Department of Physics, University of Central Florida, Orlando, FL 32816-2385, USA.
J Phys Condens Matter. 2012 Mar 14;24(10):104026. doi: 10.1088/0953-8984/24/10/104026. Epub 2012 Feb 21.
We present first-principles calculations of the vibrational density of states (VDOS), the specific heat and the mean-squared displacement of the five lowest-energy isomers of Au(13) and of two low-energy FeAu(12) nanoparticles. We find that the vibrational contributions to the Helmholtz energy do not affect the energy ordering of the isomers. As expected, for nanoparticles the vibrational density of states differs dramatically from the function proposed by the Debye model. We demonstrate that, for the nanoclusters we studied, the alternative calculations of the 'Debye temperature' yield significantly inconsistent results. We conclude that T(D) obtained from a particular thermodynamic property is neither applicable for deriving conclusions about other thermodynamic properties nor correlated with atomic bond strengths. Instead, in order to describe the temperature dependence of a nanoparticle's mean-squared displacement and its specific-heat capacity, what is necessary is its discrete phonon spectrum.
我们呈现了第一性原理计算的振动态密度（VDOS）、比热和五个最低能量构象的金（13）和两个低能的 FeAu（12）纳米粒子的均方根位移。我们发现，振动对亥姆霍兹自由能的贡献并不影响构象的能量顺序。正如预期的那样，对于纳米粒子，振动态密度与德拜模型所提出的函数有很大的不同。我们证明，对于我们研究的纳米团簇，“德拜温度”的替代计算会产生显著不一致的结果。我们得出的结论是，从特定热力学性质获得的 T(D)既不适用于得出关于其他热力学性质的结论，也与原子键强度无关。相反，为了描述纳米粒子的均方根位移和比热容量随温度的变化，需要的是其离散的声子谱。
