# On the Use of Infrared Thermography for the Estimation of Melting Enthalpy
## 2 Materials and Methods  
### Principle of the IRT-Based Method for the Estimation of Melting Enthalpy  
The principle of the method for the establishment of phase diagram has been extensively discussed at several occasions [11; 12; 13; 14; 15; 16; 17]. It consists of continuously and simultaneously recording the infrared signal of samples (droplets deposited on an aluminum plate) submitted to a slow heating ramp (1 \({}^{\circ}\)C/min) with an FLIR (Wilsonville, OR, USA) infrared camera (Model: X6580 SC, Resolution: 640 \(\times\) 512, Framerate: 7 Hz, Wavelength range: 1.5-5.5 \(\upmu\)m). The temperature and emissivity variations occurring upon phase change induce an abrupt variation in the trend of the infrared signal. Consequently, the phase diagram of a system of materials can be established in a single short experiment. Details regarding the experimental setup, the choice of parameters and the data analysis process can be found in the literature [11; 12; 13; 14; 15; 16; 17]. As the phase transition detection process in DTA and with IRT are very similar, it is anticipated that the estimation of melting enthalpy is possible based on the same working principle. On the one hand, the DTA associates phase transitions to temperature deviations between a reference and a sample submitted to a set heating ramp. The calculation of the latent heat of fusion from this experiment is made according to Equation (1):  
\[\Delta H_{i}\ =\ \frac{S_{c}}{m_{i}}\int_{t_{1}}^{t_{2}}\Delta T(t)dt \tag{1}\]  
where \(S_{c}\) is a coefficient interpolated from a prior calibration made using pure samples of known melting enthalpy, \(m_{i}\) is the mass of the sample, \(\Delta H_{i}\) is the melting enthalpy and \(\Delta T(t)\) is the temperature difference between the reference and the sample from time \(t_{1}\) to time \(t_{2}\), respectively, delimiting the beginning and the end of the melting process. On the other hand, the IRT-based method associates phase transitions to infrared signal variations in samples submitted to a heating ramp. Figure 1 shows a scheme of the experimental setup. Samples of known mass are contained in aluminum crucibles and placed on an aluminum plate whose temperature is set and monitored with a PID temperature controller, a thermocouple and a heating/cooling system. The thermocouple gives a continuous reading of the plate temperature which is assumed to be identical to the samples one under thermodynamic equilibrium. This assumption is ensured by the set slow 1 \({}^{\circ}\)C/min heating rate, whose influence has been studied in [16]. The thermocouple temperature, thus, acts as a reference temperature, and its value should only deviate from the infrared temperature upon phase change. Quantitative infrared temperature measurement is currently a predominant research topic [1; 3; 21]. The infrared signal of any infrared detector depends on a number of parameters, among which the temperature, the wavelength and the viewing angle play a major role. This signal for a given wavelength can be expressed following [PERSON]'s law as in Equation (2), assuming acute viewing angles and a negligible influence of the environment:  
\[s(\lambda,T)\;=\;R_{\lambda}(T)\;\times\;\epsilon(\lambda,T)\;\times\;\frac{2 \;\times\;h\;\times\;c^{2}}{\lambda^{5}}\;\times\;e^{1-\frac{h\epsilon_{0}}{ \lambda\times c\times t}} \tag{2}\]  
where \(s\) is the infrared signal of the detector, \(R_{\lambda}\) is a detector-specific function given for the wavelength of detection, \(\epsilon\) is the emissivity of the material, \(h\) is the Planck constant, \(c\) is the speed of light, \(k\) is the Boltzmann constant, \(\lambda\) is the wavelength and \(T\) is the temperature. In most applications of quantitative infrared temperature measurement, the study of graybodies is considered. This term refers to an object whose emissivity is independent of the wavelength.