To know the material conductivity and resistivity.

1. Prepared by

2. Content :
 INTRODUCTION
 ELECTRICAL CONDUCTIVITY & RESISTIVITY
 CONDUCTION IN PURE METALS
 FACTORS AFFECTING THE RESISTIVITY OF ELECTRICAL
METALS
 SUPERCONDUCTIVITY
 ENERGY BANDS IN SOLID
 ELECTRICAL CONDUCTIVITY AND RESISTIVITY FOR ALLOY
PHASES
 THERMAL CONDUCTIVITY OF METALS
 ELECTRICAL CONDUCTIVITY OF MULTY PHASE METALS

3. INTRODUCTION :
The most important properties of metals are their high thermal and
electrical conductivities.
Silver has the highest electrical conductivity. Copper comes next and is
similar to silver from the point of view of atomic structure ; both
belonging to the same group of periodic table.
The conductivity of copper is less than that of silver. Since supplies of
copper are not abundant in nature, Aluminum which is light and has a
high conductivity is rapidly becoming more important as a conductor
material. Gold which has a conductivity higher than that of aluminum
but lower than that of silver or copper does not find use in
electrical industry because it is expensive.
Metals having complex structures such as As, Sb, Bi, Sn , Hg have lower
conductivities which lie between those of ideal metal (very high
conductivity) and of insulators (negligible conductivities).

4. Types of Conducting Materials:
The electrical properties of materials can be divided into three
broad categories: conductors, insulators, and semiconductors. In
addition, a few materials exhibit superconductivity, but we will
not address those here.
Metals (both pure elements and alloys) are called conductors,
because they typically conduct electricity. Materials like glass,
Teflon, ceramics, and plastics are called insulators, because they
are poor conductors of electricity. The third category,
semiconductors, their properties lie between conductors and
insulators. Semiconductors are interesting, because we can
control their electrical properties.

5. ELECTRICAL CONDUCTIVITY and RESISTIVITY
The atoms of metal elements are characterized by the presence of
valence electrons .electrons in the outer shell of an atom that are
free to move about it . These free electrons are allow metals to
conduct an electric field.
The conductivity is depend on :
 Length of conductor (extrusive ).
 Cross sectional area of conductor (reverse).
 Resistivity (reverse).
Electrical conduction occurs through transport of electric charge in
response to an applied electric field .electric charge is carried by
electrons ,electron holes, and ions.
σ =L/RA

6. Electrical conductivity σ and its reciprocal ,electrical resistivity ,
ρ=1/σ ,
are physical properties of a material . While the range of values is
somewhat arbitrary , electrical conductivity is very low in
insulator , σ<10-15 S/cm ( ρ>1021 Ωcm ), intermediate in
semiconductors , σ=10-5 S/cm ( ρ= 103-1011 Ωcm ), very high in
conductors , σ= 104-106 S/cm ( ρ=1- 102 µΩcm ), and infinite in
semiconductors .
Electrical conductivity σ is defined as the product of the number of
charge carriers , n, the charge , e, and the mobility of the charge
carriers , µ .
The charge mobility is mean net velocity that’s attained within
electric field , the units of µ is (m2/V.s) .
σ =n . e .µ

7. For electronic conductors the electron charge , e=1.6 * 10-19 coulombs
is constant and independent of temperature . The mobility
usually decreases with the increases temperature due to collisions
between the moving electrons and phonons , i.e. ,lattice vibrations
. The number of charge carriers remains constant for metallic
conductors with increasing temp .
Electrical resistivity ρ is a property of a material . Resistance (Ω),
which is commonly used in circuit calculations , differs from
resistivity (Ω.m) in that resistance possesses geometrical factors
R=ρ(L/A)
Can be expressed about conductivity as a ratio of the current density
(I) and the electric field (ε) .
σ = I /ε = (A/ m2)/ (V/m)

8. Conduction in pure metals :
The charge transport in pure metals is caused by drift of free electrons .
In some metals like beryllium and zinc , the movement of charge is
considered to be due to electron holes . Free electrons have
comparatively high velocities and relatively long mean free paths until
they collide with ions constituting the crystal lattice , this process called
scattering . In a perfect periodic lattice structure , no collisions would
occur and the resistivity would be zero .
Mean free paths of the electrons are limited by :
 Ionic vibrations due to thermal energy.
 The crystal defects ,such as vacancies , dislocation , grain boundaries.
 The random substitution of impurity atoms on the pure metal sites .
As the temperature increased , the ionic vibration grow larger and
scattering increased . This offers more resistance to the flow of electrons
.

