Phase field simulations of coupled phase transformations in ferroelastic-ferroelastic nanocomposites

We use phase field simulations to study composites made of two different ferroelastics (e.g., two types of martensite). The deformation of one material due to a phase transformation can elastically affect the other constituent and induce it to transform as well. We show that the phase transformation can then occur above its normal critical temperature and even higher above this temperature in nanocomposites than in bulk composites. Microstructures depend on temperature, on the thickness of the layers, and on the crystal structure of the two constituents -- certain nanocomposites exhibit a great diversity of microstructures not found in bulk composites. Also, the periodicity of the martensite twins may vary over 1 order of magnitude based on geometry. keywords: Ginzburg-Landau, martensitic transformation, multi-ferroics, nanostructure, shape-memory alloyComment: 8 pages, 15 figure

Elastic Deformation of Polycrystals

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility induced long-range interaction between grains. The coupling of crystal orientation and elastic interactions allows for the rotation of individual grains by an external load. We apply the model to simulate uniaxial tensile loading of a 2D polycrystal within linear elasticity and a system with elastic anharmonicities that describe structural phase transformations. We investigate the constitutive response of the polycrystal and compare it to that of single crystals with crystallographic orientations that form the polycrystal.Comment: 4 pages, 4 ps figure

Domain Size Dependence of Piezoelectric Properties of Ferroelectrics

The domain size dependence of piezoelectric properties of ferroelectrics is investigated using a continuum Ginzburg-Landau model that incorporates the long-range elastic and electrostatic interactions. Microstructures with desired domain sizes are created by quenching from the paraelectric phase by biasing the initial conditions. Three different two-dimensional microstructures with different sizes of the $90^{o}$ domains are simulated. An electric field is applied along the polar as well as non-polar directions and the piezoelectric response is simulated as a function of domain size for both cases. The simulations show that the piezoelectric coefficients are enhanced by reducing the domain size, consistent with recent experimental results of Wada and Tsurumi (Brit. Ceram. Trans. {\bf 103}, 93, 2004) on domain engineered $BaTiO_{3}$Comment: submitted to Physical Review

Effect of lattice mismatch-induced strains on coupled diffusive and displacive phase transformations

Materials which can undergo slow diffusive transformations as well as fast displacive transformations are studied using the phase-field method. The model captures the essential features of the time-temperature-transformation (TTT) diagrams, continuous cooling transformation (CCT) diagrams, and microstructure formation of these alloys. In some materials systems there can exist an intrinsic volume change associated with these transformations. We show that these coherency strains can stabilize mixed microstructures (such as retained austenite-martensite and pearlite-martensite mixtures) by an interplay between diffusive and displacive mechanisms, which can alter TTT and CCT diagrams. Depending on the conditions there can be competitive or cooperative nucleation of the two kinds of phases. The model also shows that small differences in volume changes can have noticeable effects on the early stages of martensite formation and on the resulting microstructures. -- Long version of cond-mat/0605577 -- Keywords: Ginzburg-Landau, martensite, pearlite, spinodal decomposition, shape memory, microstructures, TTT diagram, CCT diagram, elastic compatibilityComment: 10 pages, 13 figures, long version of cond-mat/0605577. Physical Review B, to appear in volume 75 (2007