dielectric

A dielectric is a nonconducting substance, i.e. an insulator. The term was coined by William Whewell in response to a request from Michael Faraday.^[1] Although "dielectric" and "insulator" are generally considered synonymous, the term "dielectric" is more often used to describe materials where the dielectric polarization is important, such as the insulating material between the metallic plates of a capacitor, while "insulator" is more often used when the material is being used to prevent a current flow across it.

Dielectrics is the study of dielectric materials and involves physical models to describe how an electric field behaves inside a material. It is characterized by how an electric field interacts with an atom and is therefore possible to approach from either a classical interpretation or a quantum one.

Many phenomena in electronics, solid state and optical physics can be described using the underlying assumptions of the dielectric model. This can mean that the same mathematical objects can go by many different names.

Definitions

Electric field interaction with an atom under the classical dielectric model.

Von Hippel, in his seminal work, Dielectric Materials and Applications, stated:

Dielectrics... are not a narrow class of so-called insulators, but the broad expanse of nonmetals considered from the standpoint of their interaction with electric, magnetic, or electromagnetic fields. Thus we are concerned with gases as well as with liquids and solids, and with the storage of electric and magnetic energy as well as its dissipation.^[2]

Classical

In the classical approach to the dielectric model, a material is made up of atoms. Each atom consists of a cloud of negative charge bound to and surrounding a positive point charge at its centre. Because of the comparatively huge distance between them, none of the atoms in the dielectric material interact with one another^{[citation needed]}. Note: Remember that the model is not attempting to say anything about the structure of matter. It is only trying to describe the interaction between an electric field and matter.

In the presence of an electric field the charge cloud is distorted, as shown in the top right of the figure.

This can be reduced to a simple dipole using the superposition principle. A dipole is characterized by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behavior of the dielectric. Note: The dipole moment is shown to be pointing in the same direction as the electric field. This isn't always correct, and it is a major simplification, but it is suitable for many materials.^{[citation needed]}

When the electric field is removed the atom returns to its original state. The time required to do so is the so-called relaxation time; an exponential decay.

Behavior

This is the essence of the model in physics. The behavior of the dielectric now depends on the situation. The more complicated the situation the richer the model has to be in order to accurately describe the behavior. Important questions are:

• Is the electric field constant or does it vary with time?
  • If the electric field does vary, at what rate?
• What are the characteristics of the material?
  • Is the direction of the field important (isotropy)?
  • Is the material the same all the way through (homogeneous)?
  • Are there any boundaries/interfaces that have to be taken into account?
• Is the system linear or do nonlinearities have to be taken into account?

The relationship between the electric field E and the dipole moment M gives rise to the behavior of the dielectric, which, for a given material, can be characterized by the function F defined by the equation:

.

When both the type of electric field and the type of material have been defined, one then chooses the simplest function F that correctly predicts the phenomena of interest. Examples of possible phenomena:

• Refractive index
• Group velocity dispersion
• Birefringence
• Self-focusing
• Harmonic generation

May be modeled by choosing a suitable function F.

Dielectric model applied to vacuum

From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric.

Recall that the property which defines how a dielectric behaves is the relationship between the applied electric field and the induced dipole moment. For a vacuum the relationship is a real constant number. This constant is called the permittivity of free space, ε₀.

Dielectric dispersion

In physics, dielectric dispersion is the dependence of the permittivity of a dielectric material on the frequency of an applied electric field. Because there is always a lag between changes in polarization and changes in an electric field, the permittivity of the dielectric is a complicated, complex-valued function of frequency of the electric field. It is very important for the application of dielectric materials and the analysis of polarization systems.

This is one instance of a general phenomenon known as material dispersion: a frequency-dependent response of a medium for wave propagation.

When the frequency becomes higher:

1. it becomes impossible for dipolar polarization to follow the electric field in the microwave region around 10¹⁰ Hz;
2. in the infrared or far-infrared region around 10¹³ Hz, ionic polarization loses the response to the electric field;
3. electronic polarization loses its response in the ultraviolet region around 10¹⁵ Hz.

In the wavelength region below ultraviolet, permittivity approaches the constant ε₀ in every substance, where ε₀ is the permittivity of the free space. Because permittivity indicates the strength of the relation between an electric field and polarization, if a polarization process loses its response, permittivity decreases.

Dielectric relaxation

Dielectric relaxation is the momentary delay (or lag) in the dielectric constant of a material. This is usually caused by the delay in molecular polarization with respect to a changing electric field in a dielectric medium (e.g. inside capacitors or between two large conducting surfaces). Dielectric relaxation in changing electric fields could be considered analogous to hysteresis in changing magnetic fields (for inductors or transformers). Relaxation in general is a delay or lag in the response of a linear system, and therefore dielectric relaxation is measured relative to the expected linear steady state (equilibrium) dielectric values. The time lag between electrical field and polarization implies an irreversible degradation of free energy(G).

In physics, dielectric relaxation refers to the relaxation response of a dielectric medium to an external electric field of microwave frequencies. This relaxation is often described in terms of permittivity as a function of frequency, which can, for ideal systems, be described by the Debye equation. On the other hand, the distortion related to ionic and electronic polarization shows behavior of the resonance or oscillator type. The character of the distortion process depends on the structure, composition, and surroundings of the sample.

