# Elastic Slow Dynamics in Polycrystalline Metal Alloys
## 3 Materials and Methods  
### Samples  
Several intact metallic alloy samples have been considered in our studies. Specifically, we have analysed:  
Figure 1: Experimental result for relaxation. (**a**) Linear scale; (**b**) Semi-logarithmic scale. Results for mortar and Al and Mg based alloys are shown to allow comparison. Data from mortar have been acquired using a protocol different than that presented here, which allows to monitor earlier times of relaxation, but, being more noisy, it could not be used to analyse relaxation in metals. For metals we obtain very small variations in the wave velocity (of the order of a few per thousands), which are comparable to resonance frequency variations \(\delta f/f\) induced by slow dynamics in metals observed by [PERSON] and [PERSON] [33]. Note that for longitudinal vibrations \(\delta c/c=\delta f/f\), since the resonance frequency is proportional to the wave velocity.  
* a 3D printed titanium-alloy (sample TiAl-3 DA): A prismatic sample of dimensions \(100\times 20\times 15\) mm\({}^{3}\) was fabricated by Electron Beam Melting technology using optimal process parameters. The microstructure consists of fine lamellar Widmanstatten morphology with columnar grains extending over multiple build layers. The typical reported lath length is approx. 20 \(\upmu\)m and width in the range 0.66 \(\upmu\)m-4 \(\upmu\)m [49]. Columnar grains size can reach multiple millimeters in length [50];
* an aluminum alloy specimen (sample Alu-C20): A prismatic sample of dimensions \(100\times 20\times 8\) mm\({}^{3}\) was manufactured from a rolled sheet of D16 CT1 alloy (Al-4 Cu-1 Mg) with anisotropic microstructure and average grain size around 400 \(\upmu\)m [51]. The microstructure also contains dispersed tubular precipitates;
* a second aluminum alloy specimen (sample Alu-A01): A cylindrical sample was taken from a cold drawn round bar of 7075 Al alloy (Al-4 Zn-2 Cu). The microstructure is strongly anisotropic with typical grain size 80 \(\upmu\)m in transverse and up to 1.5 mm in longitudinal direction. Small intermetallic precipitates of Al\({}_{2}\)Fe and MgZn\({}_{2}\) are dispersed in the matrix. The sample had length 120 mm and diameter 12 mm.
* a magnesium composite specimen (sample Mg-M03): A prismatic specimen was machined from a squeeze cast magnesium AX41 alloy (Mg-4 Al-1 Ca) reinforced by 12% Saffil fibres (\(\delta\) alumina). The microstructure contains equiaxed grains with typical size 90 \(\upmu\)m, traces of intermetallic phase Mg\({}_{17}\)Al\({}_{12}\) at grain boundaries and small Al\({}_{2}\)Cu precipitates. The fibres have a planar random orientation with respect to the squeezing direction. The sample dimensions were 135 \(\times\) 20 \(\times\) 13 mm\({}^{3}\).  
The first three samples were also analysed inducing microstructural changes (damage) as discussed in Section 5.  
In addition, we have also considered data relative to a consolidated granular sample as a reference for the discussion. Data refer to mortar (sample Mor-P23), in the shape of a prism (40 \(\times\) 40\(\times\) 160 mm\({}^{3}\)), produced using Portland cement. Sand grains are in the range 0 to 2 mm size [52]. Details about data acquisition for this sample are reported in ref. [24].