Thermodynamic properties of TiC nanowire from first principles

We have investigated the thermodynamic properties of titanium carbide (TiC) nanowire within the framework of density functional theory and quasi-harmonic approximation via calculating the temperature dependence of a number of thermodynamic quantities including entropy, number of microstates, total and free energies, and specific heat. The level of disorder of the nanowire has been found to be larger than that of the bulk mainly due to expansion in only one direction, which accordingly results in acquiring more spatial degrees of freedom. A linear function of temperature has been also found for the low-temperature specific heat of the nanowire being in a remarkable agreement with the general Tn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T^{\text{n}}$$\end{document}-law for Debye systems. Results firmly establish a direct correlation between the spatial expansion of a TiC compound and its low-temperature specific heat and entropy.