Increased Thermal Conductivity of Liquid-Phase Sintering Silicon Carbide with Ytterbium Oxide and Magnesium Oxide

Abstract

Using α-SiC powder as a raw material, with ytterbium oxide and magnesium oxide as liquid-phase sintering aids, silicon carbide ceramics were prepared via spark plasma sintering (SPS) at 1900, 2000, and 2050 °C with a 10 min dwell. As the sintering temperature increased, the grain size grew from 0.54 μm to 17.59 μm, while the thermal conductivity correspondingly increased from 122.4 W/(m·K) to 231.8 W/(m·K). Microstructural analyses revealed that elevated sintering temperatures significantly accelerated the dissolution–precipitation process, thereby inducing abnormal grain growth. Grain size is identified as the dominant factor governing the thermal conductivity of SiC ceramics. Larger grains reduce grain boundary density and interfacial thermal resistance, thereby facilitating phonon transport.

1. Introduction

Silicon carbide (SiC) ceramics are essential structural materials owing to their high thermal conductivity, excellent oxidation and corrosion resistance, superior thermal and irradiation stability, and exceptional mechanical properties. Among these attributes, the outstanding thermal conductivity makes SiC ceramics attractive for applications in chemical, military, and nuclear industries, including heat exchangers, semiconductor substrates, and nuclear fuel protective coatings [1,2,3,4,5,6,7,8,9]. Several factors influence the heat conduction mechanism in SiC ceramic [10,11,12]. In covalent ceramics like SiC, the contribution of free electrons or holes to heat transport is negligible, making phonons the primary heat carriers. During phonon transport, the phonon mean free path is substantially shortened by scattering at grain boundaries, residual intergranular phases, pores, and point defects, which ultimately leads to a reduction in thermal conductivity.

Liquid-phase sintering (LPS) can achieve effective densification of SiC ceramics at temperatures below 2000 °C, owing to the higher atomic diffusion rate provided by the liquid phase. Extensive research has focused on improving the thermal conductivity of LPS-SiC ceramics. The main strategies include avoiding the introduction of aluminium impurities [13,14]; maintaining an extremely low lattice oxygen content [15,16]; promoting the formation of large-sized grains to reduce the density of grain boundaries [17,18]; minimizing heterogeneous interfaces arising from the β-SiC to α-SiC phase transition [19]; and reducing the amount of residual grain boundary phases while improving their degree of crystallization [20,21,22]. Precise regulation of the sintering process to simultaneously achieve these ideal microstructural features has therefore become a hot research topic.

Currently, rare-earth oxides are widely employed as sintering additives in LPS-SiC ceramics. During sintering, the reaction of rare-earth oxides (RE₂O₃) with the SiO₂ layer on the SiC particle surfaces produces a sufficient rare-earth silicate liquid phase, which in turn promotes densification. Concurrently, the dissolution–reprecipitation process promotes the growth of grain size [23]. Zhou et al. prepared SiC ceramics via hot pressing at 2000 °C for 2 h with 2 mol% Y₂O₃-La₂O₃ additives, achieving a thermal conductivity of 166 W/(m·K) [24]. Furthermore, it was demonstrated by Kim et al. that LPS-SiC ceramics are more likely to exhibit clean or crystalline grain boundaries when using sintering additives with smaller rare-earth ionic radii [25]. Yttrium (Y) and ytterbium (Yb) belong to the same rare-earth group. Although metallic Yb has a larger atomic radius than Y, ${\mathrm{Y}\mathrm{b}}^{3+}$ exhibits a smaller ionic radius (0.858 Å) than ${\mathrm{Y}}^{3+}$ (0.900 Å). Thus, the use of Yb₂O₃ as a sintering additive is expected to promote the formation of more favorable grain boundary structures in SiC ceramics.

Magnesium oxide (MgO), which is insoluble in the SiC lattice, was used as an effective secondary sintering additive with rare-earth oxides for LPS-SiC ceramics [26]. During sintering, MgO lowers the liquid-phase viscosity, thus facilitating the migration of SiC particles and promoting tight interparticle bonding [27]. Using β-SiC powder with Y₂O₃-MgO as sintering additives, Huang et al. obtained SiC ceramics via spark plasma sintering (SPS) at 1850 °C under 30 MPa for 1 h, which exhibited a thermal conductivity of 67 W/(m·K). A further increase in sintering temperature to 2050 °C raised the thermal conductivity to 204 W/(m·K), mainly due to the full β → α phase transition at high temperature [28]. Kim et al. similarly concluded that the β → α phase transition exerts a decisive influence on the thermal conductivity of SiC ceramics [25]. In our previous study, Yan et al. used β-SiC as starting powder and Yb₂O₃-MgO as sintering additives, and achieved a complete β → α phase transition by discharge plasma sintering under argon atmosphere at 2050 °C for 1 h, resulting in SiC ceramics with a thermal conductivity of 229 W/(m·K) [29]. Although the elimination of β/α heterogeneous interfaces through phase transformation is considered as a major factor contributing to the enhanced thermal conductivity, additional factors such as larger grains and reduced lattice oxygen content also play important roles. However, whether a fully homogeneous interface (pure α phase) can exert a positive effect on the thermal conductivity of SiC ceramics remains unclear and warrants further investigation.

