1. Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Origin of 3D Chessboard Structures: Theory and Modeling Armen G Khachaturyan, Rutgers University New Brunswick Rutgers University, DMR 0704045  Y.Ni, and A.G. Khachaturyan, “Mechanism and conditions of the chessboard structure formation.” Acta Materialia 2008, in press.  Y.Ni, and A.G. Khachaturyan, “Pseudo-spinodal decomposition: from chessboard tweed to chessboard nanowire structure.” Nature Materials, under review.  The extension of Phase Field theory and 3D modeling in the case of a coherent decomposition in strongly non-equilibrium systems resulted in a discovery of a new phenomenon, the pseudo- spinodal decomposition occurring near the diffusionless transformation point. This is a new decomposition mode producing phases of different point symmetry with gradually separating compositions. It differs significantly from what is usually expected for the conventional decomposition.  The discovery explains the observations of two structurally heterogeneous states with potentially important technological applications whose physical origin was unknown. The first one is the nano-scale tweed structure that is a new type of a precursor state. The second is the Chessboard (CB) nano-wire structure. The CB architecture consists of parallel rods of orientation domains of both phases arranged into the CB pattern.  The modeling provides the first glimpse of the 3D arrangement of the nano-domain tweed structure. It shows that under certain thermodynamic and crystallographic conditions the tweed structure (Fig.1(a)) has an underlying CB architecture (Fig 1(b)) that resulted in the formation of the coherent CB nano-wire structure in the continuing pseudo-spinodal decomposition—the tweed in this case plays a role of a template for the formation. The latter process is illustrated by Fig. 2. This finding reveals an origin of the CB nano-wire structure. Fig. 1 (a) the simulated compositionally inhomogeneous 3D tweed structure produced by the cubic  tetragonal pseudo-spinodal decomposition; (b) the Fourier filtering 3D topology of the tweed structure in (a) emphasizing its main geometrical features. (a) (b)

2. Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Origin of 3D Chessboard Structures: Theory and Modeling Armen G Khachaturyan, Rutgers University New Brunswick Rutgers University, DMR 0704045  The necessary thermodynamic conditions of the CB structure are established: the CB structure is possible near the temperature of the diffusionless equilibrium between both product phases at the same composition. The crystallographic necessary condition is the relation between crystal lattice parameters of the product phases. This relation in the case of the cubic  tetragonal transformation is the ratio ξ o =(a c -a t )/(c t -a c )~0.2 minimizing the strain energy of the CB structure where a c and a t, c t are lattice parameters of the cubic and tetragonal phases. This condition is illustrated by fig.3.  A broader impact of the discovery of the pseudo-spinodal decomposition mechanism and the origin of the CB nano-wire structures is an opening of the ways for development of new processing regimes for a spontaneous self-assembling of strongly correlated nano-wire structures. These structures can be optimal configurations for advanced multiferroic materials and for high density memory media.  The utilization of the pre-transitional nano-tweed structures also provides new ways for designing the materials with a giant anhysteretic displacive response to the applied fields (stress, magnetic and electric fields). Fig. 2 The 3D modeling of the microstructure evolution at c=0.5 (c s <~0.51) in the pseudo-spinodal decomposition of the homogeneous cubic phase producing the cubic/tetragonal two-phase CB structure. a b c d a,b,c,d Fig. 3 A plot of the estimated reduced strain energy of the CB structure as a function of the crystallographic parameter, ξ=(a c -a t )/(c t - a c ). The insertions are the simulated two phase structures for four different values of ξ at the positions a,b,c,d but the same values of other input parameters.

3. Thermodynamics and Kinetics of Phase Transformations in Complex Non-Equilibrium Systems Development of Theory of Ferroelectrics Solid Solutions Armen G Khachaturyan, Rutgers University New Brunswick Rutgers University, DMR 0704045  G.A.Rossetti, A.G. Khachaturyan, G.Akcay, Y.Ni, “Ferroelectric solid solutions with morphotropic boundaries:vanishing polarization anisotropy, adaptive, polar glass, and two-phase states.” Journal of Applied Physics 103,114113(2008). It is demonstrated that the fact that the most important ferroelectric materials are solid solutions rather than stoichiometric compounds results in important physical consequences, which have been mostly ignored before. One of them is the thermodynamic stability of two-phases states, ferroelectric+paraelectric or two ferroelectrics with different symmetry. Such two-phase ferroelectric states have been never studied before. The second consequence of a solid solution state of the ferroelectrics is expected for systems with different point symmetry of the ferroelectric phases on opposite sides of the phase diagram. This is vanishing or drastic reduction of the directional anisotropy of the polarization with respect to atomic lattice occurring along the line on the phase diagram referred as morphotropic boundary (MB). The theory revealed new angles in the understanding of the special properties of the solid solutions near MB for a particular case of generic PbZrO 3 -PbTiO 3 system with the perovskite structure. They are: A vanishing or drastic reduction of the domain wall energy resulting in a miniaturization of the domain structure near MB and formation of the mixed adaptive nano-domain states. These states produce diffraction effects mimicking the conventional diffraction from a monoclinic phase. recently observed in TEM studies.  The new interpretation of the observed giant magnetostriction near MB. According to this interpretation, the giant magnetostriction is not an intrinsic property of a single-domain crystal but rather an extrinsic effect caused by the anhysteretic reconfiguration of the nano-domains under applied electric field and similar to the pseudo-elasticity some of martensitic crystals. A manipulation of the microstructures of two-phase ferroelectric states in fact would be a new field of the ferroelectrics research. A potentiality of this approach for producing materials with exceptional physical properties can be seen from an analogy with the physical metallurgy of alloys: as is known, a similar manipulation of microstructure of two-phase states has been for more than hundred years (and still is) the main method of alloy design. So far, it produced an innumerate variety of existing advanced materials. The obtained results have an impact beyond the area of ferroelectrics– they can be also applicable to a wide variety of ferroelastic and martensitic materials.  A decoupling of the polarization and crystal lattice in some cases and thus formation of the dipole glass-kind state. The predicted nano-domain structures and curved domains typical for the glass-type state were