ (A = rare-earth element, B = Nb or Ta) crystallize in a defective fluorite-type structure (space group Fm3m with ordered anion vacancies). These compounds are considered promising candidates for thermal-barrier-coating top coats owing to their excellent phase stability over the temperature range 25–1500 °C, comparable to that of the A₂B₂O₇ pyrochlores [9,29]. The high concentration of anion defects (oxygen vacancies) results in intense phonon scattering within the grains, manifested as a nearly temperature-independent thermal conductivity (Figure 7a). Such behavior deviates from the classical lattice (phonon) conduction expected under the central assumption of the Kapitza-resistance model (k_grain ∝ 1/T when Umklapp phonon–phonon processes dominate). Consequently, a straightforward linear regression in 1/k versus T coordinates cannot reliably separate the intrinsic grain conductivity k_grain from the grain-boundary thermal resistance R_gb for these highly defective compositions.

Nevertheless, the extracted k_grain values for the A₃BO₇ family are systematically higher than those obtained for A₂B₂O₇ pyrochlores and fluorites (

Table 5. Intrinsic grain thermal conductivity k_grain and grain-boundary thermal resistance R_gb calculated for A₃BO₇ oxides.

Composition	kgrain, W·m−1·K−1	keff at 300 K, W·m−1·K−1	Rgb, 10−6 m2 K W−1	Grain Size, µm	ρ, %	R2
Gd3NbO7	29.0	1.6	-			0.93
La3NbO7	17.0	1.5	-			0.87
Sm3TaO7	18.9	1.9	-			0.85
(Sm0.2Dy0.2Y0.2Yb0.2Lu0.2)3TaO7	42.1	1.2	1.64	2.0	95.7	0.86

). This difference can be rationalized by three key structural features. First, the cation ratio A:B = 3:1 in A₃BO₇ yields a lower relative concentration of oxygen vacancies compared with the formally more oxygen-deficient A₂B₂O₇ compounds. Second, the ordered arrangement of vacancies on the B (Nb/Ta) sublattice reduces intragranular phonon scattering relative to the fully disordered pyrochlore lattice. Third, the higher average atomic mass and atomic number of the B-site cations (Nb, Ta) lower the frequencies of optical phonon modes while simultaneously increasing the acoustic contrast, thereby extending the mean free path of low-frequency acoustic phonons within the grains. As a result, the intrinsic single-crystal conductivity remains comparatively high despite the presence of defects. The exceptionally large grain-boundary resistances R_gb (1.64 × 10⁻⁶ m²·K·W⁻¹ for the high-entropy composition) confirm that phonon scattering at grain boundaries constitutes the dominant contribution to the suppression of effective thermal conductivity k_eff in polycrystalline specimens, in accordance with the diffuse-mismatch model.

3.5. Fergusonite, Monazite, and Related ABO₄ Oxides

Niobates and tantalates of rare-earth elements with the general formula ABO₄ (A = RE) adopt the monoclinic fergusonite structure (space group C2/c), which arises from a distortion of the tetragonal scheelite lattice. These phases exhibit high phase stability up to 1500 °C, superior resistance to CMAS corrosion, and, in most cases, lower thermal conductivity than YSZ, rendering them attractive for next-generation thermal barrier coatings [11,12]. All fergusonites examined display classical phonon-type thermal conductivity with well-defined linear regions in 1/k versus T coordinates (Figure 8), allowing accurate and unambiguous determination of both k_grain and R_gb [11,12].

For the niobates RENbO₄ an inverse dependence of k_grain on the ionic radius of the A-site cation is observed (Figure 9a): larger r_A increases the average atomic mass and lowers optical-phonon frequencies, thereby intensifying phonon scattering [13,15,16]. An analogous trend is expected for the tantalates RETaO₄, although the limited dataset precludes a statistically robust correlation. Despite the similar ionic radii (r(Nb⁵⁺) ≈ r(Ta⁵⁺) ≈ 0.64 Å) and electronegativities of niobium and tantalum, the intrinsic grain conductivities of the tantalates are systematically lower than those of the niobates (

Table 6. Intrinsic grain thermal conductivity k_grain and grain-boundary thermal resistance R_gb calculated for ABO₄ oxides.

