Electrical and Magnetic Properties of Materials

Dr. Emmanuel Kwesi Arthur

Email: ekarthur2005@yahoo.com

Phone #: +233541710532

Department of Materials Engineering,

Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

©2017

Course Code: MSE 455

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Lecture One

Course Description: The course spans the full rangefrom Ohm’s Law and Electrical Conductivity. The coursealso look at Magnetic Properties of Materials

The learning objectives are:To study electronic materials – insulators, dielectrics,

conductors, semiconductors, and superconductors.

To study conductivity in electronic materials.

To study the fundamental basis for responses ofcertain materials to the presence of magnetic fields.

To examine the properties and applications ofdifferent types of magnetic materials.

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Course Content Electrical conduction phenomena, Energy band structure,

Insulators and semiconductors. Femi-Dirac statistics,Density of states function, Intrinsic and extrinsic semi-conductors. Doping, n-type and p-type semi-conductors. Halleffect. Dielectric materials, Parallel plate capacitors,Dielectric displacement, Susceptibility and polarization,Polarization mechanisms Mosotti field, Clausius-Mosottiequation. Dielectric loss, Dissipation factor power factor,quality factor.

Magnetic properties of materials, Diamagnetic andparamagnetic materials, Ferromagnetic materials, Influenceof temperature on magnetic behaviour, Curie-Weiss law.Magnetic domains and hysteresis loop. Magnetic materials:Hard and soft magnetic materials, Applications.

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Text Book Rolf E. Hummel, Understanding Materials Science –History

*Properties * Application, Second Edition, ©Springer –Verlag New York, LLC, 2004.

Rolf E. Hummel, Eectronic Properties of Materials, Fourth Edition, © Springer Science + Business Media, LLC, 2011.

William D. Callister and David G. Rethwisch, Materials Science and Engineering: An Introduction, Seventh Edition, © John Wiley & Sons, Inc., 2007.

Donald R. Askeland –Pradeep P. Phulé, The Science and Engineering of Materials, Ch. 18: Electronic Materials, Fourth Edition, Power Point Lectures.

Brain S. Mitchell, An Introduction to Materials Engineering and Science, © John Wiley & Sons, Inc., Hoboken, New Jersey, 2004

.

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Syllabus:

Attendance is your job – come to class! Or our regularly scheduled time (Tuesday 8:00-9:00 am & 4:00 – 6:00

pm)

Assignments Don’t copy from others; don’t plagiarize – its just the right thing to do!!

Tutorials – by Adwoa Owusu Bia (TA) - Tuesday 8:00-9:00 am

Grading Class Attendance, Pop Quizzes and Assignments – (10% of your

grade!) Mid Semester Exams – (20%) End of Semester Exams (70%)

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Read the relevant material in the Askerland book (preferably before the lecture topic)

Review and understand the examples given in the book.Do the assigned homework. If you are having

difficulty with a particular concept, work additional problems given in the book on that topic that have the answers given in the back of the book.

Come to office hours.Seek help: tutors, etc.

Academic success is directly proportional to the amount of time devoted to study.

Suggestions for success in this class:

Time: Tuesday 8:00-9:00 am & 4:00 – 6:00 pm

Lecture Room:

Instructor: Dr. Emmanuel Kwesi ArthurDept. of Materials Engineering

Teaching Assistant: Anita Yentumi

Office: PB325

Office Hour: Monday, Tuesday, Wednesday: 10-10:55 AM,

Email: ekarthur2005@yahoo.comPhone #: +233541710532

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Electrical Properties of Materials and Electronic Materials

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Part One

Outline- Part One

Introduction

Ohm’s Law and Electrical Conductivity

Resistivity/Conductivity in Metal and Alloy

Band Structures of Solids

Superconductivity

Applications of Superconductivity

Semiconductors

Applications of Semiconductors

Insulators and Dielectric Properties

Polarization in Dielectrics

Electrostriction, Piezoelectricity, and Ferroelectricity

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Issues to Address The source of electrical conductivity

How are electrical conductance and resistance characterized ?

