Ceram Soc,73174-48190 journa Thermal Conductivity of Vapor-Liquid-Solid and Vapor-Solid Silicon Carbide Whisker-Reinforced Lithium Aluminosilicate Glass-Ceramic Composites D.. H. Hasselman' and Kimberly Y. Donaldson Thermophysical Research Laboratory, Department of Materials Science and Engineering. J. R. Thomas, Jr. Ceramic Science and Technology p, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 John J. Brennan d Technologies Research Center, East Hartford, Connecticut 06108 ty and diffu- cting ness for the tw e wo composites. JHISKER- or fiber-reinforced ceramic, glass-cer glass matrix composites offer advantages over single phase ceramics for load-bearing requirements at elevated temperatures.- Such composites will also need to be able to withstand high levels of heat flux /or rapid temperati changes. Since these conditions can lead to failure by thern D.K.Shetty- Manuscript No. 193285. Received August 22, 1994:; approved March 30, 1995 5 the composite Specimen preparation was conducted as part of Contract No. F49620-88-C-006 e 2.67 g/cm', which supported by the Air Force Office of Scientific Re conductyity Member, On sabbatical leave from the Dep nt of Mechanical Engineering, Virgi Advanced Polytechnic Institute and State U ity, Blacksburg. Virginia. Los Alamos National Laboratory. Los Alamos, NM. 742
March 1996 Thermal Conductivity ofVLS and VS Silicon Carbide Whisker-Reinforced LAS Glass-Ceramic Composites :要 民二吗 (a) Fig. 1. Optical micrographs of a 30 vol% VLS SiC whisker-reinforced lithium aluminosilicate glass:(a) parallel and (b)normal to hot-pressing suggests that the VLS whisker composite contained approxi- approximately 3%0, the data for the LAS matrix and SiC-LAS 2%0 porosity. Fig ptical micrographs of composites are identical sections of the VLS whisker composite parallel and Figures 2 and 3 show the therma ctivity data for the to the hot-pressing direction, respectively. During he natrix and the composites with the vls and vs whiskers for ressing the whiskers achieved a preferential orientation, heat flow parallel and normal to the hot-pressing direction aligned normal to the hot-pressing direction within an angle of that is significantly higher than that of the matrix. This increase symmetric). A similar preferred orientation was observed for ared with a corresponding factor of 2 for those with the VS whiskers. It should also be noted that only the thermal (2) Determination of Thermal properties conductivity values for the VLs whisker composite normal the hot-pressing direction show a significant negative tempera The thermal diffusivity was measured by the flash ture dependence. All the other sets of data shown indicate little nique, .26 using a glass-Nd laser as the flash source. The if any, dependence on temperature mens were rectangular plates approximately 5 mm x8 mm with a thickness of 3 mm. The transient temperature was moni mnhp足t Table L. Specific Heat of LAS Matrix and SiC-LAS Composite to assure linearity between the specimen temperature change Specific heat (/(gK)) and detector output. 2 Up to temperatures of approximately LAS matri 200C the thermal diffusivity measurements were made in air. Above this temperature to about 500.C the samples were con tained in a carbon-resistance furnace with a nitrogen atmosphere. The specific heat was measured by differential scanning calo- rimetry. The thermal conductivity was calculated by multi- plying the experimental thermal diffusivity data with the orresponding data for the density and specific heat, Because of 0.73 the low coefficient of thermal expansion for the matrix pha 0.894 nd composites of this study, changes in specimen dimensions with temperature had no significant effect on the thermal con ductivity values obtained in this manner 511 1.140 VS SIC-LAS IlL. Results, Analysis, and Discussion 0.745 0.9 ()Experimental Results 070 Table e weithine nthe swas tice per of the dsc method of 507 1.145
Journal of the American Ceramic Society-Hasselman et Vol. 79. No. 3 VLS SiC-reinforced silicon nitride composites, the VLS whisk- EE-2a ● VLS SiCw-LAS ers at room temperature have been estimated to have a thermal ▲ VS SiCM-LAS conductivity value of about 100 W/(mK). These estimates, however,are probably low since they were based on the assumption of perfect whisker-matrix thermal contact In view of these uncertainties, analysis of the experimental data took the following approach. The experimentally measured value of K at room temperature was used with a range of values of whisker thermal conductivity (K) and interfacial thermal conductance(he)in the expressions of Benveniste and Miloh to generate a family of curves for the room-temperature thermal conductivity parallel(K33) and perpendicular(Kn)to the axis of perfectly aligned whiskers. Comparison between the experimental data and these predicted curves should tablishing a window of reasonable values for the hermal conductivity and interfacial thermal conductance for each composite at room temperature. All calculations assumed hat both composites contained 30 vol% uniaxially aligned whiskers with a length-to-diameter ratio of 12. The thermal TEMPERATURE(°C) conductivity of the whiskers was assumed to be isotropic. All combined effects which might contribute to an interfacial ther mal barrier were assumed to be represented by a single interfa- glass matrix and for 30 vol% VLS SiC and VS Sic cial thermal conductance value. The diameter of the VLs orced lithium aluminosilicate glass matrix parallel to whiskers was taken to be 6.5 um and the diameter of the vs pressing direction whiskers was taken to be 0.7 