Linear Dielectric

10 Key excerpts on "Linear Dielectric"

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  Fundamentals of Ceramics

  • Michel Barsoum(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  14

  Linear Dielectric Properties

  It serves to bring out the actual mechanical connexions between the known electro-magnetic phenomena; so I venture to say that any one who understands the provisional and temporary character of this hypothesis will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena.

  James Maxwell, Phil. Mag., 21 :281 (1861).

  14.1 Introduction

  Dielectric materials do not conduct electricity and as such are of critical importance as capacitive elements in electronic applications and as insulators. It could be argued, with some justification, that without the discovery of new compositions with very high charge-storing capabilities, i.e., relative dielectric constants k ′ > 10,000, the impressive miniaturization of semiconductor-based devices and circuits would not have been possible. In addition, the traditional use of ceramics as insulators in high-power applications is still a substantial economic activity.

  In contrast to electrical conductivity, which involves long-range motion of charge carriers, the dielectric response results from the short-range motion of these carriers under the influence of an externally applied electric field, E. Inasmuch as all solids are comprised of positive and negative entities, the application of E to any solid will result in a separation of its charges. This separation of charge is called polarization , defined as the finite displacement of bound charges of a dielectric in response to an applied electric field. If permanent electric dipoles exist in the dielectric and are mobile, they will orient parallel to the direction of E.

  The dielectric properties can vary widely between solids and are a function of temperature, frequency of applied field, humidity, crystal structure, and other external factors. Furthermore, the response can be either linear or nonlinear

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  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  241 7 Linear Dielectric Materials 7.1 DIELECTRIC MATERIALS A dielectric material typically is a large-bandgap semiconductor ( E g ~ >4 eV) that exhibits high resistivity ( ρ ). The prefix dia means through in the Greek language. The word dielectric refers to a material that normally does not allow electricity (electrons, ions, and so on) to pass through it. There are special situations (for example, exposure to very high electric fields or changes in the composi-tion or microstructure) that may lead to a dielectric material exhibiting semiconducting or metallic behavior. However, when the term dielectric material is used, it generally is understood that the material essentially is a nonconductor of electricity. An electrical insulator is a dielectric material that exhibits a high breakdown field. 7.1.1 E LECTROSTATIC I NDUCTION To better understand the behavior of nonconducting materials, let us first examine the concept of electrostatic induction and what is meant by the terms free charge and bound charge . First, con-sider a dielectric such as a typical ceramic or a plastic that has a net positive charge on its surface. Now, assume that we bring a Conductor B near this charged Insulator A (Figure 7.1a). The electric field associated with the positively charged Insulator A pulls the electrons toward it from Conductor B. This is also described as the atoms in Conductor B being polarized or affected by the presence of an electric field. The process of the development of a negative charge on Conductor B is known as electrostatic induction. In this case, the negative charge developed on Conductor B is the bound charge because it is bound by the electric field caused by the presence of the charged Insulator A next to it. The creation of a bound negative charge on Conductor B, in turn, creates a net positive charge on the other side of the conductor because the conductor itself cannot have any net electric field within it.

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  Handbook of Electrostatic Processes

  • Jen-Shih Chang, Arnold J. Kelly, Joseph M. Crowley(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  4 Electrical Phenomena of Dielectric Materials R. Tobaz6on Centre National de la Recherche Scientifique Grenoble , France I. INTRODUCTION If we exclude metals, all remaining materials are dielectrics, whatever the state of the matter in question (solid, liquid, gas), and a permittivity e can be ascribed to any substance, with vacuum as the reference dielectric. Dielectrics can be employed either as passive devices (capacitors, ca­ bles) or in active devices (electrets, electrostatic motors), and they are required to function in our near or far environment (air, seawater, soil, space). Generally, materials are subjected to a voltage (dc, ac, impulse), and, in exceptional cases, to an electromagnetic field produced by, for example, an intense laser beam. The spatiotemporal distribution of the field inside the matter not only is imposed by the geometry of the elec­ trodes (whether to insure a uniform or a nonuniform field) and the shape of the voltage wave but also depends on space charges: charge carriers can be generated or blocked at interfaces or interphases, when different dielectric substances come into contact with each other. Among environmental constraints, we may consider the actions of pres­ sure, temperature, radiation, chemical attack, etc. Time is often a funda­ mental parameter in the study of dielectrics, e.g.: A perfect insulator would be a medium through which no conduction current could flow. In fact, the transition from “capacitive” behavior to “resistive” behavior depends on the conduction relaxation time 51 52 TOBAZEON tc = ep (insofar as a resistivity p can be ascribed to the material). Thus a dielectric may behave in a completely different manner under dc, ac, or impulse voltages.

