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In
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
, a dielectric (or dielectric medium) is an
electrical insulator An electrical insulator is a material in which electric current does not flow freely. The atoms of the insulator have tightly bound electrons which cannot readily move. Other materials—semiconductors and conductors—conduct electric current ...
that can be polarised by an applied
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
. When a dielectric material is placed in an electric field,
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
s do not flow through the material as they do in an
electrical conductor In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gener ...
, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of
dielectric polarisation In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mater ...
, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field (for example, if the field is moving parallel to the positive ''x'' axis, the negative charges will shift in the negative ''x'' direction). This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarised, but also reorient so that their symmetry axes align to the field. The study of dielectric properties concerns storage and dissipation of electric and
magnetic energy Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment \mathbf in a magnetic field \mathbf is defined as the mechanical work of the magnetic force (actually magnet ...
in materials. Dielectrics are important for explaining various phenomena in
electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
,
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
,
solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...
and
cell biophysics Cell biophysics (or cellular biophysics) is a sub-field of biophysics that focuses on physical principles underlying cell function. Sub-areas of current interest include statistical models of intracellular signaling dynamics, intracellular transport ...
.


Terminology

Although the term '' insulator'' implies low
electrical conduction Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
, ''dielectric'' typically means materials with a high
polarisability Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of all matter, considering that matter is made up of elementar ...
. The latter is expressed by a number called the
relative permittivity The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
. The term insulator is generally used to indicate electrical obstruction while the term dielectric is used to indicate the
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
storing capacity of the material (by means of polarisation). A common example of a dielectric is the electrically insulating material between the metallic plates of a
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
. The polarisation of the dielectric by the applied electric field increases the capacitor's surface charge for the given electric field strength. The term ''
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
'' was coined by
William Whewell William Whewell ( ; 24 May 17946 March 1866) was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge. In his time as a student there, he achieved dist ...
(from '' dia'' + ''electric'') in response to a request from
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
. A ''perfect dielectric'' is a material with zero electrical conductivity (
cf. The abbreviation ''cf.'' (short for the la, confer/conferatur, both meaning "compare") is used in writing to refer the reader to other material to make a comparison with the topic being discussed. Style guides recommend that ''cf.'' be used onl ...
perfect conductor A perfect conductor or perfect electric conductor (PEC) is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric). While perfect electrical conductors do not exist in nature, t ...
infinite electrical conductivity), thus exhibiting only a
displacement current In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
; therefore it stores and returns electrical energy as if it were an ideal capacitor.


Electric susceptibility

The
electric susceptibility In electricity (electromagnetism), the electric susceptibility (\chi_; Latin: ''susceptibilis'' "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applie ...
''χe'' of a dielectric material is a measure of how easily it polarises in response to an electric field. This, in turn, determines the electric
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
of the material and thus influences many other phenomena in that medium, from the capacitance of
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
s to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. It is defined as the constant of proportionality (which may be a
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
) relating an electric field E to the induced dielectric polarisation density P such that \mathbf = \varepsilon_0 \chi_e \mathbf, where ''ε''0 is the electric permittivity of free space. The susceptibility of a medium is related to its relative permittivity ''εr'' by \chi_e\ = \varepsilon_r - 1. So in the case of a vacuum, \chi_e\ = 0. The
electric displacement In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
D is related to the polarisation density P by \mathbf \ = \ \varepsilon_0 \mathbf + \mathbf \ = \ \varepsilon_0 \left(1 + \chi_e\right) \mathbf \ = \ \varepsilon_0 \varepsilon_r \mathbf.


