Download Electrical Properties of Materials

Static Charges
Matter carries electrical charges
The charges arises from the presence of protons & electrons in the
atoms that make up the matter & a force results between charged
bodies
The force on a static electrical charge are described by
Coulombs Law-
q1  q 2 
F
e
2
4o r

Where e is the unit vector in the direction to q1 from q2
1/4o=constant 10-7c2 (or) 8.99109 Nm2/coul2 or Vm/coul
Units of o (permitivity of free space)=coul2/Nm2 (or) coul/Vm
Static Charges



q1 and q2 are charges
r is the distance between charges
The forces can be :
attractive ( as in the case of a “+” and “-” charge) or
 repulsive (as in the case of two “+” charges or two “-” charges)



The most important charge in nature is that of an electron
The charge on a electron is 1.6010-19 coulombs
Electrical Fields
If two charges are separated by a distance, r, charge 1 produces a
“condition” at the location of charge 2
When a charge 2 is at the location, it ‘feels’ a force
The condition is the electric field ‘E’ and is a vector in the direction of
F and represents the force (in newtons) on a unit charge (C) at the point
considered
q1  r
E
3
4o r
So, that the force at that location is:
F=q2E
Therefore:
E=F/q2

where r=r e
Electrical Fields
The formula shown before is for an electric field created by
a single charge
If a field is created by numbers of individual charges, the
vector E fields from each charge need only be summed:
E= E1 + E2 + E3 +E4 + …
or
E
i
q1  r i
3
4o ri
Current
The flow of electrical charge is defined as current
dq
I
dt
Where I is in C/s= amperes (amps)
One ampere is 1 C/s.
Since the charge on an electron is
1.602210-19 coulombs, it is
equivalent to 6.24151018 electrons
passing a point in one second!
Electrostatic Potential (The Volt)
A Volt (V) is the potential energy per unit charge
The potential between two points is related to the work
done in carrying a charge from a to b
b ~
~
W   F  d s
a
Since the electric field is force per unit charge, the work
per unit charge (or potential) can be derived from:
V V
b
b ~
a
~
  E d s
a
The unit for electrical potential is joule (work) per coulomb (unit
charge) and is called volt
This means that a charge of one coulomb (1 C) will acquire one joule
(1 J) of energy falling through a potential difference of one (1 V)
Capacitance
Capacitance is the ability to store charge.
A capacitor usually consists of two conductors in a
circuit separated by an insulator (dielectric).
If a voltage is applied across the plates, excess charges
will build up until the voltage is enough to discharge the
capacitor across the dielectric
The relationship
of capacitance
in a parallel
plate:
C
Ko A
d
K-relative dielectric constant, o -absolute permittivity, A area of the plates, & d - distance separating the plates
Capacitance
In terms of applied voltage, capacitance can be
described as:
Q  CV
Q- the charge in coulombs
V-potentials in volts
C-capacitance in Farad
Electrical Conduction
Ohm’s Law
Resistance is a measure of resistance to flow of
electricity.
It is defined as follows:
R
Where
V
I
I = Current (Ampere or C/s)
V = Voltage (Volt or J/C)
R = Resistance (Ohm or V/A)
, resistance is in the units of volts per ampere.
One volt per ampere is called an ohm ().
Current Density
Can be expressed as
J
Where J = Current density, A/m2
E = Electric field, V/m
ρ= electrical resistivity, Ωm
Or
q
J
At
E

Where Δq is the net quantity of
charge flowing through an area A in
time Δt
Resistivity ()
RA

l
Where
l = distance between two points at which voltage is measured
A = cross-sectioned area perpendicular to the direction of current
 has the unit of m
Schematic representation of
apparatus used to measure
electrical resistivity
Electrical conductivity () is the reciprocal of
the resistivity ()

1

•  has the unit of (m)-1
• solid materials show amazing range of
conductivity over 27 orders of magnitude
• Using the conductivity : materials can be
categorized:
•Metal-Good conductor
•Insulators-Very low conductivities
•Semiconductors-Intermediate conductivities



A conductor-a substance that allows current to flow
through it
In metals, the current is composed of moving
electrons
Electrolytic solutions also conduct current but by
the movement or flow of ions
VS
Insulators have few mobile electrons or ions
The flow of current is inhibited
As fields are increased, dielectric breakdown of
insulators occurs and the current is discharged as a
surge
The dielectric strength is the maximum field an
insulator can support
Conductors/Metals :  ~ 10+7 (•m)-1
Semiconductors :  ~ 10-6 to 10+4 (•m)-1
Insulators :  ~ 10-10 to 10-20 (•m)-1
Electrical Conduction in Ionic Ceramics and in Polymers
Electrical Conductivity [(-m)-1]
Material
105
Graphite
CERAMICS
Aluminum oxide
Porcelain
Soda-lime glass
Mica
10-10- 10-12
POLYMERS
Phenol-formaldehyde
Nylon 6,6
Polymethyl methacrylate
Polyethylene
Polystyrene
Polytetrafluoroethylene
10-9- 10-10
10-10- 10-12
<
10-10
10-11- 10-15
10-9- 10-12
<
10-12
10-13- 10-17
<
10-14
< 10-16
Most polymers and ionic ceramics are insulators with Eg > 2 eV
Very small conductivity, then high resistivity
  increases with temperature

