4th Edition 2011
EEE 2203 Material Science II
`Z
ETI 2104 /EEE 2203 MATERIAL SCIENCE (II)
COURSE OUTLINE
Electrical properties: Conductors, insulators, super-ionic conductors. Semi-conduction in amorphous
material. Dielectrics, ferroelectrics, piezoelectrics, pyroelectrics, thermoelectric materials, magnetic
electrics, electro-striction.
Magnetic properties: Ferro and ferrimagnetism metals, alloys, ceramics and amorphous materials.
Paramagnetism. Domain theory. Remanence, coercivity, permeability. Support materials
Encapsulating materials, protective coating, tubing and sleeving materials. Adhesive materials.
Insulating materials. Plating circuit boards materials metalized ceramics. Etching and cleaning.
Stability of materials.
Course Outline in Point Form
1.
Electrical Properties of Materials: conductors, insulators, semi-conductors super-ionic and
superconductor materials.
2.
Dielectrics (special insulators) Materials: piezoelectric, pyroelectrics, ferroelectrics,
thermoelectric and magneto electric materials.
3.
Magnetic properties of Materials: ferromagnetic, Ferrimagnetic and Paramagnetic. Metal
alloys, ceramics and amorphous materials. Domain theory, Remanence, coercivity and
permeability.
4.
General Insulators: Support and Encapsulating Materials, Protective Coating, Tubing and
Sleeving Materials.
5.
Adhesives Materials, Plating Circuits Boards (PCBs) materials, metalized ceramics, Etching
and cleaning.
6.
Stability of Materials (electrical stability, mechanical stability, chemical stability and thermal
stability).
1.1.1 Examsfsemi
·
2 CATS [10 marks]
·
2 Assignment [5 marks]
·
2 LABs [15 marks]
·
Main Exam [70 marks]
-1-
4th Edition 2011
EEE 2203 Material Science II
Course objectives
At the end of the course;
·
The students must be able to distinguish clearly the difference between an electrical conductor,
an electrical insulator and an electrical semi-conductor.
·
The student should be able to tell and explain the various applications of electrical conductors,
electrical insulators, electrical semi-conductors, super ionic and super conducting materials.
·
The student should be able to elucidate the various dielectric materials and their practical
engineering application especially in the field of transducers or sensors.
·
The student should be able to elaborate what causes magnetism in magnetic materials and the
various applications of these magnetic materials in real life engineering.
·
The student should appreciate the materials used for electronic support structures such as
PCBs and encapsulating materials for diodes and transistors in the electronic manufacturing
industries.
Reference Books
Ø Material Science 4th edition by J.C. Anderson, K.D. Leaver and et al
Chapman and Hall publishers.
ISBN
0412341506
Ø The Science and Engineering of Materials 2nd SI Edition by Donald R. Askeland
Chapman and Hall Publishers.
ISBN 0421-34260X
Ø Physical Properties of Materials by M.C.Lovell, A.J Avery and M.W Vernon
Publisher Van Nostrand Reinhold Company.
ISBN
0442-30096-4
Ø An Introduction to Electrical Engineering Materials by C.S Indulkar and S. Thiruvengadam
ISBN 81-219-0666-0
Ø Principles of Material Science and Engineering 2nd Edition (1990) by William F. Smith,
publisher McGraw-Hill publisher Co. ISBN 0-07-059169-5,
Ø Electronic Materials (inside electronic devices) 2nd Edition (2000) by Nicholas Braithwaite &
Graham Weaver, publisher Butterworth Heineman, ISBN 0-7506-4387-0
Ø Milton Ohring (1995), Engineering materials science, Academic Press, illustrated Ed.
References
1. William F. Hosford (2007), Materials science: an intermediate text, Cambridge University Press,
illustrated Ed.
2. Eugene A. Irene (2005), Electronic Materials Science: Fundamentals, Wiley-Interscience,
illustrated Ed.
Ø And any other
-2-
4th Edition 2011
1.0.
EEE 2203 Material Science II
Electrical properties of conductors, insulators, semi conductors, super ionic and
superconducting materials.
1.1
Introduction.
Recall from physical chemistry the electronic shell arrangement of electrons in an atom can
be said to have four levels; these are n, l , ml and ms
(i).
The principal Quantum numbers n = 1, 2, 3, 4...... which is identified by the letters K, L, M,
N…. respectively. The maximum number of electrons contained in these quantum numbers
are 2, 8, 18…, respectively and in general this is given by ( 2n 2 ). This gives us the orbit
(distance) of an electron from the nucleus and it defines the total energy of an electron in a
particular state.
(ii).
The subsidiary quantum number which is a measure of the eccentricity (shape) of the electron
orbits or waves. This quantum number is designated as l = 0, 1, 2, 3..... ( n - 1) which is
identified by the letters s, p, d, f… respectively. The numbers of electrons that can be
contained in s, p, d, f states are 2, 6, 10, and 14 respectively and in general 2 ( 2l + 1) . The
l = 0 states are all seen to be perfectly spherical in shape, while the others are quite
asymmetrical. It is also associated with the angular momentum of an electron which itself is
quantized.
(iii).
The magnetic orbital quantum number which is associated with the rotation (clockwise or
anticlockwise motion) of the electron about the nucleus. It is associated with the fact that an
electron in an orbital constitutes a rotating charge and hence an electric current which has
associated magnetic field and magnetic moment. This is denoted by ml = 0,... ± l . Example
when l = p (1) , ml = 0, ± 1 , which corresponds to 6 electronic states.
(iv).
The spin quantum number ( ms ) which is associated with the spin of electrons about their own
æ1ö
axis. It gives the direction of electron spin; this can be ± 1 . Spin up ç ÷ or spin
2
è2ø
æ 1ö
down ç - ÷ .
è 2ø
Important note; the Pauli’s Exclusion Principle; which states that ‘no two electrons in an
atomic system can have the same set of four quantum numbers n, l , ml and ms that is; no two
electrons can occupy the same quantum state. The periodic table of elements may be explained by
Pauli’s Exclusion Principle.
-3-
4th Edition 2011
EEE 2203 Material Science II
Table 1.1: Electron arrangement in shells and subshells
Shell
K
n
1
Subshell
s s
0 0
l
ml
0 0
No. of states
2 2
No. of electrons 2
L
2
p
s
1
0
0, ± 1 0
6
2
8
M
3
p
1
0, ± 1
6
N
4
d
2
0, ± 1, ± 2
10
18
s
0
0
2
p
1
0, ± 1
6
d
2
0, ± 1, ± 2
10
32
f
3
0, ± 1, ± 2, ± 3
14
./
Examples of electronic configuration of some elements are given in table 1.2.
Table 1.2: electronic configuration of some elements
Element Electronic Arrangement
H
1S 1
Li
1S 2 2 S 1
Be
1S 2 2 S 2
Atomic Number of the Element
1
3
C
1S 2 2S 2 2 P 2
6
O
1S 2 2S 2 2 P 4
8
F
1S 2 2 S 2 2 P 5
9
Na
1S 2 2 S 2 2 P 6 3S 1
11
Si
1S 2 2 S 2 2 P 6 3S 2 3P 2
14
S
1S 2 2 S 2 2 P 6 3S 2 3P 4
16
4
Exercise
Write the electronic configuration of the following elements;
-
Ge atomic number 32
-
Mn atomic number 25
-
Pb atomic number 82
-
Mg atomic number 12
-
P atomic number 15
-
Ni atomic number 28
-
Cr atomic number 24
-
Cu atomic number 29
-
Al atomic number 13
-4-
4th Edition 2011
1.2.
EEE 2203 Material Science II
The energy band Theory: Valence and Conduction Bands
The outermost electrons of an atom; that is those in the shell farthermost from the nucleus are
called valence electrons and have the highest energy. It is these electrons which are most affected
when a number of atoms are brought very close together as during the formation of a solid. The
valence electrons are the ones actually used for bonding. The states of lower-energy electrons
orbiting in shells nearer to the nucleus are little, if at all, affected by this atomic proximity.
The band of energy occupied by the valence electrons is called the valence band and is
obviously the highest occupied band. It may be completely filled or partially filled with electrons, but
can obviously be never empty. The next higher permitted energy band is called the conduction band
and may either be empty or partially filled with electrons. In fact it may be defined as the lowest
unfilled energy band.
In the conduction band, electrons can move freely and hence are known as conduction
electrons. Heat and electric current conduction electrons reside in this band. The electrical behavior
of conductors, insulators and semiconductors can be explained with the help of an energy band
structure diagrams as shown in fig. 1.1.
conduction band
free
electrons
EG @ 6eV
conduction
band
EG @ 1eV
forbidden
energy
gap
valence
band
EG
holes
valence band
(a) an insulator
(b) a semiconductor
(c) a conductor
Fig. 1.1 Energy band structure of (a) an insulator (b) a semiconductor and (c) a conductor.
The range of energies which are prohibited to the electrons is called the forbidden energy gap,
often just the energy gap and is a direct measure of the amount of energy an electron needs to leave
the bonds. It is different for different materials as we shall see shortly. Application of an electrical
field to a material tends to excite valence electrons to higher energy states. The extent to which these
electrons may be excited distinguishes whether the material is a conductor, semiconductor or
insulator. To achieve electronic conduction, there must be empty energy states into which electrons
can be excited.
-5-
4th Edition 2011
1.2.1
EEE 2203 Material Science II
An insulator
This is a material with an extremely poor electrical conductivity. This is because the
conduction band is empty and the energy required to excite the electrons from valence band to
conduction is very high approximately 6eV for diamond at 00 Kelvin. This energy cannot be applied
to the material without breakdown or destruction. Hence electrical conduction is impossible.
In terms of energy bands, it means that insulators;
-have a full valence band
-have an empty conduction band
-and they have a large energy gap of several eV between valence and conduction bands.
1.2.2. A conductor
A conductor of electricity is a material with an overlapping valence and conduction bands.
The degree of overlap varies among metals with silver having the largest area of overlap. This makes
it the best metallic conductor of electricity and heat. The surface area of overlap is directly
proportional to the electron mobility. The larger is the surface area the higher the electron mobility
and vice versa.
Therefore, there is no energy gap between the valence and conduction bands in conductors.
Hence on application of an electric field the electrons may acquire additional energy and move into
higher energy states. Clearly, electrons in the conduction band can accelerate readily because empty,
higher energy levels are available to accommodate them. Thus mobility of electrons is possible. Since
mobile electrons constitute an electric current this material forms a good electrical and thermal
conductor.
In terms of energy bands a conductor, is a material;
- With no physical distinction between the two bands and hence the availability of a large number
of conduction electrons.
- That has no forbidden energy band or gap therefore does not offer a structure to establish holes.
The total current in such conductors is simply a flow of electrons. It is for this reasons that the
existence of holes was not discovered until semi-conductors were studied thoroughly.
1.2.3
Semi-conductors
This is a material whose electrical properties are in between those of insulators and good
conductors. Examples are Germanium (Ge), and Silicon (Si). The semiconductors have a small
forbidden energy gap as shown in fig 1.1 (b) typically of 1eV . This makes it possible for application
of a small thermal energy or electric field to promote electrons from valence band to conduction
band. Germanium has EG of 0.785 eV and Silicon has EG of 1.21 eV at 0 Kelvin.
-6-
4th Edition 2011
EEE 2203 Material Science II
Additional energies equal to these values of EG can’t ordinarily be obtained from applied
fields. Hence these materials in pure or intrinsic form behave as insulators at low temperatures. In
fact intrinsic semiconductors are perfect electrical insulators at absolute zero temperature. However
the conductivity increases with the increase in temperature. A pure semiconductor has poor
conductivity and is not of much use in formation of semiconductor devices. The conductivity of a
semiconductor may be greatly increased by adding a very small amount of impurity to the otherwise
pure semiconductor. The process is known as doping and consists of adding impurity atoms of either
trivalent or pentavalent materials to pure germanium or silicon. As a result allowable energy states
appear in the forbidden energy gap. These impurity levels also contribute to the electric current
conduction.
Impurities are introduced by substituting them for atoms of the host intrinsic semiconductor.
This may be done either by diffusing in foreign atoms or by introducing them during crystal growth.
If, as is usual, the valency of an impurity differs from the host, then it may have one more or less
electron to participate in bonding. If one more, the excess electron is relatively weakly bound to the
parent atom, because polarization effects screen it from the normal binding force of its parent. This
effect is represented by the relative permittivity of the medium. The binding energy of the carrier is
reduced by the factor 1
( e 0e r )
2
.
The ionization energy thus becomes extremely small; a typical value of e r is 12 for
germanium and the ionization energy for impurity atom of arsenic is 0.01eV. This atom is therefore,
ionized at quite low temperatures and at room temperature most arsenic atoms present as impurities
would be ionized.
1.2.4
Super ionic
These are materials formed by combining atoms of two or more types of elements differing
considerably in their tendencies to give off or accept electrons. They are non conductors of current in
their solid form. This is so since there is no free electron or ions to conduct.
However, when dissolved in a liquid like water, the super ionic crystals dissociate into cations
and anions and hence become an electrolyte. The movement of these ions in aqueous solution
constitutes moving charges and hence electric current. Examples of such compounds are; NaCl, KF,
CaCl2 , and HF .
The electrolyte can be strong, moderate or weak depending on the concentration of the ions in
the solution which in turn is a function of the degree of dissociation of the substance in aqueous
-7-
4th Edition 2011
EEE 2203 Material Science II
solution. Example sodium chloride is a strong electrolyte because it completely dissociate into ions in
water, however, ethanoic acid is a weak electrolyte because it only partially dissociate into ions.
1.2.5. Superconductors
A large number of metals become superconducting below a temperature near absolute zero
which is a characteristic of the particular metal. Superconducting compounds and alloys are not
necessarily formed from superconducting elements. A number of superconducting elements and
compounds are listed in table 1.3 together with their transition temperatures.
The resistivity r of a superconductor is zero. At the same time it has been observed that the
magnetic flux density B through such a substance also vanishes. It is possible to destroy
superconductivity by the application of a strong magnetic field. When the magnetic field exceeds a
certain critical value, the superconducting state disappears, the magnetic field penetrates the material
and electrical resistance is restored. A superconductor ring has a critical value of current I = 2p rH c
above which the material becomes normal. The transition temperature of a superconductor is reduced
when magnetic field is applied. A definite relationship exists between the superconducting
temperature and the magnetic field.
Table 1.3 superconducting elements and compounds
Metal Transition temperature Compounds
in degrees Kelvin
Transition temperatures in
degrees Kelvin
Al
1.14
Pb2 Au
7.0
Zn
0.786
SnSb
3.9
Sn
3.72
50% Nb - 50%Ti
8
Pb
7.26
60% Nb - 40% Zr
11
V
5
V3 Si
17
Nb
9
Nb3 Sn
18
Strontium Titanate
0.3
Barium Lead Bismuth Oxide
14
Lanthanum Barium Copper Oxide 35
In summary there are three quantities which have to be below a critical value for the material
in order for the superconducting state to exist. They are;
-8-
4th Edition 2011
EEE 2203 Material Science II
(a).
the temperature of the material (T < Tc )
(b).
the current density in the material ( I < I c )
(c).
the magnetic field around the material ( B < Bc )
If any of these criteria is not met, then the material won’t be superconducting. Consequently,
superconducting disappears;
§
If the temperature of the material is raised above critical temperature Tc
§
If a sufficiently strong magnetic field H c is applied around the material
§
When a high current density J c prevails in the conductor
Superconductivity is also sensitive to pressure, mechanical stresses and variations in internal structure
like whether the metal is cold worked or re-crystallized.
1.2.5.1.
(i).
Applications of Superconductors
Generation of high magnetic fields using superconducting solenoids, for example in magnetic
resonance imaging (MRI)
(ii).
High resolution detectors of magnetic flux using superconducting quantum interference
device magnetometers (SQUIDs)
(iii).
Small, low power electric devices based mostly on the Josephson effect like optical detectors,
high speed digital logic devices and circuits, radio frequency and microwaves devices
example millimeter wave detectors and mixers.
1.3.
Electrical conductivity of materials
The electrical conductivity of a material is the amount of electric charge transferred per unit
time
dq
dV
across unit cross sectional area A under the action of unit potential gradient
.
dt
dx
æ dq ö
ç ÷
s = è dt ø
dq
Where J =
æ dV ö
Aç
÷
è dx ø
=
J
E
(1.1)
dt equals to the current density and E equals the potential gradient E = dV or the
A
dx
electric field.
-9-
4th Edition 2011
EEE 2203 Material Science II
The electrical conductivities of materials exhibit probably the widest range of variation of all
materials properties. Ranging from Sulphur 5 ´10-16 W -1m -1 to silver 63 ´106 W -1m -1 which is of the
order 23.
The charge mobility m is defined as the velocity ( v ) in unit electric field. Mathematically:
m=
v 2 -1 -1
mV s
E
(1.2)
rl
W
A
(1.3)
The resistance ( R ) of a material is given by
R=
Where r is the resistivity in W - m and l is the length in m of the material.
Electrons can move through an ideal metallic crystal without resistance but in actual crystals,
electrons collide with ‘phonon’ (a quantum of energy of elastic waves of vibrating atoms or
electrons), dislocations, vacancies, impurity atoms and other lattice imperfections. Residual
resistivity due to solute atoms, impurities and dislocations is usually independent of temperature.
