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| [[File:Diel.gif|thumb|A dielectric medium showing orientation of charged particles creating polarization effects. Such a medium can have a higher ratio of electric flux to charge (permittivity) than empty space]]
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| In [[electromagnetism]], '''absolute permittivity''' is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an [[electric field]] affects, and is affected by, a [[dielectric]] medium. The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge in that medium. More electric flux exists in a medium with a high permittivity (per unit charge) because of polarization effects. Permittivity is directly related to [[electric susceptibility]], which is a measure of how easily a dielectric [[polarization density|polarizes]] in response to an [[electric field]]. Thus, permittivity relates to a material's ability to transmit (or "permit") an electric field.
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| In [[SI]] units, permittivity ''ε'' is measured in [[farad]]s per [[meter]] (F/m); electric susceptibility ''χ'' is dimensionless. They are related to each other through
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| :<math>\varepsilon = \varepsilon_{\text{r}} \varepsilon_0 = (1+\chi)\varepsilon_0 </math>
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| where ''ε''<sub>r</sub> is the [[relative permittivity]] of the material, and ''ε''<sub>0</sub> = 8.8541878176.. × 10<sup>−12</sup> F/m is the [[vacuum permittivity]].
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| ==Explanation==
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| In [[electromagnetism]], the [[electric displacement field]] '''D''' represents how an electric field '''E''' influences the organization of electric charges in a given medium, including charge migration and electric [[dipole]] reorientation. Its relation to permittivity in the very simple case of ''linear, homogeneous, [[isotropic]]'' materials with ''"instantaneous" response'' to changes in electric field is
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| :<math>\mathbf{D}=\varepsilon \mathbf{E}</math>
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| where the permittivity ''ε'' is a [[scalar (physics)|scalar]]. If the medium is anisotropic, the permittivity is a second rank [[tensor]].
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| In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a [[nonlinear optics|nonlinear medium]], the permittivity can depend on the strength of the electric field. Permittivity as a function of frequency can take on real or complex values.
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| In SI units, permittivity is measured in farads per meter (F/m or A<sup>2</sup>·s<sup>4</sup>·kg<sup>−1</sup>·m<sup>−3</sup>). The displacement field '''D''' is measured in units of [[coulomb]]s per [[square meter]] (C/m<sup>2</sup>), while the electric field '''E''' is measured in [[volt]]s per meter (V/m). '''D''' and '''E''' describe the interaction between charged objects. '''D''' is related to the ''charge densities'' associated with this interaction, while '''E''' is related to the ''forces'' and ''potential differences''.
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| ==Vacuum permittivity==
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| {{main|Vacuum permittivity}}
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| The vacuum permittivity ''ε''<sub>0</sub> (also called '''permittivity of free space''' or the '''electric constant''') is the ratio '''D'''/'''E''' in [[Vacuum|free space]]. It also appears in the [[Coulomb force constant]], ''k''<sub>e</sub> = 1/(4''πε''<sub>0</sub>).
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| Its value is<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?ep0 electric constant]</ref>
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| :<math>
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| \begin{align}
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| \varepsilon_0 & \stackrel{\mathrm{def}}{=}\ \frac{1}{c_0^2\mu_0} = \frac{1}{35950207149.4727056\pi}\ \frac{\text{F}}{\text{m}} \approx 8.8541878176\ldots\times 10^{-12}\ \text{F/m}
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| \end{align}
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| </math>
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| where
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| :''c<sub>0</sub>'' is the [[speed of light]] in free space,<ref>Current practice of standards organizations such as [[NIST]] and [[BIPM]] is to use ''c''<sub>0</sub>, rather than ''c'', to denote the speed of light in vacuum according to [[ISO 31]]. In the original Recommendation of 1983, the symbol ''c'' was used for this purpose. See [http://physics.nist.gov/Pubs/SP330/sp330.pdf NIST ''Special Publication 330'', Appendix 2, p. 45 ].</ref>
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| :''µ''<sub>0</sub> is the [[vacuum permeability]].
