Conductors & Insulating Materials
The electrons in the outermost orbitals of the atoms of a solid determine its electrical properties. The free electron model is introduced, starting with a brief description of the wide range of resistivity of materials. The justification for Ohm’s law is given, in terms of the free electron motion and the collisions processes in crystals. Materials for conductive and resistive functions are discussed.
Conductors are metals and alloys. Gold, silver and copper are among the best conductors of electricity. Therefore, their electrical resistivities are the lowest, as shown in table below. They are followed by aluminium whose resistivity is 60% higher than that of copper. Transition metals such as iron and nickel are not as good conductors as shown below. Still poorer conductors are the semimetals of the fifth column, e.g., antimony and bismuth. Graphite, with one of its bonding electrons resonating between the (sp2) bonds, also fall in this category of semimetals. The electrical resistivity of conductor’s ranges from 10-9 to 10-3ohm m. The electrical conductivity, being the reciprocal of resistivity, ranges from 109 ohm-1 m-01 to 103 ohm-1 m-1.
Planck’s constant h = 6.626 × 10-34 J s
Rest mass of electron m = 9.109 × 10-31 kg
Charge of electron e = 1.602 × 10-19‑ C
of resistance α
Per ohm per metre
De Broglie wavelength λ
Wave number k
metre per second
Field gradient ε
Volt per metre
Current density Je
Ampere per m2
When the resistivity is in the range 10-3-103 ohm m, we have the second category of materials known as semiconductors:- they form the base for a number of solid state devices. Here, the resistivity is a strong function of small concentrations of impurities. Doped germanium, with an impurity content of a few tens per million, can have a resistivity about two orders of magnitude lower than that of pure germanium as shown in above table. Pure silicon has a higher resistivity than pure germanium.
The third category of materials are insulators:- Common electrical insulating materials such as polyethylene, Bakelite, Lucite, mica, PVC, rubber and porcelain fall in this category. The resistivity range for this category extends from 104 to beyond 1017 ohm-m. Here, a difference in resistivity of some twelve orders of magnitude is noticeable between a silica glass and soda-lime-silica (window glass). This striking difference is a result of the ionic conductivity of window glass. The relatively loosely bound sodium and calcium cations in soda-lime glass diffuse and conduct much more readily, as compared to the tightly bound immobile silicon cations in pure silica. Ionic conduction and ionic diffusivity are closely related phenomena.
THE FREE-ELECTRON THEORY
The conducting properties of a solid are not a function of the total number of electrons in the solid, as only the outermost electrons of the atoms can take part in conduction. In the free electron model, the outermost electrons of an atom are not bound to that atom, but are free to move through the whole solid. These electrons have been variously called the free electron cloud, the free electron gas or the Fermi gas.
In the free electron theory, the basic assumption is that the potential field due to the ion cores is uniform throughout the solid. The free electron have the same potential energy everywhere in the solid. Due to the electrostatic attraction between a free electron and the ion cores, this potential energy will be a finite negative value. As we are interested only in energy differences, we can assume this constant potential to be zero. Then the only energy that we have to consider is the kinetic energy. This kinetic energy is substantially lower than that of the bound electrons in an isolated atom, as the field of motion for the free electron is considerably enlarged in the solid as compared to the field around an isolated atom.
Electrons have both particle-like and wave-like characteristics. The de Broglie wavelength of an electron λ is related to its momentum mv as
Where h is Plank’s constant, m is the mass of the free electron and ν is its velocity. The wavelength is inversely related to the magnitude of the wave number vector k:
As the velocity of the free electrons is much smaller than that of light, we can ignore relativistic effects and use the classical relation for kinetic energy E.
Substitute the above values from equations, we obtain
CONDUCTION BY FREE ELECTRONS
The wave number k takes both positive and negative values. For every electron moving with a certain speed in a direction, there is another electron moving with the same speed in the opposite direction. This equal and opposite velocity distribution in a neutral solid can be biased by an externally applied electrical field to yield a net velocity in one direction. With this biasing, the solid conducts electricity.
Figure: Electrons moving towards the positive end of the applied field acquire extra velocity, while those moving in the opposite direction lose some velocity.
The negatively charged electrons are accelerated towards the positive end of the field. The velocity of the fastest electron moving in the direction of the positive end has a larger magnitude than that of the fastest electron moving towards the negative end of the field. Such redistribution is possible, only when empty electron states are available immediately above the Fermi level. This availability is a basic characteristic of conductors, as opposed to semiconductors and insulators.