Total resistivity is the sum of residual and thermal contributions as per Matthiessen’s rule.
Increasing temperature introduces thermal vibrations which impair lattice periodicity and thus impede
movement of electrons.
Let the number of charge carriers be n per unit volume, e be the basic electric charge and v be drift
velocity. Then,
J = nev
(1.4)
J = nem E
(1.5)
s = nem
(1.6)
Putting equation (1.2) into (1.4),
Thus;
Equation (1.6) is of fundamental importance. The electrical conductivity depends on two
factors the number ( n ) of charge carriers per unit volume and their mobility ( m ) . The way in which
these two quantities vary particularly with temperature provides the key to the understanding of
electrical properties of materials.
For example, in a metal n is constant and m varies relatively slowly with temperature (T). In
semiconductors the exponential dependence of n on temperature is of primary importance while in
some insulators it is the exponential dependence of m on temperature that is significant while n is
constant.
- 10 -
4th Edition 2011
1.3.1
EEE 2203 Material Science II
Electrical conductivity of metals
One essential feature which distinguishes metallic behavior is that the d.c electrical
conductivity tends to a constant value as absolute temperature is approached T ® 0 . That is, there
are no temperature induced effects necessary for metallic conduction. In alternating current circuits,
the electrical conductivity is a function of frequency as well. At higher frequencies, the current tend
to flow closer to the surface of the conductor thus reducing the cross-sectional area for current
conduction. This is known as the skin effect. This leads to increase in resistance as per equation (1.3).
For metals the electrical conductivity is given by;
s=
1
e2 nt -1 -1
= nem =
W m
r
me
(1.7)
Where me is the mass of an electron, e electronic charge, n the number of conduction electrons per
unit volume. t is the mean free time between collisions which is about 10-14 sec for most metals.
From the equation (1.7), the two quantities which determine the resistivity are therefore, the
electron density n , and the mean free time between electron collisions t . Since the electron density
cannot vary with temperature, the whole of the temperature dependence of resistivity must be due to
changes in t .
The mobility of electrons in metals is given by;
m=
et
me
(1.8)
The drift velocity of electrons is given by;
eEt
(1.9)
me
Thus the current density in metals is gives by the following expression\
ne2 Et
J = nev =
(1.10)
me
Note that conduction in pure metals is due to electron flow only. Since the current I = JA where A is
v=
the cross sectional area of the conductor, then
I = nem EA
The three main causes of resistivity in metals are;
§
Increase in temperature: as temperature goes up, the amplitude of the atomic vibrations
increases, the deviations from lattice periodicity is enhanced, thus scattering by lattice
vibrations increases and mean free paths decreases resulting to increase in resistivity.
§
Chemical impurities
§
Imperfections in the metal lattice e.g. dislocations
- 11 -
(1.11)
4th Edition 2011
1.3.2
EEE 2203 Material Science II
Thermal conductivity as related to electrical conductivity
The electrical conductivity of a metal is given by equation (1.7). The thermal conductivity of a metal
is given by;
1 np 2 k 2Tt
(1.12)
3 me
On combining (by dividing) equations (1.7) and (1.12), we have;
K p 2k 2
(1.13)
=
T
s
3e2
Or
K p 2k 2
(1.14)
=
ºL
sT
3e2
Equation (1.14) predicts that for all metals, the ratio K
should be a universal constant. This law is
sT
called Wiedemann-Franz law. The constant is called the Lorenz number and is equal to
2.45 ´10-8 W - W - deg 2 watt- ohm- degree squared.
K=
Exercise
Question one
State two factors which determine the electrical conductivity of a material and hence discuss how
these factors are influenced by temperature to affect the electrical conductivity behavior of;
(i).
super ionic materials [2 marks]
(ii).
Metals [2 marks]
(iii).
Insulators [2 marks]
(iv).
Semiconductors [2 marks]
Question two
(i).
Define clearly from first principles what is electrical conductivity; give its formula and units
[3 marks]
(ii).
Explain why heat and current conduction electrons are only available in the conduction band
whereas bonding electrons reside in the valence band. [3 marks]
(iii).
Holes positively charged charge carriers cannot exist in the conduction band of an element
like silicon. Justify this statement. [3 marks]
(iv).
The density of copper is 8.93 ´103 kg / m3 . Calculate the number of free electrons per cubic
meter and hence their drift velocity when a current is flowing whose density is 1A / cm 2 .
1.3.3
Electrical conductivity in semiconductor
The electrical properties of semi conductors are determined by;
Ø the existence of a gap in the energy states, and
- 12 -
4th Edition 2011
EEE 2203 Material Science II
Ø the presence of impurities and other crystal defects or imperfections.
Ø temperature
Two kinds of carriers of electricity are involved in a semiconductor; that is electrons in the
conduction band and holes in the valence band. It is the possibility that these two current carriers; one
is negatively charged and the other positively charged, can exist simultaneously in a crystal and
behaves almost independently that gives rise to the interesting properties of semiconductors.
It follows that it is possible to modulate the bulk conductivity of semiconductors by changing
the concentration of electrons or holes while still maintaining charge neutrality. When a voltage is
applied to such an intrinsic semiconductor a current flows which is due the motion of holes and
electrons. The drift velocities of the two types of carriers in the electric field are different because of
their differing effective masses.
The current density J in electric field E may be written as;
J = neme E + pem h E
(1.15)
Where n and p are the electron and hole densities (numbers per unit volume) respectively,
me and mh their respective mobilities, that is drift velocities in unit electric field and e the electronic
charge. In an intrinsic semiconductor the concentration of holes is equal to the concentration of
electrons since each electron excited into the conduction band creates hole in the valence band.
The number n depends on the temperature, size of energy gap, the density of states and the
position of the Fermi level. (Fermi level is defined as the highest occupied molecular orbital in the
valence band at 0K so that there are many states available to accept electrons. Note that in
semiconductors, the position of the Fermi level relative to the band structure determines both the
density of electrons and holes. Fermi level in conductors lies in the conduction band, in insulators it
lies in the valence band and in semiconductors it falls in the gap between the conduction band and
valence band.
In an intrinsic semiconductor the Fermi level lies half away between the top of the valence
band and the bottom of the conduction band. The formula for the electron population density is;
3
æ Eg ö
æ 2p me kT ö 2 -ççè 2 kT ÷÷ø
n = 2ç
÷ e
2
è h
ø
Where;
me is the electron effective mass @ 9.1´ 10-31 kg
E g is the energy gap width in J
- 13 -
(1.16)
4th Edition 2011
EEE 2203 Material Science II
k is the Boltzmann constant 1.38 ´10-23 JK -1
T is the temperature in Kelvin
h is the Planck constant 6.62 ´ 10-34 Js
Equation (1.16) shows that the number of carriers and hence the conductivity increases rapidly with
temperature in contrast to metallic behavior. The simple rule which describes the statistical balance
between electrons and holes in extrinsic semiconductors at any given temperature is;
np = ni2
(1.17)
Where ni is electron or hole concentration in an intrinsic semiconductor at a given temperature, n is
electron concentration in an extrinsic semiconductor and p is the hole concentration in an extrinsic
semiconductor. The total current in a semiconductor is given by
I = I e + I p = J e A + J h A = ( nme + p mh ) eEA
(1.18)
Example 1
The electrical resistivity of pure silicon is 3.0 ´ 103 W - m at room temperature 270 C . The
conductivity is 2.67W -1m -1 at 2500 C . Estimate the size of the energy gap.
Solution
We know s = s 0e
-
Eg
2 kT
thus we have
E
s 3000
g
1
600 k
=
=
s
e
0
3 ´ 103
s 5230 = 2.67 = s 0e
-
(i)
Eg
1046 k
(ii)
[2 marks]
Dividing equation (i) by (ii)
- Eg
600 k
1
e
= - Eg
3 ´10 ´ 2.67
e1046 k
3
[2 marks]
Taking natural logarithm on both sides we have
1 ö
æ 1
- Eg ç
÷
è 300 523 ø , thus E = 1.735 ´ 10-19 Joules [2 marks]
-8.988 =
g
2 ´ 1.38 ´ 10-23
In terms of eV , Eg =
1.735 ´10-19
= 1.084eV » 1.1eV [2 marks]
1.6 ´10-19
- 14 -
4th Edition 2011
EEE 2203 Material Science II
Figure 1.2 (a) shows the variation of conductivity of an intrinsic semiconductor as a function
of temperature. This shows that as temperature increases above room temperature valence electrons
breaks from the covalent bonds due to thermal agitation to conduction band. This increases the
number of charge carriers in the conduction band (electrons) as well as in the valence band (holes).
Hence when all the valence electrons are promoted to conduction band, the conductivity saturates.
saturation
conductivity
s
300K
temperature
T K
Fig. 1.2 (a) Conductivity as a function of temperature for an intrinsic semiconductor.
As the figure 1.2 (b) shows at low temperature, the conductivity in extrinsic semiconductor is
contributed by the impurity atoms (electrons or holes) until saturation is attained. Above this point,
conductivity is enhanced by electrons and holes created due to thermal agitation which makes
electrons to break from the covalent bonds to conduction band, leaving behind holes also available
for conduction.
excitation across
main energy gap
(intrinsic)
conductivity
s
all
impurities
ionized
(saturation)
impurity
excitation
(extrinnsic)
0K
300K
temperature
T K
Fig 1.2 (b) Variation of conductivity of an extrinsic semiconductor with temperature.
- 15 -
4th Edition 2011
EEE 2203 Material Science II
Example 2. A conductor
A uniform copper wire has resistivity of 1.6 ´10-6 W - cm at room temperature. An electric field of
2V/m is applied along the length of the wire. If the number of conduction electrons is 5.6 ´1028 / m3 .
Calculate the electron mobility, drift velocity of electrons and their relaxation time.
Solution
The current density in a conductor is given by
J=
E
= nev
r
Then, v =
E
2
=
m / sec = 1.38 ´10-2 m / sec
28
-19
-8
ner 5.6 ´10 ´ 1.6 ´ 10 ´1.6 ´ 10
Mobility equals the drift velocity per unit electric field. Hence m =
the relaxation time is given by t =
v 1.385
=
= 6.925 ´10-3 m 2 / V - S
E
200
me m 9.1´ 10-31
=
´ 6.925 ´ 10-3 sec = 3.91´10-14 sec
e
1.61´10-19
Example 3. An intrinsic semiconductor
The resistivity of intrinsic germanium at 300 C is 0.46 W - m . Calculate the intrinsic carrier
density n at 300 C . Given that the electron mobility me is 0.38m 2 / V - s and the hole mobility
mh is 0.18m 2 / V - s
Solution
s=
1 -1 -1
W m = ne ( me + mh )
r
Therefore; n =
s
1
1
1019
=
´
=
= 2.42 ´1019 / m3
e ( m e + m h ) 0.46 1.6 ´10-19 ( 0.38 + 0.18 ) 0.46 ´1.6 ( 0.56 )
Example 4: An extrinsic semiconductor
(i).
Find the conductivity of intrinsic silicon at 300K. Given that;
·
ni at 300K is 1.5 ´ 1010 / cm3 ,
·
the mobility of electrons and holes in silicon are 1300 cm 2 / V - s and 500 cm 2 / V - s
respectively and
·
the number of Si atoms per cubic cm equals 5 ´1022 .
- 16 -
4th Edition 2011
(ii).
EEE 2203 Material Science II
If donor type impurity is added to the extent of one atom per 108 silicon atoms, find the
conductivity.
(iii).
If acceptor type impurity is added to the extent of one impurity atom per 108 silicon atoms,
find the conductivity.
Solution
(i).
n = p = ni
s = ni e ( mh + me ) = 1.5 ´1010 ´ 1.6 ´10-19 ( 500 + 1300 ) = 4.32 ´10-6 W-1 - cm -1
(ii).
If there is 1 donor atom in 108 silicon atoms, then N D =
5 ´ 1022
= 5 ´1014 atoms / cm3
108
10
ni2 (1.5 ´10 )
Further, n » N D . Hence p =
=
= 4.5 ´105 holes / cm3
14
ND
5 ´10
Since n ? p , we may neglect p in calculating the conductivity. Thus
s = neme = 5 ´1014 ´1.6 ´10-19 ´1300 = 0.104W -1 - cm -1
2
(iii).
With 1 acceptor atom per 108 silicon atoms, N A =
5 ´1022
= 5 ´ 1014 atoms / cm3
108
10
n 2 (1.5 ´10 )
Further, p » N A . Hence n = i =
= 4.5 ´ 105 electrons / cm3
14
ND
5 ´10
Since p ? n , we may neglect n in calculating the conductivity. Thus
2
s = pemh = 5 ´ 1014 ´1.6 ´10-19 ´ 500 = 0.04W -1 - cm-1
Example 5: An extrinsic semiconductor
(i).
Find the resistivity of intrinsic germanium at 300K. Given that;
·
ni at 300K is 2.5 ´1013 / cm3 .
·
the mobility of electrons and holes in germanium are 3800 cm 2 / V - s and 1800
cm 2 / V - s respectively and
·
the number of Ge atoms per cubic cm equals 4.41´1022 . [2 marks]
Solution
r=
=
1
1
1
=
=
-19
s eni ( me + mh ) 1.6 ´10 ´ 2.5 ´ 1013 ( 3800 + 1800 )
[1 mark]
1
1
=
= 44.64W - cm [1 mark]
-4
1.6 ´ 2.5 ´ 5.6 ´10
2.24 ´10-2
(ii).
If donor impurity is added to the extent of one atom per 5 ´107 germanium atoms, find the
resistivity. [2 marks]
- 17 -
4th Edition 2011
EEE 2203 Material Science II
Solution
Number of donor atoms=
4.41´1022
= 8.82 ´1014 atoms / cm3 or electrons / cm3 [0.5 mark]
7
5 ´10
N D ; ne = 8.82 ´1014 electrons / cm3
13
ni2 ( 2.5 ´10 )
number of holes nh =
=
= 7.086 ´ 1011 holes / cm3 [0.5 mark]
14
ne
8.82 ´10
2
s = e ( me ne + m h nh ) = 1.6 ´10-19 ( 8.82 ´1014 ´ 3800 + 7.086 ´1011 ´1800 )
= 1.6 ´10-19 ( 3.3516 ´1018 + 1.27548 ´1015 ) = 1.6 ´104 ( 3351.6 + 1.27548 )
= 0.53646W -1 - cm -1 Therefore, r =
(iii).
1
1
=
= 1.864W - cm [1 mark]
s 0.53646
If acceptor impurity is added to the extent of one impurity atom per 2 ´107 germanium atoms,
find the resistivity. [2 marks]
Solution
4.41´1022
Number of acceptor atoms N A =
= 2.205 ´ 1015 atoms / cm3 [0.5 marks]
7
2 ´ 10
nh ; N A = 2.205 ´ 1015 holes / cm3
13
ni2 ( 2.5 ´10 )
ne =
=
= 2.834 ´1011 electrons / cm3 [0.5 mark]
nh 2.205 ´1015
2
s = e ( me ne + m h nh ) = 1.6 ´ 10-19 ( 3800 ´ 2.834 ´1011 + 1800 ´ 2.205 ´ 1015 )
= 1.6 ´10-6 (10.7692 + 396900 ) = 1.6 ´ 3.969 ´10-1 = 0.63506W -1 - cm -1
Hence, r =
1
1
=
= 1.575W - cm [1 mark]
s 0.63501
Example 6: A Conductor
The relaxation time of conduction electrons in a material is 4 ´10-14 sec. If the density of these
electrons is 5.4 ´ 1014 per cubic meter. Calculate the resistivity of the material and the mobility of the
electrons. [4 marks]
Answer
Given t = 4 ´10-14 sec, N = 5.4 ´1014 / m3
me
9.1´10-31
r= 2
=
= 1.65 ´ 106 W - m
2
19
14
14
e Nt (1.6 ´10 ) ´ 5.4 ´10 ´ 4 ´ 10
- 18 -
[2 mark]
4th Edition 2011
m=
EEE 2203 Material Science II
et 1.6 ´10-19 ´ 4 ´ 10-14
=
me
9.1´10-31
= 7.03 ´10-3 m 2 / V - s
[2 mark]
or
m=
1
1
=
= 7.01´ 10-3 m 2 / V - s
14
-19
6
Ner 5.4 ´ 10 ´1.6 ´10 ´1.65 ´10
Exercise
1.
Magnesium has one more electron than sodium, that is its 3S band is full. Explain why Mg is
also an electrical conductor. [2 marks]
2.
An intrinsic semiconductor has a conductivity of 390W -1m -1 at 50 C and 1010W -1m -1
at 250 C .
(i). What is the size of the energy gap in eV?
(ii). What is the conductivity at 150 C ? [10 marks]
3.
Explain what is a superconductor. State at least two practical applications of superconductors.
[4 marks]
4.
The electrical conductivity of Nickel decreases when a small amount of Copper is added. This
is despite the fact that copper has a superior current conductivity than Nickel. Explain why the
resistivity increases in the Nickel-Copper alloy. [3 marks].
5.
Discuss electric current semi-conduction in amorphous materials. [3 marks].
6.
(a).
Explain why a semi conductor exhibits a negative temperature coefficient of
resistivity. [2 marks]
(b).
