G E. Youngblood et al./Composites Science and Technology 62(2002)1127-1139 lars m about -0.7 0×104s/m2.The S-term in Eq.(10) is related to the strength of the Umklapp or thermal phonon-phonon scattering resis- h=5000w(cm2K) tance. For high-purity CVD-SiC, several observations in this laboratory have indicated that Sa48+5 s/(m2K) approximately independent of irradiation defect con- W/(cm?K centrations [36]. Although these values may not be quite correct for the Tyranno SA fiber or the CvI-SiC matrix, they are representative enough to predict the correct temperature effects on Keff In Fig. 10(a), the analytic h a 50 W/(cm, K) solutions predicted for the hypothetical Tyranno SA, CVI-SiC composite are replotted as a function of tem- perature forf=0.4 and selected values h=5000, 500 and Temperature (C A well-adhered PyC fiber coating with thickness 0.2 um and thermal conductivity 10 w/m K) would have an equivalent haKa/t= 5000 W/(cm- K), a value that 空(b) represents good f/m thermal coupling. For such a case, Kef(T) ranges from a value of about 29 W/(m K)at 27C up to an apparent maximum of 34 w/(m K)at about 200C, and back down to 26 w/(m K)at 1000C The maximum in Kef at about 200C, observed for all h-values, is related to the rather steep positive tempera ture dependence of the SiC heat capacity for T<600C The two lower h-values (500 and 50 w/(cm-K) repre sent moderate and poor fim thermal coupling, respec tively.Forh≈500W/cm2K),R≈ I and Keff≈Km≈20 W/(m K)for all temperatures. Finally, for h=50 W/ h=50 (cm K), Kefr<12 W/(m K) in the 27<T<1000 oC range. This hypothetical case again emphasizes the 1000 00 mportant role that the interfacial conductance plays in determining Kef(h) when h-values fall in the transition ature resisted b y dm al for ac iai y irma ased land tio af To account fo o account for degradation of Kef(t)due to irra irradiated hypothetical 2D-Tyranno SA / CVI-SiC composite with diation damage, the K(T)and Km(T)-values were h=50.,500or5000W/cm21 lected data values: a=5 um,f=0. 4, Kr(27C)=65w/(m K)and Km(27C)=20 w/(m K). separately adjusted for expected temperature and dose effects prior to substituting them into Eq(1). The ther- mal conductivity degradation for irradiated SiC depends primarily on the radiation temperature when Thermal diffusivity data for unirradiated Tyranno Sa doses are in excess of saturation, i.e. >1 dpa for Sic Sic fiber and for a CVI-SiC matrix were generated and [32]. To estimate the degradation effect of irradiation fit to an expression with linear temperature dependence: quadratic curves were separately fit to the temperature- dependent thermal conductivity data given in reference 32] for high-purity CVD-SiC and SiCe/CVI-Sic irra l/a=P+S(1) (10) diated above saturation. For 27<T< 1000 oC. the equations K()rad=[0. 10+3.5x10-T2K,(T)and for the temperature range 300-1300 K starting with Km(T)rad=0.20+3.6x10-TKm(T were used to known values of a at 300 K. Then KiT)-and Km(T)- represent the temperature dependence of Tyranno SA values were calculated from the generated a-data using fiber and CVI-SiC matrix irradiated above saturation Eq( 8)for both cases. In Eq. (10), the P-term depends doses, respectively upon the initial purity of the SiC as well as the radiation In Fig. 10(b), the analytic solutions predicted for the concentrations. For instance, P=-(0.72+0.08) hypothetical irradiated Tyranno SA/CVI-SiC composite s/m2 for high-purity CVD-SiC as determined by are replotted as a function of temperature after the ke Senor et al. [36], while CVd-Sic irradiated above and Km values were adjusted for the effects of irradia saturation doses exhibited a P-value of about 10x10+s/ tion. In contrast to the unirradiated condition, for each m[36]. Thus, the P-term for SiC may cover a relatively selected h-value the predicted Keft-values for irradiatedThermal diffusivity data for unirradiated Tyranno SA SiC