Enhancement in specific heat by nanocrystallization: Softening of phonon frequencies mechanism

The temperature-dependent specific heat C-p(T) of nanocrystalline (NC) Cu (8 nm) and Pd (6 nm) is theoretically analyzed and compared with the specific heat of their corresponding bulk materials in the temperature range from 150 K to 300 K. It is revealed that the C-p values of NC Cu (Pd) are about 10% (40%) higher as compared to that of their corresponding bulk form, the softening of phonon frequencies at interfaces in NC materials is argumented as the main mechanism responsible for enhancement in C-p in the present work. Lattice (phonon) specific heat is obtained following an overlap repulsive potential using Debye model. In NC materials having large interface volume ratio, the phonon frequencies and Debye temperature are comparatively less at the interfaces than at the core of nanocrystal. The contributions to specific heat due to atoms present at interfaces (C-ph(IF)) and those present at the core of nanocrystal (C-ph(NC)) are estimated separately by estimating the characteristic Debye temperature (theta(D)) from elastic force constant (kappa). The temperature derivative of the internal energy yields the electronic contribution to specific heat (C-el). The present investigation based on the softening of phonon frequencies mechanism is successful to explain the enhancement in specific heat by nanocrystallization.