Discus why silver is the best metallic conductor of electricity. [2 marks]
(c).
Explain how conductivity modulation in semiconductors is used in thermistors and
photoconductors. [4 mark]
7.
List four main causes of resistivity in metals. [4 marks]
8.
The resistivity of pure silicon is 2.3 ´103 W - m at 27 0 C . Find its conductivity at
2000 C. Assume that its Eg is is 1.1eV and k = 8.65 ´10-5 eV / K answer 1.04W -1 m -1 [5 marks]
Important; A law is a concise statement of experimental results. It need not include an explanation
of them. A hypothesis is an explanation of experimental findings by means of a concept or model. A
well established hypothesis is known as a theory.
- 19 -
4th Edition 2011
2.0.
EEE 2203 Material Science II
DIELECTRICS; Piezoelectrics, Pyroelectrics, Ferroelectrics, Magneto-electrics and
Thermal electrics.
2.1.
Introduction: Dielectrics
Dielectrics (special insulators) have no free charge carriers and act as insulators. These
materials have interesting electrical properties because of the ability of an electric field to polarize the
material to create electric dipoles. A dipole is an entity in which equal positive and negative charges
are separated by a small distance as shown in fig. 2.1, the electric dipole moment p being equal
to p = qr . An electric dipole moment is the strength of the electric field associated with the electric
dipole.
-q
+q
r
Fig 2.1 Separated charges forming an electric dipole.
Therefore, dielectrics are materials in which polarization effect are important. An electric
field produces electrical polarization within the material. Dielectrics materials are invariably
substances in which the electrons are localized in the process of bonding the atoms together. Thus
covalent or ionic bonds, or a mixture of both, or van de Waals bonding between closed-shell atoms
all give rise to solids (or gases) exhibiting dielectric (insulating) properties. The energy gap is so
large that, at ordinary temperatures, thermal energy is insufficient to raise electrons from the valence
to the conduction band, which is, therefore, empty of electrons. Consequently, there are no free
charge carriers and the application of an electric field will produce no current through the material.
2.1.1. Dielectric Properties
Consider two metal plates of area A separated in vacuum by a distance d and having a battery
of voltage V connected across the plates. The electric field E between the plates is directed as shown
and has a magnitude
V
q
Vm-1 arising from the charge density Dv = on the plates.
d
A
E
V
Fig 2.2 Capacitor with vacuum dielectric
- 20 -
d
4th Edition 2011
EEE 2203 Material Science II
The relationship between charge density or electric displacement ( Dv ) in vacuum or free space and
the electric field E is
Dv = e 0 E
(2.1)
Where e 0 = 8.854 ´10-12 F / m permittivity of vacuum, Dv electric flux density, charge
density or electric displacement in C / m2 in vacuum. The capacitance of this capacitor with a
vacuum dielectric is
Cv =
Qv Dv A e 0 A
=
=
V
Ed
d
(2.2)
original
charge
V
d
E
polarization
field
'extra' charge
attracted
by charge in
dielectric
Ep
Fig 2.3 Polarized dielectric in capacitor, with dipoles giving surface charge and extra charges
attracted on to plates.
If a dielectric medium is introduced so as to just fill the space between the plates, this medium
becomes polarized by the field E and dipoles appear throughout the material lined up in the direction
of the field. This increases the charge density D and hence the capacitance C of the capacitor. This
new value of capacitance is given by;
C=
Q DA e 0e r A
=
=
V Ed
d
(2.3)
Where
D = e 0e r E = e E , e =
er =
D
is the permittivity of the dielectric material and
E
e
the relative permittivity of the dielectric media.
e0
This capacitance of the capacitor has increased due to the accumulation of positive charges on
the positive plate and negative charges on the negative plate. The positive charge will be adjacent to
the negative capacitor plate and will neutralize some of the charge on it. Similarly the negative end of
the dipole chain will neutralize some of the charge on the positive capacitor plate. The surface charge
- 21 -
4th Edition 2011
EEE 2203 Material Science II
density will increase by a factor P where P is the polarization in the dielectric or electric dipole
moment per unit volume.
Polarization is defined as the increase in charge density above that of vacuum due to the
presence of dielectric. Alternatively, P is equal to the bound charge per unit area of the dielectric
surface and is measured in coulombs per square meter, the same units as the flux density D and is a
vector quantity.
Thus we may imagine the electric flux density in a dielectric to be due to two causes: the flux
density, which would be set up in the space occupied by the dielectric by an applied electric field, and
the polarization of the dielectric which results from the electric field. Thus we may write,
D = e0E + P
(2.4)
Since charge density has increased, the capacitance has also increased. Thus,
C
D e0E + P
=
=
=
Cv Dv
e0E
ö
e 0 E æç1 + P
÷
e
E
P
è
0 ø
= 1+
e0E
e0E
(2.5)
The ratio of polarization ( P ) to the charge density Dv of the capacitor with vacuum dielectric is
called electric susceptibility c . Thus
c=
P
electric strain bound ch arg e density
=
=
e 0 E electric stress
free ch arg e density
But D = e 0e r E = e 0 E + P , therefore, e 0e r E - e 0 E = P or e r - 1 =
(2.6)
P
=c
e0E
Hence
c = e r -1
(2.7)
Or
er = c +1
Dielectric polarization is a characteristic phenomenon of ‘some’ electrical insulators. It
appears whenever electric charges have reversible displacements relative to each other. Devices
based on this phenomenon include condensers, rectifiers, resonators, amplifiers, transducers, memory
devices for computers and many others.
There are two classes of dielectrics; polar and nonpolar. A nonpolar dielectric material is one
which has no dipoles when the material is not subjected to an electric field. This material can be
electronic and atomically or ionically polarized by electric field. A polar dielectric is a dielectric
which has dipoles in the absence of electric field. These materials or molecules are permanently
- 22 -
4th Edition 2011
EEE 2203 Material Science II
polarized. A water molecule for example has the structure shown in figure 2.4 and is a good example
of a polar dielectric. Polar materials undergo orientational polarization when an electric field is
applied as the dipoles tend to line up in the direction of the field.
O
1040
H
H
Fig. 2.4 spatial of a water molecule
Example 1
Polystyrene has a relative dielectric constant of 2.5. If it is used as a dielectric in a capacitor, having
its plates 0.5mm apart. What is the polarization produced in the polystyrene if a d.c voltage of 100V
is applied between the capacitor plates?
Solution
P = e 0 E ( e r - 1) = 8.854 ´10-12 ´
100
´ ( 2.5 - 1)
5 ´ 10-4
= 2.6562 ´10-6 C / m 2 » 2.7 ´10-6 C / m 2
Example 2
A capacitor with two parallel plates 1´ 2 cm each receives 2.25V between the plates. How far apart
must be the plates to produce a charge density of D = 10-7 C / m 2
Solution
D = e0E = e0
2.2.
V
V
2.25
, d = e 0 = 8.854 ´10-12 ´ -7 » 2 ´10-4 m = 0.20mm
d
D
10
Characteristics of Dielectric Materials
There are three important parameters that characterize any dielectric material. These are;
§
Dielectric constant
§
Dielectric strength
§
Dielectric loss
2.2.1. Dielectric constant e r
This is the permittivity of a material as compared to that of vacuum or free space.
It gives a measure of how easily electric flux lines can be set up in a dielectric material.
Mathematically;
er =
- 23 -
e
e0
(2.8)
4th Edition 2011
EEE 2203 Material Science II
2.2.2. Dielectric strength
The dielectric strength is defined as the maximum amount of volts per unit length that can be
applied to a dielectric material without it breaking down i.e. the amount of voltage a dielectric can
withstand without losing its insulating properties.
Dielectric strength therefore, represents the magnitude of the electric field E necessary to produce
dielectric breakdown. Insulation or dielectric breakdown causes
o Localized melting
o Burning
o Vaporization
2.2.2.1.
Breakdown in dielectric Materials
The electric strength at breakdown is defined as the minimum electric stress usually expressed
in kV/cm which will cause rupture or breakdown of the material under specified conditions of
temperature, duration, waveform, frequency and the type of electrodes. The electric breakdown
strength of a material depends on its composition, thickness, temperature, moisture content
and to some extent on the time of application of the applied voltage. It is also affected by the
shape of the waveform and steepness of the wavefront of the applied voltage.
There is no definite relationship between these variables, but in general for sheet materials,
the electric strength is an inverse function of the thickness and time and decreases with increasing
temperature and moisture content. At breakdown, high electric stress is assumed to cause an interatomic displacement of the orbital electrons which alters the atomic structure causing heating and a
conduction path in the material.
The breakdown mechanism of gaseous, liquids and solid dielectrics are different in nature.
2.2.3. Dielectric loss
This is the energy lost from joule heating effect in the dielectric when the current J is not
exactly 900 out of phase with the applied electric field strength E .
When D varies with time, a displacement current density J flows in the dielectric due to the
fluctuating surface charges where J =
dD
in the absence of any Ohmic current; that is, for an ideal
dt
dielectric as illustrated in fig 2.5 (a).
J=
- 24 -
dD
dt
(2.9)
EEE 2203 Material Science II
J out of phase by 900
J out of phase by 900
D
displacement
current density
J
displacement
current density
J
4th Edition 2011
D
J in phase
d
Applied electric field E
D in phase
Applied electric field E
Fig. 2.5 (a) phase relationship between vectors;
Fig. 2.5 (b) phase relationship between vectors
J , D and E for a perfect dielectric.
J , D and E for a normal dielectric.
However energy dissipation will arise in the dipole relaxation (dipole rotation) process from Joule
heating if there is a component of J in phase with the electric field giving rise to a non-zero
term J .E .
As long as J is perpendicular to E , clearly there is no energy loss, but when as in fig 2.5 (b) D gets
out of phase with E , J is no longer exactly perpendicular to E and so has a component in the
direction of E .
The energy dissipated per second is; `
w 2wp
(2.10)
J · Edt
2p ò0
Where w is the angular frequency of the field E . If E = E0 cos wt , D = e 0e r E0 cos (wt - d ) where d is
the phase angle between D and E and J = -e 0e r E0w sin (wt - d ) . Therefore, energy dissipated per
second is
2p
æ w ö w
(2.11)
ç
÷ ò we 0e r E0 sin (wt - d ) · E0 cos wt dt
è 2p ø 0
Expanding sin (wt - d ) and multiplying out gives only one term which contributes to the integral, that
is the term cos 2 wt. Hence energy dissipated per second is
æw
ç
è 2p
2
æ w2
ç
è 2p
ö
2
÷ e 0e r E0 sin d
ø
2p
w
0
ö
æw
2
2
÷ sin d ò e 0e r E0 cos wt dt = ç
ø
è 2p
2
2p
ö
2
÷ e 0e r E0 sin d
ø
2p
w
é1 æ
1
öù w æ w ö
2
t
+
sin
2
w
t
÷ ú = ç ÷ e 0e r E0 sin d Joules
ê 2 ç 2w
2
øû0
è ø
ë è
- 25 -
1
ò 2 (1 + cos 2wt ) =
0
(2.12)
EEE 2203 Material Science II
we 0e r' E0
4th Edition 2011
resultant current
vector
d
we 0e r" E0
Fig 2.6 Relationship of real and imaginary parts of relative permittivity and loss angle d .
Fig 2.6 illustrates the relationship between the real and imaginary parts of e r and the dielectric loss
angle d . Thus if J lags behind by a small angle d , as is often the case, tan d =
e r"
is the measure of
e r'
the power loss and is known as the loss tangent. Note that: the lower is the tan d the better is the
material and vice versa. For a good dielectric tan d » 10-5 and for poor dielectric tan d » 0.1 .
Dielectric losses in water are the reason for food and drink getting hot in a microwave oven.
An Exercise
Discuss the following three main causes of dielectric power losses in electric power cables.
(a).
conductivity of insulation
(b).
dielectric hysteresis or dielectric absorption
(c).
Ionization or corona.
2.3.
Application of dielectrics and insulators
Dielectrics are used mainly as transducer materials and as dielectric materials in capacitors.
Materials like oils and wax impregnated paper are used as insulators in power transformers and in
electric power cables. Steatite (a compressed mixture of talc, clay, barium and calcium carbonates) as
an insulator for high voltage terminals.
For capacitors, dielectric materials include; paper, plastic film and mica sheet; oxides of
aluminium, titanium and tantalum (electrolytic capacitors) and a wide range of ceramic oxides which
are often ferroelectric dielectrics. Examples of polymer materials used as commercial dielectrics are
polyesters, polystyrenes and polycarbonates.
- 26 -
4th Edition 2011
EEE 2203 Material Science II
2.3.1. Cable Insulation
The insulating compounds used as insulants for power cables should posses the following main
properties:
1.
High insulation resistance
2.
High dielectric strength
3.
Good mechanical strength
4.
Preferable non-hygroscopic
5.
Capable of being operated at high temperatures i.e. good thermal stability
6.
Low power factor
7.
Low thermal resistance
The most commonly used dielectrics in power cables are impregnated paper, butyl rubber,
polyvinyl chloride (PVC), polythene, cross-linked polyethylene (XLPE). Paper insulated cables,
because of their relatively high current carrying capacity; long life and general reliability are
preferred.
Polythene insulated power cables are found useful for special applications. Polythene, being
non-hygroscopic is used in cable for submarine use and damp soil. Polythene cables are
comparatively lighter and have non-migratory dielectric. They are, therefore, suitable as aerial cables
and other vertical installations.
2.3.2. Cable Construction
A power cable consists of the three main components, namely, conductor, dielectric and
sheath. The conductor provides the conducting path for the current. The insulation or dielectric
withstands the service voltage, and isolates the conductor with other objects.
The sheath does not allow the moisture to enter, and protects the cable from all external
influences like chemical or electrochemical attack, fire and mechanical damage. it should be nonmagnetic if it is used for telecommunication.
2.4.
Electrostriction (electrically induced mechanical strain)
All dielectric materials undergo a strain when subjected to an applied electric field, the fields
of the dipoles induced influences the interatomic spacing resulting in a slight change in shape. The
change in length of a dielectric under the action of an electric field is termed as electrostriction. This
phenomenon is a non linear function of the applied electric field and is a unidirectional attribute.
Example 3.
A 2m F capacitor is connected across a 500 volts d.c supply. If it contains mica as the dielectric
material having relative dielectric constant e r = 5 ; find:
- 27 -
4th Edition 2011
EEE 2203 Material Science II
(i).
The energy stored in the capacitor and
(ii).
The energy stored in polarizing the dielectric material
(iii).
Repeat the calculations if the dielectric material is titanium oxide with e r = 95
Solution
(i).
the energy stored in the capacitor
1
1
2
Ec = CV 2 = ´ 2 ´10-6 ´ ( 500 ) = 0.25 J
2
2
(ii).
Energy stored in a capacitor in terms of electric field and dielectric constant of the material is
given by;
1
1 1
e 0e r vE 2 = = CV 2 where v is the volume of the dielectric material. Energy per unit
2
4 2
volume stored in polarizing the dielectric material is;
E p / v ( m3 ) =
1
PE per unit volume = 0.5e 0 ( e r - 1) E 2 J / m3
2
E p = 0.5e 0 ( e r - 1) vE 2 Joules , but vE 2 =
CV 2
e 0e r
Hence energy stored in polarization the dielectric E p = 0.5e 0 ( e r - 1)
Alternatively, energy stored in a capacitor without dielectric equal Ev =
a capacitor with dielectric equals E =
æ e -1 ö
CV 2
= 0.5CV 2 ç r
÷.
e 0e r
è er ø
1 e 0 AV 2
and that stored in
2 d
1 e 0e r AV 2
. The difference of these energies gives the energy
2
d
stored in polarizing the dielectric. That is
E p = E - Ev =
( e - 1) .
1 e 0e r AV 2 1 e 0 AV 2 1 e 0 AV 2
1 e 0e r AV 2 ( e r - 1) 1
=
e
1
=
= CV 2 r
( r )
2
d
2 d
2 d
2
d
er
2
er
On substituting the values, we get E p = 0.25 ´
(iii).
For titanium oxide; E p = 0.25 ´
5 -1
= 0.2 J
5
95 - 1
= 0.247 J
95
Example 4.
A capacitor uses an aluminium oxide as the dielectric with e r = 8 . An effective surface area of 360
square cm gives a capacitance of 6 µF. Calculate the field strength and the total dipole moment
induced in the oxide layer if a potential difference of 15 volts exists across the capacitor.
Solution Given e r = 8, A = 360 ´10-4 M 2 , C = 6 m F , V = 15V
- 28 -
4th Edition 2011
EEE 2203 Material Science II
C=
e 0e r A
ee A
it follows that d = 0 r
d
C
d=
8.854 ´10-12 ´ 8 ´ 360 ´10-4
= 4.25 ´ 10-7 m
6 ´ 10-6
Electric field strength E =
V
15
=
= 3.53 ´107 V
m
d 4.25 ´10-7
Polarization (P) equals dipole moment per unit volume, therefore,
P = e 0 ( e r - 1) E = 8.854 ´10-12 ´ 7 ´ 3.53 ´107 = 2.19 ´ 10-3 C
m2
Total dipole moment
= P ´ volume = PAd = 2.19 ´ 10-3 ´ 360 ´10-4 ´ 4.25 ´ 10-7 = 3.35 ´ 10-11 C - m
Exercise
Question One
(i).