In this study, SiC ceramics were fabricated via spark plasma sintering using α-SiC powder with Yb₂O₃–MgO as liquid-phase sintering additives. Through comprehensive analyses of phase composition, microstructure, thermal properties, and grain growth behavior, we elucidated the effects of additive content and sintering temperature on microstructural evolution, and further established its correlation with thermal conductivity. In contrast to existing studies employing Yb₂O₃–MgO-doped β-SiC with prolonged sintering, this work directly utilizes α-SiC to bypass the β→α transformation and the associated interfacial defects. Without the need to consider phase transition, the combined use of the Yb₂O₃–MgO additive system and short-duration SPS enabled the manipulation of liquid-phase sintering kinetics to drive abnormal grain growth. The sintering time was dramatically shortened compared to the conventional 1 h regime, demonstrating a promising route for the efficient preparation of high thermal conductivity SiC ceramics.

2. Materials and Methods

2.1. Sample Preparation

The starting materials were α-SiC powder (D₅₀ = 0.5 μm, Shanghai Macklin Biochemical Technology Co., Ltd., Shanghai, China, MgO (purity 99.99%, Beijing InnoChem Technology Co., Ltd., Beijing, China), and Yb₂O₃ (purity 99.99%, National Engineering Research Center for Rare Earth Metallurgy and Functional Materials, Baotou, China). SiC ceramics were prepared using Yb₂O₃-MgO (marked as YbM) as liquid-phase sintering additives. The total additive contents were 3, 5, and 7 wt.% with a fixed molar ratio of Yb₂O₃:MgO = 2:5. This study focuses on a fixed Yb₂O₃: MgO ratio to investigate the dominant role of sintering temperature in governing thermal conductivity through grain growth kinetics. The selection of this molar ratio is grounded in our prior research, which confirmed that the Yb₂O₃–MgO additive system is favorable for achieving high thermal conductivity [29]. Compared to the previously adopted 1:2 ratio, the current study slightly increases the MgO content to 2:5. This adjustment is intended to further harness the viscosity-lowering effect of MgO on the high-temperature liquid phase [27], thereby promoting more effective mass transport and grain growth under the conditions of α-SiC starting powder and ultra-short sintering.

The α-SiC powder and sintering additives were proportionally loaded into a polyurethane tank and mixed for 10 h using anhydrous ethanol as the dispersion medium and polyurethane balls as grinding media. The ball-milled slurry was vacuum-dried at 80 °C for 24 h. The dried mixture was subsequently crushed, sieved, and placed into a graphite mold with an inner diameter of 25 mm. Densification was carried out by SPS under a uniaxial pressure of 40 MPa in a vacuum atmosphere. The samples were subjected to SPS at 1900 °C, 2000 °C and 2050 °C for 10 min under a uniaxial pressure of 40 MPa in a vacuum atmosphere.

2.2. Performance Analysis

2.2.1. Density, Phase Composition, and Microstructure

The actual density and open porosity of the sintered specimens were measured using the Archimedes method with deionized water as the immersion medium. The theoretical density was calculated based on the mixing rule. Phase composition were identified by X-ray diffraction (XRD, XRD-6000, Shimadzu, Kyoto, Japan). Microstructural observations of polished surfaces were performed using a scanning electron microscope (SEM, SIGMA-500, Zeiss, Oberkochen, Germany). Grain diameters of the SiC samples were analyzed using Image-Pro Plus software (Version 6.0, Media Cybernetics Inc., Rockville, MD, USA). In SEM images, grain size was defined as the diameter of a sphere having the same surface area as the irregularly shaped grain. Transmission electron microscopy (TEM, Talos F200X, Thermo Fisher, Hillsboro, OR, USA) was used to observe the microstructure and morphology of the selected area in different imaging modes, and HRTEM was used to observe the microstructure and interfacial structure of the material. The lattice oxygen concentration was determined using an oxygen-nitrogen analyser (ON836, LecoCo., Joseph, MI, USA).

