Nuclear Science User Facilities 88 0.0025 K-1 on average.This is lower than that of bulk silver (0.0038 K-1 ), which is to be expected of the printed sensors due to their nanostructure and size. Similarly, theTCR of the printed platinum sensors is ~0.0026 K-1 . We have performed 3ω thermal conductivity measurements on alumina substrates, which have thermal conductivity values roughly in the same range of advanced nuclear fuels. Based on the alumina substrate thickness of 635 µm and the sensor width of 15 µm, the range of frequencies applicable to the 3ω slope method is ~60 to ~700 Hz. Figure 4 shows the temperature oscillation as a function of frequency for different temperature measurements.The results show an excellent linear dependence of temperature on the logarithm of applied frequency in the frequency range outlined above – a fundamental requirement of the 3ω slope method. The amplitude of temperature oscil- lations varies slightly for the different temperatures studied because slightly different current was used at each temperature.The thermal conductivity of the substrate can be determined based on the slope dV3ω d(In9ω))of the third harmonic voltageV3ω to the natural logarithm of frequency ω using the following equation: where V1ω is the voltage across the sensor at the fundamental harmonic, l is the sensor length, and R is the sensor resistance at the temperature of interest. Figure 5 shows the temperature- dependent thermal conductivity measurement results up to 400°C.The thermal conductivity of 99.5% pure alumina measured using the printed 3ω sensor agrees within about 5% of the value reported by the National Bureau of Standards.The excellent agreement validated the accuracy of the printed 3ω sensor, and demonstrates promises of the printed sensors for in-pile thermal conductivity measurement. Future Activities Figure 5. Thermal conductivity of alumina as measured by aerosol jet printed silver 3ω sensors and the recommended values reported by the National Bureau of Standards (NBS) [5]. K = (TCR) V3 1ω d(ln(ω)) , 4πlR dV3ω