Physical origin of surface energy anisotropy

Chih-Chun Wang¹, Kuo-An Wu^1*

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Kuo-An Wu, email:kuoan@phys.nthu.edu.tw

It is well established that for diffusive order-disorder interfaces the interfacial anisotropy arises due to symmetry breaking of density waves at the interface. While the interfacial anisotropy is expected to be related to the underlying lattice symmetry, the anisotropy can still differ among materials with the same lattice structure due to the difference in the interatomic potentials. To shed light on this, a general Ginzburg-Landau (GL) theory of order-disorder interfaces, based on crystal symmetry and classical density functional theory, is proposed to analytically connect the relation between lattice symmetry, the shape of the free-energy landscape, and surface energy anisotropy. Using a perturbative scheme, we show that the corresponding anisotropic form of the surface energy, depending on crystal symmetry, naturally appears in the perturbation expansion. To explore how the double-well free-energy landscape in the GL theory affects the anisotropy, we consider lattices of hexagonal
symmetry as an example, for which the shape of the free-energy landscape is shown to only depend on one parameter. The dependence of anisotropy on the free-energy landscape predicted by the perturbation scheme is shown to be in good agreement with numerical solutions of the GL theory. Finally, a universal relation between density wave profile widths and the anisotropy parameter of the surface energy is proposed and validated using a phase-field crystal method.

Keywords: interfacial anisotropy, symmetry breaking, Ginzburg-Landau theory, Order-disorder transition