Dynamical properties of a ferroelectric capacitor observed through nonlinear time series analysis

Abstract

By data analysis the ordinary differential equation for the description of an experimental electric resonance circuit with nonlinear capacitor is derived. Triglycine sulfate (TGS) was used as nonlinear dielectric material. This is the most thoroughly investigated ferroelectric with a second order phase transition. Its static dielectric small signal behavior is well described in the framework of the Landau theory, yielding a Duffing-type ordinary differential equation as a model equation of the circuit. Data analysis allows us to check carefully the validity of this model and to determine required corrections of this simplified equation. (c) 1998 American Institute of Physics.

What Can We Learn About Ferroelectrics Using Methods of Nonlinear Dynamics?

“…These signals are recorded by a digital storage oscilloscope and can be used for direct observation of the phase portrait as demonstrated in figure 2. Alternatively, it is possible to record only the signal U C and to calculate the temporal derivatives numerically [1,5].…”

“…To minimize the influence of these two elements it is necessary to fulfill the condition R 1/C 1/C NL which reminds of the Sawyer-Tower circuit. So, two signals U C ∼ D and U R ∼Ḋ = j may be derived [1,4], where D and j are the dielectric displacement and the current density, respectively. These signals are recorded by a digital storage oscilloscope and can be used for direct observation of the phase portrait as demonstrated in figure 2.…”

“…From equation (1) one gets a second order differential equation [1,5,6], that is the equation of motion in the sense of the theory of dynamic systems:…”

“…where the degree of the polynomial in D was increased up to n = 9 [1]. What follows is a short description of the fitting procedure.…”

“…Considerations of the system on the basis of simple Landautheory suggest to describe the resonance circuit by means of a Duffingequation. Because of the switching process during the nonlinear vibrations the real situation is more complicated as can be shown by nonlinear time series analysis [1]. …”