硬球晶体中的自由能、空位浓度和密度分布各向异性：密度泛函和模拟的结合研究
Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
摘要：
我们使用蒙特卡罗模拟和密度泛函理论（采用基本测度泛函）对硬球晶体中的自由能和密度分布进行了比较研究。使用最近引入的技术（Schilling和Schmid，J. Chem. Phys 131，231102（2009）），我们获得了高精度的晶体自由能。从基本测量理论的自由能是在良好的协议与模拟结果，并证明这些泛函的适用性，涉及结晶的其他问题的治疗。FMT和模拟之间的协议的水平上的自由能也反映在周围的单晶格位置的密度分布。总体而言，不同晶格方向的峰宽和各向异性符号一致，然而，发现基本测量理论给出的峰略窄，各向异性比模拟中看到的更大。在所研究的三种基本测度泛函中，只有白熊II泛函（Hansen-Goos和Roth，J. Phys.：康登斯Matter 18，8413（2006））展示了平衡空位浓度的合理结果和由固定空位浓度约束的晶体中化学势的物理行为。
英文摘要：
We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.
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