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

Abstract

The temperature-dependent specific heat C[Formula: see text](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[Formula: see text] 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[Formula: see text] 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[Formula: see text]) and those present at the core of nanocrystal (C[Formula: see text]) are estimated separately by estimating the characteristic Debye temperature ([Formula: see text]) from elastic force constant ([Formula: see text]). The temperature derivative of the internal energy yields the electronic contribution to specific heat (C[Formula: see text]). The present investigation based on the softening of phonon frequencies mechanism is successful to explain the enhancement in specific heat by nanocrystallization.