Low temperature features in the heat capacity of unary metals and intermetallics for the example of bulk aluminum and Al$_3$Sc

We explore the competition and coupling of vibrational and electronic contributions to the heat capacity of Al and Al$_3$Sc at temperatures below 50 K combining experimental calorimetry with highly converged finite temperature density functional theory calculations. We find that semilocal exchange correlation functionals accurately describe the rich feature set observed for these temperatures, including electron-phonon coupling. Using different representations of the heat capacity, we are therefore able to identify and explain deviations from the Debye behaviour in the low-temperature limit and in the temperature regime 30 - 50 K as well as the reduction of these features due to the addition of Sc.