Elasticity of two-dimensional ferroelectrics across their paraelectric phase transformation

The mechanical behavior of two-dimensional (2D) materials across 2D phase changes is unknown, and the finite temperature ($T$) elasticity paradigmatic SnSe monolayers---ferroelectric turning paraelectric as their unit cell turns from a rectangle into square---is described here in progressive manner. To begin with, $\mathrm{zero}\text{\ensuremath{-}}T$ total energy landscape gives way to (Boltzmann-like) averages which elastic determined. These estimates are complemented with results strain-fluctuation method, employs or ab initio molecular dynamics data. All approaches capture coalescence moduli $\ensuremath{\langle}{C}_{11}(T)\ensuremath{\rangle}=\ensuremath{\langle}{C}_{22}(T)\ensuremath{\rangle}$ due structural transformation. broad evolution sudden parameters $\ensuremath{\langle}{C}_{11}(T)\ensuremath{\rangle}$, $\ensuremath{\langle}{C}_{22}(T)\ensuremath{\rangle}$, $\ensuremath{\langle}{C}_{12}(T)\ensuremath{\rangle}$ these atomically thin phase-change membranes establishes heretofore overlooked connection among soft matter.