Rajeev Ahluwalia

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

Size dependence of domain patterns in a constrained ferroelectric system

90^{o}

Elastic deformation of polycrystals.

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

Power-Law Statistics for Avalanches in a Martensitic Transformation

BaTiO_{3}

Manipulating Ferroelectric Domains in Nanostructures Under Electron Beams

We have simulated the size dependence of domain patterns in a two-dimensional (square shaped) constrained ferroelectric system by means of a time-dependent Ginzburg–Landau model. The theory incorporates elastic strain in the form of an effective long-range nonlocal interaction of the polarization. A nonferroelectric layer is introduced in the free energy that enforces a decaying polarization at the surface. The results show that the number of domains decreases on decreasing the system size. We also found two critical sizes. The first one signifies a transition from a multi-domain to a single-domain state and the second indicates the disappearance of ferroelectricity.

Effect of surface induced nucleation of ferroelastic domains on polarization switching in constrained ferroelectrics

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.

Piezoelectric response of engineered domains in ferroelectrics

We devise a two dimensional model that mimics the recently observed power law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [ Vives {\it et al}, Phys. Rev. Lett. {\bf 72}, 1694 (1994)]. We include a threshold mechanism arising from the athermal nature of transformation, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis of the transformation, and more importantly, it shows that the energy is released in the form of avalanches with power law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.

Simulation of grain size effects in nanocrystalline shape memory alloys

Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. At the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable and may substitute piezoelectric effect in centrosymmetric materials. These features make flexoelectricity of growing interest during the last decade. At the same time, the available theoretical and experimental results are rather contradictory. In particular, experimentally measured flexoelectric coefficients in some ferroelectric materials largely exceed theoretically predicted values. Here, we determine the upper limits for the magnitude of the static bulk contribution to the flexoelectric effect in ferroelectrics, the contribution which was customarily considered as the dominating one. The magnitude of the upper bounds obtained suggests that the anomalously high flexoelectric coupling documented for perovskite ceramics can hardly be attributed to a manifestation of the static bulk effect.

Lateral size and thickness dependence in ferroelectric nanostructures formed by localized domain switching

Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.