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 of paradigmatic SnSe monolayers - ferroelectric 2D materials turning paraelectric as their unit cell turns from a rectangle into a square - is described here in a progressive manner. To begin with, their zero-T total energy landscape gives way to (Boltzmann-like) averages from which the elastic behavior is determined. These estimates are complemented with results from the strain-fluctuation method, which employs the energy landscape or ab initio molecular dynamics data. All approaches capture the coalescence of elastic moduli (C11(T))=(C22(T)) due to the structural transformation. The broad evolution and sudden changes of elastic parameters (C11(T)), (C22(T)), and (C12(T)) of these atomically thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.