  The growth and microstructural properties of ternary monolayers of
two-dimensional hexagonal materials are examined, including both individual
two-dimensional crystalline grains and in-plane heterostructures,
multijunctions, or superlattices. The study is conducted through the
development of a ternary phase field crystal model incorporating sublattice
ordering and the coupling among the three atomic components. The results
demonstrate that a transition of compositional pattern or modulation in this
type of two-dimensional ternary crystals, from phase separation to
geometrically frustrated lattice atomic ordering, can be controlled via the
varying degree of energetic preference of heteroelemental neighboring over the
homoelemental ones. Effects of growth and system conditions are quantitatively
identified through numerical calculations and analyses of interspecies spatial
correlations and the degree of alloy intermixing or disordering. These findings
are applied to simulating the growth of monolayer lateral heterostructures with
atomically sharp heterointerface, and via the sequential process of
edge-epitaxy, the formation of the corresponding superlattices or structures
with multiple heterojunctions, with outcomes consistent with recent experiments
of in-plane multi-heterostructures of transition metal dichalcogenides. Also
explored is a distinct type of alloy-based lateral heterostructures and
multijunctions which integrate ternary ordered alloy domains with the adjoining
blocks of binary compounds, providing a more extensive variety of
two-dimensional heterostructural materials.