Band theory, energy bands and band gap

What are the physical phenomena that distinguish conductors, semiconductors, and insulators?

Reasons for high conductivity of metals

For metals, how is conductivity affected by imperfections, temperature, and deformation?

For semiconductors, how is conductivity affected by impurities (doping) and temperature?

Semi conductivity – Intrinsic and Extrinsic

Dielectric behavior

Ferro and Piezo-electricity

Goal: Students will be able to describe various electrical properties that materials have and learn how to improve them10

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Electrical ConductionOhm‘s Law

Electrical ConductionOhm‘s Law

12

13

Electrical Conduction

Ohm's Law: V = I Rvoltage drop (volts = J/C)

C = Coulombresistance (Ohms)

current (amps = C/s)

1

Conductivity, σ

Resistivity, R: -- a material property that is independent of sample size and

geometry

RA

l

surface areaof current flow

current flow path length

Where I is current (Ampere), V is voltage (Volts) and R is the resistance (Ohms or Ω) of the conductor (Ω-m)-1

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Electrical Properties

Which will have the greater resistance?

Analogous to flow of water in a pipe

Resistance depends on sample geometry and size.

D

2D

R1 2

D

2

2

8

D2

2

R2

2D

2

2

D2

R1

8

.time

chargeI

.sec

coulomb1ampere1

A

IJ~

Current density-

Current

The current flowing through per unit cross-sectional area.

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Electrical Properties

AR

A

1R

Electrical resistance

where σ is the electrical conductivity

I

VR

/V

I/A

V

I

A

/V

J~

16

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Definitions

Further definitions

J = <= another way to state Ohm’s law

J current density

electric field potential = V/

flux a like area surface

current

A

I

Electron flux conductivity voltage gradient

J = (V/ )

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What is the minimum diameter (D) of the wire so that V < 1.5 V?

Example 1: Conductivity Problem

Cu wireI = 2.5 A- +

V

Solve to get D > 1.87 mm

< 1.5 V

2.5 A

6.07 x 107 (Ohm-m)-1

100 m

I

V

AR

4

2D

100 m

v Ev = E

where μ is the mobility

Current density - The current flowing through per unit cross-sectional area.

Electric field - The voltage gradient or volts per unit length.

Drift velocity - The average rate at which electrons or other charge carriers move through a material under the influence of an electric or magnetic field.

Mobility - The ease with which a charge carrier moves through a material.

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Terminology

When a current flows through a conductor

the electric field causes the charges to move

with a constant drift speed . This drift speed

is superimposed on the random motion of the

charges.

dv

Drift Speed

dJ nevdJ nv e

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I = nvAe

nveA

nvAe

A

IJ~

E

env

E

J~

E

v

= en 21

Electrical Conductivity

Electron Mobility

dJ nev

J E

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Some Useful Relationships, constants and units

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Source of Electrical Conductivity

(a) Charge carriers, such as electrons, are deflected by atoms or defects and take an irregular path through a conductor. The average rate at which the carriers move is the drift velocity v.

(b) Valence electrons in the metallic bond move easily.

(c) Covalent bonds must be broken in semiconductors and insulators for an electron to be able to move.

(d) Entire ions must diffuse to carry charge in many ionically bonded materials.

Mean free path – The average distance that electrons can move without being scattered by other atoms.24

Example 2- Drift Velocity of Electrons in Copper

Assuming that all of the valence electrons contribute to current flow, (a) calculate the mobility of an electron in copper and (b) calculate the average drift velocity for electrons in a 100-cm copper wire when 10 V are applied.

lattice parameter of copper is 3.6151 x 10-8 cm

Electrical conductivity of copper is 5.98x105

Example 2 SOLUTION

1. The valence of copper is one: therefore, the number of valence electrons equals the number of copper atoms in the material. The lattice parameter of copper is 3.6151 10-8 cm and, since copper is FCC, there are 4 atoms/unit cell.