2.2.2. Thermal Property Measurements

Ceramic samples were cut into blocks with dimensions of 10 mm × 10 mm × 3 mm. Thermal diffusivity and heat capacity were measured using a laser flash analyzer (LFA-467, Netzsch, Selb, Germany). Prior to measurement, both surfaces of each sample were coated with a thin layer of graphite to minimize laser reflection and enhance infrared signal sensitivity. Measurements were conducted at room temperature. Thermal conductivity was calculated using Equation (1):

$$\kappa = \alpha \rho C_P$$

(1)

where κ denotes the thermal conductivity (W/(m·K)), α is the thermal diffusion coefficient (mm²/s), ρ is the sample density (g/cm³), and C_P is the specific heat capacity (J/(g·K).

The phonon mean free path (L), defined as the average distance traveled by phonons between scattering events, was calculated using Equation (2):

$$L= {\displaystyle \frac{3\kappa }{C_P\nu }}$$

(2)

where $v$ is the phonon velocity. The sound velocity of sintered SiC used in this calculation was 11,820 m/s at room temperature [30].

3. Results and Discussion

3.1. Microstructure and Phase Analysis

Table 1 summarizes the sintering conditions and corresponding bulk densities and open porosities for SiC ceramics prepared with Yb₂O₃–MgO additives. All samples achieved nearly full densification, with bulk densities higher than 3.24 g/cm³ and open porosities lower than 0.31%. Specimen density peaked at 2000 °C before declining.

Table 1. Sintering parameters and densification results of SiC ceramics.

Sintering Temperature (°C)	Specimen lD	Sintering Additive Content (wt.%)	Bulk Density (g/cm3)	Open Porosity (%)
2050	3YbM-25	3	3.241 ± 0.004	0.10
	5YbM-25	5	3.242 ± 0.003	0.12
	7YbM-25	7	3.247 ± 0.005	0.01
2000	7YbM-20	7	3.266 ± 0.005	0.31
1900	7YbM-19	7	3.245 ± 0.004	0.12

Figure 1 shows the XRD peaks of sintered samples with varying additive contents. Both the raw SiC powder and the sintered samples predominantly consist of the 6H polytype, with a minor presence of the 4H phase. Yb₂Si₂O₇ was detected in all sintered samples, while MgSiO₃ was observed primarily in samples sintered at lower temperatures. These silicates formed through reactions between Yb₂O₃ and MgO additives and the native SiO₂ layer on the SiC particle surface, as described by the following reaction:

Yb₂O₃ + 2SiO₂ → Yb₂Si₂O₇

MgO + SiO₂ → MgSiO₃

Figure 1. XRD patterns of samples with varying sintering temperature.

Figure 2 presents SEM images of SiC ceramics containing 7 wt.% Yb₂O₃-MgO sintered at different temperatures. 7YbM-19 and 7YbM-20 exhibit uniform fine-grain equiaxed microstructures with clear and continuous grain boundaries. The liquid-phase-derived grain boundary phases uniformly coat SiC grains in a lamellar morphology. When the sintering temperature increases to 2050 °C, the grain morphology transitions from equiaxed to irregular coarse grains, with a maximum aspect ratio of 6.9, indicative of abnormal grain growth. Significant grain size disparity is observed, accompanied by a pronounced reduction in the number of grain boundaries. Rapid grain growth causes partial migration of grain boundary phases toward triple junctions, resulting in a local enrichment state.

Figure 2. SEM images for samples sintered at different temperatures: (a) 7YbM-19; (b) 7YbM-20; (c) 7YbM-25.

Figure 3 shows the grain size distribution of SiC ceramics with 7 wt.% Yb₂O₃-MgO additive sintered at different temperatures. At sintering temperatures of 1900–2000 °C, the grains remain uniform and fine, with an average size of 0.58 μm. A small fraction of coarse grains (~3 μm) form as initially larger grains preferentially absorb SiC atoms dissolved in the liquid phase via Ostwald ripening [31]. When the temperature rises to 2050 °C, both liquid-phase fluidity and atomic migration rate increase substantially. A few grains with growth advantages rapidly consume the surrounding fine grains through the dissolution–reprecipitation mechanism, leading to a sharp increase in average grain size to 17.59 μm. The grain growth behavior thus transitions from uniform coarsening to abnormal grain growth. According to the classic grain growth theory established by German [32], grain growth during liquid-phase sintering is intrinsically governed by the properties of the liquid phase. Abnormal grain growth refers to the rapid and selective growth of a minority of grains at the expense of their surrounding finer grains [33,34]. As the sintering temperature increases, the viscosity of the liquid phase decreases while its fluidity improves, enabling it to more thoroughly surround the grains and thereby increase the interfacial area available for coarsening. Concurrently, partial volatilization of the liquid phase reduces its total volume, promoting direct contact between solid grains and further accelerating coarsening through enhanced interactions. Under such conditions, a small number of grains migrate and consume the fine grains, triggering secondary recrystallization. This process results in a bimodal grain size distribution, which is a characteristic microstructural signature of abnormal grain growth.

