# Mathematical model to predict the characteristics of polarization in dielectric materials: The concept of piezoelectrcity and electrostriction

## Chukwuemeka Peter Ukpaka

### Abstract

Model was developed for the prediction of polarization characteristics in a dielectric material exhibiting piezoelectricity and electrostriction based on mathematical equations and MATLAB computer simulation software. The model was developed based on equations of polarization and piezoelectric constitutive law and the functional coefficient of Lead Zirconate Titanate (PZT) crystal material used was 2.3×10-6 m (thickness), the model further allows the input of basic material and calculation of parameters of applied voltage levels, applied stress, pressure, dielectric material properties and so on, to generate the polarization curve, strain curve and the expected deformation change in the material length charts. The mathematical model revealed that an application of 5 volts across the terminals of a 2.3×10-6 m thick dielectric material (PZT) predicted a 1.95×10-9 m change in length of the material, which indicates piezoelectric properties. Both polarization and electric field curve as well as strain and voltage curve were also generated and the result revealed a linear proportionality of the compared parameters, indicating a resultant increase in the electric field yields higher polarization of the dielectric materials atmosphere.