Are Nanoparticle Corners Round?

Experimental results for corner rounding in nanoparticles as a function of size are reported. We find that the rounding is independent of size, which appears to violate the conditions for both the thermodynamic and kinetic Wulff conditions. To understand this, we first verify that continuum concepts such as the weighted mean curvature and preferential nucleation at a twin boundary are valid at the nanoscale using density functional theory calculations. We then explain the rounding as a consequence of a nominal singularity in continuum models for sharp corners, showing that rounded or in some cases slightly truncated corners are a Lyapunov (steady-state) solution. We point out that in almost all cases the corners of materials at the nanoscale will be rounded, and also that the rounding can be exploited to measure the chemical potential during the growth conditions.