Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Transformation Sequences in the Cubic  Tetragonal Decomposition Armen G Khachaturyan, Rutgers University, DMR 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, 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). t t t Case A Case B Case C

Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Response and Microstructures of Compositionally Constrained Martensites Armen G Khachaturyan, Rutgers University, DMR  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,  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 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) 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/(Ge 2 )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.