Harmonic and Anharmonic Lattice Thermal Capacities of Molecular Wires and 0001-Oriented Cylindrical ZnO Nano-Wires

Abstract

Unique characteristics of temperature-dependent isobaric thermal capacity, Cp (T), of ‘chain and layered structures’ attracted substantial scientific interest more than seven decades ago. In particular, the low-temperature Cp (T) function(s) of linear macromolecules (microwires) apparently does not follow the Debye’s law, Cp (T) ∝ T3  , which is well established experimentally and theoretically for the bulk crystalline and amorphous solids more than a century ago. Instead, Cp (T) ∝ T and Cp (T) ∝ T2 dependencies are generally expected for those chain and layered structures (respectively) at relatively low temperatures. In addition, the low-temperature behaviour(r) of the isobaric lattice thermal capacity could be affected considerably as well by ‘cut-off ’ in the fundamental vibrational spectrum of nano-structures materials, originating appearance of their ‘low-temperature anomalies’. Framework of so-called ‘Tarasov Equation(s)’allows one to reformulate readily the basic equations of the Debye’s theory for the thermal capacity of bulk solids into similar basic equations suitable for the ‘layered’ (2D) and ‘chain’ (1D) structures.

However, even in these cases, the (acoustic) phonon spectra of those 1D and 2D structure(s) are implicitly presumed to be quasi-continuous. In other words, the spatial confinement effect and (closely related to it) phonon energy quantization are routinely not taken into account even within frameworks of dominant existing approaches to quantitative evaluations on the lattice thermal capacity of spatially non-homogeneous and low-dimensional solids, which eventually do not allow one to replicate important features of the experimental Cp (T) curves, like aforementioned ‘low-temperature anomalies’.

Herein, the static and spatially confined vibrational basis comprises of zeros of Bessel functions of the first kind in a combination with so-called ‘Fock space formalism’ are implemented at simulations on the single-particle (fundamental) and many-particle acoustic phonon spectra and temperature-dependent harmonic and anharmonic fractions of the lattice thermal capacity of nanowires (NWs) with the ‘cylindrical’ morphology. Simulation results obtained for the cylindrical 0001-oriented ZnO NWs of different transverse sizes (lengths and diameters) are compared (wherever it is possible) with predictions of 1D ‘Generalized Skettrup Model’ for the ‘molecular wires’.