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Domains of the adsorbed benzene monolayer on graphene

We consider the adsorbed benzene monolayer on graphene and show that the monolayer’s structure can be very complicated even for benzene, the simplest representative of the cyclic hydrocarbons. We base this on previous the first principal investigations, which found different energy states of the adsorbed benzene molecule. We find the existence of the six domains (star domains) for the stable molecular monolayer. The representatives of these domains (grains) at the graphene hexagonal layer are star vectors that describe transitions from symmetric high energy state into the stable low symmetric position. In the hexagon lattice of any benzene close pack domain, we introduce the primitive unit vectors, which are twice longer than the graphene primitive unit ones. The symmetry elements of the adsorbed benzene monolayer on graphene are found, left and right domains are introduced. Besides, half-translation of the benzene domains on the graphene primitive unit vectors leads to a further increase in the variety of the domain types. We introduce the selection procedure to decrease the number of the possible domains, find zero-block cells, and the complete number of the benzene domains — eight. We find all types of the structural domains and show their relation with the graphene unit cell construction.