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

Abstract

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 2T_{tr}, where T_{tr} is the ferroelastic transition temperature. The precursor effects become strong at T<1.7T_{tr}. Two effects were identified in our two-dimensional model: the symmetry-breaking strain e_{3} (ɛ_{xy}) leads to softening of the elastic modulus C_{33}, while the nonsymmetry-breaking strain e_{1}+e_{2} (ɛ_{xx}+ɛ_{yy}) leads to hardening of C_{11}. The strain e_{3} is proportional to the order parameter and scales as |e_{1}+e_{2}|∼e_{3}^{2}. 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 ΔC_{33} and ∼−1 for ΔC_{11}, Δ(C_{11}+C_{12}) and Δ(C_{11}−C_{12}). 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.