Fabrication of SiCw/Ti3SiC2 composites with improved thermal conductivity and mechanical properties using spark plasma sintering

Abstract: High strength SiC whisker-reinforced Ti3SiC2 composites (SiCw/Ti3SiC2) with an improved thermal conductivity and mechanical properties were fabricated by spark plasma sintering. The bending strength of 10 wt% SiCw/Ti3SiC2 was 635 MPa, which was approximately 50% higher than that of the monolithic Ti3SiC2 (428 MPa). The Vickers hardness and thermal conductivity (k) also increased by 36% and 25%, respectively, from the monolithic Ti3SiC2 by the incorporation of 10 wt% SiCw. This remarkable improvement both in mechanical and thermal properties was attributed to the fine-grained uniform composite microstructure along with the effects of incorporated SiCw. The SiCw/Ti3SiC2 can be a feasible candidate for the in-core structural application in nuclear reactors due to the excellent mechanical and thermal properties. 

Keywords: SiC whisker; Ti3SiC2; mechanical property; thermal conductivity; spark plasma sintering

1 Introduction

Ti3SiC2 is a typical MAX phase material (M: early transition metal, A: group A element, and X: C or N), which was developed in 1967 [1]. Because Ti3SiC2 unit cell consists of alternating covalently-bonded Ti6C octahedra and planar metallic-bonded Si layers along the c-axis direction [2], it shows combined properties of ceramics and metals, such as high elastic modulus, fracture toughness, thermal shock, and corrosion resistance [2–7]. However, the flexural strength (260–450 MPa based on four-point bending test), Vickers hardness (4 GPa), and thermal conductivity (k) of Ti3SiC2 are known to be insufficient for nuclear reactor applications, which are inferior to those of SiC [4]

One feasible way to compensate these weaknesses is the incorporation of strengthening filler, which possesses good mechanical and thermal properties [8]. Among many possible fillers, because SiC is thermodynamically stable along with excellent mechanical properties and high k [9–13], the Ti3SiC2 reinforced with SiC particles has attracted much attention [14–22]. It was reported that the Vickers hardness, fracture toughness, k, and oxidation resistance of Ti3SiC2 could be improved by the addition of SiC particles [14–16]. However, the room-temperature strength of Ti3SiC2 decreased by the addition of SiC due to the retained tensile stress in the Ti3SiC2, originating from the increased thermal expansion mismatch between SiC and Ti3SiC2 [14,16]

On the other hand, SiC whisker (SiCw) can be a promising one-dimensional filler, which can strengthen the composite by crack deflection, bridging, and whisker pull-out, due to its excellent strength combined with high aspect ratio [23]. Indeed, the bending strength of Al2O3/Ti3SiC2 was improved to 688 MPa when 20 wt% SiCw was added [24]. Furthermore, the presence of SiCw in the SiCw/TiC/Ti3SiC2 was reported to increase the room-temperature strength. Hashimoto et al. [25] reported a very high bending strength of 1 GPa for the Ti3SiC2 containing 15 vol% SiCw, which was explained by the preferential grain orientation, TiC precipitates, and the effects of SiCw. However, the presence of TiC is not desirable because it deteriorates the oxidation resistance of Ti3SiC2 [26–28]. Moreover, the Ti–Si intermetallic compounds, which are formed simultaneously upon the decomposition of Ti3SiC2 during sintering, are not desirable for nuclear applications due to their poor corrosion resistance [29]

Therefore, compared to SiC particles, one dimensional SiC whiskers have remarkable effects on the improving flexural strength of ceramics. This study aimed to investigate the effects of SiCw on the reinforcement of Ti3SiC2. The SiCw/Ti3SiC2 composites were fabricated using a heteropolar coagulation method followed by spark plasma sintering, which can minimize the decomposition of Ti3SiC2. The mechanical and thermal properties of SiCw/Ti3SiC2, as a function of SiCw content, were analyzed in comparison with the monolithic Ti3SiC2

2 Experimental 

2. 1 Starting materials 

Commercial Ti3SiC2 powder with 98.5% purity was used as a starting material (Beijing Jinhezhi Materials Co., China), which contains Al2O3 and TiC impurities. SiCw with a diameter of 0.4–0.9 μm and a length of 6–120 μm was used as a reinforcement (Union Materials Co., Republic of Korea), while polyethyleneimine (PEI, molecular weight ≈ 10,000, Aladdin Co., China) was used as a cationic dispersant to improve the uniform distribution of SiCw in the TTi3SiC2 matrix.

