Sushko Nazar, van der Schoot Paul
Laboratory of Polymer Chemistry, University of Groningen Nijenborgh 4, 9747 AG Groningen, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 2):067104. doi: 10.1103/PhysRevE.72.067104. Epub 2005 Dec 22.
As is well known, hard-sphere crystals of the fcc and hcp type differ very little in their thermodynamic properties. Nonetheless, recent computer simulations by Pronk and Frenkel indicate that the elastic response to mechanical deformation of these two types of crystal are quite different [S. Pronk and D. Frenkel, Phys. Rev. Lett. 90, 255501 (2003)]. By invoking a geometrical argument put forward by Martin some time ago [R. M. Martin, Phys. Rev. B 6, 4546 (1972)], we suggest that this is largely due to the different symmetries of the fcc and hcp crystal structures. Indeed, we find that elastic constants of the fcc hard-sphere crystal can be mapped onto the equivalent ones of the hcp crystal to very high accuracy, as a comparison with the computer simulation data of Pronk and Frenkel shows. The same procedure applied to density functional theoretical predictions for the elastic properties of the fcc hard-sphere crystal also produces remarkably accurate predictions for those of the hcp hard-sphere crystal.
众所周知，面心立方（fcc）和六方密排（hcp）型的硬球晶体在热力学性质上差异很小。尽管如此，普龙克（Pronk）和弗伦克尔（Frenkel）最近的计算机模拟表明，这两种晶体对机械变形的弹性响应有很大不同[S. 普龙克和D. 弗伦克尔，《物理评论快报》90, 255501 (2003)]。通过引用马丁（Martin）前段时间提出的一个几何观点[R. M. 马丁，《物理评论B》6, 4546 (1972)]，我们认为这在很大程度上是由于fcc和hcp晶体结构的对称性不同。实际上，正如与普龙克和弗伦克尔的计算机模拟数据比较所示，我们发现fcc硬球晶体的弹性常数可以非常精确地映射到hcp晶体的等效弹性常数上。将同样的程序应用于fcc硬球晶体弹性性质的密度泛函理论预测，也能对hcp硬球晶体的弹性性质做出非常准确的预测。