These whisker dimension were used to calculate the descriptive geometry (i,e,eccentric- ity, distance between centerline and foci of the ellipse, etc. )of (2) Analysis the ellipsoids used in Benveniste and Miloh's solutions A direct comparison of the experimental data with those calculated K,3 curves at room temperature for the VLs and VS whiskers are shown in Figs. 4(a)and 5(a), respectively predicted from theory is not possible in view of the preferred In general, for both sets of data, the composite thermal conduc- orientation and differences in the nature of the whiskers (i.e the thickness, thermal conductivity, interfacial characteristic ty increases sigmoidally with increasing he, as theoretically etc. ) The thermal conductivity values for the two Sic whisker predicted for composites with an interfacial thermal barrier types are unknown and cannot be estimated theoretically with any degree of certainty, since thermal conductivity is higl falls below Km. This result is also expected, since the interfacial sensitive to impurity and defect level. An estimate for the inter thermal contact at these low he values is so poor that the whisk facial thermal conductance is even more uncertain, although the ers cannot contribute to the heat conduction and effectively act value is probably not infinite since the approximate factor of 5 as a pore phase with zero thermal conductivity. At the highest mismatch in the elastic moduli of the Sic whiskers and the values of he, the K33 values become constant. Note, however LAS matrix promotes phonon scattering. However, the thermal that the magnitude of K3 for any value of K, falls well below conductivity value for the VS whiskers at room temperature has that predicted by the rule of mixtures. This occurs because the length-to-diameter ratio of the whiskers is finite, and the rule of been estimated from experimental data for mullite, alumina, mixtures is valid only as this ratio approaches infinity and silicon nitride matrix composites to range from about to 30 W/(mK). Similarly, from experimental data for 30 vo Figures 4(b) and 5(b) show the calculated curves for Ki characteristics similar to the ones shown in Figs. 4(a)and 5(a) with the exception that the Ku values show only a slight depen dence on the magnitude of the K, values. As easily verified ■ ◆vssc.LAs from theory, for heat flow transverse to the axis of oriented fibers or whiskers, the dependence of the composite thermal onductivity (K ) on K, i.e., d(ke)/d(K1), approaches zero The curves shown in Figs, 4 and 5 assume that the whiskers are uniaxially aligned. Since the whiskers in the composites of s study are not perfectly aligned the calculated data still annot be directly compared to the experimental data. for known values of K, (the global thermal conductivi to the hot-pressing direction) and K,(the global conductivity normal to the hot-pressing direction), the of Chou and Nomura, which assumes an axially fiber orientation transformed by rotation through an ang describe the fiber misalignment, can be used to derive sions that can be used to obtain K33 and K As shown by Chou and Nomura, K, can be expressed as TEMPERATURE(°C) [sin20K33+(1+ cos O)kulf(e)sin 6d8 id for 30 vol VLS SiC and vs SiC wh er f(0)sin 6de reinforced litl luminosilicate glass matrix normal to the hot pressing direction
March 1996 Thermal Conductivity of VLS and vS Silicon Carbide Whisker-Reinforced LAS Glass-Ceramic Composites T 00 2.0 Exper Inent al Data 150 125 日 Km 15 Km iud LuLu 05 102103104105106107106109101 h(W/m2K) LOG h(W/m2K) (b) Fig. 4. Theoretical thermal conductivity curves LS SiC whisker-reinforced voI erfectly aligned whiskers calculated for a whisk er of 6 a co values compared with room-temperature values info experimental data: (a)parallel and ular to whisker axis here 0 is the angle between the direction parallel to the hot composite theory. For instance, a distribution f()= sin 0 pressing direction and any specific whisker and f(e)is a fu resulted in a value of K> Ku. Such a result is not consister tion which describes the distribution of whisker orientation with general composite theory. The most consistent values of Similarly, K, can be described by K and K were obtained from a sin 3 0 distribution and from a distribution uniform between 0=60 and 90. These results (cos 0K33+ sin AK)f(e)sin edg calculated from the experimental data at room temperature, are summarized in Table lI Comparison of these results indicates that the calculated f(e)sin 0de values of Ku and K 3 do not differ greatly for either distribution between0<0<30. For a composite consisting of a low thermal conductivity matrix and aligned whiskers with a high For a known whisker orientation distribution and known thermal conductivity, the relative magnitudes of Ki and K33 of K and K33, Eqs. ( 1)and(2)can be used to predict shown in Table ll are consistent with composite theory mal conductivity values for a given composite. Con Comparison of the K, values in Table II with the calculated the experimental thermal conductivity data and an curves for K3 shown in Figs. 4(a)and 5(a) permits establishing assumed orientation distribution function for the whiskers will a lower bound on both the whisker thermal conductivity and permit calculation of K, and K33, which is the approach taken he interfacial conductance at room temperature. For the VLs n this study whiskers, with K33 ranging from about 16.6 to 18.0 W/(mK), For instance, for a composite with a random whisker thermal e n act i d, n ic,tt aust be f east fe o wrrm -Ka As mentioned previously, however, perfect interfacial thermal Kp-”→大3+Kn contact is unlikely in these composites due to the mismatch in the elastic properties of SiC and LAS. The Similarly, for whiskers perfectly aligned normal to the hot resulting phonon-scattering at the interface can create a signif ressing direction (i.e, 6=90) thermal conductivity values reported for particulate diamond (4a) reinforced cordierite matrix composites. 