Ferroelastic Dynamics and Strain Compatibility

T. Lookman; S. R. Shenoy; K. O. Rasmussen; A. Saxena; A. R. Bishop

doi:10.1103/PhysRevB.67.024114

paper

Ferroelastic Dynamics and Strain Compatibility

arXiv:cond-mat/0211425 · doi:10.1103/PhysRevB.67.024114

Abstract

We derive underdamped evolution equations for the order-parameter (OP) strains of a ferroelastic material undergoing a structural transition, using Lagrangian variations with Rayleigh dissipation, and a free energy as a polynomial expansion in the $N = n + N_{o p}$ symmetry-adapted strains. The $N_{o p}$ strain equations are structurally similar in form to the Lagrange-Rayleigh 1D strain dynamics of Bales and Gooding (BG), with `strain accelerations' proportional to a Laplacian acting on a sum of the free energy strain derivative and frictional strain force. The tensorial St. Venant's elastic compatibility constraints that forbid defects, are used to determine the n non-order-parameter strains in terms of the OP strains, generating anisotropic and long-range OP contributions to the free energy, friction and noise. The {\it same} OP equations are obtained by either varying the displacement vector components, or by varying the N strains subject to the $N_{c}$ compatibility constraints. A Fokker-Planck equation, based on the BG dynamics with noise terms, is set up. The BG dynamics corresponds to a set of nonidentical nonlinear (strain) oscillators labeled by wavevector $k$ , with competing short- and long-range couplings. The oscillators have different `strain-mass' densities $ρ (k) \sim 1/ k^{2}$ and dampings $\sim 1/ ρ (k) \sim k^{2}$ , so the lighter large-k oscillators equilibrate first, corresponding to earlier formation of smaller-scale oriented textures. This produces a sequential-scale scenario for post-quench nucleation, elastic patterning, and hierarchical growth. (Continued ...)

Phys. Rev. B, in press

Ferroelastic Dynamics and Strain Compatibility

Abstract

References in corpus (9)

Cited by in corpus (54)