  Spontaneous formation of geometric patterns is a fascinating, ubiquitous
process that provides fundamental insights into the roles of symmetry breaking,
anisotropy and nonlinear interactions in emergent phenomena. Here we report
dynamic, highly ordered topographic patterns on the surface of diamond that
span multiple length scales and have a symmetry controlled by the chemical
species of a precursor gas used in electron beam induced etching (EBIE). This
behavior reveals an underlying etch rate anisotropy and an electron energy
transfer pathway that has been overlooked by existing EBIE theory. We present
an etch rate kinetics model that fully explains our results and is universally
applicable to EBIE. Our findings can be exploited for controlled wetting,
optical structuring and other emerging applications that require nano and
micro-scale surface texturing.