Dispersion and causality

In general, a material cannot polarise instantaneously in response to an applied field. The more general formulation as a function of time is \mathbf(t) = \varepsilon_0 \int_^t \chi_e\left(t - t'\right) \mathbf(t')\, dt'. That is, the polarisation is a
convolution In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...
of the electric field at previous times with time-dependent susceptibility given by ''χe''(Δ''t''). The upper limit of this integral can be extended to infinity as well if one defines for . An instantaneous response corresponds to
Dirac delta function In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire ...
susceptibility . It is more convenient in a linear system to take the
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
and write this relationship as a function of frequency. Due to the
convolution theorem In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g. ...
, the integral becomes a simple product, \mathbf(\omega) = \varepsilon_0 \chi_e(\omega) \mathbf(\omega). The susceptibility (or equivalently the permittivity) is frequency dependent. The change of susceptibility with respect to frequency characterises the
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
properties of the material. Moreover, the fact that the polarisation can only depend on the electric field at previous times (i.e., for ), a consequence of
causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
, imposes Kramers–Kronig constraints on the real and imaginary parts of the susceptibility ''χe''(''ω'').


Dielectric polarisation


Basic atomic model

In the classical approach to the dielectric, the material is made up of atoms. Each atom consists of a cloud of negative charge (electrons) bound to and surrounding a positive point charge at its center. 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 In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system i ...
using the
superposition principle The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So tha ...
. A dipole is characterised 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 behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure. This isn't always the case, and is a major simplification, but is true for many materials.) 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. This is the essence of the model in physics. The behaviour of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behaviour. Important questions are: *Is the electric field constant or does it vary with time? At what rate? *Does the response depend on the direction of the applied field (
isotropy Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
of the material)? *Is the response the same everywhere (
homogeneity Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
of the material)? *Do any boundaries or interfaces have to be taken into account? *Is the response
linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
with respect to the field, or are there nonlinearities? The relationship between the electric field E and the dipole moment M gives rise to the behaviour of the dielectric, which, for a given material, can be characterised by the function F defined by the equation: \mathbf = \mathbf(\mathbf). 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 phenomena that can be so modelled include: *
Refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
*
Group velocity dispersion In optics, group velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium will affect the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the ...
*
Birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
*
Self-focusing Self-focusing is a nonlinear optics, non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as ...
*
Harmonic generation Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which n photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with n times the energy of t ...


Dipolar polarisation

Dipolar polarisation is a polarisation that is either inherent to
polar molecule In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. Polar molecules must contain one or more polar ...
s (orientation polarisation), or can be induced in any molecule in which the asymmetric distortion of the nuclei is possible (distortion polarisation). Orientation polarisation results from a permanent dipole, e.g., that arising from the 104.45° angle between the asymmetric bonds between oxygen and hydrogen atoms in the water molecule, which retains polarisation in the absence of an external electric field. The assembly of these dipoles forms a macroscopic polarisation. When an external electric field is applied, the distance between charges within each permanent dipole, which is related to
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
ing, remains constant in orientation polarisation; however, the direction of polarisation itself rotates. This rotation occurs on a timescale that depends on the
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
and surrounding local
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
of the molecules. Because the rotation is not instantaneous, dipolar polarisations lose the response to electric fields at the highest frequencies. A molecule rotates about 1 radian per picosecond in a fluid, thus this loss occurs at about 1011 Hz (in the microwave region). The delay of the response to the change of the electric field causes
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
and heat. When an external electric field is applied at
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
frequencies or less, the molecules are bent and stretched by the field and the molecular dipole moment changes. The molecular vibration frequency is roughly the inverse of the time it takes for the molecules to bend, and this distortion polarisation disappears above the infrared.


Ionic polarisation

Ionic polarisation is polarisation caused by relative displacements between positive and negative
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
s in
ionic crystal In chemistry, an ionic crystal is a crystalline form of an ionic compound. They are solids consisting of ions bound together by their electrostatic attraction into a regular Crystal structure, lattice. Examples of such crystals are the alkali hal ...
s (for example,
NaCl Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...
). If a crystal or molecule consists of atoms of more than one kind, the distribution of charges around an atom in the crystal or molecule leans to positive or negative. As a result, when lattice vibrations or molecular vibrations induce relative displacements of the atoms, the centers of positive and negative charges are also displaced. The locations of these centers are affected by the symmetry of the displacements. When the centers don't correspond, polarisation arises in molecules or crystals. This polarisation is called ionic polarisation. Ionic polarisation causes the
ferroelectric effect Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the add ...
as well as dipolar polarisation. The ferroelectric transition, which is caused by the lining up of the orientations of permanent dipoles along a particular direction, is called an order-disorder phase transition. The transition caused by ionic polarisations in crystals is called a displacive phase transition.


