## 3 Materials and Methods
### Materials
#### 3.2.2 Solar Radiation Simulation--SOLARBOX Chamber Setting  
The solar radiation simulation was conducted with a SOLARBOX 1500 CO.FO.MEGRA chamber equipped with a 295-800 nm UV outdoor filter. Specimens underwent 1 month of testing with a fixed value of solar radiation of 1000 W/m\({}^{2}\) (equipment range of 100-1000 W/m\({}^{2}\)).  
During SOLARBOX aging, the solar irradiance was reproduced, and a relation between test time (T\({}_{\rm T}\)) and hypothetical outdoor exposure (T\({}_{\rm A}\)) was defined. The test time (T\({}_{\rm T}\)) is the period in which the specimens are placed in the climatic chamber. In this study, the experiments were conducted with T\({}_{\rm T}\) = 1 month. The hypothetical outdoor exposure (T\({}_{\rm A}\)) is the time defined by the product of test time and a hypothetical acceleration factor. The term \"hypothetical\" means that the reproduction of the outdoor exposure on a climatic chamber is uncertain. This is because it is always recommended to test aging in a natural environment in order to verify the reliability of the artificial aging [50].  
As for the FITOCLIMA setting, the meteorological data of the Italian Alpine region affected by Dfc climate were chosen in terms of average global solar radiation. The Alpine Dfc areas present an average annual global solar radiation variable between 4200 and 4700 MJ/m\({}^{2}\)/year [51]. It is important to underline how this range of values is independent of the type of climate but is mainly linked to the latitude. A value of 4500 MJ/m\({}^{2}\)/year has been selected as reference for our test corresponding to 12.33 MJ/m\({}^{2}\)/day.  
Only 6% of this radiation falls in the ultraviolet region between 295 nm and 400 nm, or rather the wavelengths that create the most damage to materials' surfaces.  
A further correction of 67% is recommended and could be applied to allow the fact that not all this radiation is acting at higher summer temperatures, and so it will be less damaging to the affected surfaces [52]. This means that the Alpine Dfc area records a solar radiation of 12.33 MJ/m\({}^{2}\)/day \(\times\) 0.06 \(\times\) 0.67 = 0.49 MJ/m\({}^{2}\)/day 295-400 nm.  
The average daily solar radiation of the international standard place (Miami, FL, USA) is 1 MJ/m\({}^{2}\)/day 295-400 nm [53]. Therefore, average daily radiation in Miami is (1 MJ/m\({}^{2}\)/ day 295-400 nm/0.49 MJ/m\({}^{2}\)/day 295-400 nm) = 2.04 times the average daily radiation of Alpine Dfc areas. In this research, a radiation of 1000 W/m\({}^{2}\) was selected in the SOLARBOX.  
According to the SOLARBOX manufacturer, the chamber set at 1000 W/m\({}^{2}\) with a 295-800 nm UV outdoor filter for one day of testing (T\({}_{\rm T}\) = 1 day) reproduces 9.60 MJ/m\({}^{2}\) 295-400 nm, corresponding to 9.6 days (T\({}_{\rm A}\) = 9.6 days) of hypothetical outdoor exposure in Miami and 9.6 days \(\times\) 2.04 = 19.6 days (T\({}_{\rm A}\) = 19.6 days) in Alpine Dfc areas. Therefore, the relation T\({}_{\rm T}\)-T\({}_{\rm A}\) for Alpine Dfc areas is:  
\[\rm TA=F\times T_{T}\ (1000\ W/m^{2}\ with\ 295-800\ nm\ UV\ outdoor\ filter)\]  
where F is the acceleration factor = 19.6.  
It is essential to underline that the high temperature registered inside the SOLARBOX, as indicated by the manufacturer CO.FO.MEGRA, can accelerate the aging speed. During our experiments, the temperature inside the SOLARBOX was always in the range of 30 \(<\) T \(<\) 40 \({}^{\circ}\)C.  
Considering a period of test duration T\({}_{\rm T}\) = 1 month, with a radiation of 1000 W/m\({}^{2}\), the hypothetical solar outdoor exposure for a slate sample in the Alpine Dfc area is T\({}_{\rm A}\) = 19.6 months.