title: A heat capacity model of T3/2dependence for quantum dots.
abstract: This article addresses the heat capacity of quantum dots (QDs) using density functional theory (DFT). By analyzing the evolution of phonon density of states and heat capacity as CdSe clusters grow from a molecular cluster into larger quantum confined solids, we have shown that their heat capacity does not fit very well with the Debye T3model. We observed that the number of phonon modes, which is discrete, increases as the particles grow, and the dispersion relation shows a quadratic behavior in contrast to the bulk solids whose dispersion relation is linear and equal to the sound velocity. The phonon density of states showed a square root variation with respect to frequency whereas that of the bulk is a quadratic variation of frequency. From the observed variation in the phonon density of states and holding the fact that the atomic vibrations in solids are elastically coupled, we have re-derived the expression for total energy of the QDs and arrive at a T3/2model of heat capacity, which fits very well to the observed heat capacity data. These results give promising directions in the understanding of the evolution of the thermophysical properties of solids.
authors.affiliation: Faculty of Industrial Sciences and Technology (FIST), Universiti Malaysia Pahang (UMP), 26300 Kuantan, Malaysia. rjose@ump.edu.my.
authors.forename: Amirul Edham
authors.initials: AE
authors.lastname: Roslee
authors.affiliation: Faculty of Industrial Sciences and Technology (FIST), Universiti Malaysia Pahang (UMP), 26300 Kuantan, Malaysia. rjose@ump.edu.my.
authors.forename: Saifful Kamaluddin
authors.initials: SK
authors.lastname: Muzakir
authors.affiliation: Faculty of Industrial Sciences and Technology (FIST), Universiti Malaysia Pahang (UMP), 26300 Kuantan, Malaysia. rjose@ump.edu.my.
authors.forename: Jamil
authors.initials: J
authors.lastname: Ismail
authors.affiliation: Faculty of Industrial Sciences and Technology (FIST), Universiti Malaysia Pahang (UMP), 26300 Kuantan, Malaysia. rjose@ump.edu.my.
authors.forename: Mashitah M
authors.initials: MM
authors.lastname: Yusoff
authors.affiliation: Faculty of Industrial Sciences and Technology (FIST), Universiti Malaysia Pahang (UMP), 26300 Kuantan, Malaysia. rjose@ump.edu.my.
authors.forename: Rajan
authors.identifier: http://orcid.org/0000-0003-4540-321X
authors.initials: R
authors.lastname: Jose