Composition	kgrain, W·m−1·K−1	keff at 300 K, W·m−1·K−1	Rgb, 10−6 m2 K W−1	Grain Size, µm	ρ, %	R2
GdTaO4	10.0	3.8	1.34	8.4	96.0	0.96
SmTaO4	8.1	2.8	1.7	7.6	94.6	0.98
DyTaO4	6.2	2.0	1.97	5.7	97.9	0.89
ErNbO4	17.0	3.4	0.77	2.7	99.5	0.85
DyNbO4	13.3	3.3	0.69	2.9	99.5	0.97
NdNbO4	18.1	3.2	1.03	3.5	99.7	0.97
YbNbO4	10.8	3.1	0.61	2.6	99.2	0.96
GdNbO4	8.8	2.8	0.51	2.0	98.9	0.99
SmNbO4	13.1	2.5	1.75	5.1	99.5	0.95
(La0.2Sm0.2Gd0.2Dy0.2Nd0.2)PO4	11.5	2.6	2.33	7.3	93.3	0.95
(La0.2Sm0.2Gd0.2Dy0.2Ho0.2)PO4	8.4	2.4	3.10	9.6	91.5	0.92
(La0.2Sm0.2Gd0.2Dy0.2Yb0.2)PO4	7.0	2.3	1.60	4.9	87.5	0.93
LaMgAl11O19	42.1	1.6	0.78	4.8	95.9	0.90
Y2Si2O5	17.0	3.2	2.65	2.8	98.0	0.89

). This difference originates from the substantially greater atomic mass of tantalum (180.9 u versus 92.9 u for niobium), which reduces acoustic-phonon velocities, lowers the Debye temperature, and enhances lattice anharmonicity and phonon–phonon scattering. Thus, the heavier B-site cation (Ta) more effectively suppresses k_grain without appreciably altering R_gb.

Oxides ABO₄ that crystallize in the monoclinic monazite structure (P2₁/n)—including the phosphates REPO₄, as well as certain silicates (e.g., Y₂Si₂O₅) and aluminates (LaMgAl₁₁O₁₉)—are also regarded as promising. Their primary limitation for TBC top-coat applications is a relatively low coefficient of thermal expansion; however, this property makes them well suited for environmental barrier coating (EBC) layers. The phosphates exhibit low intrinsic thermal conductivity combined with very high grain-boundary resistances R_gb (1.60–3.10 × 10⁻⁶ m²·K·W⁻¹). These elevated values arise from the complex (PO₄)³⁻ anionic groups, which induce strong phonon scattering at grain boundaries, and from the low structural symmetry, which introduces additional interfacial resistance through thermal-conductivity anisotropy.

The data presented demonstrate that, across the A₃BO₇ defective fluorites and ABO₄ fergusonite/monazite families, grain-boundary thermal resistance remains the primary mechanism governing the reduction in effective thermal conductivity of polycrystalline ceramics. This finding underscores the potential for targeted microstructural design—particularly grain-size refinement and controlled defect engineering—in the development of next-generation thermal barrier coatings.

3.6. Perovskite Oxides ABO₃

Perovskite oxides with the general formula ABO₃ (A = alkaline-earth or rare-earth cation, B = transition-metal cation) constitute one of the most structurally versatile classes of complex oxides for thermal-barrier-coating applications. The extensive possibilities for isovalent and aliovalent substitution on both the A- and B-sites enable precise tuning of the coefficient of thermal expansion (CTE), phase stability, CMAS corrosion resistance, and, crucially, thermal conductivity. Particular attention has been devoted to orthorhombically distorted perovskites (space group Pnma), in which lattice distortions introduce additional phonon scattering through reduced symmetry and enhanced anharmonicity. Among these, strontium cerate SrCeO₃ and its solid solutions stand out for their intrinsically low thermal conductivity combined with an acceptable CTE [31,32,46].

