Fabrizio Daví

Evolution of domain walls in ferroelectric solids

Abstract The evolution of domain walls in ferroelectrics is analyzed. The placement field and the polarization vector field accounting for the microstructure of ferroelectric domains describe the body. Measures of interaction are associated to the polarization field. They have electromechanical nature and are balanced by appropriate equations. The deduction of the evolution equations for strongly anisotropic domain walls and corners (junctions among domain walls) is the main result of this paper. The model is applied to typical cases and the explicit solutions obtained fit the available experimental results on Barium Titanate. An analogous agreement is found also at the junctions.

The theory of Kirchhoff rods as an exact consequence of three-dimensional elasticity

A one-dimensional model of a linearly elastic thin rod is deduced from three-dimensional elasticity by regarding the Kirchhoff hypotheses as internal constraints prevailing in a three-dimensional tubular region. It follows from such an assumption that the displacement and the strain fields are linear in the cross-sectional coordinates. A constitutive relation that exhibits the maximal symmetry compatible with the assumed constraints is chosen and the equilibrium equations in terms of displacements are obtained.

Saint-Venant's Problem with Voigt's Hypotheses for Anisotropic Solids

We seek for a solution of Saint-Venants problem for inhomogeneous and anisotropic materials under the assumptions, introduced by Voigt, that the stress is either constant along the axis of the cylinder or depends linearly on the axial coordinate. We first prove the uniqueness of the solution in terms of resultants, then we exhibit an explicit formula for such a solution; we show finally how Clebschs hypothesis, that the stress vector on axial planes is parallel to the axis, is compatible with Voigts hypotheses provided that the symmetry group of the material comprising the cylinder contains the reflections on the cross-section.

On twinning and domain switching in ferroelectric Pb(Zr1−xTix)O3—part I: twins and domain walls

Abstract We study the electromechanical behavior of lead zirconate titanate ferroelectric ceramics (PZT), by means of a three-dimensional continuum model for deformable ferroelectric bodies in their polar phase characterized by spontaneous polarization and strain. Spontaneous polarization and strain organize into a domain structure which minimizes electrostatic and elastic energies and which can be modified by the application of electromechanical loads. Such process, which is called “domain switching”, is associated with electrical and mechanical hysteresis and can be studied as a minimization problem for a functional which reminds the micromagnetic energy of deformable ferromagnetics. In this paper, which is the first of two, we deal with the electromechanical model and related constitutive assumptions, as well as with the analysis of domain structure in PZT. In particular, following the discover of a new monoclinic phase in PZT carried by Noheda and co-workers, we analyze twinning between spontaneous strain at the various phase boundaries and show that both non-generic, non-conventional twins and finely-twinned laminates are possible, and also that the presence of a monoclinic phase may explain PZT exceptional properties.

Elastic Moduli and Optical Properties of LYSO Crystals: Theory and Experiments

In order to obtain a complete characterization and understanding of the structural, optical and mechanical properties of LYSO scintillanting crystals, we studied a mechanical, optical and photoelastic model for a cylindrical prism of square cross-section bent by applied loads. This is the starting point which is necessary in order to design a set of mechanical, electrical and optical experiments aimed to obtain the characterization of the macroscopical behavior of LYSO and similar crystals.

Photoelastic sphenoscopic analysis of crystals

Birefringent crystals are at the basis of various devices used in many fields, from high energy physics to biomedical imaging for cancer detection. Since crystals are the main elements of those devices, a great attention is paid on their quality and properties. Here, we present a methodology for the photoelastic analysis of birefringent crystals, based on a modified polariscope. Polariscopes using conoscopic observation are used to evaluate crystals residual stresses in a precise but time consuming way; in our methodology, the light beam shape, which impinges on the crystal surface, has been changed from a solid cone (conoscopy) to a wedge (sphenoscopy). Since the polarized and coherent light is focused on a line rather than on a spot, this allows a faster analysis which leads to the observation, at a glance, of a spatial distribution of stress along a line. Three samples of lead tungstate crystals have been observed using this technique, and the obtained results are compared with the conoscopic observation. The samples have been tested both in unloaded condition and in a loaded configuration induced by means of a four points bending device, which allows to induce a known stress distribution in the crystal. The obtained results confirm, in a reliable manner, the sensitivity of the methodology to the crystal structure and stress.

Singularities in Landau-Devonshire Potentials for Ferroelectric Phase-Transitions

Ferroelectrics phase transitions are studied in terms of fourth-order Landau potentials: a clever choice of the reference configuration allows for a complete description of all the possible transitions. The study of the stability conditions at the phase interface helps to explain the fairly complex nature of the observed twins.Copyright

Optimization of the photoelastic fringe pattern processing for the stress evaluation in scintillating anisotropic media

Scintillating media are used in numbers of fields, from the high-energy physics to the biomedical devices, like those for the cancer detection and characterization, passing through the laser technology and industry processes control. Their performances must be enhanced in order to accomplish to the more and more sophisticated needs of the applications. Residual stress conditions are crucial for the correct performance of these materials. Moreover, an accurate study of the internal stress leads to a proper setting of the production process and prevent unwanted fractures of the brittle media. Non-invasive photoelastic methods are particularly suitable for the purpose; producing fringe pattern images which are a signature of the crystal state. These methods have to be supported of algorithms dedicated to the image analysis, so to extract geometrical parameters of the fringe pattern. Here an optimized algorithm to analyze the fringe pattern acquired by a laser based polariscope is discussed. This algorithm has been optimized and automated so to reduce the measurement uncertainty, considering a time saving procedure. The implemented procedure makes the software able to recognize the ROI in the acquired image and reduces the uncertainty by a factor 3.5.