金属Mo和W纳米晶表面能及形成焓的计算

The calculation of surface energies and formation enthalpies of metallic Mo and W nanocrystals

D. Xie *, M. P. Wang, L. F. Cao, Y. L. Jia

School of Materials Science and Engineering, Central South University, Changsha 410083, China

* Author to whom correspondence should be addressed.

Tel.: +86-731-8830264. Fax: +86-731-8876692. E-mail: patriot_csu@

Abstract

A simple but valid equation for the higher surface energies of metallic nanocrystals is obtained, the formation enthalpies of nanocrystals are calculated by using the equation of surface energies, and the structure variation induced formation enthalpies are also discussed. The calculated surface energy values of Ag and Au nanocrystals are in excellent agreement with the corresponding newest experimental values, and the predicted formation enthalpy values are consonant with the corresponding experimental values of Mo and W nanocrystals.

Keywords：Metallic nanocrystals, Surface energy, Formation enthalpy

Since Kim et al. [1] reported the first experimental data on the formation enthalpies of Mo and W by measuring the oxidation enthalpies of nanocrystals, several authors began to investigate the important thermodynamic parameter theoretically [2-4]. Despite the success, most of the models established in the literatures under different theoretical origins, avoided to discuss the structure variations of nanocrystals which could directly influence the formation enthalpies ( for example, the structure of Mo and W nanocrystals can be changed from BCC structure to FCC structure with crystals size decreasing [1] ), and can not determine the surface induced and structural

induced formation enthalpies of nanocrystals. Recently, Qi made efforts to present a thermodynamic method to calculate the surface contribution to formation enthalpies of nanocrystals, and tried to calculate the structural induced formation enthalpies indirectly by considering the structure variations of nanocrystals [5], but unfortunately the calculations presented by the author seems wrong which we will discuss later.

In this letter, a simple but valid equation for higher surface energies of metallic nanocrystals is obtained to calculate the formation enthalpies of Mo and W nanocrystals, and the formation enthalpy induced by structure variation are also discussed.

According to the discussions on the surface and structural effects of nanocrystals by Kim et al. [1], the formation enthalpy of nanocrystal ΔH should be written as follows

surf sv H H H ∆=∆+∆ (1)

where ΔH surf denotes the formation enthalpy induced by surface, ΔH sv denotes the formation enthalpy induced by structure variation, whose absolute value could also be regarded as the value of solid structure transition energy. ΔH sv =0 when the structure of the nanocrystals has no difference from that of the corresponding bulk.

It is know that the surface induced formation enthalpy of a nanocrystal can be written as ΔH surf = S γn , where S is the surface area, γn is the surface energy per unit area at 0 K [6]. Though the γn value of free nanocrystal is supposed to be size and structure independence and equal to the corresponding bulk value by a few of authors

[5], there are lots of literatures to confirm both experimentally and theoretically that the value of γn is much higher than that of the corresponding bulk and varies with the changed structure [7-10]. For instance, the size independence surface energies of γn have been experimentally determined by Nanda et al. as 7.2 J/m 2 for free FCC Ag