Proper ferroelastic phase transitions in thin epitaxial films with symmetry-conserving and symmetry-breaking misfit strains

We study how the ferroelastic domain structure sets in in an epitaxial film of a material with second order proper ferroelastic transition. The domain structures considered are similar to either $a_{1}/a_{2}/a_{1}/a_{2}$ or $c/a/c/a$ structures in perovskite ferroelectrics. If the "extrinsic" misfit strain, not associated with the transition, does not break the symmetry of the high-temperature phase, the phase transition in the film occurs at somewhat lower temperature compared to the bulk. The loss of stability then occurs with respect to a sinusoidal strain wave, which evolves into the domain structure with practically the same geometry and approximately the same period. In the presence of the symmetry-breaking component of the misfit strain ("extrinsic" misfit) the character of the phase transition is qualitatively different. In this case it is a {\em topological} transition between single-domain and multi-domain states, which starts from a low density of the domain walls.Comment: 7 pages, 2 figures, REVTeX 3.

Deformation through Transformations

Constitutive stress-strain relations for transformational deformation are discussed. A crystal which can be in two possible phase states is considered. A phase transformation begins during the deformation after a certain amount of elastic strain. For each fixed level of strain an equilibrium polydomain microstructure is established which corresponds to a minimum in the free energy of the crystal. The equilibrium microstructure consists of plane-parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of different domains (twins) forming plane-parallel alternating layers. The volume fractions of the phases and the fractions of the different twin components in the product phase are functions of strain and temperature. The stress-strain curve which reflects the evolution of the equilibrium microstructure is calculated. For deformation under strain control the stressstrain curve has a section with negative or zero slope that corresponds to a negative or zero Young's modulus. If deformation proceeds under stress control, hysteretic stress-strain curves on loading and unloading will result from a section with negative slope

Principal Concepts of Martensitic Theory

Fundamentals of the theory of martensitic transformations are discussed. Principal theoretical concepts which are valid for all phase transformations in solids are formulated and illustrated. Some basic problems which are still unsolved are pointed out

Domain structures and high tunability in compositionally graded ferroelectric films

The domain structure and dielectric properties in multilayered compositionally graded Ba xSr 1-xTiO 3 films on SrTiO 3 substrates are studied using phase field modeling with a uniaxial ferroelectric model of an 180° domain film. The films with a strong composition gradient produce stable polydomain states with labyrinth and columnar morphologies. At zero applied field, the labyrinth structure has zero equilibrium polarization and the columnar domain structure has significant average polarization. Both structures can be obtained in the same film depending on the domain formation history. The simulation results demonstrate that graded films with the stable polydomain state stable produce a very large tunability. Copyrigh

Domain structure and P(E) hysteresis in m BaxSr (1-x)TiO3 - N BaTiO3 bilayers on SrTiO 3 substrate

The model of the P(E) hysteresis in dielectric - ferroelectric bilayers and weak - strong ferroelectric bilayers is presented with the phase field modeling of the domain structure and P(E) curves in the compositionally graded m BaxSr(1-x)TiO3 - n BaTiO3 bilayers on SrTiO3 substrate. It is shown that the hysteresis loop depends on the film composition and structure and varies from simple rectangular to complex. The coercive field and the single-domain to polydomain transition depend on the film composition and structure. There is a significant difference between the behavior of through thickness domain structures and columnar domain structures localized in one layer. Copyrigh

Modeling of martensitic transformation in adaptive composites

The formation of elastic domains in transforming constrained films is a mechanisms of relaxation of internal stresses caused by the misfi between a film and substrate. The formation and evolution of polydomain microstructure as a result of the cubic-tetragonal transformation in a constrained layer are investigated by phase-field simulation. It has been shown that the three-domain hierarchical structure can be formed in the epitaxial films. With changing a fraction of out-of-plane domain there are two types of morphological transitions: from the three-domain structure to the two-domain one and from the hierarchical three-domain structure to the cellular three-domain structure. The results of the phase-field simulatio

Phase field modeling of self-assembling nanostructures in constrained films

We present a thermodynamic analysis and phase field modeling of self-assembled multiphase nanostructures produced by phase transformations in constrained layers. Due to coherency between the phases, the elastic interactions between them and between each phase and the substrate layer play an important role in the formation of the nanostructures. It has been shown that a variety of morphologies of heterophase nanostructures can be obtained depending on the crystallographic characteristics of transformations, elastic properties of the phases, relative fractions of the phases, and the thickness of the film. The results obtained by phase-field modeling agree well with predictions of an analytical thermodynamic model. The final equilibrium structures are determined by thermodynamic parameters and do not depend on the transformation path and, therefore, the phase-field approach developed in this paper can be expanded to finding equilibrium multiphase coherent nanostructures created as a result of solid-solid or solid-liquid transformations as well as during co-deposition on a substrate

Morphological transitions of elastic domain structures in constrained layers

The phase transformation in a constrained layer is the subject of this article. The formation and evolution of polydomain microstructure under external stress in the constrained layer are investigated by phase-field simulation and analytically using homogeneous approximation. As a result of simulation, it has been shown that the three-domain hierarchical structure can be formed in the epitaxial films. Under external stress there are two types of morphological transitions: from the three-domain structure to the two-domain one and from the hierarchical three-domain structure to the cellular three-domain structure. The results of phase-field simulation are compared with conclusions of homogenous theory and with available experimental data