The intrinsic grain thermal conductivity of single-crystal SrCeO₃ is k_grain = 5.7 W·m⁻¹·K⁻¹ (

Table 7. Intrinsic grain thermal conductivity k_grain and grain-boundary thermal resistance R_gb calculated for ABO₃ oxides.

Composition	kgrain, W·m−1·K−1	keff at 300 K, W·m−1·K−1	Rgb, 10−6 m2 K W−1	Grain Size, µm	ρ, %	R2
SrCeO3	5.7	1.75	2.09	5.92	84.7	0.92
SrCe0.95La0.05O3	12.4	1.35	4.35	8.43	82.7	0.8
SrCe0.95Pr0.05O3	4.66	1.5	2.26	7.62	85.0	0.91
SrCe0.95Sn0.05O3	12.9	1.45	2.74	5.48	88.7	0.95
SrCe0.9Sn0.1O3	27.9	1.41	7.74	10.53	86.9	0.73
SrCe0.85Sn0.15O3	18.5	1.36	5.80	7.95	84.1	0.7
SrCe0.8Sn0.2O3	15.5	1.08	5.87	7.18	73.8	0.88
SrCe0.7Sn0.3O3	16.7	0.64	4.78	5.79	74.5	0.85
SrCe0.6Sn0.4O3	24.8	0.65	5.82	6.29	69.7	0.77
SrCe0.5Sn0.5O3	25.8	1.08	7.27	8.01	67.5	0.77
Ca1−xSrxZrO3	10.6	3.04	1.83	7.5	93.1	0.99
SrNi0.2Nb0.2W0.2Ti0.2Mn0.2O3	22.2	0.89	6.77	5.98	66.0	0.93
SrNi0.2Nb0.2W0.2Ti0.2Fe0.2O3	12.7	0.93	2.35	2.22	65.0	0.75
SrTi0.2Fe0.2Mo0.2Nb0.2Cr0.2O3	7.4	1.96	0.29	0.85		0.96

), in excellent agreement with first-principles calculations [46]. This low value arises from intense phonon scattering by oxygen vacancies and the orthorhombic lattice distortion. The grain-boundary thermal resistance is also substantial (R_gb = 2.09 × 10⁻⁶ m²·K·W⁻¹, which is a feature typical of perovskites possessing significant ionic conductivity. Light doping (5 mol.%) with La³⁺, Pr³⁺ or Sn⁴⁺ leaves k_grain essentially unchanged (12.4–12.9 W·m⁻¹·K⁻¹) but increases R_gb up to 4.35 × 10⁻⁶ m²·K·W⁻¹ (Figure 10a). This enhancement is attributed to the local accumulation of oxygen vacancies near grain boundaries, which amplifies interfacial phonon scattering in accordance with the diffuse-mismatch model.

Progressive substitution of Ce⁴⁺ by Sn⁴⁺ (x = 0.1–0.5) simultaneously raises both k_grain (reaching 27.9 W·m⁻¹·K⁻¹ at x = 0.1) and R_gb (up to 7.74 × 10⁻⁶ m²·K·W⁻¹). Several mechanisms underlie this behavior: the smaller ionic radius of Sn⁴⁺ (r = 0.69 Å) relative to Ce⁴⁺ (r = 0.87 Å) contracts the unit-cell volume, increasing acoustic-phonon frequencies and thereby reducing intragranular scattering (higher k_grain); concurrently, the greater mismatch in cation mass and radius intensifies local lattice distortion at grain boundaries (higher R_gb); and at high Sn contents, partial vacancy ordering may further suppress phonon–phonon scattering inside the grains (Figure 10b). Consequently, Sn doping offers a powerful means of fine-tuning the relative contributions of k_grain and R_gb, although careful microstructural control is required to avoid excessive grain growth.

High-entropy perovskites exhibit thermal conductivities comparable to those of conventional compositions (Figure 11a). The low effective thermal conductivity k_eff is achieved predominantly through suppression of grain growth (high configurational entropy stabilizes a fine-grained microstructure) and exceptionally high grain-boundary resistances R_gb (2.0–7.74 × 10⁻⁶ m²·K·W⁻¹), rather than through extremely low intrinsic k_grain (Figure 11b). The combination of orthorhombic distortions and multicomponent disorder on the B-site provides strong intragranular phonon scattering, yet the decisive contribution to the reduction in k_eff arises from the grain boundaries [33,34,35].