In cells

Ionic polarisation enables the production of energy-rich compounds in cells (the
proton pump A proton pump is an integral membrane protein pump that builds up a proton gradient across a biological membrane. Proton pumps catalyze the following reaction: : n one side of a biological membrane/sub> + energy n the other side of the membr ...
in
mitochondria A mitochondrion (; ) is an organelle found in the Cell (biology), cells of most Eukaryotes, such as animals, plants and Fungus, fungi. Mitochondria have a double lipid bilayer, membrane structure and use aerobic respiration to generate adenosi ...
) and, at the
plasma membrane The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (t ...
, the establishment of the
resting potential A relatively static membrane potential which is usually referred to as the ground value for trans-membrane voltage. The relatively static membrane potential of quiescent cells is called the resting membrane potential (or resting voltage), as oppo ...
, energetically unfavourable transport of ions, and cell-to-cell communication (the
Na+/K+-ATPase NA, N.A., Na, nA or n/a may refer to: Chemistry and physics * Sodium, symbol Na, a chemical element * Avogadro constant (''N''A) * Nucleophilic addition, a type of reaction in organic chemistry * Numerical aperture, a number that characterizes ...
). All cells in animal body tissues are electrically polarised – in other words, they maintain a voltage difference across the cell's
plasma membrane The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (t ...
, known as the
membrane potential Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges ...
. This electrical polarisation results from a complex interplay between
ion transporters An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
and
ion channels Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore. Their functions include establishing a resting membrane potential, shaping action potentials and other electrical signals by gating the flow of io ...
. In neurons, the types of ion channels in the membrane usually vary across different parts of the cell, giving the
dendrite Dendrites (from Greek δένδρον ''déndron'', "tree"), also dendrons, are branched protoplasmic extensions of a nerve cell that propagate the electrochemical stimulation received from other neural cells to the cell body, or soma, of the n ...
s,
axon An axon (from Greek ἄξων ''áxōn'', axis), or nerve fiber (or nerve fibre: see spelling differences), is a long, slender projection of a nerve cell, or neuron, in vertebrates, that typically conducts electrical impulses known as action po ...
, and
cell body The soma (pl. ''somata'' or ''somas''), perikaryon (pl. ''perikarya''), neurocyton, or cell body is the bulbous, non-process portion of a neuron or other brain cell type, containing the cell nucleus. The word 'soma' comes from the Greek '' σῶμ ...
different electrical properties. As a result, some parts of the membrane of a neuron may be excitable (capable of generating action potentials), whereas others are not.


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 a lag between changes in polarisation and changes in the electric field, the permittivity of the dielectric is a complicated function of frequency of the electric field. Dielectric dispersion is very important for the applications of dielectric materials and for the analysis of polarisation systems. This is one instance of a general phenomenon known as
material dispersion In optics, and by analogy other branches of physics dealing with wave propagation, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to o ...
: a frequency-dependent response of a medium for wave propagation. When the frequency becomes higher: # dipolar polarisation can no longer follow the oscillations of the electric field in the
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
region around 1010 Hz; # ionic polarisation and molecular distortion polarisation can no longer track the electric field past the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
or far-infrared region around 1013 Hz, ; # electronic polarisation loses its response in the ultraviolet region around 1015 Hz. In the frequency region above ultraviolet, permittivity approaches the constant ''ε''0 in every substance, where ''ε''0 is the permittivity of the free space. Because permittivity indicates the strength of the relation between an electric field and polarisation, if a polarisation process loses its response, permittivity decreases.