The force experienced by an electron of charge e in an applied field of gradient ‘ε’ can be equated to the force as defined in the classical law:
εe = ma
when m is the mass of the electron and a is the acceleration due to the applied field. The electrons that are accelerated towards the positive end of the field do not continue to increase their velocity indefinitely. They collide with obstacles on their way. Depending on the time interval between two successive collisions, the electrons acquire an average increment of velocity called drift velocity, all of which they lose during a collision, as illustrated in Fig. 14.5. The drift velocity is the extra velocity that electrons acquire over and above their normal velocity in the absence of a field.
Figure: The extra velocity acquired by an electron due to an applied field is lost on collision with an impurity, imperfection or phonon.
If the average collision time is τ and vd is the drift velocity acquired by the electrons.
m(vd/τ) = εe or vd= εeτ/m
The flux Je due to the flow of electrons is called the current density:
Where n is the number of free electrons of charge e. This is in the form of Ohm’s law. As conductivity σ is by definition the flux per unit potential gradient, we have
The electrical resistivity ρ is the reciprocal of conductivity.
Conductors and Materials
The resistivity, the temperature coefficient of resistance, the density and the tensile strength of typical conductor and resistor materials are listed in Table below.
Properties of Typical Conductors and Resistors at Room Temperature
10-8 ohm m
103 kg m-3
The tensile strength values given here are approximate, as they depend on the prior thermal and mechanical history of the metal.
For use as conductors in applications such as transmission lines and distribution lines, how I2R loss is the primary consideration and the choice would be from amongst the best conductors, keeping in view the cost, fabricability and mechanical strength. Copper and aluminium are the most likely choices. For long distance transmission lines, aluminium is chosen. As a large cross section would reduce the I2R loss, thick cables are preferred. If the elastic modulus of the aluminium cables is improved by reinforcement with steel as in ACSR (aluminium conductor steel reinforced) cables, the distance between successive poles along the transmission line can be substantially increased. More expensive copper is used for distribution lines, busbars and other energy conversion applications, OFHC (oxygen-free high conductivity) copper is often specified., Among the common solutes in copper, Fe, P and As are the most harmful in impairing the electrical conductivity.
For electrical contacts used in switches, brushes and relays, the material must possess high electrical conductivity, high thermal conductivity, high melting point and good oxidation resistance. High thermal conductivity helps to dissipate the heat effectively. High melting point is desirable so that may accidental overheating does not fuse together the contact points. Good oxidation resistance is necessary to keep the contact clean and free of insulating oxides. Copper and silver largely satisfy the above requirements. For low cost, copper is commonly used. For critical contacts such of pure silver is increased by the dispersion of fine particles of CdO.
Dislocations moving in silver have to bend around the dispersed CdO particles and a fine dispersion increases the strength. CdO improves the wear resistance of silver. It also decomposes at the melting point of silver, thereby absorbing much of the heat generated by arcing and minimizing the loss of expensive silver by evaporation.
Superconductivity is the set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor.
Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.
Figure 1: Temperature comparison
The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect.
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature.
A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too strong.
Important points of superconductors:
(i) Some elements offer zero resistance property while carrying current when worked at below certain temperature.
(ii) Direct current (DC) flowing in the coil produces strong sustained magnetic field even the current becomes zero it is maintained.
(iii) Magnetic field is utilized as stored energy.
Above the critical temperature, a superconductor has no notable effect when a magnetic field is applied, as the magnetic field is able to pass through the superconductor unhindered. If the superconductor is below its critical temperature, the applied magnetic field is expelled from inside of the superconductor and bent around it, called as Meissner effect, shown in figure. Because surface current that flows without resistance create magnetization within superconductor is equal and opposite to the applied magnetic field, resulting in cancelling out the magnetic field everywhere within the superconductor. This results in superconductor having a magnetic susceptibility of -1, that means it exhibits perfect diamagnetism.
Fig: state of metal in normal conducting state and superconducting state
Superconductors can be divided into two classes according to how this breakdown occurs.
Type-I Superconductors: There are thirty pure metals which exhibit zero resistivity at low temperatures and have the property of excluding magnetic fields from the interior of the superconductor (Meissner effect). They are called Type I superconductors.
The superconductivity exists only below their critical temperatures and below a critical magnetic field strength.
Type I superconductors are well described by the BCS theory, which relies upon electron pairs coupled by lattice vibration interactions.
Remarkably, the best conductors at room temperature (gold, silver, and copper) do not become superconducting at all. They have the smallest lattice vibrations, so their behavior correlates well with the BCS Theory.
A type I superconductor consists of basic conductive elements that are used in everything from electrical wiring to computer microchips. At present, type I superconductors have Tc between 0.000325 °K and 7.8 °K at standard pressure. Some type I superconductors require incredible amounts of pressure in order to reach the superconductive state. One such material is sulphur which requires a pressure of 9.3 million atmospheres (9.4 x 1011 N/m2) and a temperature of 17 °K to reach superconductivity. Some other examples of type I superconductors include Mercury - 4.15 °K, Lead - 7.2 °K, Aluminum - 1.175 °K and Zinc - 0.85 °K.