Figure 3. Grain size distribution plots for samples sintered at different temperatures: (a,d) 7YbM-19; (b,e) 7YbM-20; (c,f) 7YbM-25.

Figure 4 shows SEM images and corresponding grain size distributions of samples with different additive contents sintered at 2050 °C. All samples exhibit grain sizes exceeding 10 μm. Lower additive contents (3 wt.% and 5 wt.%) result in reduced liquid-phase formation. The narrowing of the “liquid-phase transport channels” limits the dissolution–precipitation process of SiC, weakens the dissolution driving force of small grains, and reduces diffusion efficiency. As a result, SiC atoms cannot fully migrate and precipitate onto larger grains, leading to an overall kinetic rate much lower than that of 7YbM-25, and consequently, smaller grain sizes.

Figure 4. SEM images and grain size distributions of samples with different additive contents: (a–c) 3YbM-25; (d–f) 5YbM-25.

Notably, at a sintering temperature of 2050 °C, despite increasing the additive content from 3 wt.% to 7 wt.%, both grain size and thermal conductivity remained at comparably high levels, indicating that within this high-temperature regime, the influence of additive content is far less significant than that of sintering temperature. This observation is primarily attributed to the substantial reduction in liquid-phase viscosity and the markedly enhanced atomic diffusion rate at elevated temperatures, which together shift the grain growth mechanism from diffusion-controlled uniform growth to interface-reaction-dominated abnormal coarsening. Under such conditions, a limited quantity of liquid phase is sufficient to sustain the rapid dissolution–reprecipitation process, thereby diminishing the capacity of liquid-phase volume variation to modulate the final grain size. As the primary factor altering the properties of the liquid phase and governing the grain growth mechanism, sintering temperature plays a dominant role in determining the microstructural evolution and, consequently, the thermal conductivity.

The microstructural features of grain boundaries are believed to exert a critical influence on thermal conductivity. According to XRD analysis, the secondary phase is identified as Yb₂Si₂O₇. Meanwhile, the presence of MgSiO₃ in samples sintered at lower temperatures suggests its evaporation at higher temperatures. The grain boundary structures of YbM samples were further characterized by transmission electron microscopy (TEM), as shown in Figure 5. Figure 5a–d present the trigranular phase and grain boundary of the 7YbM-25 sample. Figure 5c shows a high-resolution TEM (HRTEM) image of the trigranular phase together with its fast Fourier transform (FFT) image, confirming that the liquid phase has fully crystallized into Yb₂Si₂O₇ at the trifurcated grain boundary. High-angle annular dark-field (HAADF) images of the 7YbM-25 sample (Figure 5b) reveal a narrow grain boundary with a thickness of 1.46 nm. Figure 5e presents a STEM image of the SiC-SiC grain boundary film in the 7YbM-19 sample. Lattice fringe analysis using HRTEM, combined with plane identification from the corresponding FFT diffraction pattern, indicates the formation of crystalline MgSiO₃ within the SiC-SiC grain boundary region. Figure 5f shows that the thicknesses of the amorphous boundary films in the 7YbM-19 sample reach approximately 4.07 nm. The pronounced difference in intergranular film thickness between the 7YbM-25 and 7YbM-19 samples can be attributed to the following mechanism. During sintering, SiC forms a continuous liquid-phase network that promotes grain growth. As adjacent SiC grains coarsen, the intergranular phase is progressively “squeezed out” from the grain boundary regions. Consequently, the 7YbM-25 sample, which possesses the largest grain size, expels a greater fraction of the liquid phase into the trigranular junction zones, resulting in the formation of a thinner intergranular film. This reduction in interfacial film thickness effectively suppresses phonon scattering at grain boundaries, thereby contributing to the enhanced thermal conductivity.

Figure 5. TEM investigation of 7YbM-25 and 7YbM-19 samples: (a,e) STEM images; (b,f) HADDF images; (c,g) HRTEM images; (d,h) fast Fourier transform (FFT) images of marked area.

3.2. Thermal Properties

The thermal conductivity of the sintered samples are shown in Table 2. A pronounced increase from 122.2 to 231.8 W/(m·K) is observed with increasing sintering temperature from 1900 °C to 2050 °C. All samples sintered at 2050 °C exhibit thermal conductivity exceeding 210 W/(m·K). When the sintering temperature is raised from 2000 °C to 2050 °C, this incremental increase induces a fundamental shift in the grain growth mechanism from diffusion-controlled Ostwald ripening to secondary recrystallization-dominated abnormal coarsening. The elevated temperature intensifies ionic thermal motion within the RE–Mg–Si–O liquid phase, weakens cation–anion bonding, and markedly reduces the liquid-phase viscosity, thereby accelerating the dissolution–reprecipitation process [17,35]. This enables a limited number of grains with growth advantages to rapidly consume surrounding fine grains, causing the average grain size to surge from 0.58 μm to 17.59 μm, with the grain morphology evolving from equiaxed to irregular coarse structures. Concurrently, during rapid grain coarsening, a substantial portion of the intergranular phase is extruded and enriched at triple junctions, thinning the grain boundary film to 1.46 nm. This optimized interfacial architecture effectively mitigates phonon scattering. Meanwhile, the MgSiO₃ phase is almost entirely volatilized at this temperature, eliminating its modestly detrimental contribution to thermal conductivity. Through the synergistic action of these factors, the thermal conductivity of the SiC ceramics is markedly enhanced.