fiber and for a CVI-SiC matrix were generated and fit to an expression with linear temperature dependence: 1= ¼ P þ S TðÞ ð10Þ for the temperature range 300–1300 K starting with known values of  at 300 K. Then Kf(T)- and Km(T)- values were calculated from the generated a-data using Eq. (8) for both cases. In Eq. (10),the P-term depends upon the initial purity of the SiC as well as the radiation defect concentrations. For instance, P=-(0.720.08) 104 s/m2 for high-purity CVD-SiC as determined by Senor et al. [36],while CVD-SiC irradiated above saturation doses exhibited a P-value of about 10 104 s/ m2 [36]. Thus,the P-term for SiC may cover a relatively large range from about 0.7 to +10 104 s/m2 . The S-term in Eq. (10) is related to the strength of the Umklapp or thermal phonon-phonon scattering resis￾tance. For high-purity CVD-SiC,several observations in this laboratory have indicated that S 485 s/(m2 K) approximately independent of irradiation defect con￾centrations [36]. Although these values may not be quite correct for the Tyranno SA fiber or the CVI-SiC matrix, they are representative enough to predict the correct temperature effects on Keff. In Fig. 10(a),the analytic solutions predicted for the hypothetical Tyranno SA/ CVI-SiC composite are replotted as a function of tem￾perature for f=0.4 and selected values h=5000,500 and 50 W/(cm2 K). A well-adhered PyC fiber coating with thickness 0.2 mm and thermal conductivity 10 W/(m K) would have an equivalent h Kd/t=5000 W/(cm2 K),a value that represents good f/m thermal coupling. For such a case, Keff (T ) ranges from a value of about 29 W/(m K) at 27
C up to an apparent maximum of 34 W/(m K) at about 200
C,and back down to 26 W/(m K) at 1000
C. The maximum in Keff at about 200
C,observed for all h-values,is related to the rather steep positive tempera￾ture dependence of the SiC heat capacity for T<600
C. The two lower h-values (500 and 50 W/(cm2 K) repre￾sent moderate and poor f/m thermal coupling,respec￾tively. For h 500 W/(cm2 K), R 1 and Keff Km 20 W/(m K) for all temperatures. Finally,for h=50 W/ (cm2 K), Keff<12 W/(m K) in the 27<T<1000
C range. This hypothetical case again emphasizes the important role that the interfacial conductance plays in determining Keff(h) when h-values fall in the transition range (see Fig. 9). To account for degradation of Keff (T) due to irra￾diation damage,the Kf (T )- and Km(T )-values were separately adjusted for expected temperature and dose effects prior to substituting them into Eq. (1). The ther￾mal conductivity degradation for irradiated SiC depends primarily on the radiation temperature when doses are in excess of saturation,i.e. 51 dpa for SiC [32]. To estimate the degradation effect of irradiation, quadratic curves were separately fit to the temperature￾dependent thermal conductivity data given in reference [32] for high-purity CVD-SiC and SiCf/CVI-SiC irra￾diated above saturation. For 27<T<1000
C,the equations Kf (T)rad=[0.10+3.5 107 T2 ]Kf (T ) and Km(T )rad=[0.20+3.6 107 T2 ]Km(T) were used to represent the temperature dependence of Tyranno SA fiber and CVI-SiC matrix irradiated above saturation doses,respectively. In Fig. 10(b),the analytic solutions predicted for the hypothetical irradiated Tyranno SA/CVI-SiC composite are replotted as a function of temperature after the Kf￾and Km-values were adjusted for the effects of irradia￾tion. In contrast to the unirradiated condition,for each selected h-value the predicted Keff-values for irradiated Fig. 10. The transverse thermal conductivity, Keff,as a function of temperature predicted by Eq. (1) for (a) an unirradiated and (b) an irradiated hypothetical 2D-Tyranno SATM/CVI-SiC composite with h=50,500 or 5000 W/(cm2 K). Selected data values: a=5 mm, f=0.4, Kf (27
C)=65 W/(m K) and Km (27
C)=20 W/(m K). G.E. Youngbloodet al. / Composites Science andTechnology 62 (2002) 1127–1139 1137