# Improving the thermal conductivity of epoxy composites using a combustion-synthesized aggregated β-Si3N4 filler with randomly oriented grains

Sep 10, 2020

### Characterization of the combustion-synthesized aggregated β-Si3N4 filler

The XRD patterns of the CA-SN fillers are shown in Fig. 2, the inset of which shows the cross-sectional image of the CA-SN bulk product. The outer layer of this bulk product is white, whereas the inner portion appears to be gray. The XRD patterns of the inner and outer layers of the bulk product are displayed at the bottom and top, respectively. The diffraction peaks of the inner portion of the product were mainly attributed to β-Si3N4, whereas the diffraction peaks of the outer portion of the product were attributed to both α-Si3N4 and β-Si3N4. No silicon and silica peaks were observed in the inner or outer layers of the product, indicating that the silicon powder successfully reacted with nitrogen to form Si3N4 during the combustion process. The α-Si3N4 and β-Si3N4 phases are the low- and high-temperature phases, respectively. The transformation of α phase to its β counterpart occurs at temperatures above 1,300 °C15. Hirao et al. reported that α-Si3N4 is present in the surface layer of the combustion products because the combustion temperature of the surface layer was lower than that of the interior owing to the thermal loss from the side surface18. Because α-Si3N4 has lower thermal conductivity than β-Si3N415, only the inner portion of the bulk product was used in the following discussion.

The SEM images of the CA-SN filler are shown in Fig. 3A,B, respectively. The CA-SN filler shows aggregated particle of several tens of micrometers in size (Fig. 3A). The highly magnified image of the CA-SN filler (Fig. 3B) shows that the aggregate was composed of rod-like individual grains that were identified as typical, randomly oriented β-Si3N4 grains. β-Si3N4 grains grow preferentially into a typically hexagonal rod-like shape, attributed to the much faster growth rate along the [001] (or c-axis) direction than along the [210] direction, namely anisotropic or elongated grain growth. Therefore, the Lotgering orientation factor (f00l) was used to evaluate the degree of c-axis orientation in β-Si3N4 bulk, according to Eq. (1)22:

$$f=frac{P-{P}_{0}}{1-{P}_{0}}$$

(1)

where P and P0 = ΣI(001)/Σ(hkl) denote the intensities of the (hkl) reflections in the range of 2θ from 10° to 70°. The value of P was calculated from the ratio of the sum of the (00 l) intensity to that of all (hkl) intensities, and the value of P0 was calculated from the standard data of the JCPDS card (No. 3-1160). The Lotgering orientation factor was calculated to be 0.005 from the XRD pattern of CA-SN (Fig. 2, inset). This value was nearly zero, indicating that the grains are not oriented in one direction. It was also confirmed that the elongated β-Si3N4 grains were randomly oriented in the CA-SN filler.

Figure 3C shows the particle size distribution of the CA-SN filler obtained after ultrasonic dispersion (as mentioned in “Experimental section”). The CA-SN filler has an average particle size of 26 μm, which is significantly larger than the size of an individual β-Si3N4 grain. Furthermore, the aggregated structure is retained even after sonication, indicating that the individual β-Si3N4 grains were connected. Table 1 shows the characterization results of the CA-SN and commercial β-Si3N4 powders (SN-F1, Denka Co. Ltd, Japan) used as filler in a previous study20 (SEM image of the commercial β-Si3N4 powder can be found as Supplementary Fig. S1A). The mean diameters of the CA-SN and commercial β-Si3N4 powders were 26 μm and 4.5 μm, respectively. The specific surface areas of the CA-SN and commercial β-Si3N4 powders were 3.0 m2 g−1 and 4.1 m2 g−1, respectively. In general, the specific surface area increases with decreasing particle size. However, the specific surface areas of both powders were observed to be similar although the particle sizes differed by a factor of 5. This indicates that the individual β-Si3N4 grains are partially sintered with each other to form an aggregate structure, suggesting that it is this aggregate structure that allows the heat to pass more efficiently through the CA-SN filler compared to the commercially available β-Si3N4 powder. Furthermore, the total oxygen contents of the CA-SN and commercial β-Si3N4 powders were 0.29% and 1.83%, respectively, indicating that the oxygen content in β-Si3N4 was significantly reduced by combustion synthesis. It has been reported that the thermal conductivity of Si3N4 increases with a decrease in oxygen content21. Evidently, the individual β-Si3N4 grains in the CA-SN filler showed a higher thermal conductivity compared to the commercially available β-Si3N4. Therefore, we can conclude that the CA-SN filler formed large aggregates (few tens of microns in size) with random orientations of β-Si3N4 grains and a low oxygen content.