2. 2 Composite fabrication 

SiCw and Ti3SiC2 particles were added into water containing 1.5 wt% PEI, while the pH of the solution was adjusted to 3 using HCl to achieve a uniform dispersion. The pH of the suspension was then increased to 9 by adding NH4OH followed by ultrasonication for 45 min, where a uniform dispersion by hetero-coagulation between the Ti3SiC2 particles and SiCw could be achieved due to the opposite surface charge. After drying the suspension at 80 ℃ in a vacuum, a uniform SiCw and Ti3SiC2 mixture could be obtained. 

The mixture was consolidated at 1350 ℃ for 20 min using a spark plasma sintering (SPS, HP D25/1, FCT System GmbH, Germany) in an Ar atmosphere after loading the powder into a graphite die with an inner diameter of 60 mm. The heating and cooling rate was 50 ℃/min, and 50 MPa uniaxial pressure was applied during sintering. The amount of SiCw was controlled at 1 wt%, 5 wt%, and 10 wt%, which corresponded to 1.24 vol%, 6.2 vol%, and 12.4 vol%, respectively, in the SiCw/Ti3SiC2, while a pure monolithic Ti3SiC2 was also fabricated at the same condition for comparison. 

2. 3 Characterization 

The phases in the composite were analyzed with a X-ray diffractometer (XRD, D8 Advance, Bruker AXS, Germany) using Cu Kα radiation under an operating voltage 40 kV and current 30 mA. The microstructure of SiCw, powder mixture, and sintered specimen was observed with a scanning electron microscope (SEM, Hitachi S-4800, Japan) equipped with an energy dispersive spectroscope (EDS). A transmission electron microscope (TEM, JEM-2010) equipped with an EDS was also utilized to analyze the interface between SiCw and Ti3SiC2 matrix. 

A zeta potential analyzer (Zetasizer Nano ZS, Malvern, UK) was used to measure the surface charge of the SiCw and Ti3SiC2 in deionized water. The pH was controlled at 3–12 with or without PEI addition. The composite density was measured using an Archimedes’ method. Three-point bending strength was measured for rectangular specimen (20 mm × 4 mm × 2 mm) after polishing the sample surface using a diamond suspension. A universal electromechanical testing system (CMT5105, MTS, USA) was used for the strength test at room temperature with a cross-head speed of 0.5 mm/min. At least 5 samples were tested for each type of specimen. The indentation test was performed to measure the Vickers hardness at room temperature using a Vicker’s diamond indenter (HV-1000; Shanghai Lianer Testing Equipment Co., China). An indentation load (P) of 9.8 N and a dwell time of 15 s were used. At least 20 indents were tested for each specimen composition, and the mean value and standard deviation were calculated. 

A laser flash method (LFA 457, Netzsch, Germany) was used to measure the thermal diffusivity and specific heat capacity (Cp). The measurement was performed for the compacts having a diameter of 12.7 mm and a thickness of 2 mm in a nitrogen atmosphere at room temperature. The k (W/(m·K)) was calculated from Eq. (1)

k = ρλCp (1) 

where λ is the thermal diffusivity coefficient and ρ is the density of the material.

3 Results and discussion 

3. 1 SiC whisker dispersion in Ti3SiC2

The uniform distribution of SiCw in Ti3SiC2 is believed to enhance the mechanical and thermal properties of the final composite. Because PEI is a cationic surfactant with a high molecular weight, it can facilitate the dispersion of SiCw by both electrostatic and steric mechanism [30]. Figure 1 shows the zeta potential behavior of SiCw in an aqueous system with different amounts of PEI as a function of pH. The zeta potential of SiCw was increased from 22 to 58 mV at pH = 3 by adding 1.5 wt% PEI. Because the zeta potential of Ti3SiC2 (25 mV) was similar to that of SiCw without PEI at pH = 3, firstly SiCw was dispersed in water after adding 1.5 wt% PEI, and then the Ti3SiC2 powder was 
added followed by the pH adjustment to 3 to obtain the uniform dispersion of SiCw and Ti3SiC2

The pH of the suspension was then increased to 9 by adding NH4OH, followed by ultrasonication for 45 min. A uniform mixing between the Ti3SiC2 (zeta potential = –30 mV) and SiCw (zeta potential = +25 mV) was obtained by heteropolar coagulation originated from opposite surface charge. The insets in Fig. 1 compare the image of SiCw/Ti3SiC2 dispersion at pH = 3 and 9. Figure 2 shows SEM images of the SiCw and SiCw/Ti3SiC2 mixture, where the uniform distribution of SiCw in Ti3SiC2 is found due to the dispersion by electrosteric mechanism combined with heteropolar coagulation.