Electrical Conduction in Ionic Materials and in Polymers
Both cations and anions can move/migrate/diffuse under application of E
Another definition of current- a net movement of these charged ions (in
addition to electrons)
Thus, conduction:
total = electron + ion
Polymers are very insulative and mostly only electronic contribution
Conducting Polymers (with dopants)
Many applications due to low density, flexibility, and production ease
Electrodes in rechargeable batteries
Wiring in aircraft
Electronic devices (Transistors/Diodes)
Electron Conduction
in Real Mode
Influence of Temperature
 Influence of Impurities
 Influence of Plastic Deformation

Electrical Resistivity of Metals
 Resistivity: Scattering of electrons due to crystal defects
Increasing the numbers of defect raises resistivity( lowers conductivity)
 Number of defects depend on temperature, composition, specimen, and thermal history
total = t + i + d  Matthiessen’s Rule
t = thermal contribution
i = impurity contribution
d = plastic deformation
independent
Influence of Temperature
Temperature
t   0  aT
o and a are constant for metal
The temperature is dependent on thermal resistivity
component on temperature is due to the increase with
temperature in thermal vibrations and other lattices
irregularities (i.e. vacancies) which serve as electronscattering centers
Influence of Impurities
i  Aci (1  ci )
Impurities
For additions of a single impurity the impurity
resistance i is related to the impurity
concentration ci in terms of the atom fraction (at
100%)
A is a composition-independent constant that is a
function of both impurity and host metals
ENERGY BAND
A range
of energies that electrons can have in a solid. In a
single atom, electrons can exist in discrete energy levels.
In a crystal, in which large numbers of atoms are held
closely together in a lattice, electrons are influenced by a
number of adjacent nuclei and the sharply defined levels
of the atoms become bands of allowed energy; this
approach to energy levels in solids is often known as the
band theory.
Each band represents a large number of allowed quantum
states.
Between the bands are forbidden bands.
The outermost electrons of the atoms form the valence
band. This is the band, of those occupied, that has the
highest energy.
Conduction Band




The band structure of solids accounts for their electrical
properties.
In order to move through the solid, the electrons have to
change from one quantum state to another.
This can only occur if there are empty quantum state to
another. This can only occur if there are empty quantum
states with the same energy.
In general, if the valence band is full, electrons cannot
change to new quantum states in the same band. For
conduction to occur, the electron have to be in unfilled
band - conduction band
Energy Band Structure in Solids
2s
1s
Individual atom
(Quantum Numbers : n, l, m, s)
Bring 12 atoms closer
Energy Band Structure in Solids
Valence Band = the band that contains the highest energy or valence electrons
Conduction Band = the next higher energy band, most likely unoccupied by electrons
At equilibrium spacing, band may not form in innermost electrons 
Energy Band Structure in Solids
Valence band is partially
filled
(Cu)
Filled valence band
overlapping with conduction
band (Mg)
Filled valence band with
“energy band gap” Eg
(insulator/semiconductors)
 Fermi Energy Ef = the energy of the highest filled state at 0 K 
Atomic Bonding and Band Conduction
 Only electrons with E > Ef are active in electric field 
 Hole = charged electronic entity with E < Ef (found in insulators/semiconductors 
Metal
 metallic binding “electron gas”
 vacant state next to Ef
 Easy to excite  high 
Insulator
 ionic/covalent bonding
 highly localized e hard to move  large Eg
Semiconductor
 weak covalent
 Easy to move
 low Eg
Ferroelectricity
•Exhibit spontaneous polarization which is
polarization in the absence of electric field
•Materials exhibit ferroelectric properties:
Barium Titanate, Rochelle salt, potassium
dihydrogen phosphate, potassium niobate,
lead zirconate-titanate
•Have extreme high dielectric constant at
relatively low applied field frequencies
•Capacitors from this material much smaller
than other dielectric materials
Piezoelectricity
•Pressure electricity
•Polarization is induced and electric field is
established across a specimen by the
application of external forces
•Utilized in transducers. For instance, some
transducer will convert electrical energy into
mechanical strains or vice versa
•Piezoelectric materials: titanates of barium &
lead, lead zirconate, ammonium dihydrogen
phosphate & quartz
•A common application of piezoelectric material
-ultrasound transducer
From: http://www.pennhealth.com/
health_info/Surgery/
graphics/ultrasound_2.jpg
From:
http://static.howstuffworks.com/
gif/ultrasound1a.jpg