Dielectric relaxation

Dielectric relaxation is the momentary delay (or lag) in the
dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
of a material. This is usually caused by the delay in molecular polarisation with respect to a changing electric field in a dielectric medium (e.g., inside capacitors or between two large
conducting Conducting is the art of directing a musical performance, such as an orchestral or choral concert. It has been defined as "the art of directing the simultaneous performance of several players or singers by the use of gesture." The primary duti ...
surfaces). Dielectric relaxation in changing electric fields could be considered analogous to
hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
in changing
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s (e.g., in
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
or
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
cores). Relaxation in general is a delay or lag in the response of a
linear system In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction o ...
, and therefore dielectric relaxation is measured relative to the expected linear steady state (equilibrium) dielectric values. The time lag between electrical field and polarisation implies an irreversible degradation of
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...
. In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, dielectric relaxation refers to the relaxation response of a dielectric medium to an external, oscillating electric field. This relaxation is often described in terms of permittivity as a function of
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
, which can, for ideal systems, be described by the Debye equation. On the other hand, the distortion related to ionic and electronic polarisation shows behaviour of the
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
or
oscillator Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
type. The character of the distortion process depends on the structure, composition, and surroundings of the sample.


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 ''ε'' of a medium as a function of the field's
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
''ω'': \hat(\omega) = \varepsilon_ + \frac, where ''ε'' is the permittivity at the high frequency limit, where ''εs'' is the static, low frequency permittivity, and ''τ'' is the characteristic
relaxation time In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time ' ...
of the medium. Separating into the real part \varepsilon' and the imaginary part \varepsilon'' of the complex dielectric permittivity yields: \begin \varepsilon' &= \varepsilon_\infty + \frac \\ pt \varepsilon'' &= \frac \end Note that the above equation for \hat(\omega)is sometimes written with 1 - i\omega\tau in the denominator due to an ongoing sign convention ambiguity whereby many sources represent the time dependence of the complex electric field with \exp(-i\omega t) whereas others use \exp(+i\omega t). In the former convention, the functions \varepsilon' and \varepsilon'' representing real and imaginary parts are given by \hat(\omega)=\varepsilon'+ i \varepsilon'' whereas in the latter convention \hat(\omega)=\varepsilon'- i \varepsilon''. The above equation uses the latter convention. The dielectric loss is also represented by the loss tangent: \tan(\delta) = \frac = \frac This relaxation model was introduced by and named after the physicist
Peter Debye Peter Joseph William Debye (; ; March 24, 1884 – November 2, 1966) was a Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry. Biography Early life Born Petrus Josephus Wilhelmus Debije in Maastricht, Netherlands, D ...
(1913). It is characteristic for dynamic polarisation with only one relaxation time.


Variants of the Debye equation

;
Cole–Cole equation The Cole–Cole equation is a relaxation model that is often used to describe dielectric relaxation in polymers. It is given by the equation : \varepsilon^*(\omega) = \varepsilon_\infty + \frac where \varepsilon^* is the complex dielectric co ...
: This equation is used when the dielectric loss peak shows symmetric broadening. ; Cole–Davidson equation: This equation is used when the dielectric loss peak shows asymmetric broadening. ;
Havriliak–Negami relaxation The Havriliak–Negami relaxation is an empirical modification of the Debye relaxation model in electromagnetism. Unlike the Debye model, the Havriliak–Negami relaxation accounts for the asymmetry and broadness of the dielectric dispersion curv ...
: This equation considers both symmetric and asymmetric broadening. ; Kohlrausch–Williams–Watts function: Fourier transform of
stretched exponential function The stretched exponential function f_\beta (t) = e^ is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments between 0 and +∞. With , the usual exponential functio ...
. ;
Curie–von Schweidler law The Curie–von Schweidler law refers to the response of dielectric material to the step input of a direct current (DC) voltage first observed by Jacques Curie and Egon Ritter von Schweidler. Overview According to this law, the current decays acco ...
: This shows the response of dielectrics to an applied DC field to behave according to a power law, which can be expressed as an integral over weighted exponential functions..


