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arXiv · cond-mat/0211425

Ferroelastic Dynamics and Strain Compatibility

T. Lookman·S. R. Shenoy·K. O. Rasmussen·A. Saxena·A. R. Bishop
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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 $N=n+N_{op}$ symmetry-adapted strains. The $N_{op}$ 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 $\vec{k}$, 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 ...)

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T. Lookman, S. R. Shenoy, K. O. Rasmussen, A. Saxena, A. R. Bishop. 2002-11-20. Ferroelastic Dynamics and Strain Compatibility. https://doi.org/10.1103/physrevb.67.024114

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