Table 2. Thermal properties of SiC ceramics.

Sample	κs [W/(m·K)]	${\mathit{\kappa }}_{\mathit{c}}$ [W/(m·K)]	${\mathit{\kappa }}_1$ [W/(m·K)]	${\mathit{\kappa }}^{\mathit{s}}$ [W/(m·K)]	Phonon Mean Free Path (nm)
3YbM-25	215.0 ± 1.8	215.2	230.0	212.1	86.3
5YbM-25	210.3 ± 1.7	210.6	225.0	195.2	83.4
7YbM-25	231.8 ± 2.3	231.8	250.0	227.1	90.8
7YbM-20	135.5 ± 1.2	136.0	148.0	-	45.9
7YbM-19	122.4 ± 2.6	122.6	130.0	-	37.6

As a typical polycrystalline material, the microstructure of SiC ceramics primarily consists of grains and grain boundaries. In general, when the grain size substantially exceeds the phonon mean free path, phonon transport within grains is less constrained; theoretically, grain boundaries remain a significant source of phonon scattering and therefore govern the crucial role in heat conduction. The calculated phonon mean free path values (as shown in Table 2) are all smaller than the grain sizes, indicating that phonon scattering primarily occurs at grain boundaries rather than within grains. A significant increase in phonon mean free path is observed as the sintering temperature increases from 2000 °C to 2050 °C. The large phonon mean free path is beneficial for phonon transport.

To further elucidate the influence of grain boundary structure on heat conduction, this study combined XRD, TEM, and thermal property measurements to investigate the roles of the grain boundary phases Yb₂Si₂O₇ and MgSiO₃ in phonon scattering. XRD phase identification (Figure 1) confirms the presence of Yb₂Si₂O₇ in all samples, whereas MgSiO₃ is detected only in specimens sintered at 1900 °C and 2000 °C, disappearing at 2050 °C due to high-temperature volatilization. This phase evolution is consistent with microstructural observations: in the 7YbM-19 sample sintered at 1900 °C, TEM reveals an amorphous/crystalline mixed grain boundary film approximately 4.07 nm thick (Figure 5f), containing crystalline MgSiO₃ (Figure 5e). Such a relatively thick and structurally complex film induces pronounced phonon scattering and thus high interfacial thermal resistance. In contrast, in the 7YbM-25 sample sintered at 2050 °C, the grain boundary phase mainly comprises well-crystallized Yb₂Si₂O₇, which is enriched as isolated phases at triple junctions (Figure 5a–d), and the grain boundary film thickness is drastically reduced to ~1.46 nm. This reduction helps lower the frequency of phonon scattering at the interfaces, positively contributing to the enhancement of thermal conductivity.

In our previous study, Yan et al. employed β-SiC as the raw material and observed that the thermal conductivity increased from 65 W/(m·K) to 229 W/(m·K) as the sintering temperature increased from 1900 °C to 2050 °C, concomitant with the completion of the β → α phase transition at elevated temperatures [29]. Meanwhile, the grain size increased significantly from 0.32 μm to 8.51 μm. A similar trend was observed by Huang et al., who documented that SiC ceramics with Y₂O₃-MgO additives exhibited an increase in thermal conductivity from 67 to 204 W/(m·K) in conjunction with grain growth from 0.53 μm to 2.41 μm [28]. Through computational analysis, Chai et al. demonstrated that increasing the grain size from 750 nm to 1400 nm accounted for approximately 85% of the total enhancement in thermal conductivity, whereas reducing additive content contributed only about 15% [36]. These published findings indicate that large grain size serves as a core factor in enhancing thermal conductivity of sintered SiC ceramics.

In this study, the SiC phase remains 6H, indicating the absence of phase transformation during sintering. The average grain size of the SiC ceramic samples increased from 0.54 μm to 17.59 μm, while the thermal conductivity correspondingly rose from 122.2 W/(m·K) to 231.8 W/(m·K). The variation in thermal conductivity is non-linear with respect to liquid-phase content, further indicating that the enhancement of thermal conductivity is dominated by the increase in grain size. Large-size grains contribute to reduced defect density, while more homogeneous phase interfaces suppress phonon scattering, thereby improving thermal transport performance.