Paraelectricity

Paraelectricity is the nominal behaviour of dielectrics when the dielectric permittivity tensor is proportional to the unit matrix, i.e., an applied
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
causes polarisation and/or alignment of dipoles only parallel to the applied electric field. Contrary to the analogy with a paramagnetic material, no permanent
electric dipole The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The d ...
needs to exist in a paraelectric material. Removal of the fields results in the dipolar polarisation returning to zero. The mechanisms that causes paraelectric behaviour are distortion of individual
ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
(displacement of the electron cloud from the nucleus) and polarisation of molecules or combinations of ions or defects. Paraelectricity can occur in
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
phases where electric dipoles are unaligned and thus have the potential to align in an external
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
and weaken it. Most dielectric materials are paraelectrics. A specific example of a paraelectric material of high dielectric constant is
strontium titanate Strontium titanate is an oxide of strontium and titanium with the chemical formula Sr Ti O3. At room temperature, it is a centrosymmetric paraelectric material with a perovskite structure. At low temperatures it approaches a ferroelectric phase ...
. The LiNbO3 crystal is
ferroelectric Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the add ...
below 1430 K, and above this temperature it transforms into a disordered paraelectric phase. Similarly, other
perovskite Perovskite (pronunciation: ) is a calcium titanium oxide mineral composed of calcium titanate (chemical formula ). Its name is also applied to the class of compounds which have the same type of crystal structure as (XIIA2+VIB4+X2−3), known as ...
s also exhibit paraelectricity at high temperatures. Paraelectricity has been explored as a possible refrigeration mechanism; polarising a paraelectric by applying an electric field under
adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...
conditions raises the temperature, while removing the field lowers the temperature. A
heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing h ...
that operates by polarising the paraelectric, allowing it to return to ambient temperature (by dissipating the extra heat), bringing it into contact with the object to be cooled, and finally depolarising it, would result in refrigeration.


Tunability

''Tunable dielectrics'' are insulators whose ability to store electrical charge changes when a voltage is applied. Generally,
strontium titanate Strontium titanate is an oxide of strontium and titanium with the chemical formula Sr Ti O3. At room temperature, it is a centrosymmetric paraelectric material with a perovskite structure. At low temperatures it approaches a ferroelectric phase ...
() is used for devices operating at low temperatures, while
barium strontium titanate A perovskite is any material with a crystal structure following the formula ABX3, which was first discovered as the Perovskite, mineral called perovskite, which consists of calcium titanium oxide (CaTiO3). The mineral was first discovered in t ...
() substitutes for room temperature devices. Other potential materials include microwave dielectrics and carbon nanotube (CNT) composites. In 2013, multi-sheet layers of strontium titanate interleaved with single layers of
strontium oxide Strontium oxide or strontia, SrO, is formed when strontium reacts with oxygen. Burning strontium in air results in a mixture of strontium oxide and strontium nitride. It also forms from the decomposition of strontium carbonate SrCO3. It is a stron ...
produced a dielectric capable of operating at up to 125 GHz. The material was created via
molecular beam epitaxy Molecular-beam epitaxy (MBE) is an epitaxy method for thin-film deposition of single crystals. MBE is widely used in the manufacture of semiconductor devices, including transistors, and it is considered one of the fundamental tools for the devel ...
. The two have mismatched crystal spacing that produces strain within the strontium titanate layer that makes it less stable and tunable. Systems such as have a paraelectric–ferroelectric transition just below ambient temperature, providing high tunability. Films suffer significant losses arising from defects.


