Variation of the dielectric constant in alternating fieldsWe know that a dielectric becomes polarised in an electric field. Now

imagine switching the direction of the field. The direction of the

polarisation will also switch in order to align with the new field. This

cannot occur instantaneously: some time is needed for the movement of

charges or rotation of dipoles.

If the field is switched, there is a characteristic time that the orientational

polarisation (or average dipole orientation) takes to adjust, called the

relaxation time. Typical relaxation times are ~10-11 s. Therefore, if the

electric field switches direction at a frequency higher than ~1011 Hz, the

dipole orientation cannot ‘keep up’ with the alternating field, the

polarisation direction is unable to remain aligned with the field, and this

polarisation mechanism ceases to contribute to the polarisation of the

dielectric.

In an alternating electric field both the ionic and the electronic

polarisation mechanisms can be thought of as driven damped harmonic

oscillators (like a mass on a spring), and the frequency dependence is

governed by resonance phenomena. This leads to peaks in a plot of

dielectric constant versus frequency, at the resonance frequencies of the

ionic and electronic polarisation modes. A dip appears at frequencies just

above each resonance peak, which is a general phenomenon of all

damped resonance responses, corresponding to the response of the

system being out of phase with the driving force (we shall not go into the

mathematical proof of this here). In this case, in the areas of the dips, the

polarisation lags behind the field. At higher frequencies the movement of

charge cannot keep up with the alternating field, and the polarisation

mechanism ceases to contribute to the polarisation of the dielectric.

As frequency increases, the material’s net polarisation drops as each polarisation mechanism ceases to contribute, and hence its dielectric constant drops. The animation below illustrates these effects.The dielectric constantThe dielectric constant of a material provides a measure of its effect on a

capacitor. It is the ratio of the capacitance of a capacitor containing the

dielectric to that of an identical but empty capacitor.

An alternative definition of the dielectric constant relates to the

permittivity of the material. Permittivity is a quantity that describes the

effect of a material on an electric field: the higher the permittivity, the

more the material tends to reduce any field set up in it. Since the

dielectric material reduces the field by becoming polarised, an entirely

equivalent definition is that the permittivity expresses the ability of a

material to polarise in response to an applied field. The dielectric constant

(sometimes called the ‘relative permittivity’) is the ratio of the permittivity

of the dielectric to the permittivity of a vacuum, so the greater the

polarisation developed by a material in an applied field of given strength,

the greater the dielectric constant will be.

There is no standard symbol for the dielectric constant – you may see it

referred to as κ, ε, ε′ or εr. In this TLP κ shall be used to avoid confusion

with the absolute permittivity, which may also be given the symbolε.

Effect of structure on the dielectric constantWe have already seen that the more available polarisation mechanisms a

material possesses, the larger its dielectric constant will be. For example,

materials with permanent dipoles have larger dielectric constants than

similar, non-polar materials.

In addition, the more easily the various polarisation mechanisms can act,

the larger the dielectric constant will be. For example, among polymers,

the more mobile the chains are (i.e. the lower the degree ofcrystallinity )

the higher the dielectric constant will be.

For polar structures, the magnitude of the dipole also affects the

magnitude of polarisation achievable, and hence the dielectric constant.

Crystals with non-centrosymmetric structures such as barium titanatehave

especially large spontaneous polarisations and so correspondingly large

dielectric constants. Conversely, a polar gas tends to have smaller

dipoles, and its low density also means there is less to polarise, therefore

polar gases have lower dielectric constants than polar solids or liquids.

The density argument also applies for non-polar gases when compared

with non-polar solids or liquids.

Effect of temperature on the dielectric constant

For materials that possess permanent dipoles, there is a significant

variation of the dielectric constant with temperature. This is due to the

effect of heat on orientational polarisation.

e: This animation requires Adobe Flash Player 8 and later, which can

be downloaded here.

However, this does not mean that the dielectric constant will increase

continually as temperature is lowered. There are several discontinuities in

the dielectric constant as temperature changes. First of all, the dielectric

constant will change suddenly at phase boundaries. This is because the

structure changes in a phase change and, as we have seen above, the

dielectric constant is strongly dependent on the structure. Whether κ will

increase or decrease at a given phase change depends on the exact two

phases involved.

There is also a sharp decrease in κ at a temperature some distance below

the freezing point. Let us now examine the reason for this.

In a crystalline solid, there are only certain orientations permitted by the

lattice. To switch between these different orientations, a molecule must

overcome a certain energy barrier ΔE.

 

When an electric field is applied, the potential energy of orientations

aligned with the field is lowered while the energy of orientations aligned

against the field is raised. This means that less energy is required to

switch to orientations aligned with the field, and more energy required to

switch to orientations aligned against the field.

Therefore over time molecules will become aligned with the field.

However, they must still overcome an energy barrier in order to do this. If

a molecule possesses an energy less than the height of any energy

barrier, it cannot cross the energy barrier therefore cannot change its

orientation. Hence the orientational mode becomes “frozen out” and can

no longer contribute to overall polarisation, leading to a drop in the

dielectric constant.

