Nonlinear and nonlocal continuum model of transformation precursors in martensites

An intrinsic mechanism for explaining the origin of the transformation precursors observed above the transition in the parent phase of many materials undergoing a martensitic transformation is proposed. It is based on a nonlinear and nonlocal elastic continuum model for the elastic displacement field describing the parent-product deformation for the two-dimensional analog of a cubic-tetragonal transformation. By minimizing the Landau-Ginzburg free energy functional for the total elastic (strain plus strain gradient) energy a static, possibly stable, continuous, periodically modulated {110}/〈110〉 strain pattern is obtained which corresponds to alternating layers of more and of less transformed material, consistent with experimental observations. This pattern is stabilized by the balance between nonlinear and nonlocal elastic effects. Numerical application to In_1-x XT _x , alloys gives the minimum period of the modulation in the order of nanometers, in agreement with experimental observations.