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 ofC11. The strain e3 is proportional to the order parameter and scales as |e1 + e2| ∼ e23 . 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 C33 and ∼−1 for C11, (C11 +C12) and (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 non symmetry-breaking strain, we find density fluctuations which make the material harder.