Elasticity of 2D 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 (u.c.) turns from a rectangle onto a square—is described here in a progressive manner. To begin with, their zero−T elastic 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 (MD) data. Both 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.