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  Introductory Solid State Physics

  • H.P. Myers(Author)
  • 1997(Publication Date)
  • CRC Press

    (Publisher)

  12 Dielectric Media ‘Insulators’ are dielectric media, whose general characteristics usually comprise strong ionic or directed covalent bonds, brittle mechanical behaviour at ordinary temperatures, very high resistivities and in many cases transparency to visible and infrared light. A dielectric is a substance that becomes polarized in the presence of an electric field. The physical quantities of primary interest are the field vectors E and D, the polarization P, together with the electric susceptibility ț and dielectric constant İ r . If Ǽ denotes the macroscopic electric field within the medium then D=İ r İ 0 Ǽ=İ 0 Ǽ+ȇ , (12.1) ȇ=țİ 0 Ǽ, (12.2) İ r =1+ț. (12.3) An external field acting on a dielectric produces induced dipole moments, and we must consider the polarizabilities of the atoms; there is therefore some justification for beginning with a treatment of the isolated atom. 12.1 The Free Atom In an isolated atom of Na or Xe, say, the electronic charge is distributed in a spherically symmetrical manner around the nucleus, but in the presence of an external field E 0 the distribution is altered, leading to an induced dipole moment p; we say the atom becomes polarized (Fig. 12.1), and write p=Įİ 0 Ǽ loc , (12.4) where Į is the atomic polarizability (assumed independent of the electric field) and E loc the electric field acting at the site of the atom. We call this the local field. Since a dipole cannot act upon itself and because the atom is isolated, the local field is given in this case by the external field E 0 . The dipole moment arises as a result of separation of the centres of gravity of the electronic and nuclear charges, a separation that is determined by balancing the force Figure 12.1 The basis for an elementary calculation of the polarizability of the free atom. In the presence of the field E 0 the electron charge cloud and the nucleus undergo a slight relative displacement.

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  Introduction to Electrodynamics

  • David J. Griffiths(Author)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  If, for instance, we put a piece of dielectric into an external field E 0 , we cannot compute P directly from Eq. 4.30; the external field will polarize the material, and this polarization will produce its own field, which then contributes to the total field, and this in turn modifies the polarization, which . . . Breaking out of this infinite regress is not always easy. You’ll see some examples in a moment. The simplest approach is to begin with the displacement, at least in those cases where D can be deduced directly from the free charge distribution. In linear media we have D =  0 E + P =  0 E +  0 χ e E =  0 (1 + χ e )E, (4.31) so D is also proportional to E: D =  E, (4.32) where  ≡  0 (1 + χ e ). (4.33) This new constant  is called the permittivity of the material. (In vacuum, where there is no matter to polarize, the susceptibility is zero, and the permittivity is  0 . That’s why  0 is called the permittivity of free space. I dislike the term, for it suggests that the vacuum is just a special kind of Linear Dielectric, in which the permittivity happens to have the value 8.85 × 10 −12 C 2 /N· m 2 .) If you remove a factor of  0 , the remaining dimensionless quantity  r ≡ 1 + χ e =   0 (4.34) is called the relative permittivity, or dielectric constant, of the material. Dielec- tric constants for some common substances are listed in Table 4.2. (Notice that  r is greater than 1, for all ordinary materials.) Of course, the permittivity and the dielectric constant do not convey any information that was not already available in the susceptibility, nor is there anything essentially new in Eq. 4.32; the physics of Linear Dielectrics is all contained in Eq. 4.30. 8 7 In modern optical applications, especially, nonlinear materials have become increasingly important. For these there is a second term in the formula for P as a function of E—typically a cubic term.