Fig. 1 Zeta potential of Ti3SiC22 and SiCw with/without PEI dispersant in an aqueous system. The insets compare the image of SiCw/Ti3SiC2 dispersion at pH = 3 and 9

Fig. 2 SEM images of (a) well-dispersed SiCw with PEI at pH = 3 and (b) 10 wt% SiCw/Ti3SiC2 mixture intentionally agglomerated at pH = 9.

3. 2 Microstructure of SiCw/Ti3SiC2 composites 

The relative density for SiCw/Ti3SiC2 with different SiCw contents after SPS at 1350 ℃ is shown in Fig. 3, where the density ≥ 98.4% was obtained for all samples, regardless of the amount of SiCw. The theoretical composite density was calculated by considering the relative amount of SiCw and Ti3SiC2

Fig. 3 Relative density of SiCw/Ti3SiC2 as a function of SiCw after SPS at 1350 ℃. 

Figure 4 shows the XRD patterns of SiCw/Ti3SiC2 and pure Ti3SiC2 after SPS at 1350 ℃, which indicates the presence of Ti3SiC22 (JCPDS No. 65-3559) and SiC (JCPDS No. 29-1129). No trace for the second phase, such as TiC and intermetallic Ti–Si compounds, is detected. Moreover, the Ti3SiC2 in both monolith and composites seems to have a random orientation, based on a magnified XRD pattern shown in Fig. 4(b), showing characteristic peaks for various planes. This is opposite to the result for the SiCw/TiC/Ti3SiC2 system from Hashimoto et al. [25], where the Ti3SiC2 grains were preferentially aligned. Due to the grain alignment along with the TiC precipitates, the SiCw/TiC/Ti3SiC2 showed very high bending strength, especially when the composite contained 15 vol% SiCw. However, the SiCw/TiC/Ti3SiC2 revealed the decomposition of components during heat treatment, resulting in the formation of intermetallic Ti–Si compounds, such as TiSi2 and Ti5Si3, which are deleterious for nuclear applications. 

Fig. 4 XRD patterns of the SiCw/Ti3SiC2 and pure Ti3SiC2 for 2θ = (a) 20°–80° and (b) 32°–45° after SPS at 1350 ℃. 

The reason for the decomposition of Ti3SiC2 in Ref. [25] was attributed to the flake-shaped Ti3SiC2 particles formed by ball milling. Because Ti3SiC2 contains TiC octahedrons, which are aligned to (111) plane, the flake-shaped Ti3SiC2 particles promote the formation of TiC by the decomposition of Ti3SiC2. The enhanced decomposition of Ti3SiC2 can also be achieved by the mechano-chemical activation using a high energy ball milling [31]. However, the SiCw/Ti3SiC2 composites were fabricated by a soft hetero-coagulation process in this study, without exposing them to a severe milling. Therefore, no formation of TiC was observed in this study. Resultantly, the decomposition of Ti3SiC2 and the formation of TiC could be minimized because the Ti3SiC2 particles remained as randomly oriented polycrystalline.

The SiCw phase distribution in the Ti3SiC2 matrix was observed from the polished-surface of the samples with different content of SiCw. Figures 5(a)–5(c) show the SEM images for the SiCw/Ti3SiC2 containing different amounts of SiCw. The gray phase corresponds to Ti3SiC2 matrix, while the dark phase is SiCw, according to the EDS analysis (not shown here). The SiCw is distributed uniformly in the Ti3SiC2 matrix for the 1 wt% SiCw/Ti3SiC2 sample. Some agglomeration of whiskers in the 5 wt% and 10 wt% SiCw/Ti3SiC2 composites was observed (Figs. 5(b) and 5(c)). Figure 5(d) shows a high-angle annular dark-field (HAADF) image for a SiCw embedded in the Ti3SiC2 matrix. The Ti3SiC2 and SiCw can be distinguished by the intensities in the HAADF image, which are proportional to the square of atomic number [32]. No crack is found at the interface between SiCw and Ti3SiC2 matrix. 