Define what is a dielectric material?
(ii)
Explain how we quantify the electrical behavior of materials.
Question Two
A 0.1m F capacitor is connected across a 400 volts d.c supply. If the relative dielectric constant of the
material is 4, calculate
(i).
the energy stored in the capacitor and in polarizing the dielectric material (0.008 & 0.006 J).
(ii).
Repeat the calculations if the relative dielectric constant of the material is 91 (0.008 and
0.0072 J).
Question Three
A parallel plate capacitor has an area of 12 cm 2 with a separation of 0.1mm. The space is filled with
Teflon. The real part of the complex relative dielectric constant is 2.1 and the loss tangent is 2 ´10-4
calculate the capacitance and the equivalent parallel loss resistance at a frequency of
(i).
1MHz (223 pF , R = 3.57 M W, R = 35.7 k W
(ii).
æ
1 ö
100MHz ç tan d =
÷
wCRac ø
è
2.5.
Piezoelectric Materials
Assume e r' and tan d are constants at the two frequencies.
The piezoelectric effect is the production of an electric charges on the surface of a material
and hence a voltage across the material as a result of the application of mechanical stress. This occurs
in materials where the application of stress causes a change in electric polarization by separation of
- 29 -
4th Edition 2011
EEE 2203 Material Science II
the centers of positive and negative charge in a crystal. In crystalline materials, the piezoelectric
effect only occurs in a limited class of materials of low crystal symmetry in which the application of
stress deforms the crystal structure and leads to the generation of electric dipole moments. These
materials necessarily have a crystal structure which lacks a center of symmetry.
Of the thirty two crystal symmetry classes, eleven have a centre of symmetry and in one a
combination of symmetries effectively provides such a centre, leaving twenty classes which can have
asymmetric properties. All the materials in these twenty classes are piezoelectric. Materials in ten of
these twenty classes have a unique polar axis where none of the symmetric operations of the crystal
point group will turn this axis round. This is shown in fig. 2.7.
The existence of a polar axis in a crystal allows the appearance of a spontaneous electrical
polarization and these materials are pyroelectric. A restricted group of pyroelectrics have the
additional property of being ferroelectric.
Therefore, all ferroelectrics are pyroelectrics and
piezoelectrics. All pyroelectrics are piezoelectrics but the converse is not true. Example, quartz is
piezoelectric but not ferroelectric. Not all piezoelectrics are pyroelectrics and not all pyroelectrics are
ferroelectrics.
Thus a piezoelectric is a material which becomes electrically polarized in response to an
applied mechanical stress. Further the material is mechanically strained when an electric voltage is
applied. The strain is directly proportional to the applied field E . From the above statements, there
are two effects both of which have important practical applications:
(a).
Direct effect.
The application of a mechanical stress to a crystal produces a strain which results in a net
polarization.
32 Symmetry Classes
21 Non-centrosymmetric
(20 piezoelectric)
11 Centrosymmetric
10 Pyroelectric (polar)
11 Non-pyroelectric
Non-ferroelectric (polar)
Ferroelectric (polar)
Fig 2.7 Symmetry classification of piezoelectric and pyroelectric materials.
- 30 -
4th Edition 2011
(b).
EEE 2203 Material Science II
Inverse effect
The application of an electric field produces a mechanical strain whose sign depends on field
direction.
These are both linear effects. If a stress T is applied to a material resulting in a strain S, there is a
simple relation between the two quantities, involving the elastic stiffness constant c and compliance s
for the material.
T = cS or S = sT and c =
1
s
(2.13)
The stress T will produce a polarization P = g T where g is a piezoelectric strain constant. The
dielectric displacement D in the presence of a stress therefore contains an extra term given by
D = e E + g T and the inverse S = sT + g E
(2.14)
Note that these relationships are complicated by the fact that, most crystalline materials are
anisotropic.
2.5.1 APPLICATIONS
Piezoelectric crystals have been widely used to control the frequency of electronic oscillators.
If the crystal is cut in the form of a thin slab it will have a sharp mechanical resonance frequency and
in a suitable circuit, this resonance can be excited by an applied alternating voltage, the frequency of
which it then controls. This is one of the most vital applications of piezoelectricity; the quartz crystal
resonator, in which the strain amplitude can become very large when the applied A.C voltage signal
coincides with the mechanical resonance of the quartz crystal. Similarly, when the frequency of
mechanical excitation coincides with the resonant frequency, a large electrical signal is produced.
Another important field of application of piezoelectric materials is as ultrasonic transducers.
These are devices which when excited by an alternating electric field, vibrate mechanically and set up
sound waves. Conversely, sound waves falling upon suitably designed transducers will cause it to
generate alternating voltages which may be amplified, in other words it is a microphones.
Many modern record player pick-ups employ piezoelectric materials to covert mechanical
vibration from the needle to electrical signals. Other application include; gas igniters, sound
transducers e.g. microphones which changes sound (acoustic) to electrical energy, speakers, hearing
aids, earphones, filters, strain gauges, ultrasonic flaw detectors and underwater sonar transducers.
They are as well used as pressure transducers (accelerometers) in steel and aluminium rolling mills.
Examples of piezoelectric materials;
Ø Rochelle salt
Ø Quartz
- 31 -
4th Edition 2011
EEE 2203 Material Science II
Ø Ammonium Dihydrogen Phosphate (ADP)
Ø Lead Zirconate Titanate (PZT)
Ø Lithium gallate
Ø Lithium sulphate etc
2.6.
Pyroelectric Materials
Pyro means heat. Hence pyroelectric material is one which exhibits a spontaneous
polarization in the absence of an electric field and which changes its polarization on heating. Certain
crystals, such as tourmaline, acquire an electric charge when heated; they are termed as pyroelectric.
It is easy to reason that all pyroelectric crystals are piezoelectric as well because when heated the
crystal will expand and thus it will be deformed.
If the change of polarization is DP on raising the temperature by DT , then
DP = lDT
(2.15)
Where l is the pyroelectric coefficient of polarization. A good pyroelectric material should have;
high pyroelectric coefficient, low relative permittivity, physical and chemical stability, low
piezoelectric response and if ferroelectric, stability against depoling. The optical absorption should be
in the right part of the spectrum.
2.6.1 Application
a. Used in radiometry to make infra red detectors/sensors/transducers like burglar alarms which can
detect the thermal radiation from a human body, and horizon sensing proximity ‘fuses’ which can
operate at room temperature. They are extremely sensitive to temperatures of less than a
thousandth.
b. Optical pyrometry image tubes for use in the dark (commonly used material Triglycine sulphate
TGS). By using pyroelectric as the sensitive screen in a television camera tube, infrared images
can be formed from the differing heat radiation from the scene being viewed, so that the operator
can ‘see’ in the dark. These are used in a wide variety of satellite and military applications.
c. Thermistors as temperature sensors or flame detectors.
d. Fourier transform infrared spectroscopy.
2.6.2. Examples of pyroelectric Materials:
ü TGS
ü Barium titanate
ü PZT
ü ZnS (wurtzite)
- 32 -
4th Edition 2011
EEE 2203 Material Science II
ü Strontium Barium Niobate (SBN)
ü Lithium Tantalate LiTaO3
2.7.
Ferroelectric Material
These are materials which exhibits a spontaneous polarization in the absence of an electric
field which may be switched in direction by the application of a field. A crystal is said to be
ferroelectric when it has two or more orientational states of polarization, in the absence of an applied
electric field and can be switched from one to another of these states by the application of an electric
field. Ferroelectrics have high relative permittivity and high strain coefficients. In addition they
possesses high polarization-to-electric field strength ratio.
The intrinsic ferroelectric property is the possibility of reversal or change in orientation of the
polarization direction by an electric field. This leads to a hysteresis in the polarization P, electric field
relation similar to magnetic hysteresis. Hence the name ferroelectricity has arisen from the analogy
with ferromagnetism. Ferroelectrics can exhibit either piezoelectricity or electrostriction depending
on the conditions under which they are operated.
Piezoelectrics and pyroelectrics are dielectrics materials for which polarization P is a linear
function of the applied field E and heat respectively. On the other hand, we have ferroelectric
materials which;
(i).
Do not have linear polarization versus applied electric field relation (electrostriction).
(ii).
Show hysteresis effects similar to that found in ferromagnetic materials.
For a given material, ferroelectricity is generally exhibited below a specific temperature,
called the Curie temperature. Above this temperature, thermal agitation is sufficient to destroy the
cooperative ordering of the dipoles which gives rise to the spontaneous polarization. The relative
permittivity reaches a maximum at Curie temperature as shown in fig. 2.8.
Fig 2.9 shows the polarization versus electric field curve of one such ferroelectric material.
Consider a virgin specimen of such material that is a specimen with no initial polarization. On
application of a progressively increasing electric field E, the polarization increases along curve ABC.
Next let the field be reduced so that polarization reduces from its final value at C along the curve
CDFG. It may be seen that for E = 0 , there exist a certain residual polarization or remanent
polarization. ( Pr ) AD.
Stated otherwise, the material is spontaneously polarized. On further reducing the electric
field E in the negative direction, the polarization ultimately reduces to zero at E = - Ec at point F on
- 33 -
4th Edition 2011
EEE 2203 Material Science II
the curve. This electric field Ec is referred to as the coercive field (AF). The intercept AP1 where the
Polarization P
extrapolated saturated polarization cuts the P axis is called the spontaneous polarization.
er
Relative permittivity
P1
C
D
B
- E1
Tc
Temperature T
- Ec
A
Ec
E1
Electric field E
H
G
Fig. 2.8 Relative permittivity versus
Temperature
F
- P1
Fig. 2.9 Hysteresis curve of a ferroelectric material
If the electric field is made further negative, polarization also becomes negative and finally
reaches a value - P1 , at E is equal to - E1 point G. Next on increasing E from - E1 to + E1
polarization moves along the curve GHC. The closed curve CDFGHC constitutes the so called
hysteresis curve.
Any further reversal of E between the limits E1 to - E1 results in retracing of the same hysteresis
curve. The curve ABC traced during the initial polarization of the material is called the initial
polarization curve. The spontaneous polarization usually vanishes above the so-called ferroelectric
Curie temperature Tc as shown in fig. 2.10.
The hysteresis loop is a manifestation of the key property of a ferroelectric that of switching
of the direction of polarization by an electric field. The e r , T relation shown in fig. 2.8 is the
simplest observed. The permittivity shows a characteristic peak near the Curie point Tc and e r may
become very large. This is a vital property of these materials. Above Tc the curve usually follows a
Curie-Weiss law again by analogy with magnetic materials. This relation is in the form of
- 34 -
4th Edition 2011
EEE 2203 Material Science II
A
(2.16)
T - Tc
Where A and Tc are constants for a particular ferroelectric material. Equation (2.16) is known as the
Curie-Weiss temperature law.
Plarization P
e r -1 =
Tc
0
Temperature T
Fig. 2.10 Polarization as a function of temperature.
2.7.1. Classification of Ferroelectric Materials.
Ferroelectric materials may be classified into the following three groups depending on their
chemical composition and structure:
(a).
Tartrate hydrogen bonded crystals group; examples are Rochelle salt which is the sodiumpotassium tetrahydrate salt of tartaric acid ( NaKC4 H 4O6 4 H 2O ; this material has unique
property that it is ferroelectric only in the temperature range from -180 C to 230 C ), lithium
thallium
tartrate
monohydrate
and
lithium
ammonium
tartrate
monohydrate
( LiNH 4C4 H 4O6 H 2O )
(b).
Dihydrogen phosphate group which have a structure framework based of PO4 groups linked
by hydrogen bonds. Examples potassium dihydrogen phosphate
( KH 2 PO4 )
with a Curie
temperature of 1230 C and ammonium dihydrogen phosphate ( NH 4 H 2 PO4 )
(c).
Oxygen octahedron group whose structure contain repeated oxygen octahedra surrounding
another type of ion. Examples barium titanate
( BaTiO3 )
with a Curie temperature of
1200 C and cadmium pyroniobate ( Cd 2 Nb2O7 ) , PZT, Lithium Niobate, Strontium Barium
Niobate.
- 35 -
4th Edition 2011
EEE 2203 Material Science II
Ferroelectric materials can also be classified as uniaxial or multiaxial. Uniaxial are those
which can polarize only ‘up’ or ‘down’ along one crystal direction. Multiaxial are those which can
polarize along several axes that are equivalent in the non-polar state.
Examples of uniaxial ferroelectrics are;
§
Rochelle salt and related tartrates
§
Potassium Dihydrogen phosphate and related materials.
§
Triglycine Sulphate (TGS, (CH 2 NH 2COOH )3 H 2 SO4 )
Examples of multiaxial ferroelectrics are;
§
Barium Titanate ( BaTiO3 )
§
Lead Metaniobate Pb ( NbO3 ) 2
§
Ammonium Cadmium Sulphate ( NH 4 )2 Cd 2 ( SO4 )3
2.7.2. Applications
(i).
Ferroelectrics can be used to fabricate micro-capacitors for dynamic random access memories
(DRAM) which have higher charge storage density and faster access times {high charge
storage density 19.6 m C / cm 2 and small leakage current density of 1.32 ´ 10-7 A / cm 2 ). The
remanent polarization of Lead Zirconate Titanate is typically 10m C / cm 2 .
(ii).
As Microelectromechanical Machines (MEMs) like accelerometers, displacement transducers,
micro-pumps, pressure sensors and micro-actuators. Example of such material PZT
(iii).
As thermistors for those ferroelectrics which are good pyroelectrics.
Exercise
Question One
(a).
A capacitor of 1m F has effective area of 480 cm 2 and it uses a material with relative
dielectric constant of 3. If a potential difference of 40V is applied to the capacitor, calculate
the field strength and the total dipole moment induced in the dielectric material. [4 marks]
(b).
Discuss the following types of polarization in dielectric materials. [6 marks]
(i).
Ionic polarization –it is polarization which is caused by relative displacements between
positive and negative ions in ionic crystals
(ii).
Electronic Polarization
(iii).
Orientational Polarization
Question Two
- 36 -
4th Edition 2011
(a).
EEE 2203 Material Science II
Give the classification of ferroelectric materials and state the characteristic properties of
each type. [8 marks]
(b).
A parallel plate capacitor has an area of 8cm 2 with a separation of 0.08mm. The space is
filled with polystyrene. The real part of the complex relative dielectric constant is 2.56 and
the loss tangent is 0.7 ´10-4 at a frequency of 1MHz. Calculate the capacitance, the
equivalent parallel loss resistance and dielectric loss. Given E = 100 cos 2p ft V / m [8 marks]
2.7.
Magnetoelectric Materials
In "conventional" materials the electric polarization is proportional to the electric field, and
the magnetization is proportional to the magnetic field. In the magnetoelectric materials the electric
polarization can be influenced by the magnetic field and the magnetization depends upon the electric
field. Current topic of scientific interest represent materials showing simultaneously electric and
magnetic order, the multiferroics. An example of multiferroic materials is represented by rare-earth
manganites, RMnO3.
In a magneto-electric material, a magnetic field can induce a ferroelectric moment—a
displacement of the ions that creates an electric field. Similarly, an electric field can induce a change
in the material’s magnetic structure. These materials have caught the attention of technologists who
are interested in developing them as future data storage devices: it is much easier to make a compact
storage system that can be switched electrically, rather than with the current system of magnetic
read/write heads.
Unfortunately, relatively few magneto-electric materials exist, which is why Daisuke
Okuyama of the RIKEN Advanced Science Institute, Wako, and Yuichi Yamasaki of the University
of Tokyo and colleagues are aiming to better understand the connection between ferroelectricity and
magnetic structure at the microscopic level in TbMnO3. TbMnO3 is one of the most well-studied
magneto-electric materials.
2.8.
Thermoelectric Materials
These are materials in which a voltage (the thermoelectric EMF), is created in the presence of
a temperature difference between two different metals or semiconductors. This causes a continuous
current in the conductors if they form a complete loop. The voltage created is of the order of several
- 37 -
4th Edition 2011
EEE 2203 Material Science II
microvolts per kelvin difference. One such combination, copper-constantan, has a Seebeck
coefficient of 41 microvolts per kelvin at room temperature.
Thermoelectricity (thermo-electricity, abbreviated as TE) refers to a class of phenomena in
which a temperature difference creates an electric potential or an electric potential creates a
temperature difference. In modern technical usage, the term almost always refers collectively to the
Seebeck effect, Peltier effect, and the Thomson effect. In recent years, thermoelectricity sees rapidly
increasing usages in applications like portable refrigerators, beverage coolers, electronic component
coolers, metal alloy sorting devices etc. One of the most commonly used material in such application
is Bismuth telluride (Bi2Te3), a chemical compound of bismuth and tellurium.
The thermoelectric effect is the direct conversion of temperature differences to electric
voltage and vice versa. A thermoelectric device creates a voltage when there is a different
temperature on each side. Conversely when a voltage is applied to it, it creates a temperature
difference (known as the Peltier effect). At atomic scale (specifically, charge carriers), an applied
temperature gradient causes charged carriers in the material, whether they are electrons or electron
holes, to diffuse from the hot side to the cold side, similar to a classical gas that expands when
heated; hence, the thermally-induced current.
