[PoojaPadmakumar]

According to Dulong & Petit , the atomic heat capacities of crystalline solid elements are almost constant. On decreasing the temperature, the atomic heat capacities of solid elements decrease greatly. Heat capacity of an element is the heat required to attain a raise in temperature by 1 degree.How does the heat capacity DECREASE when the overall temperature is decreased

[Enthalpy]

Because some vibration modes need a minimum energy to be active I'd say.

Typically if some atoms do not belong to the crystal-wide network but are rather side chains, the associated resonance frequencies don't drop when adding more and more atoms to the crystal, so these modes are harder to excite. Or if some atoms are strongly bonded (chemical bond) and others weakly (Van der Waals) then crystal-wide modes can easily let the weak bonds vibrate but not the strong ones.

Then, at really cold temperatures, even metals have a smaller heat capacity.