746 Journal of the American Ceramic SocietyHasselman et a Vol, 79. No. 3 25 2.0 1.5 ange 10 1.0 ⊥uuuL 0 (W/m2K h(W/m2K (a) Fig. 5. Theoretical thermal conductivity curves for a VS SiC whisker-reinforced lithium aluminosilicate glass co 30 vol%o values compared with room-temperature valves ferred from experimental data:(a)parallel and (b) perpendicu e and perfectly aligned whiskers calculated for a whisker diameter of 0.7 um over a range of interfacial conductar thermal conductivity he value of 10 W/(mK) was inferred from the transverse whisker composites at 500.C, K3 can be calculated thermal conductivity data for an uncoated silicon carbide fiber from 10.0 to 10.7 W/(m-K). The theoretical curves then reinforced reaction-bonded silicon nitride. 1 The corresponding a lower bound on the whisker thermal conductivity of about value for the same composite reinforced with carbon-coated 55 W/(m K). Assuming an he value identical to the one used for fibers was found to be =10 W/(m2.K). This latter value is the room-temperature data(5 X 10 W/(m2. K), an upper bound low because, due to a mismatch in the coefficients of thermal for the thermal conductivity of the VLS whiskers at 500"C can pansion, the presence of the carbon coating promotes inter- be estimated to be 65 W/(m K). Similarly, for the VS whiskers facial separation as the composite is cooled from its processing at 500C, a lower bound of 35 W/(m K)and an upper bound temperature. For a particular diamond-reinforced cordierit ( based on an h≈7×10W/(m2.K)of90W/mK)is matrix composite at room temperature, the interfacial thermal ferred. It is of interest to note that the decrease in thermal conductance was estimated to be about 10 W/(m.K) onductivity of the whiskers over this temperature range is Thermal conductivity data measured for a SiC-particulate comparable to the corresponding decrease for polycrystalline reinforced aluminum matrix composite implied an he value of tructural SiC 28 Also note that because of the small size of the 1.5×105W(m2K).9 A comparison of these values with Fig 4(a) for the VLs VS whiskers and associated much greater effect from finite interfacial thermal conductance these whiskers have a corre whiskers indicates that for an he> 10 w/(m-K), the Ks values sponding smaller effect on the composite thermal conductivity which is approximately equal to the previously obtained lower For this reason, the temperature dependence of the composites bound,120 W/(m-K). Assuming an he value no lower than containing the VS whiskers will be closer to that of the matrix X 10 W/(m2.K), the upper bound on K, becomes s200 than for the composites with the much larger VLS whiskers, W/(m K). It would require an he value as low as 3 X 10 as observed W/(mK)to yield a K33 value of 300 W/(m'K) These results lead to some rather interesting conclusions Referring to Fig. 5(a), similar results are found for the vs the interfacial thermal conductance is high in both composites hiskers.For he 10 W/(m2.K), the K33 values approach (i.e, >10 ), the VLS whiskers appear to have a significantly ose for h→∞. For an h. value as low as7×103W/(m2-K) igher thermal conductivity than the VS whiskers, as previously K becomes≈200W/(mK). An h value as low as6×10° inferred from data assuming perfect interfacial thermal con- required to yield a K33 value of 300 W/(mK) tact. 29-3 Assuming the interfacial thermal contact in these com- Estimates for the temperature dependence of the whisker posites is not perfect, as appears likely for the reasons discussed thermal conductivity can be made in the same way. For the VLs lously, the results for the lower values of h. indicate that Table Il. Whisker Distribution Functions and Calculated Thermal Conductivity Values at Room-Temperature Parallel(K33)and Perpendicular(Ku) to Aligned Whisker Resulting thermal conductivity (w/(m'k) Resulting equations for K, and k f(0)= uniform,60<6<90°K=0.083K3+0.917K1 Kn=0.458K3+0.542K1 K=3.28 f()=sin36,60°<<90° 人=041K +0.951K1 K3=93 +0.524K1 K1=3.89