Elastic precursor softening in proper ferroelastic materials: A molecular dynamics study

Precursor elastic effects are investigated in a displacive anharmonic spring model and shown to extend greatly into the paraelastic phase. Weak precursor effects can be detected near 2Ttr, where Ttr is the ferroelastic transition temperature. The precursor effects become strong at T<1.7Ttr. Two effects were identified in our two-dimensional model: the symmetry-breaking strain e3 (ϵxy) leads to softening of the elastic modulus C33, while the nonsymmetry-breaking strain e1+e2 (ϵxx+ϵyy) leads to hardening of C11. The strain e3 is proportional to the order parameter and scales as |e1+e2| ∼e32. The temperature evolutions of the elastic moduli are surprisingly well described by power laws and Vogel-Fulcher equations. The power-law exponents are ∼-0.5 for ΔC33 and ∼-1 for ΔC11, Δ(C11+C12) and Δ(C11-C12). The Vogel-Fulcher temperatures are very similar, while the Vogel-Fulcher energies differ between the excess elastic moduli. The origin of the precursor effect is the evolution of short-range order in the paraelastic phase which gives rise to a characteristic local nanostructure. In the case of the symmetry-breaking strain, this microstructure resembles dynamical twinning patterns corresponding to the ferroelastic nanostructure, which weakens the material. In the case of the nonsymmetry-breaking strain, we find density fluctuations which make the material harder.