Dielectric Materials for Electrical Engineering E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 850

Veröffentlichungsjahr: 2013

Beschreibung

The object of this book is to provide a comprehensive reference source for the numerous scientific communities (engineers, researchers, students, etc.) in various disciplines which require detailed information in the field of dielectric materials. Part 1 focuses on physical properties, electrical ageing, and modeling - including topics such as the physics of charged dielectric materials, conduction mechanisms, dielectric relaxation, space charge, electric ageing and end of life (EOL) models, and dielectric experimental characterization. Part 2 examines applications of specific relevance to dielectric materials: insulating oils for transformers, electro-rheological fluids, electrolytic capacitors, ionic membranes, photovoltaic conversion, dielectric thermal control coatings for geostationary satellites, plastics recycling and piezoelectric polymers.

Leseprobe

Table of Contents

PART 1. GENERAL PHYSICS PHENOMENA

Chapter 1. Physics of Dielectrics

1.1. Definitions

1.2. Different types of polarization

1.3. Macroscopic aspects of the polarization

1.4. Bibliography

Chapter 2. Physics of Charged Dielectrics: Mobility and Charge Trapping

2.1. Introduction

2.2. Localization of a charge in an “ideally perfect” and pure polarizable medium

2.3. Localization and trapping of carriers in a real material

2.4. Detrapping

2.5. Bibliography

Chapter 3. Conduction Mechanisms and Numerical Modeling of Transport in Organic Insulators: Trends and Perspectives

3.1. Introduction

3.2. Molecular modeling applied to polymers

3.3. Macroscopic models

3.4. Trends and perspectives

3.5. Conclusions

3.6. Bibliography

Chapter 4. Dielectric Relaxation in Polymeric Materials

4.1. Introduction

4.2. Dynamics of polarization mechanisms

4.3. Orientation polarization in the time domain

4.4. Orientation polarization in the frequency domain

4.5. Temperature dependence

4.6. Relaxation modes of amorphous polymers

4.7. Relaxation modes of semi-crystalline polymers

4.8. Conclusion

4.9. Bibliography

Chapter 5. Electrification

5.1. Introduction

5.2. Electrification of solid bodies by separation/contact

5.3. Electrification of solid particles

5.4. Conclusion

5.5. Bibliography

PART 2. PHENOMENA ASSOCIATED WITH ENVIRONMENTAL STRESS – AGEING

Chapter 6. Space Charges: Definition, History, Measurement

6.1. Introduction

6.2. History

6.3. Space charge measurement methods in solid insulators

6.4. Trends and perspectives

6.5. Bibliography

Chapter 7. Dielectric Materials under Electron Irradiation in a Scanning Electron Microscope

7.1. Introduction

7.2. Fundamental aspects of electron irradiation of solids

7.3. Physics of insulators

7.4. Applications: measurement of the trapped charge or the surface potential

7.5. Conclusion

7.6. Bibliography

Chapter 8. Precursory Phenomena and Dielectric Breakdown of Solids

8.1. Introduction

8.2. Electrical breakdown

8.3. Precursory phenomena

8.4. Conclusion

8.5. Bibliography

Chapter 9. Models for Ageing of Electrical Insulation: Trends and Perspectives

9.1. Introduction

9.2. Kinetic approach according to Zhurkov

9.3. Thermodynamic approach according to Crine

9.4. Microscopic approach according to Dissado–Mazzanti–Montanari

9.5. Conclusions and perspectives

9.6. Bibliography

PART 3. CHARACTERIZATION METHODS AND MEASUREMENT

Chapter 10. Response of an Insulating Material to an Electric Charge: Measurement and Modeling

10.1. Introduction

10.2. Standard experiments

10.3. Basic electrostatic equations

10.4. Dipolar polarization

10.5. Intrinsic conduction

10.6. Space charge, injection and charge transport

10.7. Which model for which material?

10.8. Bibliography

Chapter 11. Pulsed Electroacoustic Method: Evolution and Development Perspectives for Space Charge Measurement

11.1. Introduction

11.2. Principle of the method

11.3. Performance of the method

11.4. Diverse measurement systems

11.5. Development perspectives and conclusions

11.6. Bibliography

Chapter 12. FLIMM and FLAMM Methods: Localization of 3-D Space Charges at the Micrometer Scale