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| Constants ''c''<sub>0</sub> and ''μ''<sub>0</sub> are defined in SI units to have exact numerical values, shifting responsibility of experiment to the determination of the meter and the [[ampere]].<ref>[http://physics.nist.gov/cuu/Constants/index.html Latest (2006) values of the constants (NIST)]</ref> (The approximation in the second value of ''ε''<sub>0</sub> above stems from ''π'' being an [[irrational number]].)
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| ==Relative permittivity==
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| {{main|Relative permittivity}}
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| The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity ''ε''<sub>r</sub> (also called [[dielectric constant]], although this sometimes only refers to the static, zero-frequency relative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing [[birefringence]]. The actual permittivity is then calculated by multiplying the relative permittivity by ''ε''<sub>0</sub>:
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| :<math>\varepsilon = \varepsilon_{\text{r}} \varepsilon_0 = (1+\chi)\varepsilon_0,</math>
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| where χ (frequently written χ<sub>e</sub>) is the electric susceptibility of the material.
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| The susceptibility is defined as the constant of proportionality (which may be a [[tensor]]) relating an [[electric field]] '''E''' to the induced [[dielectric]] [[polarization (electrostatics)|polarization density]] '''P''' such that
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| :<math>
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| \mathbf{P} = \varepsilon_0\chi\mathbf{E},
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| </math>
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| where ''ε''<sub>0</sub> is the [[Vacuum permittivity|electric permittivity of free space]].
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| The susceptibility of a medium is related to its relative permittivity ''ε''<sub>r</sub> by
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| :<math>\chi = \varepsilon_{\text{r}} - 1.</math>
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| So in the case of a vacuum,
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| :<math>\chi = 0. </math>
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| The susceptibility is also related to the [[polarizability]] of individual particles in the medium by the [[Clausius-Mossotti relation]].
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| The [[electric displacement]] '''D''' is related to the polarization density '''P''' by
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| :<math>
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| \mathbf{D} = \varepsilon_0\mathbf{E} + \mathbf{P} = \varepsilon_0 (1+\chi) \mathbf{E} = \varepsilon_{\text{r}} \varepsilon_0 \mathbf{E}.
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| </math>
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| The permittivity ''ε'' and [[permeability (electromagnetism)|permeability]] ''µ'' of a medium together determine the [[phase velocity]] ''v'' = ''c''/''n'' of [[electromagnetic radiation]] through that medium:
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| :<math>\varepsilon \mu = \frac{1}{v^2}.</math>
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| ==Dispersion and causality==
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| 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
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| :<math>\mathbf{P}(t)=\varepsilon_0 \int_{-\infty}^t \chi(t-t') \mathbf{E}(t') \, dt'.</math>
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| That is, the polarization is a [[convolution]] of the electric field at previous times with time-dependent susceptibility given by ''χ''(Δ''t''). The upper limit of this integral can be extended to infinity as well if one defines ''χ''(Δ''t'') = 0 for Δ''t'' < 0. An instantaneous response corresponds to [[Dirac delta function]] susceptibility ''χ''(Δ''t'') = ''χ δ''(Δ''t'').
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| It is more convenient in a linear system to take the [[continuous Fourier transform|Fourier transform]] and write this relationship as a function of frequency. Because of the [[convolution theorem]], the integral becomes a simple product,
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| :<math>\mathbf{P}(\omega)=\varepsilon_0 \chi(\omega) \mathbf{E}(\omega).</math>
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| 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 (optics)|dispersion]] properties of the material.
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| Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. ''χ''(Δ''t'') = 0 for Δ''t'' < 0), a consequence of [[causality]], imposes [[Kramers–Kronig relation|Kramers–Kronig constraints]] on the susceptibility ''χ''(0).
