Babylon University College of Materials EngineeringMetals Eng. Department

METALLIC CONDUCTORS

Prepared by

ENG.AHMED SALIH ABD AL-HUSSEIN

Content :

INTRODUCTIONELECTRICAL CONDUCTIVITY & RESISTIVITYCONDUCTION IN PURE METALSFACTORS AFFECTING THE RESISTIVITY OF

ELECTRICAL METALSSUPERCONDUCTIVITYENERGY BANDS IN SOLIDELECTRICAL CONDUCTIVITY AND RESISTIVITY FOR

ALLOY PHASES THERMAL CONDUCTIVITY OF METALS ELECTRICAL CONDUCTIVITY OF MULTY PHASE

METALS

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).

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.

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

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

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)

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 .

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.

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:

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 .

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.

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.

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).

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.

FIG. CONDITIONS FOR SUPER CONDUCTION.

ZERO RESISTIVITY AND NEGLIGIBLE

MAGNETIC PERMEABILITY OCCUR

WHEN SUPERCONDUCTING METALS ARE IN LOW MAGNETIC FIELD AT LOW TEMPERATURE .

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

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.

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.m99%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.

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 .

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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

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/m32. V, the average velocity of the electrons 3. dW/dx , the energy gradient 4. A, the area of cross-section

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

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 Κ= c (1- ƒd ) / (1+ ƒd/2)When Κ c < 0.1 Κd Κ Κ= c (1+ 2ƒd) / (1- ƒd )

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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