Applications


Capacitors

Commercially manufactured capacitors typically use a
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
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''. 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 In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
allows a greater stored charge 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 ''σε''. In this case the charge density is given by \sigma_=\varepsilon\frac and the
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
per unit area by c=\frac=\frac 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
ionisation Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...
. This allows the capacitor to operate at higher voltages before the insulating dielectric ionises and begins to allow undesirable current.


Dielectric resonator

A ''dielectric resonator oscillator'' (DRO) is an electronic component that exhibits
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
of the polarisation response for a narrow range of frequencies, generally in the microwave band. It consists of a "puck" of ceramic that has a large dielectric constant and a low
dissipation factor In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or d ...
. Such resonators are often used to provide a frequency reference in an oscillator circuit. An unshielded dielectric resonator can be used as a dielectric resonator antenna (DRA).


BST thin films

From 2002 to 2004, the United States
Army Research Laboratory The U.S. Army Combat Capabilities Development Command Army Research Laboratory (DEVCOM ARL) is the U.S. Army's foundational research laboratory. ARL is headquartered at the Adelphi Laboratory Center (ALC) in Adelphi, Maryland. Its largest singl ...
(ARL) conducted research on thin film technology. Barium strontium titanate (BST), a ferroelectric thin film, was studied for the fabrication of radio frequency and microwave components, such as voltage-controlled oscillators, tunable filters and phase shifters. The research was part of an effort to provide the Army with highly-tunable, microwave-compatible materials for broadband electric-field tunable devices, which operate consistently in extreme temperatures. This work improved tunability of bulk barium strontium titanate, which is a thin film enabler for electronics components. In a 2004 research paper, U.S. ARL researchers explored how small concentrations of acceptor dopants can dramatically modify the properties of ferroelectric materials such as BST. Researchers "doped" BST thin films with magnesium, analyzing the "structure, microstructure, surface morphology and film/substrate compositional quality" of the result. The Mg doped BST films showed "improved dielectric properties, low leakage current, and good tunability", meriting potential for use in microwave tunable devices.


Some practical dielectrics

Dielectric materials can be solids, liquids, or gases. (A high
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
can also be a useful, nearly lossless dielectric even though its relative
dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
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 Porcelain () is a ceramic material made by heating substances, generally including materials such as kaolinite, in a kiln to temperatures between . The strength and translucence of porcelain, relative to other types of pottery, arises mainl ...
,
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
, and most
plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...
s. Air,
nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
and
sulfur hexafluoride Sulfur hexafluoride or sulphur hexafluoride (British spelling) is an inorganic compound with the formula SF6. It is a colorless, odorless, non- flammable, and non-toxic gas. has an octahedral geometry, consisting of six fluorine atoms attached ...
are the three most commonly used
gaseous dielectric A dielectric gas, or insulating gas, is a dielectric material in gaseous state. Its main purpose is to prevent or rapidly quench electric discharges. Dielectric gases are used as electrical insulators in high voltage applications, e.g. transformers ...
s. *
Industrial coating A coating is a covering that is applied to the surface of an object, usually referred to as the substrate. The purpose of applying the coating may be decorative, functional, or both. Coatings may be applied as liquids, gases or solids e.g. Powde ...
s such as
Parylene Parylene is the common name of a polymer whose backbone consists of ''para''- benzenediyl rings –– connected by 1,2-ethanediyl bridges –––. It can be obtained by polymerization of ''para''-xylylene . The name is also used for se ...
provide a dielectric barrier between the substrate and its environment. *
Mineral oil Mineral oil is any of various colorless, odorless, light mixtures of higher alkanes from a mineral source, particularly a distillate of petroleum, as distinct from usually edible vegetable oils. The name 'mineral oil' by itself is imprecise, ...
is used extensively inside electrical
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
s as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade
castor oil Castor oil is a vegetable oil pressed from castor beans. It is a colourless or pale yellow liquid with a distinct taste and odor. Its boiling point is and its density is 0.961 g/cm3. It includes a mixture of triglycerides in which about ...
, are often used in
high voltage High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and conductors that carry high voltage warrant spec ...
capacitors to help prevent
corona discharge A corona discharge is an electrical discharge caused by the ionization of a fluid such as air surrounding a conductor carrying a high voltage. It represents a local region where the air (or other fluid) has undergone electrical breakdown ...
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 The triboelectric effect (also known as triboelectric charging) is a type of contact electrification on which certain materials become electrically charged after they are separated from a different material with which they were in contact. Rubb ...
). This can be useful, as in a
Van de Graaff generator A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage direct ...
or
electrophorus In electromagnetism, an electrophorus or electrophore is a simple, manual, capacitive, electrostatic generator used to produce charge via the process of electrostatic induction. A first version of it was invented in 1762 by Swedish professor Jo ...
, or it can be potentially destructive as in the case of
electrostatic discharge Electrostatic discharge (ESD) is a sudden and momentary flow of electric current between two electrically charged objects caused by contact, an short circuit, electrical short or dielectric breakdown. A buildup of static electricity can be caused ...
. *Specially processed dielectrics, called
electret An electret (formed as a portmanteau of ''electr-'' from "electricity" and ''-et'' from "magnet") is a dielectric material that has a quasi-permanent electric charge or dipole polarisation. An electret generates internal and external electric fi ...
s (which should not be confused with
ferroelectric Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the add ...
s), may retain excess internal charge or "frozen in" polarisation. Electrets have a semi-permanent 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 Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
, or (equivalently) change physical shape if an external voltage is applied across the material. This property is called
piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
. Piezoelectric materials are another class of very useful dielectrics. *Some ionic
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s and
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
dielectrics exhibit a spontaneous dipole moment, which can be reversed by an externally applied electric field. This behaviour is called the
ferroelectric effect Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the add ...
. These materials are analogous to the way
ferromagnetic materials Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...
behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.