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| ===Complex permittivity===
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| [[Image:Dielectric responses.svg|thumb|right|454px|A dielectric permittivity spectrum over a wide range of frequencies. ''ε''′ and ''ε''″ denote the real and the imaginary part of the permittivity, respectively. Various processes are labeled on the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies.<ref>[http://www.psrc.usm.edu/mauritz/dilect.html Dielectric Spectroscopy]</ref>]]
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| As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the [[frequency]] of the field. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field. The response must always be ''causal'' (arising after the applied field) which can be represented by a phase difference. For this reason, permittivity is often treated as a complex function of the [[Angular frequency|(angular) frequency]] of the applied field ''ω'': <math>\varepsilon \rightarrow \widehat{\varepsilon}(\omega)</math> (since complex numbers allow specification of magnitude and phase). The definition of permittivity therefore becomes
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| :<math>D_0 e^{-i \omega t} = \widehat{\varepsilon}(\omega) E_0 e^{-i \omega t},</math>
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| where
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| :''D''<sub>0</sub> and ''E''<sub>0</sub> are the amplitudes of the displacement and electric fields, respectively,
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| :''i'' is the [[imaginary unit]], ''i''<sup>2</sup> = −1.
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| The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity ''ε''<sub>s</sub> (also ''ε''<sub>DC</sub>
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| ):
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| :<math>\varepsilon_{\text{s}} = \lim_{\omega \rightarrow 0} \widehat{\varepsilon}(\omega).</math>
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| At the high-frequency limit, the complex permittivity is commonly referred to as ''ε''<sub>∞</sub>. At the [[plasma frequency]] and above, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for alternating fields of low frequencies, and as the frequency increases a measurable phase difference ''δ'' emerges between '''D''' and '''E'''. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength (''E''<sub>0</sub>), '''D''' and '''E''' remain proportional, and
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| :<math>\widehat{\varepsilon} = \frac{D_0}{E_0} = |\varepsilon|e^{i\delta}.</math>
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| Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:
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| :<math>\widehat{\varepsilon}(\omega) = \varepsilon'(\omega) + i\varepsilon''(\omega) = \frac{D_0}{E_0} \left( \cos\delta + i\sin\delta \right). </math>
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| where
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| :''ε''’ is the real part of the permittivity, which is related to the stored energy within the medium;
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| :''ε''” is the imaginary part of the permittivity, which is related to the dissipation (or loss) of energy within the medium;
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| :''δ'' is the [[loss angle]].
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| It is important to realize that the choice of sign for time-dependence, exp(-''iωt''), dictates the sign convention for the imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas for the engineering convention one should reverse all imaginary quantities.
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| The complex permittivity is usually a complicated function of frequency ''ω'', since it is a superimposed description of [[dispersion (optics)|dispersion]] phenomena occurring at multiple frequencies. The dielectric function ''ε''(''ω'') must have poles only for frequencies with positive imaginary parts, and therefore satisfies the [[Kramers–Kronig relation]]s. However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model functions.
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| At a given frequency, the imaginary part of <math>\widehat{\varepsilon}</math> leads to absorption loss if it is positive (in the above sign convention) and gain if it is negative. More generally, the imaginary parts of the [[eigenvalue]]s of the anisotropic dielectric tensor should be considered.
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| In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantity that characterizes the electronic structure of any crystalline material is the probability of [[photon]] absorption, which is directly related to the imaginary part of the optical dielectric function ''ε''(''ω''). The optical dielectric function is given by the fundamental expression:<ref name=Cardona>
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| {{cite book
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| |author=Peter Y. Yu, Manuel Cardona
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| |title=Fundamentals of Semiconductors: Physics and Materials Properties
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| |year= 2001
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| |page=261
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| |publisher=Springer
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| |location=Berlin
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| |isbn=3-540-25470-6
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| |url=http://books.google.com/?id=W9pdJZoAeyEC&pg=PA261}}
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| </ref>
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| : <math>\varepsilon(\omega)=1+\frac{8\pi^2e^2}{m^2}\sum_{c,v}\int W_{c,v}(E) \left[ \varphi (\hbar \omega - E)-\varphi( \hbar \omega +E) \right ] \, dx. </math>
