Phase stability of two-dimensional monolayer As1-x Px solid solutions revealed by a first-principles cluster expansion

Abstract

The phase stability of two-dimensional monolayer As1-xPx solid solutions, exhibiting the puckered (α phase) and buckled (β phase) structures are investigated using a first-principles cluster-expansion method. Canonical Monte Carlo simulations, together with harmonic approximation, are performed to capture the influences of thermally induced configurational disorder and lattice vibrations on the phase stability of monolayer As1-xPx. We first demonstrate that, as the temperature approaches 0 K, the monolayer As1-xPx displays a tendency toward phase separation into its constituent elemental phases, and thus no stable ordered structures of As1-xPx, both α and β phases, are predicted to be thermodynamically stable. We further reveal with the inclusion of the lattice vibrational contributions that β-As1-xPx is thermodynamically favored over α-As1-xPx across the entire composition range even at 0 K and increasingly so at higher temperature, and a continuous series of disordered solid solution of β-As1-xPx, where 0≤x≤1, is predicted at the temperature above 550 K. These findings not only indicate that the ordered structures of monolayer α-As1-xPx and β-As1-xPx, frequently studied in the literature, may not exist in nature, but also presumably suggest that monolayer α-As1-xPx is metastable with respect to monolayer β-As1-xPx.