# Applicability of Infrared Thermography for the Detection of Phase Transitions in Metal Alloys
## 2 Materials and Methods
### IRT Method  
The IRT method has first been described by [PERSON] et al. [8] and further developed in several instances [9; 10; 11]. Figure 1 shows a scheme of its experimental setup. The functioning principle of the method is similar to Differential Thermal Analysis (DTA). The proposed method consists in simultaneously observing, using a X6580 SC FLIR (Wilsonville, OR, USA) infrared camera, the melting of a large number of small samples of the studied system with different compositions. To do so, the samples are deposited in droplet form on a flat metal substrate and heated at a slow and constant speed (heating ramp of 1 \({}^{\circ}\)C/min). The temperature profile in the experiment is set as a slow heating ramp of 1 \({}^{\circ}\)C/min in order to minimize the temperature difference between the supporting plate \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metals** & **Acronym** & \
\begin{tabular}{c} **CAS** \\ **Number** \\ \end{tabular} & **Supplier** & **Purity 1 (\%)** &
\begin{tabular}{c} **Melting** \\ **Temperature 1 (\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline Gallium & Ga & 7440-55-3 & Setaram & \textgreater{}99.999\% & 29.8 \\ Indium & In & 7440-74-6 & Setaram & \textgreater{}99.995\% & 156.6 \\ \hline \hline \end{tabular}  
* As given by the supplier.  
\end{table} 
Table 1: General information about the studied metals. Figure 1: Scheme of the experimental setup. and the samples. This temperature is controlled and monitored through a heating/cooling system consisting of a heating plate, a cooling heat exchanger, and PID temperature controller adjusting the load of the heating plate according to the temperature difference between the setpoint and the temperature given by a thermocouple attached to the support plate. The PID coefficients used for temperature control in this work are: proportional gain \(\mathrm{K_{p}}=31.85\), integral gain \(\mathrm{K_{i}}=1.30\), and derivative gain \(\mathrm{K_{d}}=194.67\). During the previous studies carried out, it was observed that the signals recorded by the infrared camera show first order discontinuities when a sample crosses a transition line. As the phase transition process is isothermal, discontinuities in the evolution of the infrared signal of a sample correspond to a change in the thermal emissivity and the temperature of the sample. This is the basis of the proposed phase diagram establishment method. The signal of a sample then consists of as many individual signals as there are pixels for a sample. Reliably detecting a transition within such a large cluster of data is challenging. Therefore, before the interpretation of the results, two steps are required. First, an image treatment is applied to distinguish samples from the background (segmentation) and to sort individual samples (labeling). A visualization of the image treatment process can be seen in Figure 2. Raw infrared images are extracted following the experiment. Those images cannot be interpreted as is, as they contain the data of several samples simultaneously but also data belonging to the background (such as the support plate and the thermocouple in Figure 2a). A segmentation process based on shape detection and contrast level enables the dissociation between samples and background as can be seen in Figure 2b. From there, samples are individually labelled according to their position on the images (Figure 2c) to facilitate the data treatment process. Following the image treatment step, a mathematical process of Singular Value Decomposition is implemented. This process is commonly used when dealing with large multi-variables datasets [18] and has many applications in image processing. In this case, it allows separating the time-dependence and space-dependence of the problem and highlights trend variations in the signal. The SVD of the signals of sample can be expressed as in Equation (1).