Parametrization of linear dielectric response
W A B Evans1, D M Heyes, J G Powles
1School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom. w.a.b.evans@kent.ac.uk
Summary
This study reveals inherent constraints on dielectric susceptibility fit-functions derived from quantum linear response theory. These findings are crucial for accurately modeling dielectric behavior and ferroelectric transitions.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Theoretical Chemistry
Background:
- Dielectric susceptibility and impulse response functions are key measured properties of dielectric materials.
- Analysis often involves fitting experimental data to parametric functional forms, known as fit-functions.
- Existing fit-functions may not always adhere to fundamental physical constraints.
Purpose of the Study:
- To derive general constraints on dielectric susceptibility forms from a linear response formalism.
- To evaluate common dielectric function parametrizations against these derived constraints.
- To explore the implications for ferroelectric transitions and model building.
Main Methods:
- Utilized a general linear response formalism, specifically the Madden-Kivelson approach, considering a uniform external electric field.
- Derived relationships between quasipermittivity (ζ(ω)) and normal permittivity (χ(ω)).
- Investigated common parametric 'fit-function' forms for compliance with theoretical constraints.
Main Results:
- Established definite relations between quasipermittivity and normal permittivity.
- Identified a condition for the divergence of normal susceptibility, signaling potential ferroelectric transitions.
- Demonstrated that some common fit-functions do not inherently satisfy the derived theoretical constraints.
Conclusions:
- Theoretical constraints on dielectric susceptibility forms are derivable from fundamental linear response theory.
- Incorporating these constraints into fit-functions is recommended for accurate dielectric modeling.
- The findings provide a framework for understanding ferroelectric transitions and improving dielectric material analysis.
Related Concept Videos
01:26Susceptibility, Permittivity and Dielectric Constant
When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.
01:31Dielectric Polarization in a Capacitor
The presence of a dielectric medium in a capacitor not only changes the voltage and capacitance but also affects the electric field. In general, dielectrics can be of two types: polar and nonpolar. In a polar dielectric, the positive and negative charges in the molecules are separated by a distance and hence have a permanent dipole moment. In contrast, no such charge separation exists in a nonpolar dielectric, however the nonpolar molecules get polarized in the presence of an external electric...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
01:17Gauss's Law in Dielectrics
Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
01:29Potential Due to a Polarized Object
A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
01:27Electrostatic Boundary Conditions in Dielectrics
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.