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  Principles of Engineering Physics 2

  • Md Nazoor Khan, Simanchala Panigrahi(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  The dielectric constant of a material under given conditions reflects the extent to which it concentrates electric flux. It is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum. The dielectric constant depends on the composition, microstructure, temperature and frequency of the applied field. 9.3.2 Electric dipole moment µ  e The dipole moment of a dipole is defined as the product of magnitude of charge of one pole and the distance between the two opposite charges constituting the electric dipole. It is a vector quantity with direction from the negative to the positive charge of the dipole (Fig. 9.4). Mathematically, it is defined by µ =   e qr (9.2) Figure 9.4 The electric dipole moment µ  e . It is a vector quantity with direction from the negative to the positive charge of the dipole 9.3.3 Dielectric polarization Polarization vector  P in its quantitative meaning is defined as the amount of induced dipole moments per unit volume of a polarized dielectric material. Mathematically, polarization vector  P is defined as µ =   e P N (9.3) Dielectric Materials 293 where µ  e = dipole moment of a single polarized molecule. N = number of polarized molecules per unit volume of the polarized dielectric. The direction of the polarization vector is the same as the direction of the dipole moment. The SI unit of the polarization vector  P is Cm –2 . The extent of polarization of a dielectric is described by the polarization vector  P . As shown in Fig. 9.3, the opposite surfaces of the polarized dielectric slab contains equal and opposite charges and hence, the dielectric slab as a whole may be treated as a electric dipole. Figure 9.5 shows a polarized elemental dielectric slab of width  . Let dq i = induced charges on either surfaces of the dielectric on an elemental area  ds .

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  Introduction to Electromagnetism

  • M. Sibley(Author)
  • 1995(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  What we ha¥e not yet examined is the effect of a dielectric on'a capacitor , Figure 6.3(a) shows a capacito r with a dielectric between its plates . When the upper plate has a positive charge on it, flux radiates down across the air gap and into the dielectric. The E field in the capacito r will polarize the dielectric, so producing a negative charge on the upper surface of the dielectric. A similar situation occurs on the lower plate, and so we can take the macroscopi c view as Fig. 63(b) shows . So, the exterEa l field induces polarization in the dielectric with the dipole moment s pointing towards the lower plate. This implies a polarization vector which we can deine as follows, Let ns conside r a smal volume of dielectric, SV, that is large enough to enclose a large numbe r of atoms . If the numbe r of atoms per unit volume is N, the numbe r of atoms in this volume is NW, Now, let us assume that all of these atoms are polarized in the same direction -acting downwards , Each atom has a dipole momen t of p = q x d f Cm and so the total polarization of the volume W is NWXqdCm Thus the polarization per unit volume, P, is (6.5) (6.6) 154 Dielectrics polarizationof & V p=. 8V NOV x qd -----_.~~ 8V which gives P = NqdCm2 (6.7) So, we have a new vector,the polarization,with unitsof coulomb per m 2 acting in the samedirection as the E field. This meanswe can modify ourequation linking D and E to give (6.8) Materialsin which the dipolemomentis directlyproportionalto the E field are known aslinear materials,and most dielectrics we come across are linear in form. Thus we can write (6.9) where Xis aconstantof proportionalitycalledthe electricsusceptibilityof the material.We can now writeEquation(6.8) as D = EoE + XEoE = (1 + X)E(jE Thus therelativepermittivity of the materialis E, = 1 + X (6.10) i.e. E, dependson the electric susceptibilityof the material,which is itself a measureof the polarizabilityof the dielectric.

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  Infrared and Millimeter Waves V8

  Electromagnetic Waves in Matter, Part I

  • Kenneth J. Button(Author)
  • 1983(Publication Date)
  • Academic Press

    (Publisher)

  INFRARED AND MILLIMETER WAVES, VOL. 8 CHAPTER 1 Properties of Dielectric Materials G. W. Chantry National Physical Laboratory Teddington, Middlesex United Kingdom I. II. III. IV. V. INTRODUCTION THE MACROSCOPIC THEORY A. The Response Function B. The Correlation Function and the Cole-Cole Plot C. Corrections for the Internal Field D. Causality and the Kramers-Kronig Relations THE MICROSCOPIC THEORY EXPERIMENTAL METHODS SOME ILLUSTRATIVE EXAMPLES OF SUBMILLIMETER DIELECTRIC MEASUREMENTS A. Polar Liquids B. Nonpolar Liquids C. Solutions of Polar Molecules in Nonpolar Solvents D. Polymers E. Plastic Crystals F. Glasses REFERENCES 1 5 5 9 15 16 21 26 30 30 31 35 38 45 46 47 I. Introduction The study of liquids and polymers by means of far-infrared and submilli-meter spectroscopy forms part of the much larger topic of dielectric physics. A dielectric medium is one in which there are no free charges so the dc conductivity is zero, but the medium can sustain displacement currents and these may have lossy components. Thus dielectrics are all materials that are not metallic, semiconducting, or ionized. If an external field E is applied to a dielectric, the field inside the dielectric is given by D = (e/e 0 )E, (1) where ε is the permittivity of the dielectric and ε 0 the absolute permittivity of free space (8.85418 X 10 12 F/m). In nearly all dielectric work, however, it is customary to write ε = ε/ε 0 to avoid the constant apperance of the ε 0 factor; then ε so defined is the relative permittivity of the medium, i.e., the permit-1 Copyright © 1983 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-147708-8 2 G. W. CHANTRY tivity relative to that of the vacuum. The relative permittivity is complex because it will have a lossy component, and one therefore usually writes g = β ' -/ β , (2) where the caret is used to signify an explicitly complex quantity.