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| In this expression, ''W<sub>c,v</sub>''(''E'') represents the product of the [[Brillouin zone]]-averaged transition probability at the energy ''E'' with the joint [[density of states]],<ref name=Bausa>
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| {{cite book
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| |author=José García Solé, Jose Solé, Luisa Bausa,
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| |title=An introduction to the optical spectroscopy of inorganic solids
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| |year= 2001
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| |page=Appendix A1, pp, 263
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| |publisher=Wiley
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| |isbn=0-470-86885-6
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| |url=http://books.google.com/?id=c6pkqC50QMgC&pg=PA263
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| |nopp=true}}
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| </ref><ref name=Moore>
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| {{cite book
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| |author=John H. Moore, Nicholas D. Spencer
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| |title=Encyclopedia of chemical physics and physical chemistry
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| |year= 2001
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| |page=105
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| |publisher=Taylor and Francis
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| |isbn=0-7503-0798-6
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| |url=http://books.google.com/?id=Pn2edky6uJ8C&pg=PA108}}
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| </ref> ''J<sub>c,v</sub>''(''E''); ''φ'' is a broadening function, representing the role of scattering in smearing out the energy levels.<ref name=Bausa2>
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| {{cite book
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| |title=Solé and Bausa
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| |page=10
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| |isbn=3-540-25470-6
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| |url=http://books.google.com/?id=c6pkqC50QMgC&pg=PA10
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| |author1=Solé, José García
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| |author2=Bausá, Louisa E
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| |author3=Jaque, Daniel
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| |date=2005-03-22}}
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| </ref> In general, the broadening is intermediate between [[Lorentzian function|Lorentzian]] and [[Gaussian]];<ref name=Haug>
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| {{cite book
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| |author=Hartmut Haug, Stephan W. Koch
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| |title=Quantum Theory of the Optical and Electronic Properties of Semiconductors
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| |year= 1994
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| |page=196
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| |publisher=World Scientific
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| |isbn=981-02-1864-8
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| |url=http://books.google.com/?id=Ab2WnFyGwhcC&pg=PA196}}
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| </ref><ref name=Razeghi>
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| {{cite book
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| |author= Manijeh Razeghi
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| |title=Fundamentals of Solid State Engineering
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| |year= 2006
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| |page=383
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| |publisher=Birkhauser
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| |isbn=0-387-28152-5
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| |url=http://books.google.com/?id=6x07E9PSzr8C&pg=PA383}}
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| </ref> for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale.
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| ===Tensorial permittivity===
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| According to the [[Drude model]] of magnetized plasma, a more general expression which takes into account the interaction of the carriers with an alternating electric field at millimeter and microwave frequencies in an axially magnetized semiconductor requires the expression of the permittivity as a non-diagonal tensor.<ref>[http://www.ingentaconnect.com/content/vsp/jew/2003/00000017/00000008/art00011] Prati E. (2003) "Propagation in gyroelectromagnetic guiding systems", ''J. of Electr. Wav. and Appl.'' '''17, 8''', 1177</ref> (see also [[Electro-gyration]]).
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| :<math>\begin{align}
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| \mathbf{D}(\omega) & = \begin{vmatrix}
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| \varepsilon_{1} & -i \varepsilon_{2} & 0\\
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| i \varepsilon_{2} & \varepsilon_{1} & 0\\
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| 0 & 0 & \varepsilon_{z}\\
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| \end{vmatrix} \mathbf{E}(\omega)\\
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| \end{align}</math>
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| If <math> \varepsilon_{2} </math> vanishes, then the tensor is diagonal but not proportional to the identity and the medium is said an [[uniaxial medium]].
