## 2 Materials and Methods
### Alloy Fabrication and Thermomechanical Treatment to Obtain Thin Cu-Al-Mn SMA Sheets  
Since the intended final application of the Cu-Al-Mn thin sheets in question is primarily for vibration damping, the target composition during casting and subsequent thermomechanical treatments were chosen to optimize for damping performance while simultaneously allowing enough cold workability of the alloy that would be necessary to go from an as-cast ingot to an SMA sheet with a thickness below 1 mm. Both the alloy damping capacity and material workability were previously shown to be highly dependent on the ratio of alloying elements Al and Mn presenting within the cast [18]. In terms of damping applications, the intention is to study both active and passive damping application potentials of the Cu-Al-Mn SMA thin sheets. For purposes of active damping, this means that it would be necessary to have a practical way of achieving temperature-induced phase transformation of the SMA, during which a peak in damping capacity, i.e., the loss factor, is observed in the material [5]. As the alloy primarily consists of highly conductive copper, the transformation temperatures of the SMA would need to be close enough to room temperature so that a practical method of triggering such transformation would be possible. However, they also need to be sufficiently above room temperature to ensure that the phase transformation would not be accidentally induced during use. It was determined that this would require the A\({}_{\text{s}}\) and A\({}_{\text{f}}\), austenitic and martensitic phase transformation temperatures, respectively, to be within the range of 50-100 \({}^{\circ}\)C. Furthermore, once the ingot was cast, it was necessary to perform thermomechanical treatments to obtain thin sheets. Based on a review of the literature, a Cu-Al-Mn alloy with an aluminum content lower than 18% at. was selected due to its high degree of cold workability, which comes from a reduced degree of order within the material, reaching workability rates up to 70% at 16% at. of aluminum [10; 18; 19; 20]. Based on the required material performance criteria described above, the nominal target composition of the Cu-Al-Mn alloy for the casting process was around Cu-16 Al-10 Mn % at., i.e., Cu-7.6 Al-9.67 Mn % wt. [18]. The entire casting process, which consisted of two phases, was performed at the facilities of CNR-ICMATE in Lecco, Italy. During the first phase of the casting process, a Cu-Mn pre-alloy was cast using an arc melting furnace under vacuum due to the high reactivity of manganese with oxygen. Combining the obtained Cu-Mn pre-alloy and the necessary additions of the required quantities of copper and aluminum to obtain the final composition, the second phase was performed in an Ages-Galloni induction melting furnace. Composition measurements were performed after each phase of the casting process using EDX analysis. The final products of the casting process were two ingots of Cu-Al-Mn, each with a thickness of approximately 10 mm. The raw materials used in the casting process, their chemical purity, and form can be found in Table 1. Within the raw copper, an expected small amount of phosphorus was indicated, since it is commonly used in the copper production processes to avoid copper oxidation. Once the casting process was finalized and the Cu-Al-Mn ingots were obtained, a set of thermomechanical treatments was needed to reduce the ingots thickness down to a target of \(\sim\)0.4 mm. These treatments are fully described in the text below. In Figure 1, the isothermal diagram of Cu-Al-Mn that was used as a reference when selecting the temperatures for each thermomechanical treatment that was applied to the material is shown. Additionally, in Figure 1, the point at which the target alloy composition would fall squarely within the secondary \(\beta\)-phase region is around \(\sim\)900 \({}^{\circ}\)C. Hence, this temperature was selected as the betatization and hot-rolling treatment temperature, as marked by the letters HR/BET. Each