# Temperature Estimation during Pulsed Laser Sintering of Silver Nanoparticles
## 4 Results and Discussion
However, the maximum temperature is attained after the laser irradiation of 0.1 s. As soon as the pulse is relaxed (no heat source) the underlying NPs start to cool, and it takes 0.905 s (0.9 s of no heat source and 5 ms of step time delay) to reach to near room temperature until the next pulse hits. For the first laser pulse in Figure 4, the temperature in the underlying Ag NPs layer increases and the Ag NPs layer is thermally sintered, subsequently, increasing the corresponding thermal conductivity of the Ag NPs. In the following pulse relaxation period, the process temperature drops, and the thermal conductivity of the heated zone is initialized with the value of the corresponding maximum temperature induced in the previous laser shot. The plot shows that a peak temperature of about 204 \({}^{\circ}\)C is obtained at around 52 s. The peak temperature of around 207 \({}^{\circ}\)C produced by the first pulse is slightly higher than the following peak temperature of about 201 \({}^{\circ}\)C. The slightly lower following peak temperature of 201 \({}^{\circ}\)C is due to the absorption into 50 % of the already irradiated area. As a result, half of the laser irradiation is absorbed by the area with high thermal conductivity. This resulted from the high thermal diffusivity which was caused by a slightly higher temperature from the previous laser pulse. Typically, the heat relaxation time depends upon thermal diffusivity caused from the increase in thermal conductivity and the decrease in heat capacitance. The abrupt cooling rate within the initial time step after the peak temperature and the relatively moderate cooling rates afterward, can be elaborated by the 2D surface plots as shown in Figure 5. The time steps and the cooling rates for Figure 5 are extracted from Figure 4. The reason for an abrupt cooling rate is due to the relatively small heat capacitance of silver nanoparticles (bulk Ag, \(c_{p}\) = 245 J/kg\(\cdot\)K [34]) adopted in this study and high thermal conductivity induced after the laser shot. The thermal conductivity of the glass substrate was known to be very low at 1.05 W/m\(\cdot\)K, which could not effectively act as a heat sink to help a faster heat relaxation in the Ag NPs layer [46; 47]. Therefore, the cooling via radiative and convective cooling might be responsible for this fast cooling rate. In Figure 6, the transient temperature behavior is depicted at a single point graph in which a local maximum temperature is recorded at 27.05 s (at the center of the laser beam). The previous temperature peaks appeared from the effect of previous laser pulses at this point. The temperature history depicts that the previous laser beams have caused the peaks at 26.05 s, 25.05 s, etc., and the peaks after 27.05 s are affected by the subsequent laser beams. The corresponding maximum temperatures (\(T_{\rm max}\)) from the previous laser shots, are stored for determining the corresponding thermal conductivity values for the next temperature calculation. After 27.05 s the maximum temperature is fixed at 204 \({}^{\circ}\)C,hence the corresponding thermal conductivity is maintained in spite of the reduction in temperature. The effect of higher thermal conductivity becomes immediately observable after the 27.05 s. The peak at 28.05 s is shorter than the peak at 26.05 s. The temperature at 26.05 s is approximately 117 \({}^{\circ}\)C while that at 28.05 s is approximately 105 \({}^{\circ}\)C.  
In Figure 7, the spatial distributions of thermal conductivity are presented at three points located in the start, middle, and the end of the printed line. Due to the nature of the Gaussian beam, a decrease in the temperature was witnessed away from the center of the beam [48].