Fig. 5 SEM images for the polished surface of (a) 1 wt%, (b) 5 wt%, and (c) 10 wt% SiCw/Ti3SiC2. (d) HAADF image for the 10 wt% SiCw/Ti3SiC2 and (e–g) EDS results for the points marked in (d). 

Figures 5(e)–5(g) show the semi-quantitative EDS analysis results for points 1, 2, and 3 shown in Fig. 5(d). Only Si and C are detected for point 1, as shown in Fig. 5(e), which is the SiCw. Ti3SiC2 is the phase present for point 2, while Al and O are detected at point 3, as shown in Fig. 5(g). Because Al was intentionally added to facilitate the synthesis of Ti3SiC2, it seems that Al is segregated at point 3 after oxidation into Al2O3. The presence of Al2O3 is reported to improve the oxidation resistance, strength, and fracture toughness of Ti3SiC2, while decreasing the possibility for the formation of TiC [33,34]

Both TEM and EDS results indicate that there is no obvious interfacial reaction between the SiCw and Ti3SiC2 matrix. Spencer et al. [35] could not observe the reaction between SiC fibers and Ti3SiC2 up to 1550 ℃ either. This thermochemical stability between SiCw and Ti3SiC2 would be beneficial for improving the mechanical and thermal properties of the composites. 

Randomly oriented Ti3SiC2 grains can be observed with the fractured surface images for both monolithic Ti3SiC2 and SiCw/Ti3SiC2, as shown in Fig. 6. Ti3SiC2 grains typically show plate shape because of the layered TiC and Si structure. Abnormally grown Ti3SiC2 grains were observed for the pure Ti3SiC2 and composites containing up to 5 wt% SiCw, as shown in Figs. 6(a)–6(c). The abnormal grain size of Ti3SiC2 decreased with increasing SiCw content. The very large abnormal grains seemed to be mostly impinging each other and dominated the microstructure of the monolithic Ti3SiC2, but as SiCw was added, they were reduced in terms of the occurrence and size so that they became isolated in the fine Ti3SiC2 matrix grains. 

Fig. 6 SEM images for the fractured surfaces of SiCw/Ti3SiC2 containing different amount of SiCw after SPS at 1350 ℃: (a) 0 wt%, (b) 1 wt%, (c) 5 wt%, and (d) 10 wt%. 

The largest abnormal grain size for monolithic Ti3SiC2 is 150 μm approximately, while those for SiCw/Ti3SiC2 are 52, 56, and 19 μm for the SiCw content of 1 wt%, 5 wt%, and 10 wt%, respectively, when four low magnification SEM photomicrographs of random 0.25 mm × 0.22 mm area fracture surfaces (not shown here) were examined for each specimen. Notably, only 1 wt% SiCw addition suppresses the abnormal grain growth significantly similar to that of 5 wt% SiCw addition, which might be attributed to the good dispersion of SiCw. The abnormal grain growth persisted until the SiC whisker content increased to 10 wt%, where a fine-grained uniform microstructure could be obtained (Fig. 6(d)). Moreover, the addition of SiCw seemed to affect not only the abnormal grain growth but the overall microstructure, which resulted in finer Ti3SiC2 matrix as more SiCw was added. Besides, the toughening mechanisms, such as the whisker bending and whisker pull-out as well as interface debonding could be observed in the high magnification SEM image of the fracture surface of the 10 wt% SiCw/Ti3SiC2 sample (Fig. 7). It implies that the interface bonding strength between SiCw and Ti3SiC2 is not that strong. 

Fig. 7 SEM image of the fractured surface for the SiCw/Ti3SiC2 containing 10 wt% SiCw

3. 3 Mechanical properties of SiCw/Ti3SiC2 composites 

3.3.1 Bending strength 

Figure 8 presents the bending strength of the SiCw/Ti3SiC2 composites at room temperature as a function of SiCw content. Considering the bending strength of the monolithic Ti3SiC2 was 428 MPa, the strength of composite did not change much up to 5 wt% SiCw. On the other hand, the bending strength of composite containing 10 wt% SiCw reached to 636 MPa, which is significantly improved from the monolithic Ti3SiC2 by 48%. 

