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

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.

LOW TEMPERATURE BEHAVIOR OF DEBYE CHARACTERISTIC TEMPERATURES

The low temperature behavior of the characteristic Debye temperature is investigated using the six- and nine-direction Houston approximation and by way of illustration, the lattice dynamics of Born and Begbie (nearest neighbors only). We study the values of θ0 and B2 for Cu, Au, Ag, Al, and Pb in the formula θT = θ0 θ. The existence in Pb of a shallow maximum before the usual minimum, found earlier by Bhatia and Horton, is confirmed. The method is quite general and may be used for non-metals and with other theoretical models.