12.1. Introduction

12.2. The FLIMM method

12.3. The FLAMM method

12.4. Modeling of the thermal gradient

12.5. Mathematical deconvolution

12.6. Results

12.7. Conclusion

12.8. Bibliography

Chapter 13. Space Charge Measurement by the Laser-Induced Pressure Pulse Technique

13.1. Introduction

13.2. History

13.3. Establishment of fundamental equations for the determination of space charge distribution

13.4. Experimental setup

13.5. Performances and limitations

13.6. Examples of use of the method

13.7. Use of the LIPP method for surface charge measurement

13.8. Perspectives

13.9. Bibliography

Chapter 14. The Thermal Step Method for Space Charge Measurements

14.1. Introduction

14.2. Principle of the thermal step method (TSM)

14.3. Numerical resolution methods

14.4. Experimental set-up

14.5. Applications

14.6. Conclusion

14.7. Bibliography

Chapter 15. Physico-Chemical Characterization Techniques of Dielectrics

15.1. Introduction

15.2. Domains of application

15.3. The materials themselves

15.4. Conclusion

15.5. Bibliography

Chapter 16. Insulating Oils for Transformers

16.1. Introduction

16.2. Generalities

16.3. Mineral oils

16.4. Synthetic esters or pentaerythritol ester

16.5. Silicone oils or PDMS

16.6. Halogenated hydrocarbons or PCB

16.7. Natural esters or vegetable oils

16.8. Security of employment of insulating oils

16.9. Conclusion and perspectives

16.10. Bibliography

Chapter 17. Electrorheological Fluids

17.1. Introduction

17.2. Electrorheology

17.3. Mechanisms and modeling of the electrorheological effect

17.4. The conduction model

17.5. Giant electrorheological effect

17.6. Conclusion

17.7. Bibliography

Chapter 18. Electrolytic Capacitors

18.1. Introduction

18.2. Generalities

18.3. Electrolytic capacitors

18.4. Aluminum liquid electrolytic capacitors

18.5.(Solid electrolyte) tantalum electrolytic capacitors

18.6. Models and characteristics

18.7. Failures of electrolytic capacitors

18.8. Conclusion and perspectives

18.9. Bibliography

Chapter 19. Ion Exchange Membranes for Low Temperature Fuel Cells

19.1. Introduction

19.2. Homogenous cation-exchange membranes

19.3. Heterogenous ion exchange membranes

19.4. Polymer/acid membranes

19.5. Characterization of membranes

19.6. Experimental characterization of ion exchange membranes

19.7. Determination of membrane morphology using the SEM technique

19.8. Thermal stability

19.9. Acknowledgements

19.10. Bibliography

Chapter 20. Semiconducting Organic Materials for Electroluminescent Devices and Photovoltaic Conversion

20.1. Brief history

20.2. Origin of conduction in organic semiconductors

20.3. Electrical and optical characteristics of organic semiconductors

20.4. Application to electroluminescent devices

20.5. Application to photovoltaic conversion

20.6. The processing of organic semiconductors

20.7. Conclusion

20.8. Bibliography

Chapter 21. Dielectric Coatings for the Thermal Control of Geostationary Satellites: Trends and Problems

21.1. Introduction

21.2. Space environment

21.3. The thermal control of space vehicles

21.4. Electrostatic phenomena in materials

21.5. Conclusion

21.6. Bibliography

Chapter 22. Recycling of Plastic Materials

22.1. Introduction

22.2. Plastic materials

22.3. Plastic residues

22.4. Bibliography

Chapter 23. Piezoelectric Polymers and their Applications

23.1. Introduction

23.2. Piezoelectric polymeric materials

23.3. Electro-active properties of piezoelectric polymers

23.4. Piezoelectricity applications

23.5. Transducers

23.6. Conclusion

23.7. Bibliography

Chapter 24. Polymeric Insulators in the Electrical Engineering Industry: Examples of Applications, Constraints and Perspectives

24.1. Introduction

24.2. Equipment

24.3. Power transformer insulation

24.4. Perspectives

24.5. Conclusion

24.6. Bibliography

List of Authors

Index

First published 2007 in France by Hermes Science/Lavoisier in two volumes entitled: Matériaux diélectriques pour le génie électrique © LAVOISIER 2007 First published 2010 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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Library of Congress Cataloging-in-Publication Data

Matériaux diélectriques pour le génie électrique.