See also

* Classification of materials based on permittivity *
Paramagnetism Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, ...
* Clausius-Mossotti relation *
Dielectric absorption Dielectric absorption is the name given to the effect by which a capacitor, that has been charged for a long time, discharges only incompletely when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, r ...
*
Dielectric losses Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle ''δ'' or the corresponding loss tangent tan ''δ''. Both refer to the p ...
*
Dielectric strength In physics, the term dielectric strength has the following meanings: *for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becom ...
*
Dielectric spectroscopy Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 200 ...
* EIA Class 1 dielectric *
EIA Class 2 dielectric A ceramic capacitor is a fixed-value capacitor where the ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material de ...
*
High-κ dielectric The term high-κ dielectric refers to a material with a high dielectric constant (κ, kappa), as compared to silicon dioxide. High-κ dielectrics are used in semiconductor manufacturing processes where they are usually used to replace a silicon dio ...
*
Low-κ dielectric In semiconductor manufacturing, a low-κ is a material with a small relative dielectric constant (κ, kappa) relative to silicon dioxide. Low-κ dielectric material implementation is one of several strategies used to allow continued scaling of micr ...
* leakage *
Linear response function A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in information ...
*
Metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
*
RC delay The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e. : \tau = RC econds It is the time required to ...
*
Rotational Brownian motion Rotational Brownian motion is the random change in the orientation of a polar molecule due to collisions with other molecules. It is an important element of theories of dielectric materials. The Polarization density, polarization of a dielectric ...
*
Paschen's law Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. It is named after Friedrich Paschen who ...
– variation of dielectric strength of gas related to pressure *
Separator (electricity) A separator is a permeable membrane placed between a battery's anode and cathode. The main function of a separator is to keep the two electrodes apart to prevent electrical short circuits while also allowing the transport of ionic charge carriers ...


References


Further reading

* *


External links


Feynman's lecture on dielectricsDielectric Sphere in an Electric FieldDissemination of IT for the Promotion of Materials Science (DoITPoMS) Teaching and Learning Package "Dielectric Materials"
from the
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
* {{Authority control Electric and magnetic fields in matter