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  Color Imaging

  Fundamentals and Applications

  • Erik Reinhard, Erum Arif Khan, Ahmet Oguz Akyuz, Garrett Johnson(Authors)
  • 2008(Publication Date)
  • A K Peters/CRC Press

    (Publisher)

  In the presence of an electromagnetic field, electrons remain bound, but may be displaced. In such cases, the electrons may be thought of as orbiting around a point that is some 3.6. Polarization in Dielectric Materials 183 distance away from the nucleus. As a result, the negative charge of the electrons is slightly offset with respect to the positive charge of the nucleus. An atom under the influence of an electromagnetic field may thus form an electric dipole . The atom is said to be polarized under these conditions. Some dielectrics are known as polar substances, where the molecular struc-ture is such that dipoles exist even in the absence of an external electromagnetic field. This is for instance the case with water. However, for polar substances, the orientation of each molecule is random, and therefore the net polarization of the material in bulk is zero. When an electric field is applied, the forces acting upon the molecules will align them with the field, and the material will become polarized. This phenomenon is called orientational polarization . Some materials consist of ions that are bound together. As an example, sodium chloride NaCl consists of positive and negative ions. Application of an external electric field will separate the ions and thus form electric dipoles. The result is called ionic polarization . A polarized atom may be modeled as a positive point charge + Q and a neg-ative point charge − Q separated by a distance r . The dipole moment p is then defined as p = Q r . (3.78) It would be difficult to model the interaction of an electromagnetic wave with a material if the dipole moments of each individual atom or molecule need to be considered. It is more convenient to compute the average behavior of the material at the microscopic scale.

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  Fundamentals of Rock Physics

  • Nikolai Bagdassarov(Author)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  Nevertheless, it is common to introduce the so-called dielectric displacement field D → , which is defined as an electric field caused only by the given free charges using analogy to P → : ∂ D → ∂x þ ∂ D → ∂y þ ∂ D → ∂z ¼ divD → ¼ ρ f (9.2) Figure 9.1 (a) Dielectric material is placed between two plate electrodes. Bound charges on the plates cause a reorientation of dipoles and building of dipole chains within a dielectricum having the dipole orientation p → opposite to the plate charges. (b) For calculation of the dipole field, the distance d between two charges q is taken to be small, and at the same time its charge q is getting larger, so that the dipole moment p → ¼ q  j d → j remains finite. The vector of the dipole moment p → is directed from −q to +q. (Adapted from von Hippel, 1954.) 362 DIELECTRIC PROPERTIES In this case, one may say that the external electric field E → causes polarization and displacement fields, and it is responsible for the total electric charge density ρ t . So, it may be expressed as follows: ε 0  ∂ E → ∂x þ ∂ E → ∂y þ ∂ E → ∂z  ! ¼ ε 0  div E → ¼ ρ f þ ρ b ¼ ρ t (9.3a). Comparing (9.1–9.3a), one comes to the relationship div D → ¼ ε 0  div E → þ div P → , which is equivalent to the relationship ρ f ¼ ρ t þ ρ b . When displacements of charges are small, then the displacement field D → and polarization P → are proportional to the external field E → : D → ¼ ε  E → ¼ ε 0  ε r  E → ¼ ε 0  E → þ ε 0  χ e  E → (9.3b) If one defines the relative dielectric constant of a material as a dimensionless ratio ε r ¼ ρ f þ ρ b ρ f , then ε r ¼ ε ε 0 ¼ 1 þ χ e , where χ e is the electric susceptibility. In the general case, ε r is dependent on the frequency of the external electric field E → . Frequency- dependent variables may be represented as complex numbers having two components, cos and sin.

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