English Dielectric materials for electrical engineering / edited by Juan Martinez-Vega.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-165-0

1. Dielectric devices. I. Martinez-Vega, Juan. II. Title.

TK7872.D53M3813 2010

621.3--dc22

2009041391

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-165-0

PART 1General Physics Phenomena

Chapter 1

Physics of Dielectrics1

1.1. Definitions

A dielectric material is a more or less insulating material (with high resistivity and with a band gap of a few eV), that is polarizable, i.e. in which electrostatic dipoles exist or form under the influence of an electric field.

Like any material, it is an assembly of ions with positive and negative charges which balance, for a supposedly perfect solid, so as to ensure electrical neutrality. This neutrality is observed at the scale of the elementary structural motifs which constitute solids with ionocovalent bonding (ceramics, for example) and on the molecular scale in molecular solids (polymers and organic solids).

The action of an electric field at the level of these element constituent of solids manifests itself by dielectric polarization effects. Let us remember that the dipole moment of a charge q with respect to a fixed system of reference centered in O is:

[1.1]

where is the vector which connects the point O to the charge’s position.

If due to a force (caused, for example, by a magnetic field), the charge moves , then the variation of the moment will be:

[1.2]

represents the polarization effect of the field on the charge. The generalization of expressions [1.1] and [1.2] to a collection of charges occurs by vectorial summation of the moments of each charge. An important case is that of a set of two charges ±q, whose positions are defined by and (see Figure 1.1). The application of [1.1] to the two charges gives:

Setting , we get:

[1.3]

is called the dipole moment formed by the two charges, oriented from the negative charge to the positive charge (see Figure1.1).

The dipole moment appearing in a solid, during the application of a field , is (to a first approximation) proportional to it. We can then write:

[1.4]

In this equation, α characterizes the polarisability of the species which gave the dipole and e0 the vacuum permittivity.

Figure 1.1.Calculation of the dipole moment formed by 2 charges +q and −q

1.2. Different types of polarization

To study dielectrics, it is necessary to first of all describe the different types of polarization. In order to do so, we must distinguish two types of solids: polar solids and non-polar solids.

1.2.1. Non-polar solids

In the case of non-polar solids, the centers of gravity of positive and negative charges coincide, and the dipole moment is therefore null (in the absence of a field). This is the case for solids with metallic bonding, or of numerous ionocovalent solids (ceramic Al2O3, ZrO2, ZnO, SiO2, etc.). Thus, the tetrahedron SiO4 which constitutes the motif of quartz has a null dipole moment. It is the distortion of this tetrahedron, under the effect of a mechanical stress, which will make a polarization and the piezoelectric effect appear (see Figure 1.2).

Figure 1.2.(a) Quartz cristal at rest; it posesses a symmetry axis of order 3. The arrows represent the dipole moments whose resultant is null. (b) Subject to a mechanical stress according to the direction indicated, the network is distorted and the resulting dipole moment (small vertical arrow), is no longer null: an electric field appears

1.2.2. Polar solids

Polar solids are composed of polar molecules for which the centers of gravity of the positive and negative charges do not coincide (for example a water molecule); this is molecular polarization. This is the case for most molecular solids and ferroelectric solids, which present a spontaneous polarization. Figure 1.3 gives, for example, the structure of barium titanate, a typical case of a ferroelectric body (and therefore also piezoelectric).

1.2.3. Electronic polarization

Let us consider the spherical orbital of an electron. Under the influence of an external electric field , the electrons are subject to a force -e and the orbital gets distorted (see Figure 1.4). Consequently, the centers of gravity of the positive and negative charges which were initially merged, no longer are: this is electric polarization, and this leads to the formation of an electrostatic dipole; therefore, a dipole moment internal to the atom is characterized by:

[1.5]

which opposes itself to the field . αelect is called the electronic polarisability. The polarization disappears if the field is removed.