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| ===Classification of materials===
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| {| class="wikitable" style="float:right; text-align:center;margin:10pt;"
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| |-
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| ! ''σ''/(''ωε''’) !! Current conduction !! Field propagation
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| |-
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| | 0 || || perfect dielectric<br>lossless medium
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| |-
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| | ≪ 1 || low-conductivity material<br>poor conductor ||low-loss medium<br>good dielectric
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| |-
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| | ≈ 1 || lossy conducting material || lossy propagation medium
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| |-
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| | ≫ 1 || high-conductivity material<br>good conductor ||high-loss medium<br>poor dielectric
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| |-
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| | ∞ || [[perfect conductor]] ||
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| |}
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| Materials can be classified according to their complex-valued permittivity ''ε'', upon comparison of its real ''ε''’ and imaginary ''ε''" components (or, equivalently, [[Electric conductivity|conductivity]], ''σ'', when it's accounted for in the latter). A ''[[perfect conductor]]'' has infinite conductivity, ''σ''=∞, while a ''[[perfect dielectric]]'' is a material that has no conductivity at all, ''σ''=0; this latter case, of real-valued permittivity (or complex-valued permittivity with zero imaginary component) is also associated with the name ''lossless media''.<ref>http://www.ece.rutgers.edu/~orfanidi/ewa/ch01.pdf</ref> Generally, when ''σ''/(''ωε''’) ≪ 1 we consider the material to be a ''low-loss dielectric'' (nearly though not exactly lossless), whereas ''σ''/(''ωε''’) ≫ 1 is associated with a ''good conductor''; such materials with non-negligible conductivity yield a large amount of [[dielectric loss|loss]] that inhibit the propagation of electromagnetic waves, thus are also said to be ''lossy media''. Those materials that do not fall under either limit are considered to be general media.
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| ===Lossy medium===
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| In the case of lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is:
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| :<math> J_\text{tot} = J_{\text{c}} + J_{\text{d}} = \sigma E - i \omega \varepsilon' E = -i \omega \widehat{\varepsilon} E </math>
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| where
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| :''σ'' is the [[electrical conductivity|conductivity]] of the medium;
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| :''ε''’ is the real part of the permittivity.
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| :<math>\widehat{\varepsilon}</math> is the complex permittivity
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| The size of the [[displacement current]] is dependent on the [[frequency]] ω of the applied field ''E''; there is no displacement current in a constant field.
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| In this formalism, the complex permittivity is defined as:<ref>John S. Seybold (2005) Introduction to RF propagation. 330 pp, eq.(2.6), p.22.</ref>
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| :<math> \widehat{\varepsilon} = \varepsilon' + i \frac{\sigma}{\omega} </math>
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| In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms that influence the shape of the permittivity as a function of frequency:
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| *First, are the [[Dielectric#Dielectric relaxation|relaxation]] effects associated with permanent and induced [[Dipole|molecular dipoles]]. At low frequencies the field changes slowly enough to allow dipoles to reach [[Wiktionary:equilibrium|equilibrium]] before the field has measurably changed. For frequencies at which dipole orientations cannot follow the applied field because of the [[viscosity]] of the medium, absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called [[Dielectric#Dielectric relaxation|dielectric relaxation]] and for ideal dipoles is described by classic [[Debye relaxation]].
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| *Second are the [[resonance| resonance effects]], which arise from the rotations or vibrations of atoms, [[ion]]s, or [[electron]]s. These processes are observed in the neighborhood of their characteristic [[Absorption (electromagnetic radiation)|absorption frequencies]].
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| The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorption refers to the inability of a capacitor that has been charged for a long time to completely discharge when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors will develop a small voltage, a phenomenon that is also called ''soakage'' or ''battery action''. For some dielectrics, such as many polymer films, the resulting voltage may be less than 1-2% of the original voltage. However, it can be as much as 15 - 25% in the case of [[electrolytic capacitor]]s or [[supercapacitor]]s.
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| ===Quantum-mechanical interpretation===
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| In terms of [[quantum mechanics]], permittivity is explained by [[atom]]ic and [[molecule|molecular]] interactions.
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| At low frequencies, molecules in polar dielectrics are polarized by an applied electric field, which induces periodic rotations. For example, at the [[microwave]] frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break [[hydrogen bond]]s. The field does work against the bonds and the energy is absorbed by the material as [[heat]]. This is why microwave ovens work very well for materials containing water. There are two maxima of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) frequency. Both of these resonances are at higher frequencies than the operating frequency of microwave ovens.
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| At moderate frequencies, the energy is too high to cause rotation, yet too low to affect electrons directly, and is absorbed in the form of resonant molecular vibrations. In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime).
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| At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms, exciting [[electron]] energy levels. Thus, these frequencies are classified as [[ionizing radiation]].
