The difference AZD2171 ic50 between two V 3ω values (i.e., V 3ω1 and V 3ω2) is equated to the temperature drop across the Fe3O4 film and is used to calculate the cross-plane thermal conductivity, which is defined by the following equation:
(1) Here, V 0 and R 0 are the applied voltage and electrical resistance, respectively, along the heater wire of length l. and are the third-harmonic voltages at input current frequencies of ω 1 and ω 2, respectively, and dR/dT (temperature coefficient resistance, TCR) is the rate of the resistance change of the heater at temperatures of 20 to 300 K. Figure 3a shows a schematic of the four-point probe electrodes patterned onto SiO x /Fe3O4/SiO2/Si substrate for thermal conductivity measurements using the 3-ω method. To confirm our results of thermal conductivity measured using the four-point probe 3-ω method, we used bismuth (Bi) films (50 nm in thickness) whose thermal conductivity is well known, as a reference sample. We determined its thermal conductivity to be 2.7 to 2.9 W/m · K, which is in good agreement with the previous reported results by Völklein and Kessler  and Völklein et al.  who reported that the thermal conductivity of 60-nm Bi thin films was approximately 3.6 W/m · K at 300 K. Thus, our experimental
setup and the associated analysis via the four-point probe 3-ω method were clearly validated through a comparison with the results for reference sample. Figure 3b shows temperature-dependent resistances of the three Fe3O4 thin films (100, 300, 400 nm in thickness) in the temperature range of 20 to 300 K. The relationship between the resistance see more changes in the heater wire and the temperature is linear. Figure 3b shows that the TCR for the 100-, 300-, and 400-nm Fe3O4 thin films is approximately 0.104 Ω/K, approximately 0.041 Ω/K, and approximately 0.026
Ω/K, respectively. These values can be used for estimating thermal conductivity as defined in Equation 1. Figure 3 Four-point probe 3- ω method and temperature-dependent resistances. (a) Schematic view of the four-point probe 3-ω method where the out-of-plane thermal conductivity can be measured. (b) The temperature-dependent resistances of three Fe3O4 thin films (100, 300, 400 nm in thickness) at temperature ranges of 20 to 300 K. Results and discussion O-methylated flavonoid To ensure that the measured V 3ω signal is generated by the Fe3O4 thin film, we investigated the variation in the signal with the applied frequency (ln ω) from the 3-ω measurements. This applied frequency usually provides a suitable current range for an estimation of the V 3ω signal from the sample. As discussed previously by Selleck Autophagy inhibitor Cahill , the linear relationship of ln ω with V 3ω should be satisfied as shown in Figure 4a. Figure 4a presents the V 3ω distribution of the 100-nm Fe3O4 thin film for different applied frequencies.