This effect can be used to generate electricity, to measure temperature, to cool objects, or to
heat them or cook them. Because the direction of heating and cooling is determined by the sign of the
applied voltage, thermoelectric devices make very convenient temperature controllers.
Exercise
(a).
Discuss the following materials and state their practical engineering applications: [9 marks]
§
Thermoelectric materials like thermocouple materials.
§
Magneto- electric materials
§
Piezo-magnetic materials
(b).
Differentiate piezo-electric effect from electrostriction effect. [4 marks]
(c).
With clear examples discuss the various applications of piezoelectrics. [8 marks]
END of Chapter 2
- 38 -
4th Edition 2011
EEE 2203 Material Science II
3.0
MAGNETIC PROPERTIES OF MATERIALS
3.1
Introduction
The magnetic properties are a special sub-group of the electronic properties of materials
which really form a separate subject. Nevertheless, they can also be considered as an integral part of
the electronic properties of materials. Magnetic materials are used to operate electrical motors,
generators and transformers, to store and retrieve information on magnetic tapes in computers, serve
as actuators and sensors, to focus electron beams, to assist in medical diagnostic devices e.t.c.
The most important and interesting magnetic state of a material is known as ferromagnetism.
In this case the relative permeability can be very high. This makes these materials useful in
transformers and inductors. Another property of Ferro magnets is their retention of magnetization.
This is utilized in permanent magnets for both motors and generators.
In addition particulate and thin film magnetic materials are used for magnetic recording purposes.
This application represents a very large market, both for magnetic materials and the associated
electronic support systems for magnetic recording.
3.2
Magnetism in materials
Magnetic behavior is determined primarily by the electronic structure of a material, which
provides magnetic dipoles. Interactions between these dipoles determine the type of magnetic
behavior that is observed. This behavior can be modified by chemical composition, microstructure,
and processing of these materials.
The magnetism properties almost arise exclusively from the motion of the electrons. This
motion in form of electrons spin, and electron orbital motion, generates a magnetic moment
associated with the electron. Much weaker magnetic moment arises from the nucleus spin, but these
are three orders of magnitude smaller. The nuclear magneton m n = 5.051´10-27 Am 2 whereas the Bohr
(electron) magneton m B = 9.274 ´10-24 Am 2
A magnetic moment is the strength of the magnetic field associated with the electron.
Recall that at the beginning of this unit we discussed electronic structure and quantum number
of atoms and we pointed out that each discrete energy level could contain two electrons, each having
an opposite spin. The magnetic moments of each electron pair in an energy level are opposed and,
consequently, whenever an energy level is completely full, there is no net magnetic moment. Based
on this reasoning, we expect any atom of an element with an odd atomic number to have a net
- 39 -
4th Edition 2011
EEE 2203 Material Science II
magnetic moment from the unpaired electron. However, this is not the case. In most of these
elements, the unpaired electron is a valence electron. Because the valence electrons from each atom
interact, the magnetic moments, on average, cancel and no net magnetic moment is associated with
the material.
However, certain elements, such as the transition metals, have an inner energy level that is not
completely filled. The elements scandium through copper, whose electronic structures are shown in
table 3.1 are typical. Except for chromium and copper, the valence electrons in the 4s level are
paired; the unpaired electrons in chromium and copper are canceled by interactions with other atoms.
Copper also has a completely filled 3d shell and thus does not display a net moment. The electrons
in the 3d level of the remaining transition elements do not enter the shell in pairs. Instead, as in
manganese, the first five electrons have the same spin. Only after half of the 3d level is filled do
pairs with opposing spins form. Therefore, each atom in a transition metal has a permanent magnetic
dipole moment, equal in strength to the number of unpaired electrons. Each atom behaves as a
magnetic dipole.
Table 3.1: the electron spins in 3d and 4s energy levels in transition metals, with arrows
indicating the direction of spin.
Metal
Atomic No.
Scandium
21
Titanium
22
3d
4s
Vanadium 23
Chromium 24
Maganese
25
Iron
26
Cobalt
27
Nickel
28
Copper
29
Note that instead of the outmost electrons of potassium ( K ) and calcium ( Ca ) entering the
3d shell, they go into the 4s shell. Only when the 4s shell is full do electrons begin to enter the 3d
shell- there is one 3d electron in scandium, two in titanium and so on. The reason for this behavior is
that the 4s levels have lower energy than the 3d levels so that they fill first in keeping with the
minimum energy principle. Another irregularity is at 24 chromium ( Cr ) and 29 copper ( Cu ) , each
of which contains one 4s electron instead of two. This is due to the fact that the exactly half-filled
- 40 -
4th Edition 2011
EEE 2203 Material Science II
3d shell and the filled 3d shell are particularly stable configurations, that is; they have lower energy
compared to the neighboring occupancies of four (four in 3d shell and two in
4s shell ) and nine
(nine in 3d shell and two in 4s shell ) electrons respectively.
3.3.
Origin of Ferromagnetism
Consider the free atom shown in figure 3.1. In this atom, equal number of electrons spin in the
clockwise and anticlockwise directions in shells K, L and N. these shells are, therefore, magnetically
neutral. In shell M however, 9 electrons spin in a clockwise direction and 5 electrons spin in the
anticlockwise direction. There is therefore, a net effect due to four spinning electrons in clockwise
direction. The magnetic field produced at a point outside the atom would now be 4 times that which
would be produced by a single spinning electron or the magnetic moment of the atom would be 4
Bohr magnetons (1 Bohr magneton = ±
eh
or 9.27 ´ 10-24 Am 2 ).
4p me
On this basis a cobalt atom has a magnetic moment of 3 Bohr magnetons and a nickel atom
has a magnetic moment of 2 Bohr magnetons. This applies to free atoms. However n solids, the
electrons spin in the M shell which is near the periphery of the atom is affected due to the proximity
of other atoms and therefore, the actual magnetic moments are smaller than those given above. The
average values for iron (atomic number 26), cobalt (atomic number 27) and nickel (atomic number
28) are 2.22, 1.71 and 0.606 Bohr magnetons respectively.
N
M
L
K
2 8
14 2
+26
electrons
nucleus
Fig. 3.1 Free iron atom.
When atoms of an element combine to form the element, there exists some force which aligns
the spins of adjacent atoms. According to quantum theory, forces known as exchange forces or forces
of interaction are found to exist between neighboring spinning electrons. These forces are much
stronger than those existing between electrostatic charges and the electromagnetic forces between
circulating currents of electrons. The exchange force tends to make the neighboring spins parallel or
anti-parallel depending upon the number of electrons and the distance between individual atoms.
- 41 -
4th Edition 2011
EEE 2203 Material Science II
Let D be the distance between the centers of neighboring atoms and let d be the diameter of
the electron shell which is responsible for the magnetic properties in the atom. This is the M shell for
the atoms of iron, cobalt or nickel. The curve in fig. 3.2 shows a plot of the exchange force between
D
which varies for crystals of different elements. The positive exchange
d
electrons versus the ratio
force causes the neighboring electron spins in the same direction and the negative exchange force
causes them to be in opposite direction, or anti-parallel. When
When
D
» 1.5 the exchange force is zero.
d
D
< 1.5 , the exchange force is negative and the neighboring atomic moments would be antid
parallel and the material would be anti-ferromagnetic . When
D
> 1.5 , the exchange force would be
d
positive and the neighboring atomic moments would be parallel and the material would be
ferromagnetic.
Co
Exchange Force
+ve
Ni
Fe
1
Mn
Gd
3
2
D
atomic seperation
=
d diameter of 3d orbital
-Ve
Fig. 3.2 a plot of exchange force versus the
D
ratio
d
3.3.1. Magnetic field and magnetic induction
A magnetic field is generated whenever there an electric charge is in motion. Let denote this
field with the symbol H. the magnetic field generated by an elemental length of the conductor
dl carrying a current I is given by the Biot-Savart Law
dH =
- 42 -
I
dl ´ u
4p r 2
(3.1)
4th Edition 2011
EEE 2203 Material Science II
Where r is the radial distance from the conductor at which d H is measured u is a unit vector along
the radial direction, dl is vector along the direction of the length of the conductor and d H is the
elemental contribution to the total field at r .
The magnetic induction B is the response of a medium to the presence of a magnetic field H .
Therefore, for a given field strength H , the magnetic induction B can be different in different media.
When we place a material within the magnetic field, the magnetic inductance is determined by the
manner in which induced and permanent magnetic dipoles interact with the field. The relationship
between the magnetic induction and the magnetic field is called the permeability m of the medium.
B = m H = m0 m r H
(3.2)
Where m is the magnetic permeability of the material in the field. If the magnetic moments reinforce
the applied field, m > m0 ; but if the magnetic moments oppose the field, m < m0 . Where m 0 is the
permeability of the free space whose value is m0 = 4p ´10-7 H / m . Therefore, for free space
B = m0 H
And the relative permeability m r of any other media is mathematically defined as
m
mr =
m0
3.3.2. Magnetization
(3.3)
(3.4)
This is defined as the magnetic moment per unit volume and is denoted by the symbol M .
The magnetization increases as more electronic magnetic moments are aligned in the same direction.
when all magnetic moments within a solid are aligned in the same direction, the magnetization can
not get any higher. We call this saturation level.
The magnetization M contributes together with the magnetic field H , to the magnetic
induction B . Therefore we can write the total general equation relating M , H , and B ,
B = m0 ( H + M )
(3.5)
Where
m 0 H is the induction which would be generated by the field H in free space and m 0 M is the
additional induction contributed by the presence of the magnetic material. The units of magnetization
are A / m just like H .
The ratio of M to H is called magnetic susceptibility c .
c=
Hence
- 43 -
M
H
(3.6)
4th Edition 2011
EEE 2203 Material Science II
m = m0 (1 + c )
(3.7)
And
(3.8)
c = mr - 1
The magnetic susceptibility is a measure of how much magnetic field has been increased by the
magnetic material.
3.4. Classification of magnetic materials
There are five classes into which magnetic materials can be grouped. This classification is
mainly based on the magnetic susceptibility, relative permeability and the presence of permanent or
no permanent magnetic dipoles moments. Based on these three factors, the materials are classified as:
(i)
Diamagnetic
(ii)
Paramagnetic
(iii)
Ferromagnetic
(iv)
Antiferromagnetic
(v)
Ferrimagnetic
3.4.2. Diamagnetic Materials
These are materials with inferior magnetic properties compared to free space.
Their characteristics are:
v
Small and negative c ; -10-6
v
mr < 1 approximately mr ; 1 to 10-5
v
No permanent magnetic dipoles and hence have no special application as magnetic materials.
v
They are repulsed by permanent magnetic poles
v
Induced magnetic dipoles align themselves opposite to the applied field as shown in fig. 3.3.
applied magnetic field
induced magnetic
dipoles
Fig 3.3 Induced magnetic dipoles alignment in a diamagnetic material
v
Their susceptibility increase with increase in atomic number of an element.
c = - NZ m0
()
e2
r
6me
2
Where N is the number of atoms per unit volume or per cell
Z is the atomic number
- 44 -
(3.9)
4th Edition 2011
(r )
2
EEE 2203 Material Science II
is the mean square distance of electrons from the nucleus.
me electron mass and e the electronic charge
Examples of atoms and ions which contain two or more electrons having anti-parallel spins in
addition to a completed shell e.g. Zn, Be, Ca and Pb ++ .
3.4.3. Paramagnetic Materials
These are materials with slightly better magnetic properties compared to free space.
Their characteristics are:
Ø
They are weakly attracted by permanent magnets
Ø
Their induced magnetism disappears as soon as the magnetizing field is removed.
Ø
mr is slightly greater than 1.
Ø
c ³ 0 but very small.
Ø
The paramagnetic material susceptibility varies inversely as the absolute temperature.
c=
C
T
(3.10)
Equation (3.10) is known as Curie’s law. C is a constant known as Curie constant.
Ø
They have net magnetic dipoles which tend to align themselves with applied magnetic field as
shown in fig 3.4.
applied magnetic field
induced magnetic
dipoles
Fig 3.4 Induced magnetic dipoles alignment in a paramagnetic material
Ø
Their overall net magnetization M in a field H at temperature T is given by an expression due to
Langevin
æ
æ mH
M = N m ç Coth ç
è kT
è
ö kT ö
÷÷
ø mH ø
(3.11)
Where m is the magnetic moment of the paramagnetic atoms and N is number of atoms per unit
volume. M 0 = N m is the saturation magnetization
Ø
Have no engineering importance as magnetic materials.
Ø
Examples are atoms and ions of elements having one electron over and above a completed shell
like atoms of the alkali elements, atoms of the transition elements and ions of the rare earth
elements with incomplete shell. E.g. Al , Pt , Ti, Na, O2 , N and Pa .
- 45 -
4th Edition 2011
EEE 2203 Material Science II
3.4.4. Ferromagnetic materials
Key properties of these materials are;
§
Highly attracted by permanent magnets and retain magnetism even when the magnetizing field
is removed
§
Very large and positive c ? 1
§
Large magnetization are obtained even for small magnetic field, giving relative
permeability m r ? 1 as high as 106
§
Their permanent magnetic dipoles align strongly in the direction of the applied magnetic field
as illustrated in fig. 3.5. This is due to the mutual reinforcement of the dipoles.
applied magnetic field
strongly aligned magnetic
dipoles moments
Fig 3.5 Permanent magnetic dipoles alignment in a ferromagnetic material
§
When strongly heated they lose their ferromagnetism to became paramagnetic as the CurieWeiss law
c=
C
T -q
(3.12)
Where q is a constant for a given ferromagnetic material known as Curie temperature as shown in
table 3.2. The material losses its magnetism as per figure 3.6 because the thermal energy supplied
susceptibility
provides the necessary activity which permits randomization of domain/ magnetic dipole alignment.
c
c=
very large
0
C
T -q
Tc = q
Temperature T
Fig 3.6 Temperature dependence of magnetic susceptibility c for a ferromagnetic material above
and below Curie point Tc .
- 46 -
4th Edition 2011
§
EEE 2203 Material Science II
Have very critical application in engineering as magnetic materials.
Examples are Iron, Cobalt, Nickel and Gadolinium
Table 3.2
Curie temperatures for selected magnetic materials
Ferromagnetic Material Curie Temperature
Gadolinium (Gd)
16 to 20
Nickel (Ni)
358
Iron (Fe)
770
Cobalt (Co)
1131
( C)
0
3.4.5. Antiferromagnetic Materials
Key characteristics;
§
Have equal permanent magnetic dipole moments oriented in anti-parallel direction as shown in
figure 3.7;
equal strength
magnetic moments
aligned in opposite
direction
Fig 3.7 Permanent magnetic dipoles alignment in a antiferromagnetic material
§
c is small almost equals to zero but positive and decreases with increase in temperature.
c=
C
T +q
(3.13)
Where C and q are constants.
§
mr is greater than one
§
Have no effects on permanent magnet, hence almost zero magnetization.
Have little if any magnetic engineering applications.
Examples of antiferromagnetic materials are; manganese, chromium, Cr2O3 (chromium oxide),
MnO , NiO , Al2O3 , and FeTiO3 (ilmenite). Note Mn 2 + - O 2 - = 0
3.4.6. Ferrimagnetic Materials (ferrites)
Ferrimagnetism is a phenomenon exhibited by many transition metal oxides like the mineral
magnetite FeOFe2O3 ; the detailed atomic-scale mechanism differs from that of ferromagnetism but at
the domain level there is little apparent difference.
- 47 -
4th Edition 2011
EEE 2203 Material Science II
Ferrites are ceramic materials in which different ions have different magnetic moments. In a
magnetic field, the dipoles of ion A may line up with the field while dipoles of ion B oppose the field.
But because the strength of the dipoles are not equal, a net magnetization results.
Alternatively; a ferrite can be defined as a hard, brittle non-porous ceramic material (an
alloy of transition metal oxide) which has the insulating ability of a ceramic but a magnetic
permeability of similar to a ferromagnetic material.
Major characteristics
§
Have unequal anti-parallel permanent magnetic dipole moments as shown in figure 3.8.
unequal strength
magnetic moments
aligned in opposite
direction
Fig 3.8 Permanent magnetic dipoles alignment in a Ferrimagnetic material.
§
They are highly attracted by permanent magnets
§
Have large magnetic susceptibility c ? 1
§
Have large relative permeability m r ? 1
§
Their magnetism disappears above the Curie temperature.
§
Their magnetic dipoles align themselves in the applied magnetic field as shown in figure 3.9.
applied magnetic field
unequal strength
magnetic moments
alignment in
applied magnetic
field
Fig 3.9 ferrite magnetic dipoles align themselves in the applied magnetic field.
Examples of ferrites are compounds having the large formula ( M 2 + O 2 - ) ( Fe2O3 ) . Where M is a
divalent metal ion which may or may not be magnetic like ZnOFe2O3 , NiFe2O4 , BaO6 Fe2O3 .
3.5. Magnetic Ceramics and alloys
These are ferrites materials manufactured from pressed and sintered ceramic powders. Sintering
is the bonding together of fine powder particles when heated to high temperatures. In these materials
anisotropic properties may be obtained in such a powder by applying a magnetic field appropriately
during the firing and cooling processes.