Figure 1.3.Non-centrosymmetric crystalline structure of barium titanate BaTiO3

Figure 1.4.(a) Orbital in the absence of electric field; (b) distortion of the orbital and appearance of electronic polarizationin the presence of a field

1.2.4. Ionic polarization

In the case of ionic crystals, the average position of positive and negative ions changes under the influence of a field . Suppose the ion is perfectly rigid from every angle. The action of the field will be to move it a quantity with respect to a fixed mark centered in O; hence a variation of the polar moment:

[1.6]

This is the induced ionic polarization, proportional to the field (elastic distortions); where αion is the ionic polarisability.

The total dipole moment attached to the displacement of the ion and to the distortion of the electronic orbitals is, to a first approximation, the sum of [1.5] and [1.6], that is to say:

[1.7]

1.2.5. Orientation polarization

When we subject a polar molecule, carrier of a permanent dipole moment , to an electric field , its dipole tends to turn towards the direction of the field, which leads to a distortion of the molecule related to a torque: this is orientation polarization. This distortion is not instantaneous. There is the appearance of a hysteresis, on the one hand because the molecular forces tend to block its motion and, on the other hand, the thermal agitation will tend to disorient the molecules with respect to one another.

If makes an angle θ with the direction of the field, the torque is:

The application of a field will have the effect on each molecule of producing a polar component in the direction of the field, whose first-order expression is:

[1.8]

α or is called orientational polarisability. In general,

1.2.6. Interfacial or space-charge polarization

This type of polarization plays a part when the material possesses different phases or permittivity zones. Subject to a low-frequency electric field (from 10−1 to 102 Hz), this material will behave as though it contains electric charges with interfaces separating the zones. However, these charges are not real charges, but known as “polarization” charges (see section 1.3.3).

1.2.7. Comments

Units: a dipole moment is the product of a charge by a distance; it is therefore measured in Cm. A commonly used unit is the Debye:

A dipole moment is measurable, unlike q and l. The dipole moment must be taken as an entity, in the same way as an electric charge.

Polarization vector: this is the dipole moment per unit volume. By analogy with a capacitor, we can write:

[1.9]

where ε0 is the vacuum permittivity, εr is the dielectric constant of the material and χ =(εr −1) is its dielectric susceptibility.

1.3. Macroscopic aspects of the polarization

1.3.1. Polarization of solids with metallic bonding

Rather than address non-conductive materials, it is interesting first of all to describe the polarization phenomena appearing in a metal. In this case, each ion of the solid is neutralized on the scale of the atomic volume by “free” electrons. The ions do not move under the action of the field and subsequently do not introduce any dipole moment. On the other hand, the conduction electrons go up the field (polarisability α ࢐ ∞) until they reach the limit of the solid: the electrons accumulate on the surface of the solid by which the field enters, leaving an excess of positive charges on the surface by which it comes out (see Figure 1.5). This giant dipole creates an internal field within the solid which opposes itself to the applied field . The motion of charges takes place until the total field is null:

[1.10]

We say that the free charges come to screen the applied field. The total charge of the solid is null but its surface is positively charged on one side and negatively on the other.

1.3.2. Polarization of iono-covalent solids

Unlike metals, there are no free charges in a perfect iono-covalent solid: there is therefore no screen with the applied field. Each ion of the elementary structural motif is subject to a polarization, such that the solid presents a dipolar structure at the atomic or molecular scale (see Figure 1.6). The solid being neutral, the internal field at a point is the sum of the applied field and the field created by all of the dipoles.

[1.11]

Figure 1.5.Polarization of a solid with metallic bonding

Figure 1.6.Polarization of an iono-covalent solid

This internal field is called the local field (). It is this field which is responsible for the polarization of the medium whose description was given in section 1.2.

If each atom, i, of a solid with a cubic lattice of parameter, a, carries a dipolar moment, , the polarization vector is defined by:

[1.12]

where N is the number of atoms per cell.

If d3r is the dipole moment at point of an element with continuous volume d3r, the potential created by this dipole moment at a point (see Figure 1.7) is:

[1.13]

Let us consider a continuous solid of volume ν and surface S, totally neutral (with no excess charges in the medium), subject to an external field (see Figure 1.7). It presents a polarization . The potential created at point by the dipole moment d3r is (from [1.13]):

[1.14]

and the created field has a value of:

[1.15]

Using mathematical operations (Ostrogradski and Green), we get:

[1.16]

Figure 1.7.Representation of a solid (V), of surface (S) subject to an external field

1.3.3. Notion of polarization charges

The two integrals of [1.16] are interpreted as being Coulomb integrals. Indeed, we can write the second integral of [1.16] as: , with Pn being the projection of following the direction of the surface element, directed towards the outside (see Figure 1.7). Pn has the dimension of a surface charge density σp. Similarly for the first integral represents a density per unit volume of charges. The densities σp and σp are known as polarization charge densities.