9. FACTORS AFFECTING THE RESISTIVITY OF ELECTRICAL
METALS:
1. Temperature : The electrical resistance of most metals
increases with increase of temperature because of increasing
temperature lead to increase the capacity of vibration of atoms
and thus increase the number of collisions between free electron
and atoms ,which leads to impede the movement of electrons
and the loss of part of its kinetic energy , while those of
semiconductors and electrolytes decreases with increase of
temperature. Many metals have vanishing resistivity at
absolute zero of temperature which is known as
superconductivity.
2. Alloying : A solid solution has a less regular structure than a
pure metal. Consequently, the electrical conductivity of a solid
solution alloy drops off rapidly with increased alloy content. The
addition of small amount of impurities leads to considerable
increase in resistivity.

10. 3. Cold Work : Mechanical distortion of the crystal structure
decrease the conductivity of a metal because the localized strains
interfere with electron movement.
4. Age Hardening : It increases the resistivity of an alloy.
As show in fig below:

12. SUPERCONDUCTIVITY :
The phenomenon of superconductivity was discovered in 1911 by
Kamer- lingh Onnes when he observed that the electrical resistance
of mercury vanished below 4.15 K. Instead of the expected resistivity
temperature dependence for normal metals, an anomalous drop in
conductivity for the superconductor occurred. Actually, the
resistivity was not exactly (0) Ω-cm, but rather estimated
not to exceed (10^-20) Ω-cm.
This is some 14 orders of magnitude below that of normal metals.
The promise of low-Joule heating losses in electric power and
transmission systems accounts for the intense interest in
superconductors.

13. Of the several material properties that influence the viability of
superconductors in engineering applications, there are four key
ones:
1. Critical Temperature (Tc). Above Tc superconductivity is
extinguished and the material goes normal. Liquid helium
(4.2 K) cooling systems are not cheap and therefore a high Tc
value is imperative. Progress in raising Tc over the years (until
about 1986) had been slow.
2. Critical magnetic field (HcJ. Superconductivity disappears when
the magnetic field (more correctly, magnetic flux density) rises
above Hc.; therefore, high values of the latter are desired.

14. 3. Critical current density ( Jc), A superconductor cannot carry a
current density in excess of Jc without going normal; the high
magnetic fields the currents produce are the reason. If each of the
three critical properties is plotted on the coordinate axes, the
enveloping surface, in phase diagram-Uke fashion, distinguishes
between superconducting and normal states. It is obviously
desirable to extend this surface outward as far as possible in all
three variables.
4. Fabricability. The ability to fabricate the superconductor into
required conductor shapes and lengths is essential.

15. Since 1911 superconductivity has been found to occur in some 26
metallic elements and in hundreds, or perhaps thousands, of
alloys and compounds; some of these are listed in Table 11-4
together with the key properties of interest. There are two kinds
of superconductors: type I (or soft) and type II (or hard).

16. Superconductors are obvious choices in applications requiring high
current densities, very large magnetic fields, and devices that must
be energy efficient.
Low-energy-loss, superconducting power transmission lines are
always desir-able but only practical in special cases where the
necessary refrigeration systems are cost effective. Powerful
electromagnets consisting of dc powered coils of multiturn
superconducting wire are commercially used in both magnetic reso-
nance spectrometers and medical imaging systems. Type II
superconductors (e.g., NbTi, Nb3Sn) are exclusively used for these
purposes because of their high H^ values. The greatest potential for
superconductor usage, however,appears to be in transportation
systems. Strong magnetic fields that levitate trains (MAGLEV) are a
viable way to achieve high-speed rail transportation without friction
and hence minimum energy expenditure.

