Lai Fuming, Chen Yigang, Guo Haibo
School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China.
Phys Chem Chem Phys. 2019 Jul 31;21(30):16486-16496. doi: 10.1039/c9cp01975h.
The Wulff construction is a well-known method for studying the morphologies of nanocrystal particles. The underlying Gibbs-Wulff theorem relies on Wulff points or particle centers, which are invalid for non-centrosymmetric crystals. In this study, we extend the method of inverse Wulff construction to study surface free energies of non-centrosymmetric crystals. A nonpolar (4[combining macron]3m) and a polar crystal system (6mm) are selected to show the difficulties and constraints caused by the lack of inversion centers. In addition to analytical and numerical results, we also present a general four-parameter function to simplify calculations of surface free energies from observed micro- or nanoparticle morphologies. The results reveal that non-centrosymmetric crystal morphologies entail the surface thermodynamics of coupling polar surfaces, with certain limitations originating from the combination of geometrical shapes and crystal symmetries.
伍尔夫构造是研究纳米晶体颗粒形态的一种著名方法。其 underlying Gibbs-Wulff 定理依赖于伍尔夫点或颗粒中心，这对于非中心对称晶体是无效的。在本研究中，我们扩展了逆伍尔夫构造方法以研究非中心对称晶体的表面自由能。选择了一个非极性（4[combining macron]3m）和一个极性晶体系统（6mm）来展示由缺乏反演中心所导致的困难和限制。除了分析和数值结果外，我们还提出了一个通用的四参数函数，以简化从观察到的微米或纳米颗粒形态计算表面自由能的过程。结果表明，非中心对称晶体形态需要耦合极性表面的表面热力学，并且由于几何形状和晶体对称性的组合存在一定限制。