The Type I superconductors have been of limited practical usefulness because the critical magnetic fields are so small and the superconducting state disappears suddenly at that temperature.
Type-II Superconductors: Starting in 1930 with lead-bismuth alloys, a number of alloys were found which exhibited superconductivity; they are called Type II superconductors. They reach a superconductive state at much higher temperatures when compared to Type I superconductors.
They were found to have much higher critical fields and therefore could carry much higher current densities while remaining in the superconducting state.
Type I superconductors are sometimes called "soft" superconductors while the Type II are "hard", maintaining the superconducting state to higher temperatures and magnetic fields. Type II superconductors can also be penetrated by a magnetic field whereas a type I cannot.
Figure 2: Magnetic field variation of Type Ӏ (A) and Type ӀӀ (B) superconductor
The superconducting state cannot exist in the presence of a magnetic field greater than a critical value, even at absolute zero. This critical magnetic field is strongly correlated with the critical temperature for the superconductor, which is in turn correlated with the band gap. Type II superconductors show two critical magnetic field values, one at the onset of a mixed superconducting and normal state and one where superconductivity ceases.
It is the nature of superconductors to exclude magnetic fields (Meissner effect) so long as the applied field does not exceed their critical magnetic field. This critical magnetic field is tabulated for 0K and decreases from that magnitude with increasing temperature, reaching zero at the critical temperature for superconductivity. The critical magnetic field at any temperature below the critical temperature is given by the relationship:-
INTRODUCTION TO INSULATING MATERIALS
Electrical insulating materials are defined as materials which offer a very large resistance to flow of current, and for that reason they are used to keep the current in its proper path along the conductor.
A large number of substances and materials may be classified as insulators, many of which have to be employed in practice, as no single substance or material can satisfy all the requirements involved in the numerous and varied applications of insulators in electronics & electrical engineering. Such requirements involve consideration of physical properties, reliability, cost, availability, adaptability to machining operations etc.
Thus in some applications the insulating material in addition to its function as an insulator may have to act as a rigid mechanical support to the conductor and may be installed out of doors, in which case the insulating qualities must be retained under all atmospheric conditions, in other cases extreme flexibility is required.
Again, in electric heaters the insulating materials must maintain their insulating qualities over a wide range of temperatures extending in some cases to 1100°C, and for radio purposes the insulating qualities must be maintained upto very high frequencies.
In electrical machines and transformers, the insulating materials applied to the conductors are required to be flexible, to have high specific electric strength (to reduce thickness to minimum) and ability to withstand unlimited cycles of heating and cooling.
CHARACTERISTICS OF A GOOD INSULATING MATERIAL
A good insulating material should possess the following characteristics:
- Large insulating resistance.
- Highdialectic strength.
- Uniform viscosity—it gives uniform electrical and thermal properties.
- Should be uniform throughout—it keeps the electric losses as low as possible and electric stresses uniform under high voltage difference.
- Least thermal expansion.
- When exposed to arcing should be non-ignitable.
- Should be resistance to oils or liquids, gas fumes, acids and alkalies.
- Should have no deteriorating effect on the material, in contact with it.
- High mechanical strength.
- Low dissipation factor (loss tangent).
High thermal conductivity.
High thermal strength.
Free from gaseous insulation to avoid discharges (for solids and gases).
Should be resistant to thermal and chemical deterioration.
- Should be homogeneous to avoid local stress concentration.
CLASSIFICATION OF INSULATING MATERIALS
The insulating materials can be classified in the following two ways:
- Classification according to substances and materials.
- Classification according to temperature.
A. Classification According to Substances and Materials:
- Solids (Inorganic and Organic):
Mica, wood, slate, glass, porcelain, rubber, cotton, silk, rayon, terylene, paper and cellulose materials etc.
2. Liquids (Oils and Varnishes):
Linseed oil, refined hydrocarbon mineral oils, spirit and synthetic varnishes etc.
Dry air, carbon dioxide, argon, nitrogen etc.
B. Classification According to Temperature:
Insulating materials Included
Assigned limiting Insulating temperature
Cotton, silk, paper, cellulose, wood, etc., neither impregnated nor immersed in oil. Materials of Y class are unsuitable for electrical machines and apparatus as they deteriorate rapidly and are extremely hygroscopic.
Materials of class Y impregnated with natural resin, cellulose esters, insulating oils etc. Also included in this list are laminated wool, varnished paper.
