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 2 T tr , where T tr is the ferroelastic transition temperature. The precursor effects become strong at T < 1.7 T tr . Two effects were identified in our two-dimensional model: the symmetry-breaking strain e 3 ( ɛ x y ) 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 Δ C 33 and ∼−1 for Δ C 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. Published by the American Physical Society 2024