These polarization charges, in a neutral medium (without excess charges) are not real electric charges; it is a convenient equivalence.

1.3.4. Average field in a neutral medium

To the potential given by [1.16], due to the polarization, we must add the potential due to the applied electric field. The potential in is therefore:

[1.17]

And the field in is given, by using the polarization charges, by:

[1.18]

is the field due to surface polarization charges whose effect within the dielectric is to oppose itself to the applied field . As a result of this, it is called the depolarization field. is the field created by the volume polarization charges.

is the average field. It is the usual macroscopic field defined at all points of the medium and the one that we measure (for capacities, for example). By analogy with [1.9] we can write:

[1.19]

where χ is the dielectric susceptibility.

The volume polarization charges ensuing from [1.19] have a density of:

[1.20]

with, from [1.18],

The sources of the fields and are either outside, or at the periphery of the medium, subsequently: .

As for the field, , due to the polarization charges, its divergence has the expression: and, subsequently:

[1.21]

Plugging [1.21] into [1.20], the polarization charge is written:

[1.22]

Subsequently, in a neutral medium, the polarization charges are due to the gradient of dielectric susceptibility. In other words, a medium in which susceptibility varies presents volume polarization charges.

The electric induction is defined by:

[1.23]

So, taking into account [1.19]: , and setting ε=ε0 (1 + χ):

[1.24]

where ε is the dielectric permittivity of the material, sometimes called the dielectric constant.

From [1.21] and [1.23], it follows:

In a neutral medium the divergence of the induction is null ( is at conservative flux). Equally, we can theorize the proportionality between and the depolarization field:

[1.25]

The minus sign indicates that has an opposite effect to that of on the polarization, i.e. it has a depolarizing effect. The fact that reduces the polarization produced by implies that .

1.3.5. Medium containing excess charges

Let ρa be the charge density of charges and , the field they produce. This field must be added to the expression [1.18], so:

[1.26]

The presence of charges in the medium imposes .

The problem can be tackled in two ways:

– we can treat these excess charges as charges external to the dielectric and associate their field with the applied field whose sources are outside the medium. We will therefore set: and subsequently ,

– we can also integrate these charges to the medium because, as we will see, these excess charges are generally trapped charges, which affect the physical characteristics of the medium considerably. We then set:

The final result is identical according to both approaches with:

where ρ is the total density of charges (polarization charges plus excess charges).

The application of [1.23] gives the expression for the induction:

Thus, in a charged medium, the divergence of the induction is equal to the density of excess charges.

1.3.6. Local field

We have seen (in equation [1.11]) that, within a dielectric subject to an applied field , an internal field (known as a local field) prevails, such as:

where is the field created by all of the dipoles.

Each ion of a solid is therefore solicited by this local field different to the applied field. The dipole moment which appears on a site j of the lattice is therefore expressed by:

where αj is the induced or orientational polarisability, depending on the material. The field created by all of the dipoles in j is the vectorial sum of the fields of each dipole, that is to say:

Each dipole i will create a potential at the point j whose expression is similar to equation [1.13].

1.3.7. Frequency response of a dielectric

When the applied field varies over time (harmonic field E(ω,t)), this field induces a polarization P(ω,t), defined from the expression [1.19]:

This polarization is the sum of each type of polarization. But the reaction of a material to a type of polarization is not instantaneous. Thus, there is a phase difference δ between an alternative electric field (E= E0sinωt) and the polarization P=P0 sin((ω-δ). In complex notation, we can write P*= P0 exp(i(ωt-δ)) and E*= E0 exp(iωt). The values of the polarization and of the dielectric constant depend on the ease with which the dipole moments reorient themselves when the direction of the field varies. The time required for this reorientation to take place is called relaxation time, τ, and its inverse the relaxation frequency, f

Given that the relaxations are related to thermal agitation, the frequency, f, of the material is a function of the temperature (f increases with T). When the frequency electric field is much stronger than the relaxation frequency of a type of polarization, this polarization cannot be produced. Conversely, if the frequency of a field is much less than the relaxation frequency, the polarization is produced instantaneously and the phase difference between P and E is null. But if the frequency of the field and the relaxation frequency are close, the phase difference, δ, increases to reach a maximum value. In this case, the curves D=f(E) or P=f(E) form a hysteresis buckle. The area of this buckle represents the energy loss per cycle and per unit volume of the material.

