Case A

1. Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium SystemsTransformation Sequences in the CubicTetragonal DecompositionArmen G Khachaturyan, Rutgers University, DMR 0704045 Case A t The presented selected results of the Phase Field Microelasticity modeling address a practically unknown area of the materials research– the displacive transformations in a compositionally heterogeneous system obtained by the priory decomposition. The interest to this problem is stemmed from recent observations of a giant magneto-striction in Fe-Ga alloys and observation of giant piezoelectricity of perovskite ferroelectrics near morphotropic boundaries. The purpose of this research is an attempt to fill a gap in our understanding the specific structural features responsible for the giant response of the materials with these features to the stress/magnetic/electric fields. The presented visualizations of the modeling results demonstrate that depending on the composition of the system and the free energies of the phases, a precipitation of the tetragonal phase from the cubic matrix can develop according to the three possible scenarios: A conventional process with direct nucleation of the tetragonal phase from its cubic parent phase (Case A), as is usually assumed in the textbook, and two unconventional scenarios with a two-stage process. The transformation in Case B starts as a cubiccubic+cubicdecomposition and later undergoes the cubictetragonal displacive transformation within precipitates of the solute-rich cubic phase. The sequence of transformation in Case C is revetrsed—it starts from the cubictetragonal displacive transformation that is followed by the decomposition. The PFM modeling does not impose a preset constraints on the transformation path and describes a spontaneous self-assembling of a nano-scale structure driven by the stress-relaxation of the system. Y.Ni, Y.M. Jin and A.G. Khachaturyan, “The transformation sequences in the cubictetragonal decomposition,” Acta Mater., 55, 4903, 2007. Case B t Case C t Three scenarios of the temporal microstructure evolution during the generic cubictetragonal decomposition predicted by Phase Field Microelasticity modeling (black and white represent different compositions; red and green represent different orientation domains of the tetragonal phase). Note a multilayer domain structure of precipitates (cases A and B) and checkerboard structure (case A).

2. Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Response and Microstructures of Compositionally Constrained MartensitesArmen G Khachaturyan, Rutgers University, DMR 0704045 The goal of this part of the research is to find structural conditions leading to an anhysteretic strain response of a system of structural domains to the applied fields—the anhysteretic behavior is a valuable property that can be utilized in many technologically important devices. The 3-D Phase Field Microelasticity modeling results presented in the slides illustrate (i) the effect of confinement of the cubictetragonal displacive transformation within precipitates on the architecture of orientation domains of the tetragonal phase and (ii) the response of configuration of these domains and the domain-generated macroscopic strain to applied field (stress, magnetic field in ferroelectrics, and electric field in the ferroelectrics). This spatial confinement produces a restoration driving force that reverses the rearranged domain structure (and the domain structure-induced macroscopic strain) to its initial configuration upon removal of the applied field and leads to anhysteretic behavior of the macroscopic strain illustrated by a plot on figure (d). (a) (b) (c) (d) • A.G. Khachaturyan and D.Viehland, “Structurally Heterogeneous Model of Extrinsic Magnetostriction for Fe-Ga and Similar Magnetic Alloys:Part I. Decomposition and Confined Displacive Transformation; Part II. Giant Magnetostriction and Elastic Softening, Metall Mater Trans A 38,2308; 38, 2317, 2007. • Y.Ni, Y.M. Jin and A.G. Khachaturyan, “Theory and Modeling of Martensitic Transformation within Precipitates and its Response to the Applied Field ,” to be submitted in 2007. Figure (a)-(c) are the self-assembled domain microstructures formed by the displacive transformation in a spherical particle without applied stress. The structures are shown in correspondence with the increasing value of the parameter g/(Ge2)D where D is the diameter of the precipitate, G is shear modulus, e is the tetragonality strain, an g is the domain wall energy. Figure (d) simulated the strain response and the corresponding 3D domain structures for a confined martensite within precipitates under a cyclic applied stress. A-D disignate the domain structures related to the corresponding points at the hysteresis loop.