Being relatively easy and cheap to manufacture, these materials may be used for all application
of metallic magnets with the particular advantage of high resistivity and low eddy current losses.
These materials can be tailored to the particular application by careful control of the composition,
structure and orientation.
- 48 -
4th Edition 2011
EEE 2203 Material Science II
Note: all magnetic materials exhibits a decrease in permeability with increase in frequency of
operation.
3.6. Applications of Ferrimagnetic Materials
Ferrimagnetic materials, primarily ceramic ferrites may be grouped into four classes as per their
applications. These are:
§
Magnetically hard ferrites for permanent magnets
§
Magnetically soft ferrites for transformers and inductors cores.
§
Rectangular loop ferrites for data storage and
§
Ferrites and garnets for microwaves applications
3.6.2. Permanent magnets (hard ferrites)
These materials use barium ferrite BaFe12O19 , strontium ferrite SrFe12O19 , Alnico I (21% Ni,
12% Al, 5% Co, and balance Fe), Alnico V (24% Co, 14% Ni, 8% Al, 3% Cu, balance Fe), Cunico
(50% Cu, 29% Co, 21% Ni) and many more. These materials are characterized by a high value of the
uniaxial anisotropy field and a high coercive force.
In addition their resistivity is high typically 106 W - m. The high coercive force allows these
materials to be used where there are strong demagnetizing fields for example as focusing magnets in
television tubes. The high resistivity permits their use as permanent magnets where there is additional
alternating high frequency magnetic flux without eddy current losses. Other uses include loud
speakers, telephone receivers and holding devices for door closers.
3.6.3. Soft ferrites
They account for a major use of ferrite materials. They include cores of electromagnets, inductors
cores, transformers cores, particularly line out put transformers in television sets and rod aerials. The
essential requirement is for materials of high permeability, low coercive force, low eddy current
losses and ability to operate upto frequency of 10MHz with special requirements extending to 1GHz .
Examples of soft ferrites are Ferroxcube 3 (Mn Zn ferrite) and Ferroxplanas, Ba2 Mg 2 Fe12O22 . Other
uses are hard disks and floppy disks materials in computers and magnetic tapes.
3.6.4. Rectangular loop ferrites
These are ferrites having hysteresis loops which are almost rectangular in shape as shown in figure
3.10. This property makes them suitable for use as magnetic memory core as well as switching
devices in computers.
- 49 -
4th Edition 2011
EEE 2203 Material Science II
B
P1
D
C
A
E
0
F
P0
H
G
Fig 3.10 An ideal rectangular loop ferrite hysteresis curve.
Two stable states of magnetization P1 and P0. Used in digital storage of information.
H ³ H A P1(1) Digital 1 is stored and when - H ³ H E P0 ( 0 ) digital 0 is stored.
Examples of rectangular loop ferrites: manganese-magnesium Ferrite, magnesium-copper ferrite and
lithium-nickel ferrite.
3.6.5. Microwave Ferrites
Examples of these ferrites are MnFe2O4 , CoFe2O4 and Y3 Fe5O12 (yttrium-iron garnet or YIG).
They are used to process some electromagnetic waves in the frequency range 1 to 100GHz. This
processing depends on the interaction of the electromagnetic wave with electron spin magnetic
moments in the ferrite. The discussion will be limited to one of the most important of these processes
known as Faraday rotation. This is the rotation of the plane of polarization of a plane
electromagnetic wave as it travels through the ferrite in the direction of applied magnetic field. This
is used in waveguides to accept or reject plane polarized waves. These materials have low eddy
current and hysteresis losses. Microwave devices which use ferrites include Isolators and Circulators.
In addition ferrites are used in dispersive delay lines and tunable filters in telecommunication.
3.7. Magnetization and Demagnetization of Ferromagnetic Materials.
One of the characteristic features of a ferromagnetic below its Curie temperature is the relation
between magnetization M or magnetic induction B and the applied field H which shows a hysteresis.
Hysteresis describes the relationship between magnetic induction and magnetic field. Hysteresis
means lagging in response of material in change of applied field. Thus susceptibility cannot be
defined uniquely below a temperature equal to q without knowing the state of the specimen.
- 50 -
4th Edition 2011
EEE 2203 Material Science II
A typical hysteresis curve is shown in figure 3.11 and refers to a ferromagnetic specimen being
initially magnetized and in an initial state corresponding to the point O. As H is increased positively,
the path OJ upto saturation point A is followed. From A as the field H is reduced and increased
negatively, AGCD curve is followed. The susceptibility at any point is the slope dB
corresponding B-H curve, dB
dH
dH
. For the
will be the instantaneous permeability. The slope at the origin is
called the initial susceptibility or permeability. OG is known as remanence magnetization (max
remanence can be achieved by using the same elongated single domain particles) and OC is the
coercive force ( H c ) . This coercive force is affected by design and the material from which the
magnet is made of. The energy dissipated in magnetizing the material per cycle is given by;
E=Ñ
ò HdB
(3.14)
This energy is known as hysteresis energy losses and it is due to dissipated energy required to push
the domain walls back and forth during the magnetization and demagnetization of the magnetic
material. The presence of impurities, crystalline imperfections and precipitates in soft magnetic
materials all act as barriers to impede domain wall movement during the magnetization cycle and so
increases these losses. The incremental permeability is defined as DB
DH
about a given point on the
Induction B
loop. Sometimes the term differential permeability is used.
dB
dH
M1
A
G
J
- H1
DB
= m0 m r
DH
incremental
permeability
C
-Hc
DB
DH
O
E
F
H1
Magnetic field
H
m0 mr = initial permeability
-M1
D
Fig. 3.11 Magnetization (or Induction B) versus applied magnetic field H for a ferromagnetic
material.
- 51 -
4th Edition 2011
EEE 2203 Material Science II
Figure 3.12 show that susceptibility has a low value at weak fields. As the field intensity is
increased, the susceptibility increases, reaches a maximum value and then begins to drop, ultimately
reaching a constant value on saturation.
max c
c
saturation
H
Fig. 3.12 Susceptibility versus applied magnetic field H for a ferromagnetic material.
3.8. Magnetic Anisotropy
In general the properties of magnetic materials vary with direction. Iron has a BCC structure
and the main crystallographic directions are shown in figure 3.13 (a) while the corresponding
magnetization as a function of applied field for these directions is given in figure 3.13 (b). The curves
show that there are preferred directions of magnetization in the crystal, so it costs more in energy to
choose some directions for magnetization rather than others. The crystal is said to show magnetic
[110]
[111]
[100]
Fig. 3.13(a)
Magnetization ´10
6
Am-1
anisotropy.
[100] cube edge
[100]
1.5
1
[110]
[111]
[110] face diagonal
[111] cube diagonal
0.5
0
8
16
24 32 40 48
3
Applied field H ´10
Am -1
fig. 3.13 (b)
Fig. 3.13(a) Principal crystallographic directions in a cubic crystal (b) Magnetization versus field for
these directions in a single crystal of iron. Note: figures not drawn to scale.
- 52 -
4th Edition 2011
EEE 2203 Material Science II
Anisotropy can be induced by rolling or other stress- building operations and this anisotropy
may counter or supplement the crystals inherent magnetic anisotropy that is its magneto-crystalline
anisotropy.
3.8.2. h (magnetically induced mechanical strain)
When the magnetic dipole moments in a solid are rotated into alignment, the fields of the
dipoles influence the interatomic spacing. This leads to the change in the bond length between the
atoms in a magnetic material when their electron-spin dipole moments are rotated into alignment
during magnetization. The fields of the dipoles may attract or repel each other, leading to the
contraction or expansion of the metal during magnetization.
Therefore, the shape and volume of ferromagnetic solid changes as it is magnetized. The
principal change is a positive or negative reversible strain along the axis of magnetization. This is
what is known as magnetostriction. Magnetostrictive effects in a magnetic material can be controlled
by composition and processing.
Exercise
1.
What is magnetic anisotropy energy?
2.
Explain why magnetostriction is anisotropic.
3.
Elaborate the factors that affect the magnitude of coercive force and hence the remanence
flux density.
4.
Elucidate clearly the reasons why iron crystal expands when magnetized in the easy
direction of magnetization and contracts when magnetized in the hard direction of
magnetization.
5.
Discuss the procedure that would you recommend for making the materials required for
permanent magnets.
6.
What causes humming noise in a power transformer? How can the hysteresis and eddy
current losses in such devices be minimized?
7.
What is Curie temperature? Give its value for the ferromagnetic elements and hence
explain why these elements become paramagnetic at and above this temperature.
8.
The rectangular hysteresis curve of a material has a coercity of 50Am -1 and a remanence
of 0.5T . Estimate the hysteresis loss per cubic meter of the material that is dissipated
when the material is driven around one complete hysteresis cycle. If this material is used
in a toroidal inductor core of mean circumference 0.05m with a cross-sectional area
of 0.25 ´ 10-4 m 2 , calculate the hysteresis power loss at a frequency of 60Hz. Is this the
- 53 -
4th Edition 2011
EEE 2203 Material Science II
total power loss in the inductor at this frequency? What materials properties would you
take into account in selecting a material as an inductor core?
3.8.3. Ferromagnetic Domains (Domain Theory)
Domains are a number of distinct regions each of which is magnetically saturated in a different
direction such that the material as a whole has a net zero magnetization in absence of applied
magnetic field. They can also be defined as regions possibly not more than 0.05mmm in diameter, in
which atoms are aligned so that their magnetic orientations are in the same direction. This is
illustrated in figure 3.14.
Fig. 3.14 Random arrangement of magnetic domains in unmagnetized material.
The effect of an external applied field is to align domains so that there is a net moment. At
low fields this alignment occurs through the growth of some domains at the expense of less favorably
oriented ones and the intensity of magnetization increases rapidly.
Domain growth ceases as the saturation region is approached and rotation of the remaining
unfavorably aligned domains occurs. Domains rotation requires more energy than domain growth and
hence the slope of the M-H curve decreases at this stage. This explains the initial magnetization curve
in fig. 3.11 but not the hysteresis.
Hysteresis is explained as follows. Most materials contain large number of imperfections
which act as obstacles to domain rotation and domain wall motion. When the field is increased, the
obstacles are overcomed by the energy supplied by the field. On removal of the field, the defects
prevent the walls returning to their previous positions. Thus to return the domain structure to a
random array, with zero net magnetic moment, it is necessary to supply more energy.
3.8.4. Applications of Ferromagnetic Materials.
Ferromagnetic materials are categorized into two groups depending on how easily they can be
magnetized or demagnetized. These are as discussed below.
- 54 -
4th Edition 2011
EEE 2203 Material Science II
3.8.4.1.1. Soft Ferromagnetic Magnetic Materials
These are materials which are easy to magnetize and demagnetize. They retain their
magnetism only in the presence of a magnetic field. Require applications of small magnetic field to
produce magnetic saturation as shown in figure 3.15. In general they have the following key
properties;
B (M)
0
H
Fig. 3.15 Hysteresis curve of a soft ferromagnetic material.
§
High magnetic susceptibility
§
High permeability
§
Low coercive force
§
Low remanence flux density
§
Low hysteresis and low eddy current (when suitably laminated and insulated) losses
§
Low resistance to magnetization and demagnetization. Can operate at 10MHz frequency and
above.
Examples: Permalloy (45% Ni, 55% Fe), Isoperm (50% Ni, 50% Fe), Superpermalloy (Ni + Fe +
small amount of Mo, Mn), Si-Fe silicon steel alloy and Mu-metal (Ni + Fe small amount of Cr
and Co).
Applications: used to produce cores of; power transformers, current transformers, generators,
motors, electromagnets and inductors.
3.8.3.2.
Hard Ferromagnetic Magnetic Materials
These are materials which are hard to magnetize and demagnetize. Require large magnetic
field to produce magnetic saturation as shown in figure 3.16. They are mainly used to produce
permanent magnets used in loud speakers, telephone receivers, synchronous and brushless motors
and automotive starting motors. Their key properties are:
§
High coercive force
§
High remanence flux density
- 55 -
4th Edition 2011
EEE 2203 Material Science II
§
Large anisotropy constant
§
High hysteresis losses due to large hysteresis loop
§
Low permeability
§
Large BH product
§
High resistance to magnetization and demagnetization
B(M)
0
H
Fig. 3.16 Hysteresis curve of a hard ferromagnetic material.
To achieve hardness of demagnetization, hard magnets are made out of very fine particles to
eliminate the movement of domain walls. Also non-magnetic inclusions are introduced in the
material to prevent the domains from realigning randomly once the magnetizing field is removed.
Additional hardness is affected by introduction of mechanical strains.
Example; Martensite (mainly Fe-Mn-C), Tungsten steel alloy (Fe-W), Alnico and Platinum-Cobalt.
Exercise
1.
What is magnetostriction? State its cause and list one advantage and one disadvantage of
magnetostriction. [5 marks]
2.
Explain why power transformers cores are made from cold rolled grain oriented silicon
steel alloy. [7 marks]
3.
The following are typical metallic alloys and ceramic materials used in magnetic
applications; discuss their applications and how their properties and behavior can be
enhanced. [21 marks]
(i).
Magnetic metals
(ii).
Iron-Nickel Alloys
(iii).
Silicon Iron
(iv).
Composite Magnets
- 56 -
4th Edition 2011
EEE 2203 Material Science II
(v).
Metallic Glasses
(vi).
Magnetic Tape
(vii).
Complex Metallic Alloys for Permanent Magnets
3.9. Magnetic Materials for Electrical Applications
Ferromagnetic materials are used to enhance the magnetic filed produced when an electric
current is passed through the material. The magnetic field is then expected to do work. Applications
include cores for electromagnets, electric motors, transformers, generators and other electrical
equipment. These devices utilize an alternating field, so that the core material is continually cycled
through the hysteresis loop.
Electrical magnetic materials often called soft magnets should have several characteristics. A
high saturation magnetization is desired, permitting the material to do the most work, while a high
permeability permits this saturation magnetization to be obtained with small imposed fields. A small
coercive force indicating that the domains can be reoriented with small fields, is also desired. A small
remanence is desired so that no magnetism remains when the fields is removed. These characteristics
also lead to a small hysteresis loop, therefore minimizing energy losses during operation.
In addition, the frequency at which the material operates is important. If the frequency is so
high that the domains cannot be realigned in each cycle, the device may heat, just as in dielectric
materials, due to dipole friction. Furthermore, higher frequencies naturally produce more heating
because the material cycles through the hysteresis loop more often, losing energy during each cycle.
For high-frequency applications, materials must be selected that permits the dipoles to be aligned at
exceptionally rapid rates.
Energy can also be lost by heating if eddy currents are produced. During operation, electrical
currents can be induced into the magnetic material. This currents produce power losses and joule,
or I 2 R , heating. Eddy current losses are particularly severe when the material operates at high
frequencies. If the electrical resistivity is high, eddy current losses can be held to a minimum. Most
magnets produced from ceramic materials (ferrites) have a high resistivity and there are less likely to
heat than metallic magnets. Lamination or use of insulated sheet structure in the magnetic core also
reduces these currents.
3.9.2. Magnetic Materials for Computer Memories.
Magnetic materials are used to store bits of information in computer. Memory is stored by
magnetizing the material in a certain direction. For example, if the North Pole is up, the bit of
information stored is 1. If the North Pole is down, then a 0 is stored.
- 57 -
4th Edition 2011
EEE 2203 Material Science II
For this application, material with a square hysteresis loop, a low remanence, a low saturation
magnetization and a low coercive field are preferred. Ferrites containing manganese, magnesium or
cobalt may satisfy these requirements. The square loop assures that a bit of information placed in the
material by a field remains stored; a steep and abrupt change in magnetization is required to remove
the information from storage in the ferromagnet.
Furthermore, saturation magnetization, and
remanence should be low.
3.9.3. Magnetic Materials for Permanent Magnets
Finally magnetic materials are used to make strong permanent. Permanent magnets require
high remanence, high permeability, high coercive fields and high power. The power of the magnet is
related to the size of the hysteresis loop, or the maximum product of B and H. the area of the largest
rectangle that can be drawn in the second or fourth quadrants of the B-H curve is related to the energy
required to demagnetize the magnet fig. 3.17. For the product to be large, both the remanence and the
coercive field should be large.
Flux Density
BH max product
Magnetic Field
Fig. 3.17 the largest rectangle drawn in the second or fourth quadrant of the BH curve gives
the maximum power of the magnet
Development of strong permanent magnets, often said to be magnetically hard, is aimed at
improving both the magnetic permeability and the stability of the domains. We shall see in the
following section how this achieved.
3.9.4. Magnetic Materials
Let’s look at typical metallic alloys and ceramic materials used in magnetic applications and discuss
how their properties and behavior can be enhanced.
- 58 -
4th Edition 2011
(a).
EEE 2203 Material Science II
Magnetic Metals; pure iron, nickel and cobalt are not usually used for electrical applications;
they have high electrical conductivities and relatively large hysteresis loops, leading to excessive
power losses. On the other hand, they are relatively poor permanent magnets; the domains are easily
reoriented and both remanence and the BH product are small compared with those of more complex
alloys.