The number of possible wavelengths of emitted radiation due to dielectric relaxation can be equated using Hemmings 1st Law

where

n: number of different possible wavelengths of emitted radiation

l: number of energy levels (inc. ground level).

Debye relaxation

Debye relaxation is the dielectric relaxation response of an ideal, noninteracting population of dipoles to an alternating external electric field. It is usually expressed in the complex permittivity of a medium as a function of the field's frequency ω:

where is the permittivity at the high frequency limit, where is the static, low frequency permittivity, and τ is the characteristic relaxation time of the medium.

This relaxation model was named after the chemist Peter Debye.

Variants of the Debye equation

• Cole-Cole equation
• Cole-Davidson equation
• Havriliak-Negami relaxation
• Kohlrausch-Williams-Watts function (Fourier transform of stretched exponential function)

Electric susceptibility

The electric susceptibility χ_e of a dielectric material is a measure of how easily it polarizes in response to an electric field. This, in turn, determines the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

It is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that

where is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity by

So in the case of a vacuum,

The electric displacement D is related to the polarization density P by

Dispersion and causality

In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by χ_e(Δt). The upper limit of this integral can be extended to infinity as well if one defines χ_e(Δt) = 0 for Δt < 0. An instantaneous response corresponds to Dirac delta function susceptibility χ_e(Δt) = χ_eδ(Δt).

It is more convenient in a linear system to take the Fourier transform and write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product,

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material.

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. χ_e(Δt) = 0 for Δt < 0), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility χ_e(0).

Applications

Capacitors

Commercially manufactured capacitors typically use a solid dielectric material with high permittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as the "capacitor dielectric" ^[3] . The most obvious advantage to using such a dielectric material is that it prevents the conducting plates on which the charges are stored from coming into direct electrical contact. More significantly however, a high permittivity allows a greater charge to be stored at a given voltage. This can be seen by treating the case of a linear dielectric with permittivity ε and thickness d between two conducting plates with uniform charge density σ_ε. In this case, the charge density is given by

and the capacitance per unit area by

From this, it can easily be seen that a larger ε leads to greater charge stored and thus greater capacitance.

Dielectric materials used for capacitors are also chosen such that they are resistant to ionization. This allows the capacitor to operate at higher voltages before the insulating dielectric ionizes and begins to allow undesirable current flow.

Dielectric resonator

A dielectric resonator is an electronic component that exhibits resonance for a narrow range of frequencies, generally in the microwave band. The resonance is similar to that of a circular hollow metallic waveguide, except that the boundary is defined by large change in permittivity rather than by a conductor. Dielectric resonators generally consist of a "puck" of ceramic that has a large dielectric constant and a low dissipation factor. The resonance frequency is determined by the overall physical dimensions of the puck and the dielectric constant of the material.

Dielectric resonators are often used to provide a frequency reference in an oscillator circuit.

A dielectric resonator is generally enclosed in an RF shield to prevent it radiating. An unshielded dielectric resonator can be used as an antenna. This type of antenna is usually called a DRA (Dielectric Resonator Antenna).

Cable insulation

The term "dielectric" may also refer to the insulation used in power and RF cables^{[citation needed]}. Common materials used as electrical insulations are electrical insulation paper and plastics.

Some practical dielectrics

Dielectric materials can be solids, liquids, or gases. In addition, a high vacuum can also be a useful, lossless dielectric even though its relative dielectric constant is only unity.

Solid dielectrics are perhaps the most commonly used dielectrics in electrical engineering, and many solids are very good insulators. Some examples include porcelain, glass, and most plastics. Air, nitrogen and sulfur hexafluoride are the three most commonly used gaseous dielectrics.

• Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment.
• Mineral oil is used extensively inside electrical transformers as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade castor oil, are often used in high voltage capacitors to help prevent corona discharge and increase capacitance.
• Because dielectrics resist the flow of electricity, the surface of a dielectric may retain stranded excess electrical charges. This may occur accidentally when the dielectric is rubbed (the triboelectric effect). This can be useful, as in a Van de Graaff generator or electrophorus, or it can be potentially destructive as in the case of electrostatic discharge.
• Specially processed dielectrics, called electrets (also known as ferroelectrics), may retain excess internal charge or "frozen in" polarization. Electrets have a semipermanent external electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry.
• Some dielectrics can generate a potential difference when subjected to mechanical stress, or change physical shape if an external voltage is applied across the material. This property is called piezoelectricity. Piezoelectric materials are another class of very useful dielectrics.
• Some ionic crystals and polymer dielectrics exhibit a spontaneous dipole moment which can be reversed by an externally applied electric field. This behavior is called the ferroelectric effect. These materials are analogous to the way ferromagnetic materials behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.

See also

References

• Classical Electrodynamics,John David Jackson Published by Wiley,1998 ISBN7130932X,780471309321

External links

• Electromagnetism - A chapter from an online textbook
• Dielectric Sphere in an Electric Field