The following discussion is intended to elucidate the influence of grain size on thermal conductivity and its underlying mechanism.

Pores are a common defect in SiC ceramics, and the thermal conductivity typically decreases with increasing porosity. The thermal conductivity of fully dense ceramics is calculated using Equation (3), derived from the Maxwell model.

$${\kappa }_c={\kappa }_s{\displaystyle \frac{1-V_P}{1+0.5V_P}}$$

(3)

Here, κ_s is the experimentally measured thermal conductivity of sintered SiC ceramics; V_P is the porosity of sintered SiC ceramics (expressed solely as open porosity in this study). The experimental thermal conductivity closely matches the calculated thermal conductivity of fully dense SiC ceramic, indicating that pores play a minor role in heat conduction under the present conditions [37].

A macroscopic model is subsequently employed to determine the thermal conductivity of the continuous matrix-dilute second-phase composite. Equation (4) presents the mathematical formulation of this model [38]. At the interface between the secondary phase and the SiC matrix, phonon scattering occurs, thereby reducing thermal conductivity; consequently, the model incorporates interfacial thermal resistance.

$${\kappa }_e={\kappa }_1\left[{\displaystyle \frac{2\left(\frac{{\kappa }_2}{{\kappa }_1}-\frac{{\kappa }_2}{a{h}_c}-1\right){\nu }_2+\frac{{\kappa }_2}{{\kappa }_1}+\frac{2{\kappa }_2}{a{h}_c}+2}{\left(1-\frac{{\kappa }_2}{{\kappa }_1}+\frac{{\kappa }_2}{a{h}_c}\right){\nu }_2+\frac{{\kappa }_2}{{\kappa }_1}+\frac{2{\kappa }_2}{a{h}_c}+2}}\right]$$

(4)

where $h_c$ denotes interfacial thermal conductance (the reciprocal of interfacial thermal resistance), $v_2$ and a represent the volume fraction and radius of the discrete secondary phase, respectively. ${\kappa }_e$ is the effective thermal conductivity of the composite. ${\kappa }_1$ and ${\kappa }_2$ correspond to the thermal conductivities of the continuous phase and the discrete secondary phase, respectively.

When applying the macroscopic model (Equation (4)), it is first necessary to determine the thermal conductance (reciprocal of thermal resistance) at the interface between SiC and the secondary phase. The thermal boundary resistance, a form of interfacial thermal resistance, was estimated using the Acoustic Mismatch Model (AMM) [39]. This resistance originates from disparities in acoustic impedance, which is defined as the product of mass density and phonon group velocity. This arises from mismatches in acoustic impedance, defined as the product of mass density and phonon group velocity. Within the AMM framework, phonons are treated as plane waves traveling through a continuous, amorphous material before incidentally striking the interface [40]. The calculated phonon group velocities of Yb₂Si₂O₇, SiC, and additional parameters required for calculating thermal boundary conductance using the AMM are listed in Table 3.

Moreover, the calculation of thermal conductivity using Equation (4) further necessitates the values of thermal conductivity and characteristic radius for the discrete secondary phase distributed at the triple junctions of the sintered SiC ceramics. Based on combined TEM observation and XRD analysis, the triple junction phase is identified as Yb₂Si₂O₇, which exhibits a thermal conductivity of 4.31 W/(m·K) [41]. The volume fraction of the secondary phase (v₂) is calculated solely from the content of the added sintering additives. Corresponding SEM images were used to measure the radius of the secondary phase present in the sintered SiC ceramics.

Table 3. Parameters for calculating thermal boundary conductance (reciprocal of thermal boundary resistance) of the interface between SiC and Yb₂Si₂O₇ based on AMM.

Specimens	Phonon Group Velocity 1 (m/s)	Specific Heat 2 [J/(g·K)]	Density (g/cm3)	Thermal Boundary Conductance (W·m−2·K−1)
Yb2Si2O7	3613	0.398	5.71	4.77 × 108
SiC	8268	0.677	3.22	(AMM)

¹ Phonon group velocities for Yb₂Si₂O₇ and SiC are obtained from reference [42,43] and [30]. ² Specific heats for Yb₂Si₂O₇ and SiC are obtained from reference [44] and [19], respectively.

Table 3. Parameters for calculating thermal boundary conductance (reciprocal of thermal boundary resistance) of the interface between SiC and Yb₂Si₂O₇ based on AMM.

Specimens	Phonon Group Velocity 1 (m/s)	Specific Heat 2 [J/(g·K)]	Density (g/cm3)	Thermal Boundary Conductance (W·m−2·K−1)
Yb2Si2O7	3613	0.398	5.71	4.77 × 108
SiC	8268	0.677	3.22	(AMM)

¹ Phonon group velocities for Yb₂Si₂O₇ and SiC are obtained from reference [42,43] and [30]. ² Specific heats for Yb₂Si₂O₇ and SiC are obtained from reference [44] and [19], respectively.