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| While carrying out a complete ''[[ab initio]]'' (that is, first-principles) modelling is now computationally possible, it has not been widely applied yet. Thus, a phenomenological model is accepted as being an adequate method of capturing experimental behaviors. The [[Debye relaxation|Debye model]] and the [[Lorentz model]] use a 1st-order and 2nd-order (respectively) lumped system parameter linear representation (such as an RC and an LRC resonant circuit).
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| ==Measurement==
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| {{main|dielectric spectroscopy}}
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| The dielectric constant of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated over a wide range of frequencies by using different variants of [[dielectric spectroscopy]], covering nearly 21 orders of magnitude from 10<sup>−6</sup> to 10<sup>15</sup> [[Hertz|Hz]]. Also, by using [[cryostat]]s and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. In order to study systems for such diverse excitation fields, a number of measurement setups are used, each adequate for a special frequency range.
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| Various microwave measurement techniques are outlined in Chen ''et al.''.<ref name=Chen>{{cite book |title=Microwave electronics |author=Linfeng Chen, V. V. Varadan, C. K. Ong, Chye Poh Neo |chapter=Microwave theory and techniques for materials characterization |isbn=0-470-84492-2 |publisher=Wiley |year=2004 |url=http://books.google.com/?id=2oA3po4coUoC&pg=PA37|page=37}}</ref> Typical errors for the [[Hakki-Coleman method]] employing a puck of material between conducting planes are about 0.3%.<ref name=Sebastian>{{cite book |title=Dielectric Materials foress Communication |page=19 |author=Mailadil T. Sebastian |url=http://books.google.com/?id=eShDR4_YyM8C&pg=PA19 |isbn=0-08-045330-9 |year=2008 |publisher=Elsevier}}</ref>
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| *Low-frequency [[time domain]] measurements (10<sup>−6</sup>-10<sup>3</sup> Hz)
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| *Low-frequency [[frequency domain]] measurements (10<sup>−5</sup>-10<sup>6</sup> Hz)
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| *Reflective coaxial methods (10<sup>6</sup>-10<sup>10</sup> Hz)
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| *Transmission coaxial method (10<sup>8</sup>-10<sup>11</sup> Hz)
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| *[[Quasi-optical]] methods (10<sup>9</sup>-10<sup>10</sup> Hz)
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| *[[Terahertz time-domain spectroscopy]] (10<sup>11</sup>-10<sup>13</sup> Hz)
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| *Fourier-transform methods (10<sup>11</sup>-10<sup>15</sup> Hz)
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| At infrared and optical frequencies, a common technique is [[ellipsometry]]. [[Dual polarisation interferometry]] is also used to measure the complex refractive index for very thin films at optical frequencies.
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| ==See also==
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| *[[Acoustic attenuation]]
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| *[[Density functional theory]]
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| *[[Electric-field screening]]
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| *[[Green-Kubo relations]]
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| *[[Green's function (many-body theory)]]
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| *[[Linear response function]]
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| *[[Rotational Brownian motion]]
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| *[[Permeability (electromagnetism)|Electromagnetic permeability]]
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| ==References==
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| {{reflist|2}}
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| ==Further reading==
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| *''Theory of Electric Polarization: Dielectric Polarization'', C.J.F. Böttcher, ISBN 0-444-41579-3
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| *''Dielectrics and Waves'' edited by von Hippel, Arthur R., ISBN 0-89006-803-8
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| *''Dielectric Materials and Applications '' edited by Arthur von Hippel, ISBN 0-89006-805-4.
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| ==External links==
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| *[http://lightandmatter.com/html_books/0sn/ch11/ch11.html Electromagnetism], a chapter from an online textbook
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| *[http://keith-snook.info/capacitor-soakage.html What's all this trapped charge stuff . . .], A different approach to some capacitor problems
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| *[http://falsecolour.com/aw/eps_plots/eps_plots.pdf Complex Permittivites of Metals], Plots of the complex permittivity and refractive index for many different metals.
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| <!--Categories-->
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| [[Category:Condensed matter physics]]
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| [[Category:Electric and magnetic fields in matter]]
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| [[Category:Physical quantities]]
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| [[Category:Concepts in physics]]
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| [[lt:Dielektrinė skvarba]]
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