Heterogeneous Nucleation of an Embryo in the Shape of Square Prism: Effect of Surface Roughness.

Abstract

The solution-based synthesis in a confined space between two parallel plates has been demonstrated to be a potential approach to grow single-crystal perovskite films of large sizes, such as CH3NH3PbX3 (X = Br and I) single-crystal films. In this work, we study the effects of surface roughness on the separation between two parallel, rough plates, and heterogeneous nucleation of an embryo in the shape of square prism for the Wenzel contact between the embryo and the rough surface. Analytical relations are derived for the separation of two parallel, rough plates under mechanical loading and the critical dimensions of a square embryo on a rough surface. The analytical relation reveals that one can control the thickness of perovskite films grown between two parallel plates by changing the surface tension of the precursor solution and mechanical loading. The critical dimensions of a square embryo and the corresponding formation energy are dependent on interface energies and the root mean square of surface roughness. There exists a critical root mean square of surface roughness, above which it is very difficult to form an embryo in the shape of square prism. The results illustrate the important roles of the interface energies and surface roughness of substrates in the growth of single-crystal films, including perovskites and ionic crystals, and the need to include the anisotropic characteristics of surface/interface energies in the nucleation analysis of crystalline materials.