We consider a model of two-dimensional binary substitutional solid solution based on a graphene-type crystal lattice. The question is as follows: how do doped metal atoms and carbon atoms distribute at the sites of graphene-type lattice (for a given temperature and concentration)—by means of ordered or disordered manner? Statistical-thermodynamics and kinetics models are proposed for atomic ordering in two-dimensional plane graphene-type lattice with stoichiometric concentrations, 1/8, 1/4, 1/2. (The unified ‘physical nature’, which causes mechanisms of atomic ordering in nanoscale and macroscopic mixed systems, is assumed.) Impossibility of atomically ordered distribution with stoichiometries of 1/6, 1/3 in such lattice is ascertained (at least, in case of a short-range interactions between substitutional atoms). If stoichiometry is 1/4, the structure with one long-range order (LRO) parameter is more advantageous thermodynamically than with two or three parameters. As revealed, kinetics curves of LRO parameters can be non-monotonic for structures described by two or three LRO parameters (because graphene-type crystal lattice consists of two sublattices and ‘mixing’ energies are different for them). Kinetics results confirm statistical-thermodynamic ones: firstly, equilibrium values of LRO parameter coincide within the both models; secondly, equilibrium (and instantaneous) values of LRO parameter in non-stoichiometric binary two-dimensional graphene-based phase can be higher than they are in stoichiometric one.

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