Fig. 8 Bending strength of the SiCw/Ti3SiC2 containing different amount of SiCw

This strength behavior as a function of SiCw might be affected by the microstructure shown in Fig. 6, where the largest abnormal grain size decreased from 150 to 19 μm by increasing the SiCw content from 0 to 10 wt%. Because the critical flaw size generally decreases with the decrease in the largest grain size, it is reasonable that the SiCw/Ti3SiC2 with 10 wt% SiCw showed the highest bending strength because the strength of ceramics is limited by the critical flaw size. Besides, the higher strength also resulted from the finer grain size according to the Hall–Petch relationship and Ref. [36]. Therefore, the uniform and fine grain sizes with 10 wt% SiCw, as shown in Fig. 6, seemed to contribute to the significantly improved strength. Hashimoto et al. [25] also reported a similar trend for the SiCw/TiC/Ti3SiC2 by varying the content of SiCw. However, it is notable that the composites containing up to 5 wt% SiCw showed similar strength compared to monolithic Ti3SiC2 despite of microstructural difference shown in Fig. 6. Therefore, the bending strength behavior of the composites cannot be explained with the grain size in the microstructural alone. 

A few more factors other than the microstructure must be considered to better understand the effects of the SiCw on the composite strength. The crack bridging by the SiCw in the wakes behind the tips of cracks can be another reason (Fig. 9(d)), in addition to the fine microstructure, to increase the SiCw/Ti3SiC2 composite strength [37]. On the other hand, there are two possible opposing effects of whiskers to decrease the strength of the composite. Ti3SiC2 is non-cubic and has a layered structure, resulting in extensive grain bridging. That is why Ti3SiC2 intrinsically has relatively high fracture toughness. However, the addition of SiCw decreased this matrix grain bridging effect significantly, as most of the large abnormal grains disappeared, and bridging grain sizes became much smaller, as shown in Fig. 6. The reduced grain bridging would harm the composite strength [38]. Besides, as Wan et al. [16] observed in the SiC-particulate composites, the strength of the composite could be decreased as a result of the residual tensile stresses in the matrix due to the thermal expansion mismatch with the SiCw

Fig. 9 SEM images of the surface after indentation test for (a, b) monolithic Ti3SiC2 and (c, d) 10 wt% SiCw/Ti3SiC2

Thus, the effects of SiCw on the strength of the SiCw/Ti3SiC2 composites may be complicated by these various phenomena occurring at the same time. Therefore, for the composites containing 5 wt% SiCw or less, it is speculated that the strengthening effects of the smaller grain sizes and the crack bridging by the SiCw might have been balanced by the negative effects caused by the reduced matrix grain bridging and residual tensile stresses in the matrix. As a result, the strength of the composites containing up to 5 wt% SiCw was at the same level as that of the monolithic Ti3SiC2. When the SiCw content increased to 10 wt%, the fine-grained uniform microstructure and crack bridging by the SiCw (Fig. 9(d)) dominated over the negative effects, and hence the significant strengthening was observed.

The addition of 10 wt% SiCw in Ti3SiC2 increased the bending strength by 50% compared to the pure Ti3SiC2. However, the addition of particulate SiC to Ti3SiC2 or Ti3Si(Al)C2 resulted in the decrease of flexural strength [14–16], where the degree of strength reduction increased with the increase in SiC particle content. This difference in reinforcement between SiC particle and whisker comes from the toughening mechanisms by whiskers, such as crack bridging, whisker bending and whisker pull-out, and interfacial debonding. 

3.3.2 Vickers hardness 

Figure 9 shows SEM images of the surface after the indentation test for monolithic Ti3SiC2 and 10 wt% SiCw/Ti3SiC2. The indent shape was irregular with exfoliated surfaces and deformed particles for monolithic Ti3SiC2, as shown in Figs. 9(a) and 9(b). Even though the extended cracks are usually observed at the corners of the indent for brittle ceramics, such cracks were difficult to found in this study, owing to the ductile nature of Ti3SiC2

The deformation around the indent was asymmetric, while the damaged region extended approximately 50% from the indent. Some specimens showed exfoliated directional Ti3SiC2 grains around the indent. When the basal Ti3SiC2 plane was parallel to the load, laminated fracture due to the kink, delamination, and slipping was observed, as shown in Fig. 9(b). Besides, exfoliation occurred when the basal plane of Ti3SiC2 grain was perpendicular to the shear stress, as shown in Fig. 9(a). The deformation during the indentation of Ti3SiC2 is generally caused by the basal plane slipping and debonding at the Ti3C2 octahedron and Si layer interface [4,15].

