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.

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A thermal conductivity of LaCoCuO 3 ceramic oxides is analyzed using phonon scattering effects by incorporating the scattering of phonons with point defects, grain boundaries and phonons in the model Hamiltonian. Phonons are the sole careers for the heat in the test material and the behavior of thermal conductivity is an artifact of strong phonon-defects, phonon-grain boundaries and phonon-phonon scattering mechanism. The thermal conductivity has been modeled in terms of the relaxation-time approximation, characterized by Debye temperature  D . It is seen that the phonon-phonon scattering is dominating and mainly responsible for decrease in thermal conductivity at higher temperatures.