Some improvement in the magnetic properties is gained by introducing defects into the
structure. Dislocations, grain boundaries, boundaries between multiple phases and point defects may
help to pin domain boundaries, thus keeping the domains aligned when the original magnetizing field
is removed. However, complex alloys are more suitable for producing powerful permanent magnets.
(b).
Iron-Nickel Alloys; some iron-nickel alloys such as Permalloy, have high permeabilities,
making them useful as soft magnets. One example of an application for these magnets is the ‘head’
that stores or reads information on a computer disk. As the disk rotates beneath the head, a current
produces a magnetic field in the head. The magnetic field in the head in turn magnetizes a portion of
the disk.
The direction of the field produced in the head determines the orientation of the magnetic
particles embedded in the disk and consequently stores information. The information can be retrieved
by again spinning the disk beneath the head. The magnetized region in the disk induces a current in
the head; the direction of the current depends on the direction of the magnetic field in the disk.
Addition of small amounts of other elements to nickel-iron alloys improves their magnetic
properties in certain directions. Thus cobalt reduces hysteresis, manganese reduces coercivity and
molybdenum increases the initial permeability and reduces the iron losses. Since the saturation flux
density of Ni-Fe alloys is low, they are not used in electrical machines but are widely used for
transformer cores and loading coils for telephone circuits, instrument transformers like current
transformers, for the magnetic circuits of measuring instruments, and for magnetic screens of
electronic equipment.
(c).
Silicon Iron alloy; introduction of 3% to 5% silicon into iron produces an alloy that, after
proper processing, is useful in electrical applications such as motors, current transformers for power
system protection and generators.
We take advantage of the anisotropic magnetic behavior of silicon iron to obtain the best
performance. Unusually small hysteresis loops and coercive fields are obtained when the crystal
structure of the silicon iron is lined up with the field in the most easily magnetized direction as shown
in fig. 3.18. As a result of the rolling and subsequent annealing, a sheet texture is formed in which the
[100] directions in each grain are aligned. Because the silicon iron is most easily magnetized in [100]
- 59 -
4th Edition 2011
EEE 2203 Material Science II
directions, the fields required to give saturation magnetization is very small and both a small
hysteresis loop and a small remanence are observed.
In addition, the silicon enters the iron as a solid solution alloying element, therefore reducing
the electrical conductivity. While the low conductivity helps to reduce eddy current losses, the silicon
also reduces the saturation magnetization and the Curie temperature.
Flux Density
[100]
[110]
[111]
Magnetic Field
Fig. 3.18 The initial magnetization curve for silicon iron which is highly anisotropic.
In summary; silicon in iron does the following;
§
Increases electrical resistivity thus reduces eddy current losses.
§
Decreases the magneto-anisotropy energy of iron and increases magnetic permeability thus
decreasing hysteresis losses.
§
Decreases magnetostriction and lower hysteresis energy losses and transformers hum noise.
§
However, silicon decreases the ductility of iron, the saturation induction and Curie
temperature.
§
(d).
Both anisotropy constant and the appropriate saturation magnetostriction constant decreases.
Composite Magnets; Composite material techniques have been used to further reduce eddy
current losses. Thin sheets of silicon iron are laminated around a layer of an insulating material. The
laminated layers are then built up to the desired overall thickness. The laminant thereby increase the
resistivity of the composite magnets. The laminates are successful at low and intermediate
frequencies.
At very high frequencies, eddy current losses are even more significant because the domains
do not have time to realign. In this case, a composite material containing domain sized magnetic
particles in a polymer matrix may be used. The particles, or domains, rotate easily in the soft
polymer, while eddy current losses are minimized because of the high resistivity of the polymer.
- 60 -
4th Edition 2011
(e).
EEE 2203 Material Science II
Metallic Glasses; amorphous metallic glasses, often complex iron-boron alloys are produced
by employing extraordinarily high cooling rates during solidification. The metallic glasses can be
produced in the form of thin tapes, which can be stacked together to produce larger material. These
materials behave as soft magnets with a high magnetic permeability; the absence of grain boundaries
may permit easy movement of the domains, while a high electrical resistivity minimizes eddy current
losses.
(f).
Magnetic Tape; magnetic materials for information storage must have a square loop and a
low coercive field, permitting very rapid transmission of information. Magnetic tape for audio or
video application is produced by evaporating, sputtering, or plating particles of a magnetic material
such as Fe2O3 onto a polymer tape.
Both floppy disks and hard disks for computer data storage are produced in a similar manner.
In a hard disk, magnetic particles are embedded in a polymer film on a flat aluminium substrate.
Because of the polymer matrix and the small particles, the domains can rotate quickly in response to
a magnetic field.
(g).
Complex Metallic Alloys for Permanent Magnets; improved permanent magnets are
produced by making the grain size so small that only one domain is present in each grain. Now the
boundaries between domains are grain boundaries rather than Bloch walls; the domains can change
their orientation only by rotating, which requires greater energy than domain growth.
Two techniques are used to produce these magnetic materials-phase transformations and
powder metallurgy. Alnico, one of the most common of the complex metallic alloys, has a singlephase BCC structure at high temperatures. But when Alnico slowly cools below 8000 C , a second
BCC phase rich in iron and cobalt precipitates. This second phase is so fine that each precipitate
particle is a single domain, producing a very high remanence, coercive field and power.
3.10.
Curie Temperature
When the temperature of a ferromagnetic material is increased, the added thermal energy
increases the mobility of the domains, making it easier for them to be come aligned but also
preventing them from remaining aligned when the magnetizing field is removed. Consequently,
saturation magnetization, remanence, and the coercive field are all reduced at high temperatures as
shown in fig. 3.19. If the temperature exceeds the Curie temperature, ferromagnetic behavior is no
longer observed. The Curie temperature depends on the type of magnetic material and can be
changed by alloying elements.
- 61 -
4th Edition 2011
EEE 2203 Material Science II
High
Temperature
Magnetic Field
Moderate
Temperature
Saturation Magnetization
Flux Density
Low
Temperature
Temperature
Curie Temp.
(b)
(a)
Fig. 3.19 The effect of temperature on (a) the hysteresis loop and (b) the saturation magnetization.
The dipoles can still be aligned in a magnetic field above the Curie temperature, but the
dipoles become randomly aligned when the field is removed. Above this temperature, the material
becomes paramagnetic in nature.
Exercise
(i).
Elaborate why Diamagnetic materials are repelled by permanent magnets. [2 marks]
(ii).
Discuss how a high coercivity is achieved in permanent magnets. [3 marks]
(iii).
What is magnetic susceptibility? List two factors which may influence the magnetic
susceptibility of a magnetic material. [3 marks]
(iv).
A 200 turns 40m coil is carrying a current of 20A. It is wound on a material with a relative
permeability of 5000. Calculate the magnetization (M) and inductance (B) in the material.
[4 marks]
Define with an example the following materials and discuss their main applications in
(v).
engineering. [12 marks]
§
Dielectric materials
§
Electrical conducting materials
§
Magnetic materials
§
Electrical Insulating materials
Some important definitions.
Ferrites are insulators being ionic-covalent compounds frequently incorporating oxygen.
- 62 -
4th Edition 2011
EEE 2203 Material Science II
The anisotropy constant is a measure of the energy required to rotate the magnetization direction
uniformly away from a structurally preferred direction, such as a crystal axis along which it
normally lies in the absence of any external influence. Like the [111] direction in the nickel sample.
The saturation magnetostriction constant is a measure of the sensitivity of the state of magnetization
to stresses internal to the material. It is defined as the strain of the material when magnetized from
zero flux density to saturation and it varies with the crystallographic direction of the magnetization.
As the magnetization direction changes in a region through which a domain wall moves, their is an
associated change in the lattice shape. That is there is a strain, which is proportional to the size of
the magnetostriction constant.
The exciting current is the cause of the current ratio and phase angle errors in a CT. Nickel-iron
cores CTs are mainly used for measuring CTs as the high permeability results in a low exciting
current and low errors. Also, the almost absolute saturation at relatively low flux density (and
secondary voltage) prevents excessive currents being fed to the instruments during system faults.
Silicon steel, mostly of the CRGOSS type is used for protective CTs which must not saturate even at
high secondary currents and yet must have reasonably small exciting currents and errors.
End of chapter 3
- 63 -
4th Edition 2011
4.0.
EEE 2203 Material Science II
General Insulators For Printed Circuit Boards and Associated Electronics
4.1.
Introduction
The main agenda of this section is to learn how to choose and deploy insulators for modern
circuits in the electrical and electronic industry, and to draw out the manifold material requirements
of their production methods. The fantastic market surge in electronics in recent decades reflects a
circuit building revolution. Expectations of function are ever increasing, demanding more complex,
more reliable, more compact and cheaper circuits than were possible in the early days of electronics.
For example the circuit board is a polymer material otherwise known as substrate which is used for
both the insulation between conductors and for their mechanical support.
Printed Circuit Boards (PCBs) are sort of circuit assembly whereby wire terminations of
mounted devices poke through holes from the blank side of the board and are soldered to the
conducting regions on the other side. Hybrid circuits mix the ideas of ICs and PCBs. Some of the
circuit devices are simultaneously grown onto the substrate, while others are placed on and soldered.
Hybrid circuits use ceramic substrates; conducting tracks, resistors and insulating layers are made by
depositing glassy enamel on the substrate. These enamels are placed by screen printing (the process
by which the geometry of conductors, resistors and insulating layers is defined for hybrid circuits) as
‘inks’ and fired to fix them and bring them to their functional condition (conducting or insulating).
The substrate, being refractory, can withstand these firings. Part of attraction of this method,
compared with PCBs, is the simpler logistics of component handling. Hybrids also have a reputation
for reliability, can dissipate significant power, and are remarkably robust in chemically, thermally
and mechanically hostile environments. They can be advantageous for analogue circuits needing very
precise resistor values (0.1%) and are also good at microwave frequencies above 1 GHz. PCBs and
hybrids have in common the idea that metal conductors are laid onto an insulating substrate, either
polymer or ceramic. Conductors and insulators each have their own implications for materialsselection issues
4.2.
Polymers
Polymers are macromolecules that is, large molecules formed by the linking together of large
number of small molecules called monomers. The process involved in the joining of these monomers
is called polymerization. The common characteristics of these materials are their ability to soften and
even melt, ability to pass into liquid state, insolubility in water and solubility in one or more organic
solvents. The mechanical properties of polymers vary widely, some can be spun into fibers like nylon
and terylene and others can be moulded and are hard and glass-like in mechanical properties. Yet
another group shows rubber-like properties.
- 64 -
4th Edition 2011
EEE 2203 Material Science II
Plastics are a group of synthetic polymers made up of chains of atoms or molecules. The long
molecular chains contain various combinations of oxygen, hydrogen, nitrogen, carbon, silicon,
chlorine, fluorine and Sulphur. The properties of polymers such as hygroscopicity, mechanical
strength and insulating characteristics depend to a considerable extent on their chemical composition
and molecular structure.
4.2.1. Types of polymers
Polymers can be differentiated by the way in which their monomers are joined together, that
is addition or condensation polymerization. Further, the molecular chains are linked by successive
addition of one monomer to another. In additional polymerization, the carbon atoms of the monomer
should have double bonds which can be broken under suitable conditions to allow the neighboring
monomers to link with each other to form linear or chain polymer molecules. This is illustrated fig.
4.1 for styrene with the molecular formula C8 H 8 .
H
H
C
C
H
C6 H 5
Fig. 4.1 Styrene monomer.
Styrene molecule polymerizes readily by breaking the double bond of carbon atoms and
combining with the neighboring styrene molecules forming what is known as polystyrene. The
polystyrene has the molecular structure as shown in fig. 4.2.
H
H
H
H
C
C
C
C
H
C6 H 5
H
C6 H 5
Fig. 4.2 Polystyrene molecule.
Other typical additional polymers are polyolefins, acrylics, vinyls, polyethylene,
polypropylene, polytetrafluoroethylene (PTFE), polyethene and fluoroplastics.
Condensation polymers are prepared by the reaction of two different molecules, each having
two reactive end groups. Molecular weight is built up by the linking together of these end groups and
- 65 -
4th Edition 2011
EEE 2203 Material Science II
the elimination of a small molecule; which must be removed from the reaction medium to attain a
high molecular weight. Examples include nylons, polyesters, polyurethanes, bakelite and epoxy.
OH
OH
CH 2
OH
CH 2
CH 2
OH
n
nHCHO
Phenol
CH 2 + nH 2O
CH 2
OH
Methanal
CH 2
CH 2
CH 2
OH
OH
Bakelite
Fig. 4.3 The structural formula of Bakelite
Polymers occur naturally in materials such as rubber, resin, cotton, wool and wood. They are
widely used in the plastic industry. In the home, for example they may be used as plastic dustbins,
washing-up bowls, light fittings and wrapping papers, in addition to nylon stocks. Plastics also make
good thermal and electrical insulators, have low density, great toughness and resist corrosion.
They are easy to mould and cheap to produce, which is a considerable advantage. Their
disadvantages are a low Young modulus of elasticity and low tensile strength, making them
unsuitable for many load-bearing applications. Their mechanical properties depend considerably on
their temperature and they also tend to melt relatively at low temperatures accompanied by dangerous
fumes.
4.3.
Plastics
These are polymers that are deformable in their manufacturing processes.
4.3.1. Thermosetting Plastics
These are polymers which have cross-links between chains of molecules. They are rigid and cannot
be re-moulded by heating. They are prepared by the process of condensation polymerization.
Examples are Bakelite, Melamine and epoxide resin.
1.
Epoxies; trade name epon, epirex, or araldite
Properties
·
Good moisture resistance
·
Superior adhesive to most substances
- 66 -
4th Edition 2011
EEE 2203 Material Science II
·
Relatively inexpensive
·
optimum electrical dielectric insulation and thermal stability properties
·
Good chemical resistance
·
Good fire retardancy
Applications
Used as adhesive material, protective coating, embedment of component for transformers, motors,
switch gear, coils, capacitors and resistors.
2.
Phenolics; trade name Bakelite, Durez and Resinox
Properties
·
Excellent weather resistant
·
Excellent thermal stability
·
Cheap
Application
Used as adhesive materials, materials for telephone heads and electrical automotive distribution
boards.
3.
Polyesters; trade name paraplex, laminae
Properties
·
Low cost
·
Excellent electrical insulation properties
Applications
Used in manufacture of helmets, chairs and auto body car components.
4.3.2. Thermoplastics
These are polymers which have no cross-links between chains of molecules. They become soft on
reheating and can be re-moulded. They are prepared by the process of additional polymerization
Polyethylene, polystyrene, polyvinyl chloride (PVC) and nylon are examples of thermoplastics. The
mechanical properties of these materials are more sensitive to temperature change.
1.
Acrylics; trade name lucites, plexiglass or perspex
Properties
·
Superior optical properties of transmitting light
·
Resistant to moist environment
Applications
Used in making fiber optic cables, transparent aircraft enclosures and lens.
- 67 -
4th Edition 2011
2.
EEE 2203 Material Science II
Fluorocarbons; trade name teflons or halons
Properties
·
Excellent electrical insulating properties like low loss tangent
·
Chemically inert
·
Relatively mechanically weak
·
Extreme heat resistance
Applications
Used in the manufacturing of chemical pipes, high temperature electronic parts, capacitor dielectric
and anti adhesive coating e.g. non-stick frying pans.
3.
Vinyls; trade name P.V.C or tygon
Properties
·
They are cheap
·
They melt at relatively low temperatures
·
They are flexible but mechanically weak
Applications
Floor covering tiles, insulation in electrical and telephone wires, as conduits and horse pipes.
4.4.
·
Other Materials included to mould plastics to improve their characteristics are;
Fillers; these are fibrous or powdered materials like wood, flour, talcum, silicates and
carbonates that are used to increase bulk and reduce cost.
·
Fibers; materials which produces mechanical reinforcement. Examples are cotton, metals and
metal alloy fibers.
·
Plasticizers; materials that are used to reduce brittleness and increase flexibility. These are
special organic liquid with high boiling point.
·
Dyes and pigments that are used to give the plastic different aesthetic colors for sales appeal.
·
Other methods includes; addition of antioxidants to prevent damage by ultraviolet light,
stabilizers to inhibit degradation by oxygen or heat, blowing agents to produce a porous
interior sandwiched between solid plastic skins and give high strength to weight ratio, finishes
to give the material a good sales appeal or wear, scratch and chemical resistance. Plastics can
be plated, metalized or enameled.
- 68 -
4th Edition 2011
4.5.
·
EEE 2203 Material Science II
Four important requirements of a good insulating material.
Electrical Stability:
The insulating material should electrically have high resistivity to reduce the leakage current
and high dielectric strength (several kV/mm) to enable it to withstand higher voltages without being
punctured or broken down. Further the insulator should have small dielectric loss and especially
when used for high frequency (above 10 MHz) applications.
·
Thermal Stability:
This is important for liquids and gaseous insulators that are used as coolants. For example,
transformer oil, hydrogen and helium used both for insulation and cooling purposes in large (greater
than 500 MVA) generators and transformers. For such materials good thermal conductivity is a
desirable property. The insulators should also have small thermal expansion to prevent mechanical
damage. In addition it should be non-ignitable or if ignitable it should be self extinguishable.