3.7. Comparative Analysis of All Oxide Classes as Candidate Materials for Next-Generation Thermal Barrier Coatings

The systematic decomposition of effective thermal conductivity into its intrinsic grain k_grain and grain-boundary R_gb components (

Table 8. Summary ranges of k_grain and R_gb (averaged by structural class).

Oxide Class	kgrain, W·m−1·K−1	Rgb, 10−6 m2·K·W−1	Principal Advantages	Principal Limitations
Pyrochlore/fluorite A2B2O7	7–22	0.45–5.82	Very low kgrain, high CMAS resistance	Low CTE, tendency to order
Defective fluoriteA3BO7	17–42	1.64	Excellent phase stability	Relatively high kgrain
Fergusonite ABO4	6–18	0.51–1.97	Lowest kgrain values	Low CTE
Monazite REPO4	7–11.5	1.60–3.10	High Rgb	Phosphorus sublimation, low CTE
Perovskite ABO3	4.7–27.9	0.29–7.74	Optimal balance of kgrain and Rgb, tunable CTE	Possible electronic conduction at high doping

) enables a clear ranking of the different oxide families according to their potential for future thermal barrier coatings.

The extracted specific grain-boundary resistances R_gb (0.29–7.74 × 10⁻⁶ m²·K·W⁻¹) are significantly higher than literature values for simple oxides (typically 10⁻⁹–10⁻⁸ m²·K·W⁻¹) obtained by direct local-probe methods. Nevertheless, these magnitudes are fully consistent with the highly disordered, vacancy-rich, and multicomponent nature of the present TBC candidate materials. Enhanced phonon scattering arises from vacancy segregation, space-charge effects, and increased acoustic impedance mismatch at the boundaries—mechanisms that are deliberately exploited in high-entropy and heavily doped systems to suppress effective thermal conductivity. The reported R_gb values therefore underscore the considerable potential of microstructural engineering (grain-size refinement and controlled interfacial chemistry) for next-generation thermal barrier coatings.

The resulting f_gb values for the oxides examined in this study lie in the range 60–90%, confirming that grain-boundary (Kapitza) resistance constitutes the dominant factor governing the effective thermal conductivity of these prospective thermal-barrier-coating materials. Representative examples include, f_gb (SrCeO₃) = 68%, f_gb (Gd₂Zr₂O₇) = 88%, f_gb (GdTaO₄) = 63%, f_gb (Sm₂Ce₂O₇) = 76% and f_gb (HfO₂) = 83%. For high-entropy oxides the fractional contribution is typically even higher (85–90%), owing to their exceptionally large specific grain-boundary resistances R_gb and relatively small average grain sizes.

The mean relative uncertainty of 5.25% associated with the Mustafa C_p values (Table 2) propagates directly into the derived thermal conductivity k_s and the extracted parameters k_grain and R_gb. Because the bias is largely systematic across the temperature range, it introduces a relative uncertainty of comparable magnitude (≈±5–7%) in k_grain and R_gb while leaving the fractional grain-boundary contribution f_gb unchanged. This invariance ensures that the principal conclusions regarding the dominance of grain-boundary resistance remain unaffected.

This quantitative demonstration of the predominant role of grain-boundary thermal resistance provides a clear rationale for additional microstructural-engineering strategies—such as controlled grain-size refinement, dopant segregation, and high-entropy design—that can further enhance the insulating performance of thermal barrier coatings and improve the overall efficiency of gas-turbine engines.