The incorporation of SiCw decreased the indent size, as shown in Fig. 9. Although the basic deformation behavior was similar to that of the monolithic Ti3SiC2, the degree of grain buckling and fracturing of the SiCw/Ti3SiC2 is less severe, probably due to finer grain size and the presence of whisker. Notably, the presence of SiCw did not decrease significantly the ductile nature of Ti3SiC2. The interfacial debonding between SiCw and Ti3SiC2 matrix seemed to have similar effects on the mechanical properties of SiCw/Ti3SiC2 to the basal plane slipping and debonding between the Ti3C2 octahedron and Si layer occurring in the Ti3SiC2 unit cell. 

Figure 10 shows the Vickers hardness of SiCw/Ti3SiC2 as a function of SiCw content. The hardness of 5.8 GPa for pure Ti3SiC2 increased to 7.9 GPa for the 10 wt% SiCw/Ti3SiC2 composite. The relatively low hardness of pure Ti3SiC2 is attributed to the weak bonding between the Ti–C–Ti–C–Ti chain and Si layer [39,40]. Continuous increase in hardness was found with the increase in SiCw content, as shown in Fig. 10. The significant microstructural change by adding only 1 wt% SiCw, as shown in Fig. 5, would be the reason for a drastic increase in hardness from pure Ti3SiC2 to 1 wt% SiCw/Ti3SiC2. Because hardness is known to follow the Hall–Petch relationship for microcrystalline ceramics [41], the finer microstructure of 1 wt% SiCw/Ti3SiC2 compared to the pure Ti3SiC2 caused the increase in hardness. By increasing the amount of SiCw further, however, the overall grain size gradually decreased, showing a modest linear increase in hardness, as shown in Fig. 1

Fig. 10 Variation of Vickers hardness in the SiCw/Ti3SiC2 as a function of SiCw content. 

3. 4 k of SiCw/Ti3SiC2 composites 

k is very important for nuclear application of SiCw/Ti3SiC2, which directly influences the energy exchange efficiency of the reactor. Figure 11 compares the thermal conductivities of SiCw/Ti3SiC2 composites to the monolithic Ti3SiC2. The k increased with the increase in SiCw content, where the theoretical k of single-crystal SiC is approximately 490 W/(m·K) [42]. The k of 10 wt% SiCw/Ti3SiC2 was 40.3 W/(m·K), which is almost 25% higher than that of the monolithic Ti3SiC2 (32.4 W/(m·K)). Zhang et al. [14] measured the k of Ti3SiC2 composites reinforced with SiC nanoparticles. When the amount of SiC nanoparticles was 30 vol%, the highest k of 39 W/(m·K) was obtained, which was slightly lower than that of the composite containing 10 wt% SiCw in this study. Therefore, it seems that the effect of SiCw is significantly higher than that of nanoparticles on the enhancement of thermal conductivity, which may be attributed to the large aspect ratio of SiCw.

Fig. 11 k of SiCw/Ti3SiC2 as a function of SiCw content. 

4 Conclusions 

SiCw/Ti3SiC2 with high strength and k were fabricated using SPS. The effects of SiCw on the strength of the composites were complicated by multiple phenomena occurring at the same time. As a result, the strengths of the composites containing up to 5 wt% SiCw remained at a similar level as that of the monolithic Ti3SiC2. However, when the SiCw content increased to 10 wt%, the bending strength of the composite (635 MPa) was approximately 50% higher than that of the monolithic Ti3SiC2 (428 MPa). The remarkable strengthening effect with 10 wt% SiCw was attributed to the finegrained uniform microstructure and crack bridging by SiCw in the composite. The Vickers hardness also increased to 7.9 GPa with 10 wt% SiCw from 5.8 GPa for pure Ti3SiC2. Furthermore, the addition of 10 wt% SiCw also increased the k by 25%, which is attributed to the high k of the SiCw and the one-dimensional nature of the long whiskers. 

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