2 On the other hand, if K were equal t to the maximum value K,=sK3++aKI (4b) for high-purity single-crystal SiC, 3 the lower bound on h would be inferred to be about2.5×105W/(m2·K) A similar comparison of the results for the vs whiskers For the composites and whisker distribution of this study, the nggests a lower bound on K at room temperature of the order values of K and K, are expected to lie between the values given of 40 W/(m K). This value is some 50% higher than values by eqs. (3)and estimated for vs whiskers from data for various other ceramic A numerically detailed whisker orientation distribution func- matrix composites assuming perfect thermal contact. If K, for tion for these composites was not obtained. However, as the whiskers is assumed to be 490 w/(m K), a lower bound on reported earlier, microstructural examination indicated that the h is found to be about 6x 105 w/(m2.K) whiskers were aligned within about 30 from the plane normal An estimate on the upper bound of K33 must rely on specula to the hot-pressing direction. A number of orientation distribu- tion. Investigation of data available for other co tion functions were tried over this range with the resulting hould yield information on reasonable expected values of h values for K, and K33 examined for general consistency with For instance, at room temperature and atmospheric pressure, an
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
March 1996 Thermal Conductivity of VLS and vS Silicon Carbide Whisker-Reinforced LAS Glass-Ceramic Composites the thermal contact between the LAS matrix and these two was found to be lower in the direction of hot pressing than isker types does not differ greatly. This contact is also appar in the direction normal to hot pressing, due to the preferred ently not significantly affected by the carbon-rich surface of rientation of the whiskers. Furthermore, the composites rein- skers. Any differences measured in the thermal forced with the VLS whiskers exhibited higher thermal con onductivity of composites containing these whiskers therefore ductivity values than those reinforced with the Vs whiskers nust be attributed primarily to the order of itude differ Analysis of the experimental data indicated that the Vs and ce in the thickness of these whiskers rather than to inherent VLS whiskers have nearly equal room-temperature thermal differences in their thermal conductivity. conductivity values of about 200 W/(m K). The differences in For both ites, the Ku values at room temperature thermal conductivity values for the composites must be attrib- listed in Table II significantly exceed any values calculate uted to the existence of a matrix-whisker interfacial thermal from Benveniste and Miloh's solution (refer to Figs. 4(b) barrier and the about 1 order of magnitude difference in and 5(b),even for perfect thermal contact (i.e. he = oo)and a whisker diameter thermal conductivity value of ss490 W/(m K). This difference nnot be attributed to the choice of numerical values used for the calculation, since the magnitude of Ku is relatively Reference D.B.Marshall and A G. Evans. " The Tensile Strength of Uniaxially Rein insensitive to the whisker aspect ratio, the magnitude of the interfacial conductance when h.- oo and the whisker thermal Ceramics, 7. Edited by R C. Bradt, A G. Evans, D P H Hasselman, and F. conductivity values for K >> Km. 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At least qualitatively, this indicates that depending on the distribution of the reinforcing phase, the "Effect of Thermal Expansion Mismatch on the Thermal Diffusivity of Glass-Ni contribution of percolation to composite thermal conductivity Composites. "J. Am. Ceram, Soc., 6[9-10]581-86(1980) is a function of the direction of heat flow. Consequently, the ID. P. H. Hasselman, L. F Heat Conduction Characteristics of Carbon Fiber- Reinforced Lithia Alumino- thermal conductivity value for one direction can exceed the silicate Glass-Ceramic,".Mater. Sci, 22, 701-709(199 theoretical value obtained from composite theory, while this IA. G. Every, Y. Tzou, D. P. H. Hasselman, and R. Raj, "The Effect of effect does not occur in another direction. This latter conjecture Microstructure on th ity of Particulate ZnS/ Diamond Com- is supported by the results of Balberg et al., who used Monte posites "Acta Metall. Mater, 40[1]123-29(1992 Carlo computer simulation to study electrical conduction by A. L. Geiger, Effect of R forcement Particle Size on the Thermal Conductivity of a Particulate Silico percolation in an insulating matrix containing preferentially Carbide Reinforced Aluminum Matrix Composite, "J. Am. Ceram. Soc., 75 [ oriented conducting sticks. For this reason the contribution to 2D. P H Hasselman, K. Y, Donaldson, J. Liu, L. J. Gauckler, and P. D expected to be greater for heat flow transverse to the plane of Ownby. "Thermal Conductivity of a Particulate the whiskers(i.e, parallel to the hot-pressing direction) rather Matrix Composite, "J,Am, oC,77[7]1757-60(1994) direction which involves heat 21312-16(1990) be noted, however, that promoting heat transfer by percolation H. Bhatt, K. Y. Donaldson, D. P. H. Hasselman, and R. T. 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