These effects are summarised in the graph below.

Loss in dielectricsAn efficient dielectric supports a varying charge with minimal dissipation

of energy in the form of heat. There are two main forms of loss that may

dissipate energy within a dielectric. In conduction loss, a flow of charge

through the material causes energy dissipation. Dielectric loss is the

dissipation of energy through the movement of charges in an alternating

electromagnetic field as polarisation switches direction.

Dielectric loss is especially high around the relaxation or resonance frequencies of the polarisation mechanisms as the polarisation lags behind the applied field, causing an interaction between the field and the dielectric’s polarisation that results in heating. This is illustrated by the diagram below (recall that the dielectric constant drops as each polarisation mechanism becomes unable to keep up with the switching electric field.)

Dielectric loss tends to be higher in materials with higher dielectric

constants. This is the downside of using these materials in practical

applications.

Dielectric loss is utilised to heat food in a microwave oven: the frequency

of the microwaves used is close to the relaxation frequency of the

orientational polarisation mechanism in water, meaning that any water

present absorbs a lot of energy that is then dissipated as heat. The exact

frequency used is slightly away from the frequency at which maximum

dielectric loss occurs in water to ensure that the microwaves are not all

absorbed by the first layer of water they encounter, therefore allowing

more even heating of the food.

Dielectric breakdownAt high electric fields, a material that is normally an electrical insulator

may begin to conduct electricity – i.e. it ceases to act as a dielectric. This

phenomenon is known as dielectric breakdown.

The mechanism behind dielectric breakdown can best be understood

using band theory. A detailed explanation of this can be found in the TLP

on semiconductors although not all of this is relevant to the content of this

TLP, therefore the aspects of band theory needed to understand dielectric

breakdown are presented here.

Applications of dielectrics

A major use of dielectrics is in fabricating capacitors. These have many

uses including storage of energy in the electric field between the plates,

filtering out noise from signals as part of a resonant circuit, and supplying

a burst of power to another component. The TLP on ferroelectrics shows

how the last of these functions is utilised in a camera flash system.

The larger the dielectric constant, the more charge the capacitor can

store in a given field, therefore ceramics with non-centrosymmetric

structures, such as the titanates of group 2 metals, are commonly used. 

In practice, the material in a capacitor is in fact often a mixture of several

such ceramics. This is due to the variation of the dielectric constant with

temperature discussed earlier. It is generally desirable for the capacitance

to be relatively independent of temperature; therefore modern capacitors

combine several materials with different temperature dependences,

resulting in a capacitance that shows only small, approximately linear

temperature-related variations.

Of course in some cases a low dielectric loss is more important than a

high capacitance, and therefore materials with lower values of κ – and

correspondingly lower dielectric losses – may be used for these situations.

Some applications of dielectrics rely on their electrically insulating

properties rather than ability to store charge, so high electrical resistivity

and low dielectric loss are the most desirable properties here. The most

obvious of these uses is insulation for wires, cables etc., but there are also

applications in sensor devices. For example, it is possible to make a type

of strain gauge by evaporating a small amount of metal onto the surface

of a thin sheet of dielectric material.

Electrons may travel across the metal by normal conduction, and through

the intervening dielectric material by a phenomenon known as quantum

tunnelling. A mathematical treatment of this phenomenon is outside the

scope of this TLP; simply note that it allows particles to travel between

two “permitted” regions that are separated by a “forbidden” region and

that the extent to which tunnelling occurs decreases sharply as distance

between the permitted regions increases. In this case the permitted

regions are the solidified metal droplets, and the forbidden region is the

high-resistance dielectric material.

If the dielectric material is strained, it will bow causing the distances

between the metal islands to change. This has a large impact on the

extent to which electrons can tunnel between the islands, and thus a

large change in current is observed. Therefore the above device makes an

effective strain gauge.

Summary Dielectrics are electrical insulators that support charge.

The properties of dielectrics are due to polarisation.

There are three main mechanisms by which polarisation arises on the

microscopic scale: electronic (distortion of the electron cloud in an

atom), ionic (movement of ions) and orientational (rotation of

permanent dipoles).

A capacitor is a device that stores charge, usually with the aid of a

dielectric material. Its capacitance is defined by Q = C V

The dielectric constant κ indicates the ability of the dielectric to

polarise. It can be defined as the ratio of the dielectric’s permittivity

to the permittivity of a vacuum.

Each of the polarisation mechanisms has a characteristic relaxation or

resonance frequency. In an alternating field, at each of these

(materials dependent) frequencies, the dielectric constant will sharply

drop.

The dielectric constant is also affected by structure, as this affects the

ability of the material to polarise.

Polar dielectrics show a decrease in the dielectric constant as

temperature increases.

Dielectric loss is the absorption of energy by movement of charges in

an alternating field, and is particularly high around the relaxation and

resonance frequencies of the polarisation mechanisms.

Sufficiently high electric fields can cause a material to undergo

dielectric breakdown and become conducting.