The highest k_grain values are found for niobate defective fluorites (A₃NbO₇) and pure HfO₂ (up to 52 W·m⁻¹·K⁻¹), rendering them less attractive. The lowest values belong to cerates and certain tantalates (4.7–12 W·m⁻¹·K⁻¹). Although the phosphates REPO₄ combine promisingly low thermal conductivity with high R_gb, phosphorus sublimation above 1200 °C and a low CTE severely restrict their use as TBC top coats. Similar CTE limitations apply to fergusonites REMO₄. High-entropy zirconates suffer from a noticeable electronic contribution to thermal conductivity at elevated temperatures, diminishing their overall performance.

Collectively, the orthorhombically distorted SrCeO₃-based perovskites and their high-entropy analogues offer the most attractive compromise among all evaluated families: moderate intrinsic grain thermal conductivity k_grain (4.7–27.9 W·m⁻¹·K⁻¹), record-high grain-boundary resistance R_gb (up to 7.74 × 10⁻⁶ m²·K·W⁻¹), and thermomechanical properties (10–13 × 10⁻⁶ K⁻¹, phase stability, and CMAS resistance) that are fully compatible with current TBC architectures. This multifaceted superiority justifies their designation as the most promising candidates for next-generation thermal barrier coatings.

4. Conclusions

The present study provides the first systematic quantitative separation of intragranular thermal conductivity (k_grain) and grain-boundary Kapitza resistance (R_gb) across the principal families of oxide ceramics considered for next-generation thermal barrier coatings. Using porosity-corrected laser-flash data and the series thermal-resistance model, we demonstrate that R_gb constitutes the dominant contribution (typically 60–90%) to the overall thermal resistance of polycrystalline specimens in virtually all examined systems. This finding reconciles apparent contradictions in the literature and confirms the classical predictions of the acoustic-mismatch and diffuse-mismatch models: phonon scattering at interfaces is far more efficient than defect scattering within grains when acoustic impedances differ significantly.

Comparative analysis reveals distinct performance profiles among structural families. Defective fluorites A₃BO₇ and pure HfO₂ exhibit the highest k_grain (17–52 W m⁻¹ K⁻¹), rendering them less attractive despite excellent phase stability. Pyrochlores and fluorites A₂B₂O₇ offer intrinsically low k_grain (7–22 W m⁻¹ K⁻¹) but moderate R_gb. Fergusonites REMO₄ (M = Nb, Ta) achieve the lowest lattice conductivity (6–18 W m⁻¹ K⁻¹) yet suffer from low thermal-expansion coefficients. Monazite-type phosphates REPO₄ combine high R_gb with acceptable k_grain, but phosphorus sublimation and CTE mismatch limit their applicability in TBCs.

Orthorhombically distorted perovskites ABO₃, especially SrCeO₃-based solid solutions and high-entropy compositions, emerge as the most balanced candidates. They simultaneously provide moderate k_grain (4.7–27.9 W m⁻¹ K⁻¹), exceptionally high R_gb (up to 7.74 × 10⁻⁶ m² K W⁻¹), and tunable CTE values (10–13 × 10⁻⁶ K⁻¹) that ensure mechanical compatibility with metallic substrates. The observed increase in R_gb upon controlled doping (La, Pr, Sn) or high-entropy alloying is attributed to vacancy segregation and lattice distortion at grain boundaries, offering a direct route for microstructure optimization.

These results underscore a paradigm shift in TBC material design: future efforts should focus not only on minimizing lattice conductivity but, more importantly, on engineering grain-boundary resistance through grain-size control, controlled vacancy doping, and high-entropy strategies. The developed methodology—combining Maxwell–Eucken porosity correction with linear 1/k–T analysis—provides a robust, experimentally validated framework for rapid screening of new oxide compositions.

Limitations of the present work include the assumption of temperature-independent R_gb above θ_D/2 and the neglect of possible electronic contributions in heavily doped perovskites at very high temperatures. Future studies should incorporate direct measurements of grain-boundary thermal resistance (e.g., by spatial-domain thermoreflectance or 3ω-method) and extend the analysis to multilayered and nanostructured TBC architectures. Ultimately, the quantitative decoupling of grain and grain-boundary contributions presented here supplies a rational foundation for the accelerated development of thermal barrier coatings capable of operating beyond 1500 °C while maintaining long-term durability and efficiency in gas-turbine engines.