18. ENERGY BANDS IN SOLID :
To know why some insulation materials and others conductors of
electric current to note that the energy levels are distributed of
electrons . Its materials in the form of energy band and the
distance between the energy band can not exist of electrons .
There are two types of energy bands, one know valance bands and
the electrons within these band restricted atom and don’t share
the electrical conduction .
When the valance electrons get on sufficient energy extend that its
free from the association atom, they jump to the next band ,
which is

19. Conduction band and electrons found in the band , its will share of
electrical conductivity .
There is found between valance band and conduction and restricted
area cant be found electrons called energy gap.

20. ELECTRICAL CONDUCTIVITY AND RESISTIVITY FOR ALLOY
PHASES:
The conductivities of solid solutions are always less than those of the
pure metal .for example ,as nickel dissolves in f.c.c copper,
Pure copper σ= 60*106 Ω-1 .m-1 , ρ=0.017*10-6 Ω.m
99%Cu – 1%Ni σ= 35*106 Ω-1 .m-1 , ρ=0.029*10-6 Ω.m
Fig : electrical conductivity of sold
solution alloys, the Conductivity is
reduced when nickel is added to Cu
, and when copper added to Ni.

21. We cannot interpolate linearly between the conductivities of the two
component metals since the conductivities of both decreases as
they are alloyed .also, observe that while brass is stronger and
cheaper than copper , the brass is unsuitable for most electrical
wires .
Brass has only 27% of the conductivity and 3.7 times the resistivity of
pure copper .
.

22. THERMAL CONDUCTIVITY OF METALS :
It is observed that metals which are good conductors of electricity
are also good conductors of heat.
When a homogenous isotropic materials is subjected to a
temperature gradient, a flow of heat results in a direction opposite
to the gradient. Thus if dT/dx represents the temperature
gradient, the quantity of heat flowing per second is found from
the expression.
If Q is expressed in watts, dT/dx in K per meter and the area of cross
section A in m^2, then the coefficient of thermal conductivity, K is
given in watts/m* K.
In insulating solids, the heat is carried by the lattice vibrations. This
in part is also the case in metals, but the thermal conductivity
due to the conduction electrons predominates in both
insulators and conductors.
Q=K.A dT/dx

23. The electrons in the hot end has a higher thermal energy. They move
to the cold end where the excess energy is released to the
atoms whereby the thermal agitation of the atoms and the
temperature increase. The electrons of the cold end have less
kinetic energy; so in passing to the hot end they decrease the
thermal agitation and the temperature. Since the same electrons
also conduct electric current, the transfer of heat and the
conduction of current must be closely related processes.
Finally, the total energy transferred across a cross-section is
dependent upon :
1. N, the number of electrons/m3
2. V, the average velocity of the electrons
3. dW/dx , the energy gradient
4. A, the area of cross-section

24. ELECTRICAL CONDUCTIVITY OF MULTY PHASE
METALS:
A material that contains a mixture of two or more phases doesn’t
follow eq - ρᵪ = yᵪ x (1-x) . That eq gave the resistivity of a solid
solution within a single alloy phase . The conductivity of
multiphase mixture depends not only upon the amounts of several
phases but also upon their distribution . As a result , a calculation
could became complex .
The special case of fig 17-5.1 (a) has mixture in parallel . This leads to
a mixture rule that is linear with volume fraction ,ƒ, of the two
phases . For thermal conductivity, Κ=ƒ₁Κ₁+ƒ₂Κ₂
For electrical conductivity , σ=ƒ₁σ₁+ƒ₂σ₂
For fig , 17-5.1 (b). This leads to a mixture rule that relates the
reciprocals of the conductivities .
For thermal conductivity, 1/Κ=ƒ₁/Κ₁+ƒ₂/Κ₂

25. or for electrical conductivity, 1/σ=ƒ₁/σ₁+ƒ₂/σ₂
The corresponding mixture rule takes on two empirical forms ,
depending on whether the continuous (matrix) phase ,C , is
markedly more , or markedly less , conductive than the dispersed
phase ,d
(fig 17-5.2) when Κc > 10 Κd
Κ=͂Κc (1- ƒd ) / (1+ ƒd/2)
When Κc < 0.1 Κd
Κ=͂Κc (1+ 2ƒd) / (1- ƒd )

26. The relationships below apply to the conductivities of both metallic
and non – metallic mixtures since they don’t depend on the
mechanism of conductivity.
Κ =͂ ∑ ƒᵢ Κᵢ

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