For samples with small grain sizes (7YbM-19, 7YbM-20), the calculated thermal conductivity showed good agreement with experimental values (the error range is 7.6–12.5 W/(m·K)), whereas for samples with large grain sizes (YbM-25), significant deviations are observed between calculated and experimental results (the error range is 14.7–18.2 W/(m·K)). In SiC ceramics with smaller grains, a continuous liquid phase (as shown in Figure 2) forms along the grain boundaries, resulting in a large grain boundary volume fraction. This microstructural feature leads to frequent scattering at grain boundaries during propagation. The enhanced scattering significantly reduces the phonon mean free path, impedes phonon transport, and increases energy dissipation, thereby decreasing the macroscopic thermal conductivity. In this regime, interfacial thermal resistance is the determining factor governing thermal conductivity. In contrast, in samples with large grain sizes, the low-viscosity liquid phase significantly promotes SiC grain growth, causing the secondary phase to isolate and disperse at grain boundaries. This microstructural evolution weakens phonon scattering by the second phase and allows grain size to emerge as the primary factor driving thermal conductivity. Notably, in coarse-grained samples, despite the substantial reduction in grain boundary density, the disparity between the theoretically calculated thermal conductivity and the experimental values remains pronounced. As outlined above, the model is built upon several idealizing assumptions: (1) spherical and uniformly dispersed secondary-phase particles; (2) atomically flat ideal interfaces whose thermal resistance originates solely from acoustic mismatch; and (3) applicability only to dilute dispersions, with particle–particle interactions neglected. In the current framework, beyond the omission of grain boundary scattering effects, additional non-negligible errors arise in coarse-grained systems from the estimation of interfacial thermal resistance, the simplification of secondary-phase morphology, and the gap between the idealized acoustic mismatch model and the true complexity of the interfacial structure. Furthermore, for coarse-grained specimens, the model does not account for grain size effects, further amplifying the deviation between the calculated and the experimental measurements.

The between thermal conductivity and grain size in polycrystalline silicon carbide can be further interpreted via the classical series model (Equation (5)). Grounded in the physical hypothesis that grain and grain boundary thermal resistances are connected in series, this model reveals that grain size determines thermal conductivity by adjusting the relative contribution of grain boundary thermal resistance.

$${\kappa }^s={\displaystyle \frac{{\kappa }_o}{1+{\kappa }_o\frac{R_{\kappa }}{d}}}$$

(5)

In the equation, ${\kappa }^s$ denotes the thermal conductivity of polycrystalline material, ${\kappa }_o$ denotes the thermal conductivity of single-crystal silicon carbide, $R_{\kappa }$ denotes the average Kapitza resistance, and d denotes the average grain size.

The thermal conductivity of the SiC ceramics in this work was estimated by means of Equation (5), with the intrinsic thermal conductivity κ_o taken as 490 W/(m·K). The idealized grain boundary structures commonly used in molecular dynamics simulations substantially underestimate the actual grain boundary thermal resistance in real systems. To match experimental data, the grain boundary thermal resistance must be amplified by a factor of 80; accordingly, Kapitza resistance $R_{\kappa }$ was determined to be 4 × 10⁻⁸ m²·K/W [45]. The computational results indicate that the fundamental mechanism responsible for the improvement in thermal conductivity as grain size increases is the accompanying decrease in the ${\kappa }_o{\displaystyle \frac{R_{\kappa }}{d}}$ term, corresponding to a weakened Kapitza thermal resistance effect. For large-grain samples (d ≥ 13 μm), the reduced number of grain boundaries and the enrichment of the secondary phase at triple-grain boundaries result in a negligible contribution from the heterointerface thermal resistance originating from the SiC/Yb₂Si₂O₇ interface. Under these conditions, the thermal conduction behavior approaches a one-dimensional series model of “grain–grain boundary”, yielding strong agreement between computational and experimental values. The calculated value of 227.1 W/(m·K) exhibits a relative error of 1.34%.

For fine-grained samples (d ≤ 1 μm), transmission electron microscopy reveals the formation of MgSiO₃ at SiC-SiC grain boundary films. The extremely high density of grain boundaries and the widespread presence of the secondary phase render Kapitza thermal resistance at the SiC/liquid-phase heterointerface the primary phonon-scattering source. In this regime, complex effects arising from multi-boundary interactions and enhanced phonon scattering exceed the applicability of simple series models, leading to substantial deviations between calculated and experimental values. This pattern aligns with the previous findings, which shows that series models tend to underestimate thermal conductivity for fine-grained ceramics. Moreover, experimental observations indicate that although reducing additive content can diminish the content of the secondary phase at grain boundaries, the accompanying grain refinement offsets this benefit, resulting in no significant thermal conductivity enhancement. Notably, even in the 7YbM-25 sample with the highest lattice oxygen concentration (0.36 wt.%), the thermal conductivity attains 231 W/(m·K), confirming that the positive influence of grain growth far outweighs the phonon scattering induced by point defects.

