Size effect on thermodynamic properties of free nanocrystals

Abstract

We demonstrate that the discrete character of the vibrational spectrum of a small crystal accounts for size dependence of its thermodynamic properties and melting temperature. Using a self-consistent statistical method [Phys. Rev. B 66, 054302 (2002)] we derive the Gibbs free energy of free nanocrystalline plates and calculate the thermodynamic parameters as functions of plate thickness for Cu.

Melting and thermodynamic properties of rare gas nanocrystals

“…Similar consideration for metallic nanoplates was carried out in Ref. 35. We show that taking into account the finite size of the nanocrystal results in quantization of its vibrational spectrum which becomes essentially discrete.…”

Specifics of thermodynamic description of nanocrystals

“…With decreasing particle size, the expression for the nl dependence is more complex, and for nanoclasters consisting of several tens atoms 0 n l n [28]. To calculate the equilibrium free energy, phonon gas pressure and thermodynamic properties of nanocrystals, let us employ a variational approach [26,27] developed to study thermodynamic properties of bulk crystals and extended also to the description of nanocrystals [19,20,28]. To write down the free energy functional we need approximated potential of interatomic interaction.…”

“…This feature, together with simple form of the potential (8), allows one to use the Morse potential to describe not only thermodynamic properties of simple crystals at ambient pressure [23,26], but also properties of crystals under high pressure [27]. At high temperature, a nanocrystal of mesoscopic size consisting of N atoms can be described with the functional of the Helmholz free energy [19,20] …”

“…Assuming that excessive pressure in nanocrystals is related to the phonon gas pressure only (20), and assuming 0 P , and using equation (3) which relates a change in the phase transformation temperature and a change in the pressure in the system, we can obtain an explicit expression for size dependence of the phase transformation temperature:…”

“…to changes in the surface energy under a change of the phase state of the particle [5][6][7][8]. Recently, it was demonstrated [19,20] that size reduction of a crystal is accompanied by quantization (and increasing) of its vibrational energy, making the pressure of the phonon gas of the crystal increase. A force corresponding to such excess pressure of the phonon gas is directed outwards the crystal, i. e. additional pressure in a nanoparticle is negative.…”