The most classical solicitations are mechanical or electrical. In the first case, we find the anelasticity phenomenon encountered for the mechanical properties of the materials. We note G’ and G” the real and complex modules which lead to the mechanical loss angle δm. For a dielectric, we consider the real permittivity ε’ and the complex permittivity ε” and the dielectric loss angle δe.

Electronic and ionic polarizations, which bring about short-distance rearrangements, persist in a large range of frequencies. On the other hand, for molecular materials, the orientation polarization imposes reorientations of the dipoles at the molecular scale. It can’t take place above a certain frequency, determined by the size of the molecules and by the molecular dipole moments. We must then take into account the variations of the dielectric constant and the loss factor according to the frequency.

From an experimental point of view, the mechanical solicitations have frequencies in the range 10−6 and 107 hertz, which permits them to act especially on the molecular chains in polymers. The electrical solicitations can have larger ranges of frequencies, up to 1015 hertz, which allows ionic and electronic vibrations to be analyzed.

1.4. Bibliography

[JON 83] JONSCHER A.K., Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983.

[KEL 89] KELDYSH L.V., KIRZHNITZ D.A., MARADUDIN A.A. (Eds), The Dielectric Function of Condensed Systems: Modern Problems in Condensed Matter Sciences, North Holland, Elsevier Science Ltd, 1989.

[LAN 69] LANDAU L., LIFCHITZ E., Electrodynamique des milieux continus, éditions MIR, 1969.

[SCA 89] SCAIFE B.K.P., Principles of Dielectrics, Clarendon Press, 1989.

1 Chapter written by Guy BLAISE and Daniel TREHEUX.

Chapter 2

Physics of Charged Dielectrics: Mobility and Charge Trapping1

2.1. Introduction

For the lay person, an insulating material is a material which does not conduct electricity. In fact, however, it is necessary to analyse this assertion more closely.

The conductivity of a material is defined by:

[2.1]

where n is the density of the charge carriers and μ the mobility.

Table 2.1 gives the values, at room temperature, of the conductivity and mobility of the electrons in high purity copper and alumina (aluminum oxide). We note that there are 23 regions between the two conductivities, but the mobility is twice as high in alumina as in copper. These values, which could be surprising, are due to the fact that, from [2.1], alumina contains much less than an electron per cm3 which is used for conduction while copper has about 4.5 × 1022 electrons per cm3 used for conduction (Table 2.1).

Alumina has, therefore, a very weak conductivity because it has practically no free charges to conduct (and not because it is inept at conducting charges). For a pure material with a large band gap, we have, then, an insulating state, through lack of charge carriers.

For conduction to be observed in an insulator, we need to inject charges into it. Unlike a metal, the bulk of which remains neutral during conduction, an insulating material is thus charged. The injection of charges can be done in many different ways, as will be developed in later chapters of this book. Here, we mention, for example, irradiation (electronic, radiative, etc.), corona discharge, the application of an electrical constraint, and also mechanical or tribological ones.

When we manage to inject charges in a conduction band, the strong mobility of these charges (Table 2.1) is explained by the fact that the electron-electron interactions are reduced to nothing, as a result of the weak density of the free charges. In a perfect insulator, only the electron-phonon interaction remains to limit mobility. But, if the solid contains impurities, they will also reduce the mobility. This explains, as we shall see, the very important role which impurities take in the properties of insulators.

Table 2.1.Conductivity σ and mobility μ of pure monocrystalline copper and alumina

Copper

Alumina

σ(Ω

−1

cm

−1

)

5.8.10

5

10

−18

μ (cm

2

.V

−1

.s

−1

)

80

200

n (e

−1

.cm

−3

)

4.5.10

22

3.1.10

−2

2.2. Localization of a charge in an “ideally perfect” and pure polarizable medium