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.

Phonon Scattering Mechanism for Size‐Dependent Thermoelectric Properties of Bi2Te3 Nanoparticles

“…The model has phonon frequency (ω) as one important characteristic parameter whose value depends on the size of nanoparticles. Phonon frequencies also depend on the interatomic distance and interface volume ratio, which is consistent with phenomena of softening of phonon frequencies in the nanomaterials [53] . The optimum value of ω and λ for which the function in equation (3) has the highest value depends on the size of the nanoparticles.…”

“…Therefore, the present model successfully explains the size dependence of thermoelectric properties which is introduced through phonon frequencies and interface volume ratio. Such dependence of physical properties of various nanomaterials on the phonon frequencies ω and size of nanoparticles have been reported earlier [52–54] …”

“…Such dependence of physical properties of various nanomaterials on the phonon frequencies ω and size of nanoparticles have been reported earlier. [52][53][54] Figure 5 represents the temperature and size dependence of ZT. Temperature-dependent ZT shows a broad peak around 420 K, i. e., in the vicinity of phonon peak.…”

“…Phonon frequencies also depend on the interatomic distance and interface volume ratio, which is consistent with phenomena of softening of phonon frequencies in the nanomaterials. [53] The optimum value of ω and λ for which the function in equation ( 3) has the highest value depends on the size of the nanoparticles. Therefore, the present model successfully explains the size dependence of thermoelectric properties which is introduced through phonon frequencies and interface volume ratio.…”

Effect of nano-crystallization and atomic substitution on electronic and heat properties of Bi2Te3

“…The charge carrier contribution to heat capacity is given as the temperature derivative of internal energy [12] Cel = మ ଷ k ଶ N(E )T=γT (4) Here, N (EF) denotes the density of state near Fermi level and γ is Somerfield constant.…”