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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
1
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.
2
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.
3
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
.
4
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%)
5
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
8
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
14
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.
15
Electrical Properties
AR
A
1R
Electrical resistance
where σ is the electrical conductivity
I
VR
/V
I/A
V
I
A
/V
J~
16
17
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
20
I = nvAe
nveA
nvAe
A
IJ~
E
env
E
J~
E
v
= en 21
Electrical Conductivity
Electron Mobility
dJ nev
J E
22
Some Useful Relationships, constants and units
23
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.
25
Example 2 SOLUTION (Continued)
2.The electric field is:
26
27
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
28
Energy Band Structures in Solids
©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under
license.29
30
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
32
Energy Band Structures in Solids
33
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.
35
(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.
36
Energy Bands of An Insulator
37
(> 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
40
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
42
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?
43
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