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Example 2 SOLUTION (Continued)

2.The electric field is:

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Electron Energy Band Structures Electrons occupy energy states in atomic orbitals

When several atoms are brought close to each other in a solid these energy states split in to a series of energy states (molecular orbitals).

The spacing between these states are so small that they overlap to form an energy band.

Energy levels of Molecule

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Energy Band Structures in Solids

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under

license.29

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Electron Energy Band Structures

Adapted from Fig. 18.2, Callister & Rethwisch 8e.

Schematic plot of electron energy versus interatomic separation for an aggregate of

12 atoms (N=12). Upon close approach, each of the 1s and 2s atomic states splits to

form an electron energy band consisting of 12 states.31

Energy Band Structures in Solids

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Energy Band Structures in Solids

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Band Structure Representation Valence band - The energy levels filled by electrons in their lowest

energy states.

Conduction band - The unfilled energy levels into which electrons can be excited to provide conductivity.

Energy gap (Bandgap) - The energy between the top of the valence band and the bottom of the conduction band that a charge carrier must obtain before it can transfer a charge.

Adapted from Fig. 18.3,

Callister & Rethwisch 8e.34

Band Theory The furthest band from the nucleus is filled with valence electrons

and is called the valence band.

The empty band is called the conduction band.

The energy of the highest filled state is called Fermi energy.

There is a certain energy gap, called band gap, between valence and conduction bands.

Primarily four types of band structure exist in solids.

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(Cu)

(Mg) 1s22s22p63s2

Band Theory In metals the valence band is either partially filled (Cu)

or the valence and conduction bands overlap (Mg).

Insulators and semiconductors have completely filled valence band and empty conduction band.

It is the magnitude of band gap which separates metals, semiconductors and insulators in terms of their electrical conductivity.

The band gap is relatively smaller in semiconductors while it is very large in insulators.

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Energy Bands of An Insulator

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(> 2 eV)

©2003 Brooks/Cole, a division of Thomson Learning, Inc.

Thomson Learning™ is a trademark used herein under license.38

2 eV 2 eV

39

Conduction & Electron Transport

• Metals (Conductors):-- for metals empty energy states are adjacent to filled states.

-- two types of band structures for metals

-- thermal energy excites electrons into empty higher energy states.

- partially filled band

- empty band that overlaps filled band

filled band

Energy

partly filled band

empty band

GAP

filled s

tate

s

Partially filled band

Energy

filled band

filled band

empty band

filled s

tate

s

Overlapping bands

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Energy Band Structures: Insulators & Semiconductors

• Insulators:-- wide band gap (> 2 eV)-- few electrons excited

across band gap

Energy

filled band

filled valence band

fille

d s

tate

s

GAP

empty

bandconduction

• Semiconductors:-- narrow band gap (< 2 eV)-- more electrons excited

across band gap

Energy

filled band

filled valence band

filled s

tate

s

GAP?

empty

bandconduction

Conduction Mechanism

An electron has to be excited from the filled to the empty states above Fermi level (Ef) for it to become free and a charge carrier.

In metals large number of free valence electrons are available and they can be easily excited to the empty states due to their band structure.

On the other hand a large excitation energy is needed to excite electrons in Insulators and semiconductors due the large band gap.

Conduction in Metals 41

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Charge Carriers in Insulators and Semiconductors

Two types of electronic charge carriers:

Free Electron

– negative charge

– in conduction band

Hole

– positive charge– vacant electron state in

the valence band

Adapted from Fig. 18.6(b),

Callister & Rethwisch 8e. Move at different speeds - drift velocities

Holes are in the valence band.

Conduction electrons are in the conduction band.

Holes - Unfilled energy levels in the valence band. Because electrons move to fill these holes, the holes move and produce a current.

Quiz

1. What is Ohm’s Law?

2. What is resistivity?

3. Briefly explain the band theory of electrical conduction.

4. What is Fermi energy?

5. Why are metals highly conductive?

6. Briefly explain the conduction mechanism in metals?

7. What is the difference between band structure of Cu and Mg?

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