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 < C-11(T)> = < C-22(T)> due to the structural transformation. The broad evolution and sudden changes of elastic parameters < C-11(T)>, < C-22(T)>, and < C-12(T)> of these atomically thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.