Graduate School in Nonlinear Science

Sponsored by The Danish Research Agency

MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and 
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen 
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark


by Kim Rasmussen
Theoretical Division, T-11, MS-B262,
Los Alamos National Laboratory,
Los Alamos, NM 87545, USA,

MIDIT-seminar 485

Thursday, March 29, 2001, 15.00 h
at IMM, Bldg. 305, Room 018, DTU

Abstract: I will discuss how the St.Venant elastic compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a ``landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of compatibility. Our results are also applicable to structural phase transitions in improper ferroelastics such as ferroelectrics and magnetoelastics, where strain acts as a secondary order parameter.