Synthetic resin enamels, cotton and paper laminates with formaldehyde bounding etc.
Mica, glass fibres, asbestos with suitable bonding substance, built up mica, glass fibre and asbestos laminates.
Materials of class B with bonding materials of higher thermal stability.
Glass fibre and asbestos materials, and built up mica, with silicon resins.
Mica, ceramics, glass quartz without binders or with silicon resins of higher thermal stability.
AIR SPACES IN INSULATION
When an insulation is designed every attempt is made to avoid the existence of air spaces in it. Though, it is difficult to avoid air spaces in materials such as fabricated and impregnated insulation yet these may be prevented by vacuum impregnation or by gas or oil filling under pressure.
The air spaces exercise harmful effects in the following way:
When a solid insulation containing air spaces is subjected to voltage, ionization occurs (the phenomenon being known as corona).
Consequences of ionization include-
- A great power loss in the insulation;
- Thermal instability;
- Lowering of the breakdown voltage of the insulation;
- There is carbonization, decomposition and mechanical damage to the insulating material.
Thus, when there are air spaces in the insulation, it should not be overstressed and the material should have corona resistance properties.
EFFECT OF MOISTURE ON INSULATION
When an insulating material is placed in a humid atmosphere it absorbs a certain amount of moisture. The water vapours, at first, are absorbed on the surface, then they diffuse tending to reduce moisture concentration gradient and finally they are desorbed into lower vapour concentration region.
In an insulating material moisture diffusion, as a rule, takes place when the electrical equipment is inoperative. When the current is carried by the electrical equipment, the moisture diffuses from the insulating material (i.e., material dries up).
All solid dielectrics, on the basis of absorption of moisture in highly humid atmosphere, can be classified as under:
- Hygroscopic and wet table materials.
- Non-hygroscopic and wet table materials.
- Non-hygroscopic and non wet table materials.
The air having high humidity is a source of troubles in electrical insulation and can even cause failure of electrical equipment.
The effect of moisture on insulating materials brings about the following changes:
- Changes in electrical properties.
- Chemical changes.
- Physical and mechanical changes.
- Changes in Electrical Properties:
- The moisture absorbed by an insulating material causes- (a) a decrease in the volume resistivity, and especially surface resistivity (b) an increase in the dissipation factor and a certain increase in dielectric constant (c) decrease in dielectric strength due to a change in field distribution within the insulating material.
- Conducting bridges may appear across the surface of the insulating material under high humidity and electric tension current.
In some cases the thin films formed of the moisture on the insulating material dries up when the equipment is working. Such places get a carbonized spot and such spots may join together with time and build up a conducting bridge, thus a short circuit may result.
2. Chemical Changes:
- High humidity often cause hydrolysis.
- High humidity favours the growth of fungi in some insulating materials, which in turn degrade organic insulating materials.
3. Physical and Mechanical Changes:
- Some materials like plastics, polymers and materials filled with cellulose filters swell in the presence of high humidity.
- Mechanical strength of the insulating material is reduced in the presence of moisture.
PROTECTION OF INSULATION AGAINST MOISTURE
The insulation can be protected against moisture by following methods
(i) Impregnation of Winding:
The windings of all low voltage equipments are impregnated with baking varnishes (sometimes compounds are also used). Impregnating varnishes and compounds raise the moisture resistance of windings.
Impregnation treatment solidifies the windings, increases their thermal conductivity, improves their electrical and mechanical strength and heat resistance.
(ii) Making Insulation Hydrophobic (Waterproof):
The insulating materials assemblies sometimes are rendered hydrophobic to protect them against moisture. This type of treatment is specifically effective for polymers containing hydroxyls and for cellulose base insulating materials.
In comparison to old widely used techniques employing asphalts, bitumens, waxes, water-proofing by means of some hydrophobic silicon compositions free of hydroxyls and carboxyls is finding ever increasing favour. Paper, cotton fabric are rendered hydrophobic by dipping them in the solution of methyl butoxidiamine silane in carbon tetra-chloride or methyl triethoxisilane in absolute alcohol.
(iii) Hermetic Sealing:
Hermetic sealing (sealing by means of compounds) is widely used to protect insulation against moisture and help in maintaining adequate insulation properties of parts and protect them against mechanical damage. This treatment is normally affected by coating, impregnation and potting in compounds.
The sealing methods in use are- Dipping, Moulding, Injection, Encapsulation etc. The compounds most widely used in sealing the insulation of low voltage equipment are polyester-styrene, butyl methacrylate, styrene, polyurethane, silicon base compounds.
The insulating material or part to be sealed must be thoroughly dried out. The wax, asphalt or bitumens were used in old sealing methods.
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