### Characterization of epoxy composite loaded with combustion-synthesized aggregated β-Si3N4 filler

The thermal conductivity in the perpendicular direction and the relative density of the CA-SN-loaded composites as a function of CA-SN filler content are plotted as black solid circles and black solid squares, respectively, in Fig. 4. The filler content in Fig. 4 was calculated from the weight–loss curve for up to 600 °C because the β-Si3N4 was stable until 600 °C and only the epoxy resin burned out near 600 °C (typical weight–loss curve at 53 vol% can be found as Supplementary Fig. S2). The gray solid curve shows the thermal conductivity of the commercial β-Si3N4/epoxy composites obtained using our previous work as a Ref.20, wherein the thermal conductivity was also measured in the perpendicular direction. The gray dotted curve represents the theoretical thermal conductivity of β-Si3N4/epoxy composite using the Bruggeman model. The experimental value of the thermal conductivity of CA-SN composites showed a gradual increase with increase in powder content of up to 40 vol%, and it increased rapidly up to 53 vol%. The maximum thermal conductivity of 4.7 W m−1 K−1 was observed at 53 vol%. Additionally, we measured the thermal conductivity in the parallel direction at 53 vol%, yielding a value of 4.8 W m−1 K−1. The similarity in the measured values of the thermal conductivity along the parallel and perpendicular directions indicates the isotropic nature of the CA-SN composite’s thermal conductivity. After reaching 53 vol%, thermal conductivity decreased with further increase in the powder content. The composites show a higher relative density (~ 95%) until the volume fraction of the CA-SN filler reaches 53 vol%. A further increase in the powder volume fraction to 61 vol% and 70 vol% resulted in a decrease in the relative density of the composites to 80% and 71%, respectively. Such a decrease in the relative density was attributed to the incomplete molding of the composite. Compared to the commercial β-Si3N4-loaded composites from our previous study20, the thermal conductivity values of the CA-SN composites were similar to that of commercial β-Si3N4 composites until 40 vol%; however, above 40 vol%, the thermal conductivity of the CA-SN composites was higher than that of commercial β-Si3N4 composites. The thermal conductivities of the commercial β-Si3N4 composite at 53 vol% (Si3N4) along the perpendicular and parallel directions were 1.9 W m−1 K−1 and 2.1 W m−1 K−1, respectively. As the commercial β-Si3N4 was in the form of crushed powder (see Supplementary Fig. S1A), the thermal conductivity difference between the parallel and perpendicular directions was moderate. At 53 vol%, the thermal conductivity of the CA-SN composite was approximately 2.4 times higher than that of the commercial β-Si3N4 composite. These experimental results were compared to the theoretical thermal conductivity obtained using the Bruggeman model, shown as the gray dotted curve in Fig. 4. The Bruggeman model is based on the hypothesis that the spherical particles are distributed homogeneously in a matrix and that they are separated from each other (i.e., there is no contact between the particles)23. Using this model, the thermal conductivity of a composite is described in Eq. (2):

$$1-frac{varphi }{100}=frac{left({lambda }_{c}-{lambda }_{f}right)}{left({lambda }_{r}-{lambda }_{f}right)}times {left(frac{{lambda }_{r}}{{lambda }_{c}}right)}^{1/3}$$

(2)

where λf is the thermal conductivity of β-Si3N4 (W m−1 K−1), λr is the thermal conductivity of the epoxy resin (W m−1 K−1), λc is the thermal conductivity of the composite (W m−1 K−1), and φ is the content of β-Si3N4 (vol%). The thermal conductivity of the epoxy resin (λr) is 0.2 W m−1 K−1 based on our experimental results, and the thermal conductivity of λf for β-Si3N4 is 106 W m−1 K−1, which was estimated by calculating the simple arithmetic mean of thermal conductivity values measured along three coordinate axes based on Li et al.’s work15. The experimental thermal conductivity of the CA-SN composites showed a good fit with the theoretical values calculated using the Bruggeman model below 40 vol%, which suggests that the CA-SN fillers are homogeneously distributed in the epoxy resin matrix (Fig. 4). Furthermore, the CA-SN filler has a minimal effect on the thermal conductivity of the composite for the lower filler content volume percentages because the heat flow through the Si3N4 filler is hindered by the epoxy resin owing to the low thermal conductivity (~ 0.2 W m−1 K−1) of the resin matrix. In the CA-SN filler range of 40–53 vol%, the theoretical model deviates significantly from the experimental values of thermal conductivity; the higher experimental values may be attributed to the formation of a percolation network among the CA-SN fillers. The percolation network is a system where the powder particles are in physical contact, forming a network in the matrix24,25. The thermal conductivity of the composites is dominated by the conduction path formed in the matrix. As is evident from Fig. 4, thermal conductivity increases rapidly with an increase in the powder content up to 53 vol% due to the formation of the thermal conduction path in the matrix. This behavior of the CA-SN-loaded composites is clearly distinct from that of commercial β-Si3N4-loaded composites.