·
Chemical Stability:
Chemically the insulators should be resistant to oils, liquids, gas fumes, acids and alkalis. It
should not deteriorate by the action of chemicals in soils or by contact with other metals. The
insulator should not absorb water particles since water lowers the insulation resistance and the
dielectric strength.
·
Mechanical Stability:
Insulating materials should have certain mechanical properties depending on the use to which
they are put. Thus when used for electrical machine insulation (e.g. Micanite used as an electrical
insulator between commutator segments in motors and generators), the insulator should have
sufficient mechanical strength to withstand vibrations. The porcelain and glass strain insulators used
in power system distribution and transmission lines should be able to withstand tensile or
compressive forces of the conductor. This should be achieved without compromising the other
insulating properties of the material.
4.6.
Adhesive Materials (Bonding Materials)
Adhesives are substances often called glues or cements used to stick or bond things together.
Lamination is common process that relies on adhesives; here thin sheets called lamina are bonded
together using an adhesive. a good example is the transformer core which consists of thin sheets of
silicon steel bonded together. Glue is a popularly used name for adhesives but applies particularly to
animal-based products. Note that sometimes solder paste is used where components are only mounted
on the top of a board and where the soldering process does not require the board to be inverted.
- 69 -
4th Edition 2011
EEE 2203 Material Science II
In general pure adhesive is typically used where components are to be mounted on the bottom of
a board or where the board is to be turned upside down in any subsequent operation (as solder paste
will not prevent components falling off by gravity). A number of features are important in any
adhesive used in mounting of components including;
·
It must not react with either the component or the board material
·
It must not conduct current
·
It must be tacky enough to retain the component until cured or hardened.
·
It must be capable of withstanding the heat of soldering
·
It must allow removal of the component for later repair or servicing
·
It must be non-toxic and solvent-free
·
A short curing time is desirable for a rapid throughput of assemblies.
The main families of adhesives include but not limited to;
1.
Acrylics
Normally toughened acrylics are used which have two parts; the acrylic as an adhesive and a catalyst
which is needed to cure the adhesive.
2.
Epoxides
Based on epoxide resins, these adhesive usually are of two part form although one-part, heat-cured
epoxides are available, too. Toughened versions are available giving greatly increased performance.
3.
Phenolics
Based on phenol-formaldehyde resins is one of the oldest man-made adhesives.
4.
Polyurethanes
Generally two part like epoxides with similar performance but greater susceptibility to moisture.
5.
Silicone
Silicones offer good adhesive properties with superb dielectric properties, a non corrosive cure, flame
retardancy, high temperature resistance, a wide range of operating temperatures, excellent thermal
cycling and vibration resistance.
Note that adhesives are found in many applicatory guises like emulsion, solution, powder,
stick and so on and there are several grades within each family.
4.6.
Environmental Protection of Assemblies and Components
Assemblies and components may be subjected to either a corrosive environment or a
mechanically stressful environment. Effects of one or both of these environments may be reduced to
acceptable levels though never eliminated by encapsulating assemblies. Assembly encapsulation is a
- 70 -
4th Edition 2011
EEE 2203 Material Science II
generic term referring to techniques using resin-like materials to package the assembly. There are
four main methods of encapsulation;
·
Conformal Coating
·
Embedding
·
Impregnation
·
Potting
4.6.1. Conformal Coating
This is by far the most common method of encapsulation; conformal coating, sometimes
called surface coating or surface sealing, uses thin (between 0.005 mm to 0.075 mm) transparent
coats of materials to provide an electrically insulating protective barrier against humidity, dirty,
vaporous contaminants and foreign bodies such as metal filings. Conformal coating material is
applied to electronic circuitry to act as protection against moisture, dust, chemicals and temperature
extremes that if uncoated (non-protected) could result in a complete failure of the electronic system.
For example, in a chip-on-board assembly process, a silicon die is mounted on board with an
adhesive or a soldering process, and then electrically connected by wire bonding, typically 0.001 inch
diameter gold or aluminium wire. The chip and the wire are very delicate, so they are encapsulated in
a version of conformal coating called ‘glob top’. This prevents accidental contact from damaging the
wires or the chip. Another use of conformal coating is to increase the voltage rating of a dense circuit
assembly; an insulating coating can withstand a much stronger electric field than air, particularly at
high altitude.
Typical coating materials include; acrylic, epoxy, urethanes, oleo resin, polystyrene, silicone and
silicone rubber.
4.6.2. Potting
In most cases an assembly is placed in a case or shell and then a liquid potting compound is
poured over the assembly. The main purpose of the Potting Compound is usually to protect an
electronic assembly from moisture, excessive heat, chemicals, dirt or other contaminants. The Potting
Compound may also provide other properties such as heat dissipation, flame retardancy, or vibration
resistance.
The main application of potting is casting of sensitive electronic components, potting
telecommunication equipment, thermal cut-out switches, relays, coils, transformers, power supplies,
resistors, solenoids, transistors, sensors e.t.c.
- 71 -
4th Edition 2011
EEE 2203 Material Science II
Epoxies, urethanes and silicones are good examples of potting compounds used to bond heat
sinks, encapsulate power supplies and individual components and protect motors from overheating.
Exercise
Discuss the remaining types of encapsulation methods.
- 72 -
4th Edition 2011
EEE 2203 Material Science II
5. Soldering, Cleaning and Etching
5.1.
Soldering is used in the electronic industry to bond components together forming one or more
electrical connections. Hence soldering serves two functions;
·
Mechanical support, holding the components of an assembly
·
Electrical support, forming the required electrical connections of a circuit
Most components in an assembly use the mechanical support of soldered joints alone to give
adequate fixing into the assembly. A few isolated components (notably, larger, heavier components)
may require additional mechanical support, such as straps, nuts and bolts and so on. Solder is an alloy
usually of tin and lead with selected impurities to give changes in properties as required. In
electronics assembly, the most typical soldered joints are in the printed circuit assembly, when
components leads are soldered to the copper track of the board.
Soldering is the most fault-prone step in circuit building. Basically there are two kinds of
mishap: the solder fails to make electrical contact where it should; or solder makes electrical contact
where it should not. The first can happen if::
§
The solder does not melt or misses the point of application.
§
Surfaces to be joined are greasy or tarnished and do not ‘wet’.
§
A joint cracks during cooling owing to relative movement of the parts.
The second can happen if:
§
Too much solder has been applied.
§
A solder-wettable surface extends beyond the intended joint area.
§
Movement of the circuit relative to the solder drags a ‘wick’ of solder from the join onto an
adjacent site.
5.2.
Flux is a substance used to clean the surfaces to be soldered and so aid wetting. However,
clean they are all metals with the exception of the noble metals oxidize to form an oxide layer on
their surfaces. Other tarnish products may occur, too. Presence of any tarnish layer will prevent
wetting. Flux reacts with the tarnish layers, leaving a pure base metal surface for the solder to wet. A
secondary function of flux is to reduce the solder’s surface tension, so increasing the solder fluidity
and aiding wetting. Examples of flux materials are; oxalic acid, malonic acid, formic acid,
dimethylammonium chloride (DMA HCl), zinc chloride and hydrochloric acid.
5.3.
Etching is the process of removing the unwanted copper from the PCB. The etchant used
depends largely on board type. Simple print and etch boards are usually etched with ferric chloride,
or cupric chloride where a regeneration of etchants is required. Boards which are tin/lead plated,
- 73 -
4th Edition 2011
EEE 2203 Material Science II
particularly those with plated-through holes requires the tin/lead to be unaffected by the etchant. So
ammonical etchants are normally used.
- 74 -
4th Edition 2011
EEE 2203 Material Science II
6. Main Materials for Printed Circuit Board Bases
6.1.
Introduction
A printed circuit board, or PCB, is used to mechanically support and electrically connect
electronic components using conductive pathways, or traces, etched from copper sheets laminated
onto a non-conductive substrate. It is also referred to as printed wiring board (PWB) or etched
wiring board. A PCB populated with electronic components is a printed circuit assembly (PCA),
also known as a printed circuit board assembly (PCBA).
PCBs are inexpensive, and can be highly reliable. They require much more layout effort and
higher initial cost than either wire-wrapped or point-to-point constructed circuits, but are much
cheaper and faster for high-volume production.
Most materials used for printed circuit board bases are thermoplastic, thermosetting or
reinforced plastic. Reinforcing materials include sheet paper, glass fiber cloth, cotton fabric and
nylon. Choice should be made regarding such factors like chemical, electrical, mechanical and
thermal stability characteristics of the PCBs. The resins most commonly used for rigid base materials
are epoxy, phenolic and silicon. Epoxy resins take the lion’s share of the market, with the norm being
epoxy-resin reinforced with glass fiber cloth.
6.2.
Hybrids and Surface Mounted Assembly Bases
A special case in point is the range of bases, normally called substrate, used for hybrid and
sometimes surface mounted assemblies. It is usually the problems associated with the generation of
heat and its dissipation which define the substrate used. Typical substrates are of alumina, porcelainenameled steel and glass-ceramic coated metal-cores. By no means are these substrates limited to
purely hybrid or surface mounted assemblies, however, although, their cost may be a significant
factor in preventing their use in through-hole PCB assemblies. Hybrid and surface mounted
assemblies can have peculiar problems with regard to heat. Internally generated heat from the
components themselves and external heat from the ambient environment can affect assemblies in two
main ways;
·
Excessive heat can internally damage a circuit
·
Different thermal coefficient of expansion of components and substrates can cause stresses
which may fracture the soldered joints or the components themselves.
For these reasons, substrates used for such assemblies must dissipate heat well and must have a
thermal coefficient of expansion which closely matches that of the components used.
- 75 -
4th Edition 2011
6.3.
EEE 2203 Material Science II
Choosing a board material
The circuit board must be an insulator, so polymers or polymer composite materials are appropriate.
But a successful PCB substrate material needs many other virtues, chemical, thermal, mechanical and
dielectrical. Here is a list:
§
Conducting tracks must adhere to it, but solder should not.
§
It must not char during soldering.
§
It must be proof against the chemicals used in processing.
§
It should not absorb water (would spoil the insulation).
§
It should be immune to damage by ultraviolet light.
§
It should not suffer thermal damage such as distortion during soldering or in service.
§
It should have appropriate thermal expansion characteristics. This could be important in
determining how the assembly responds to stresses caused by temperature changes or for
ensuring the components stay in place during soldering.
§
Boards should be mechanically stiff and strong, even though quite thin, and they must be
manufacturable as flat sheets, sometimes as large as 30cm by 20cm.
§
The board material should be hard enough to be mechanically cleaned: tiny holes have to be
drilled or punched without burring, smearing or clogging the drills.
§
Low relative permittivity is preferred
§
Dielectric strengths of several kV/mm are required. Even in low voltage circuits, as
conductors are brought together the dielectric limit might be approached. The specification
usually imposes a safety margin against high-voltage surges in the circuit, such as might be
produced by current interruption in inductive components. Apart from the need to withstand
the surge itself, if the insulator does break down momentarily its subsequent quality may be
seriously impaired.
§
It must be cheap.
Thermosetting resins offer the obvious solution to the problem of high solder temperature,
provided they are adequately cross-linked. Phenol formaldehyde resin and epoxy resin are
satisfactory in all respects except for their brittleness. This is overcomed by reinforcing them.
‘Paxolin’, paper reinforced phenolic resin, is cheap and finds wide application in domestic electrical
goods. Glass fabric reinforced epoxy resin is perfect! It accounts for the majority of circuit boards for
quality electronics. Both are made by impregnating the reinforcement with resin which is
polymerized under pressure between hot, polished, steel platens. Buried conductors can be included
at this stage.
- 76 -
4th Edition 2011
6.4.
EEE 2203 Material Science II
Electrical Considerations in Selecting Material for PCB
♦ Dielectric Constant (relative permittivity)
- The more stable, the better
- Lower values may be more suitable for high layer counts
- Higher values may be more suitable for some RF structures
♦ Loss Tangent
- The lower, the better
- Becomes more of an issue at higher frequencies
♦ Moisture Absorption
- The lower, the better
- Can affect dielectric constant and loss tangent
♦ Voltage Breakdown / dielectric strength
- The higher, the better
- Typically not an issue, except in high voltage applications
♦ Resistivity
- The higher, the better
- Typically not an issue, except in low leakage applications
- 77 -
4th Edition 2011
EEE 2203 Material Science II
7. Ceramic Materials
7.1.
Introduction
Ceramics are inorganic materials which consist of metallic and non-metallic materials bonded
together by ionic and covalent bonds that are rigid than the metallic bonds. However, since these
bonds are very strong, the ceramic materials have greater heat and chemical resistance than organic
materials. Ceramics are also usually good electrical and thermal insulators. Local stress
concentrations may exceed the bond strength, however, and cause a brittle failure. These materials,
unlike metals, have few slips planes to absorb local stresses, which is the reason that ceramics are
brittle materials.
Ceramic materials have high compression strength, but low tensile strength. This feature
makes them useful for load bearing and supporting structures in building construction. Most ceramics
cannot be machined by traditional methods; modern machining methods include ultrasonic, abrasive
jet, electron beam and laser beam. Most ceramics materials are either silicates, aluminates, oxides,
carbides, borides, nitrides or hydrides.
7.2.
General Properties of Ceramics
·
Ceramics are hard, strong and dense
·
They offer strong opposition to chemical attack of strong acids and alkalis.
·
Posses a high compression strength compared with tension
·
Most ceramic such as refractories can withstand high temperature and are completely stable at
such temperatures.
·
7.3.
Ceramics offer excellent insulating properties.
Classes
Ceramics may be classified into three broad categories. These are;
7.3.1. Crystalline Ceramics
These are ceramics which do not have large number of free electrons like metals but the
electrons are either co-valently shared with adjacent atoms or transferred from one atom to another to
produce ionic bond resulting in ionized or charged atoms. The bonds so formed are stable, transparent
and offer poor electrical conductivity. Examples of crystalline ceramics are;
·
Aluminium Oxide (Alumina)
·
Magnesium Oxide
·
Manganese Sulphide
·
Silicon Nitride
- 78 -
4th Edition 2011
·
EEE 2203 Material Science II
Silicon Carbide
Aluminium Oxide
Characteristics
·
Can withstand rapid changes in temperature and pressure.
·
Can withstand high voltages; that is has high dielectric strength
·
High melting point
·
It also has a high compressive strength and wear resistant.
Application
Used in making spark plug insulating materials in a car starter, used as a refractory material in
lining of furnaces. Used in tool tips and cutting or grinding tools as well as in making artificial teeth
and as a bone filler.
Silicon nitride
Characteristics
·
Low thermal conductivity
·
Low thermal expansion
·
High thermal shock resistance
·
High mechanical strength
·
Good corrosion resistance
Applications
Used in the manufacture of rotors of gas turbines and missile radomes, heat exchangers,
furnace refractory material, laboratory ware like crucibles and high temperature bearings.
Silicon Carbide ( SiC )
Characteristics
·
High thermal conductivity
·
Low thermal expansion
·
Good wear resistant
Applications
Used in making of high temperature furnace refractory material, rocket nozzles and combustion tubes
and lightning arrestors.
7.3.2. Amorphous Ceramics
These are ceramics which posses properties of liquids and solids. That is their molecules are
not arranged properly in a regular repetitive manner. They are known as super-cooled solids or glass.
- 79 -
4th Edition 2011
EEE 2203 Material Science II
Glass can be defined as a rigid super-cooled liquid having no definite melting point and a high
viscosity to prevent crystallization. It has the advantages of being optically transparent and can be
changed easily from solid to liquid at 6500 C - 8150 C
Note that amorphous means having no form or structure. Amorphous solids do not form
crystals with regular shapes because there is no regularity in the way in which their atoms are packed
together. Be warned that not all solids which do not form regular geometrical crystals are amorphous.
Properties of glass
·
Transparent
·
Excellent corrosion resistance to chemicals (except to hydrofluoric acid, which is often used
to etch glass objects).
·
Hard at room temperature
·
Brittle
·
Poor electrical and heat conductor
·
Excellent color ability; either translucent or opaque.
Note that; coloring can be imparted to glass products and additives can be added to alter the glass
characteristics.
Typical examples of glass
Soda lime glass
A glass which softens at lower temperatures and is used for window glass, glass ware (containers)
and light bulbs. The principal materials is sand ( SiO2 ), additives soda ash and limestone.
Lead alkali silicate glass
It is also known as flint glass. It is used for optical purposes (lenses and prisms) and crystal glass
for table ware.
Borosilicate glass
This glass has low thermal expansion and does not tend to crack when evenly heated. It is
therefore used for household cookware, laboratory glassware, large telescope mirrors and chemical
pipes in industries.
7.3.3. Bonding Ceramics (Composite Ceramics)
They are made of both crystalline and amorphous materials like clay used in making bricks
and in building construction and for firebrick. The ordinary clays are composed of alumina and silica
in various proportions, with other impurities present, such as iron oxide (which gives it a red color),
manganese oxide, potash, magnesium and lime. Kaolin, a white clay that is mostly composed of
- 80 -
4th Edition 2011
EEE 2203 Material Science II
alumina and silica is used in the manufacture of earthen ware (like sanitary ware), fine china,
porcelain, paper products and firebricks.
Other bonding materials include cement, mortar and concrete. These are very important
materials in the civil engineering world.
End of EEE 2203 Syllabus.
- 81 -