(c) STM image of a branch of a fractal. The sample bias is 0.5 V and the tunnel current is 0.2 nA. (d) Differential conductivity recorded at the environment of the fractal, red curve (region (i) of (c)), and on the fractal, blue curve (region (i) of (c)), and on the fractal, blue curve (region (ii) of (c)). The sample bias for both curves is 0.5 V and the tunnel current is 0.2 nA.

**Abstract**

The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to blame for this failure. Here, we study the growth of fractal nanostructures in a two-dimensional (2D) system, intercalated between mica and graphene. Based on our scanning tunneling spectroscopy data, we provide compelling evidence that these fractals are 2D ice. They grow while they are *in material *contact with the atmosphere at 20 ºC and *without* significant *thermal* contact to the ambient. The growth is studied *in situ*, in real time and space at the nanoscale. We find that the growing 2D ice nanocrystals assume a fractal shape, which is conventionally attributed to Diffusion Limited Aggregation (DLA). However, DLA requires a *low mass density* mother phase, in contrast to the actual currently present *high mass density* mother phase. Latent heat effects and consequent transport of heat and molecules are found to be the key ingredients for understanding the evolution of the snow (ice) flakes. We conclude that not the local availability of water molecules (DLA), but rather them having the locally required orientation is the key factor for incorporation into the 2D ice nanocrystal. In combination with the transport of latent heat, we attribute the evolution of fractal 2D ice nanocrystals to local temperature dependent rotation limited aggregation. The ice growth occurs under extreme supersaturation, i.e., the conditions closely resemble the natural ones for the growth of complex 2D snow (ice) flakes and we consider our findings crucial for solving the “perennial” snow (ice) flake enigma. © 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4926467]

**Reference:**

Journal of Chemical Physics **143**, 034702 (2015)

**Credits:**

Pantelis Bampoulis,^{1,2,a)} Martin H. Siekman,^{1} E. Stefan Kooij,^{1} Detlef Lohse,^{2} Harold J. W. Zandvliet,^{1} and Bene Poelsema^{1}

^{1}*Physics of Interfaces and Nanomaterials, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands*

^{2}*Physics of Fluids and J. M. Burgers Centre for Fluid Mechanics, MESA+ Institute of Nanotechnology, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands*

**Microscope:**

RHK UHV3500 STM/AFM with Inverted Viewport

**Control System:**

RHK SPM1000