Nan and Birringer reported that under coarse-grained conditions (>10 μm), thermal conductivity approaches that of single-crystal SiC, rendering grain boundary thermal resistance negligible. Conversely, in fine-grained systems (<10 nm), thermal conduction is almost entirely governed by grain boundary thermal resistance, while in the intermediate grain-size range (10 nm – 10 μm), thermal conductivity declines sharply as grain size is reduced [46]. Our finding confirms the critical part played by grain size in governing thermal conduction in polycrystalline SiC.

The primary advantages of the Yb₂O₃–MgO additive system lie in its ability to form a low-viscosity, highly fluid liquid phase that enables near-full densification of SiC ceramics (open porosity < 0.31%) at reduced temperatures within short dwell times, while simultaneously accelerating the dissolution–reprecipitation process to drive abnormal grain growth (up to 17.59 μm). This significantly reduces grain boundary density and promotes crystallization of the intergranular phase and its migration to triple junctions, thereby suppressing phonon scattering and boosting thermal conductivity to 231.8 W/(m·K). However, the system also exhibits certain limitations: the inevitable introduction of secondary phases at grain boundaries may still create additional phonon-scattering interfaces, even when these phases are crystallized and isolated at elevated temperatures. Excessive additive content tends to form a continuous grain boundary network that impedes thermal transport, whereas insufficient addition fails to achieve adequate densification and grain growth. Thus, while the Yb₂O₃–MgO system offers substantial benefits in optimizing liquid-phase sintering kinetics for efficient densification and high thermal conductivity, its ultimate performance is highly dependent on the synergistic interplay of sintering temperature, holding time, and additive content.

Notably, both Huang et al. and Yan et al. employed β-SiC as the starting powder and sintered for 1 h to obtain SiC ceramics. In contrast, our work achieved a comparable thermal conductivity of 231.8 W/(m·K) with only 10 min of sintering using α-SiC. The enhanced thermal conductivity in their studies was primarily attributed to the completion of the β→α phase transition, which reduces interfacial thermal resistance at heterogeneous boundaries and concurrently mitigates sluggish grain growth. Our results demonstrate that an equivalent level of thermal conductivity can be attained solely through grain coarsening, even in the absence of phase transformation. This finding validates the feasibility of preparing high thermal conductivity SiC ceramics directly from α-SiC without relying on phase transition engineering. More importantly, within an extremely short sintering window of just 10 min, we achieved grain sizes exceeding 10 μm by tailoring the temperature-dependent viscosity and kinetic behavior of the Yb–Mg–Si–O liquid phase. This approach not only avoids transformation-induced interfacial defects but also substantially enhances fabrication efficiency, offering distinct advantages for the industrial-scale production of SiC ceramics.

Furthermore, the achievement of high thermal conductivity SiC ceramics within a short sintering time was realized in this study, with the resulting thermal conductivity exceeding 230 W/(m·K), rendering it potentially suitable for applications demanding stringent heat dissipation capabilities. By employing lower-cost α-SiC as the starting material, the constraints imposed by phase transformation on the sintering process were circumvented, and the short-duration sintering approach offers a viable pathway toward reduced production costs and shortened processing cycles.

4. Conclusions

Spark plasma sintering of α-SiC powder at 1900, 2000, and 2050 °C for 10 min yielded high-density SiC ceramics. The influences of densification behavior and microstructural evolution on the thermal conductivity of SiC ceramics were systematically explored.

Sintering temperature strongly regulates grain growth behavior by controlling dissolution–precipitation kinetics, and grain size was identified as the key factor determining the thermal conductivity of SiC ceramics. At 2050 °C, large grains (13.03–17.59 μm) were formed. The isolated and dispersed secondary phases, together with the low-viscosity liquid phase, jointly refined grain boundaries, reduced defect density, and suppressed phonon-grain boundary scattering. Consequently, the phonon mean free path increased to 83.4–90.8 nm, enabling efficient phonon transport. In contrast, samples sintered at lower temperatures (7YbM-19 and 7YbM-20) exhibited fine-grained structures (grain sizes 0.5–0.6 μm), where uniformly distributed secondary phases formed continuous scattering networks. The resulting increase in interfacial thermal resistance limited the phonon mean free path to 37.6–45.9 nm and led to significantly lower thermal conductivity. Notably, even in the absence of a β→α phase transformation, SiC ceramics prepared in this study achieved a high thermal conductivity of 231 W/(m·K), underscoring the dominant role of grain size engineering in optimizing thermal transport in polycrystalline SiC.