  The structure of amorphous materials has been debated since the 1930's as a
binary question: amorphous materials are either Zachariasen continuous random
networks (Z-CRNs) or Z-CRNs containing crystallites. It was recently
demonstrated, however, that amorphous diamond can be synthesized in either
form. Here we address the question of the structure of single-atom-thick
amorphous monolayers. We reanalyze the results of prior simulations for
amorphous graphene and report kinetic Monte Carlo simulations based on
alternative algorithms. We find that crystallite-containing Z-CRN is the
favored structure of elemental amorphous graphene, as recently fabricated,
whereas the most likely structure of binary monolayer amorphous BN is
altogether different than either of the two long-debated options: it is a
compositionally disordered "pseudo-CRN" comprising a mix of B-N and
noncanonical B-B and N-N bonds and containing "pseudocrystallites", namely
honeycomb regions made of noncanonical hexagons. Implications for other
non-elemental 2D and bulk amorphous materials are discussed.
