Ñêà÷àòü ïîëíóþ âåðñèþ ñòàòüè (â PDF ôîðìàòå)
T. M. RADCHENKO and V. A. TATARENKO
«Statistical Thermodynamics and Kinetics of Atomic Order in Doped Graphene. I. Substitutional Solution»
867–910 (2008)
PACS numbers: 61.48.De, 61.72.Cc, 64.60.Cn, 64.70.Nd, 68.65.-k, 81.05.Uw, 81.30.Hd
The statistical-thermodynamics and kinetics models of substitutional atomic order in the two-dimensional graphene-based crystal lattices with stoichiometries of 1/8, 1/4, and 1/2 types are proposed. Impossibility of the stable ordering in the structures with stoichiometries of 1/6 and 1/3 is ascertained (at least, in case of a short-range interaction of atoms). If graphene is doped with the short-range-interacting substitutional atoms, the (super)structures described only by one long-range order (LRO) parameter are possible, and if it is doped with the long-range-interacting atoms, other (super)structures with two or three LRO parameters may appear as well. If stoichiometry is 1/4, the structure with one LRO parameter is more thermodynamically ‘favourable’ than that with one or two parameters. The dominance of intersublattice ‘mixing’ energies at their ‘competition’ with intrasublattice ones results in the non-monotony of kinetic curves of the LRO parameters for graphene-based structures described by two or three LRO parameters. As shown, the atomic ordering of carbon and substitutional dopant in graphene-based lattice is the most ‘effective’ in a structure where atomic fractions of both components are equal, and minimal ‘ordering effect’ corresponds to the structure where difference of atomic fractions of carbon and dopant is maximal. Kinetics results confirm statistical-thermodynamic ones: firstly, asymptotic and equilibrium values of the LRO parameters within the framework of these models, respectively, coincide; secondly, equilibrium (and instantaneous) value of the LRO parameter in nonstoichiometric binary graphene-based structure (where atomic fraction of the dopant deviates from the stoichiometry to the higher-concentration range) can be higher than it is in the stoichiometric phase.
|