Figure 5 shows the SEM images with backscattered electrons (BSEs) of the CA-SN composites at 40 vol% (Fig. 5A,D), 53 vol% (Fig. 5B,E,F), and 62 vol% (Fig. 5C) CA-SN filler content.(For comparison, SEM image with BSE of commercial β-Si3N4 loaded composite at 53 vol.% filler content can be found in Supplementary Fig. S1B). The small voids observed in Fig. 5A,B,D–F, were due to the shedding of Si3N4 grains when polishing the surface of the composite for SEM observation. As shown in Fig. 4, the relative density of the composites was high, namely ~ 96% until 53 vol% of the CA-SN filler content; hence, the composites were highly dense. The SEM images shown in Fig. 5A–C were captured at lower magnification, whereas the images in Fig. 5D–F were captured at higher magnification. The BSE images provide information regarding the material composition because heavier atoms (with high atomic numbers) scatter electrons more effectively than the lighter atoms (with low atomic numbers). In the BSE images of the CA-SN composites shown in Fig. 5, the CA-SN fillers and epoxy resin appear as lighter and darker regions, respectively. The low-magnification SEM images show that the CA-SN filler was uniformly distributed in the epoxy resin matrix of the composite at 40 vol% and 53 vol% CA-SN filler content; however, larger voids were observed in the composite at 62 vol% powder content owing to the incomplete molding of the composite. The highly magnified SEM image (Fig. 5D) shows that the CA-SN fillers were relatively mono-dispersed in the matrix at 40 vol%, whereas the CA-SN fillers appear to be in contact with each other at 53 vol% (Fig. 5E), thereby confirming the formation of a percolation network among the CA-SN filler particles. Figure 5F shows the detailed morphology of the percolation network formed among the CA-SN filler particles. The CA-SN filler particles were in contact with each other in the composite. In some parts of the CA-SN filler, the rod-like β-Si3N4 grains (indicated using black arrows in Fig. 5F) between the CA-SN fillers appeared slightly to enter the fillers instead of simply contacting at the points, thereby making the structure intricate. Table 2 shows the summary of the reported thermal conductivities of epoxy composite loaded with Si3N4 and AlN. While Si3N4 and AlN have similar particle sizes as CA-SN, AlN is known to have a higher thermal conductivity compared to Si3N4; for example, the thermal conductivity of commercial AlN substrate was measured to be approximately twice as high as that of commercial Si3N4 substrate26. The loaded content of AlN was ~ 55–60 vol%, which was slightly higher than that of the CA-SN composites (53 vol%) at the maximum value of thermal conductivity. The reported thermal conductivity values of Si3N4 and AlN composites were ~ 3.0 W m−1 K−1 and ~ 3.4–4.0 W m−1 K−1, respectively. Compared to Si3N4 and AlN, as per the data listed in Table 2, CA-SN provides the best results with regard to the enhancement of thermal conductivity of the epoxy composite. This improvement in the thermal conductivity of our samples may be attributed to two major reasons: the oxygen content and morphology of the powdered particles. As shown in Table 1, CA-SN has a lower oxygen content compared to commercial Si3N4. The thermal conductivity of Si3N4 increases with a decrease in oxygen content21. However, the thermal conductivity of the CA-SN-loaded composite was higher than the reported values for the AlN-loaded composites. Therefore, this enhancement cannot be only explained in the context of lower oxygen content. Hence, the morphology of the powdered (filler) particles would be a more significant factor in explaining this behavior. Figure 6 presents the schematic view of the composite loaded with CA-SN fillers (Fig. 6A) and commercial Si3N4 fillers (Fig. 6B). In the commercial Si3N4-loaded composites (Fig. 6B), the β-Si3N4 fillers came in contact with each other when the percolation network among them was formed, leading to an increase in the thermal conductivity of the composite. However, the CA-SN filler is an aggregate filler wherein the rod-like β-Si3N4 grains were partially sintered with each other (Fig. 6A). This morphology allows the heat to be conducted even more efficiently between the β-Si3N4 grains in the CA-SN filler compared to commercial β-Si3N4 filler, where they are only in contact. Furthermore, the individual β-Si3N4 grains in the CA-SN filler have a lower impurity oxygen content, suggesting that CA-SN has a higher thermal conductivity than commercial β-Si3N4.