Lecture1 electrical conduction physical metallurgy and physical properties
- 2. Dual Wave/Particle Nature Light : *Electromagnetic wave packets (bursts) moving like “flying needles” and acting like particles. *Each wave packet is a Photon with energy E = hn Electrons : *Particles which act like waves since they are diffracted
- 3. General Definitions *An electron in the closest orbit to the nucleus is in its lowest energy state, occupying the lowest energy level. *The number of possible energy levels (or states) is determined by a set of four Quantum Numbers (QN). The Pauli Exclusion Principle: *Each electronic state has its own set of the 4 QN’s and can be occupied by no more than one electron. *Each energy level can be occupied by no more than two electrons of different states.
- 4. Electronic Orbitals Shell defined by the Principal QN, n = 1, 2, 3, … s p d Subshells defined by the subsidiary QN, l = 0, 1, 2,.. n-1 Orbitals defined by the magnetic QN, ml = - l,…, +l
- 5. n = 1, l = 0 (s) n = 2, l = 0, 1 (s,p) n = 3, l = 0,1,2 (s, p, d) n = 4, l = 0, 1, 2, 3 (s, p, d, f) l = 0, ml = 0 l = 1, ml = -1, 0, 1 l = 2, ml = -2, -1, 0, 1, 2 ms = + 1/2 and - 1/2 Quantum Numbers
- 6. Sodium Atom 11 electrons 2 1s states (n= 1, l = 0(s), one orbital) 2 2s states (n= 2, l = 0(s), one orbital) 6 2p states (n= 2, l = 1(p), three orbitals) 1 3s state (n= 3, l = 0(s), one orbital)
- 7. *Electronic Configurations Ex: Fe , Atomic number = 26 3d 6 4s2 valence electrons 1s 2s 2p K-shell n = 1 L-shell n = 2 3s 3p M-shell n = 3 3d 4s 4p 4d Energy N-shell n = 4
- 8. Electrical conduction *Electrical conduction is the movement of electrically charged particles through a transmission medium. *The movement can form an electric current in response to an electric field. * The underlying mechanism for this movement depends on the material. *Conduction in metals and resistors is well described by Ohm's Law, which states that the current is proportional to the applied electric field. The ease with which current density (current per area) j appears in a material is measured by the conductivity σ, defined as: j = σ E or its reciprocal resistivity ρ: j = E / ρ In linear anisotropic materials, σ and ρ are tensors.
- 9. Electrical properties * The electrical conductivity of a metal (or its reciprocal, electrical resistivity) is determined by the ease of movement of electrons past the atoms under the influence of an electric field. This movement is particularly easy in copper, silver, gold, and aluminum—all of which are well-known conductors of electricity. * The conductivity of a given metal is decreased by phenomena that deflect, or scatter, the moving electrons. These can be anything that destroys the local perfection of the atomic arrangement—for example, impurity atoms, grain boundaries, or the random oscillation of atoms induced by thermal energy. * This last example explains why the conductivity of a metal increases substantially with falling temperature: in a pure metal at room temperature, most resistance to the motion of free electrons comes from the thermal vibration of the atoms; if the temperature is reduced to almost absolute zero, where thermal motion essentially stops, conductivity can increase several thousandfold.
- 10. Formation of Energy Bands *In an isolated atom, the electrons in each orbit possess definite energy. But, in the case of solids, the energy level of the outermost orbit electrons is affected by the neighboring atoms. *When two isolated charges are brought close to each other, the electrons in the outermost orbit experience an attractive force from the nearest or neighboring atomic nucleus. Due to this reason, the energies of the electrons will not be at the same level, the energy levels of electrons are changed to a value that is higher or lower than that of the original energy level of the electron. *The electrons in the same orbit exhibit different energy levels. The grouping of these different energy levels is known as the energy band. *However, the energy of the inner orbit electrons is not much affected by the presence of neighboring atoms.
- 13. Energy band structures for Na and Mg
- 14. Classification of Energy Bands Valence Band The electrons in the outermost shell are known as valence electrons. These valence electrons contain a series of energy levels and form an energy band known as the valence band. The valence band has the highest occupied energy. Conduction Band The valence electrons are not tightly held to the nucleus due to which a few of these valence electrons leave the outermost orbit even at room temperature and become free electrons. The free electrons conduct current in conductors and are therefore known as conduction electrons. The conduction band contains conduction electrons and has the lowest occupied energy levels. Forbidden Energy Gap The gap between the valence band and the conduction band is referred to as the forbidden gap. As the name suggests, the forbidden gap doesn’t have any energy and no electrons stay in this band. If the forbidden energy gap is greater, then the valence band electrons are tightly bound or firmly attached to the nucleus. We require some amount of external energy that is equal to the forbidden energy gap.
- 16. *Solids (including insulating solids) * In crystalline solids, atoms interact with their neighbors, and the energy levels of the electrons in isolated atoms turn into bands. Whether a material conducts or not is determined by its band structure. * Electrons, being fermions, follow the Pauli exclusion principle, meaning that two electrons in the same interacting system cannot occupy the same state, which further means that their four quantum numbers have to be different. Thus electrons in a solid fill up the energy bands up to a certain level, called the Fermi energy. * Bands that are completely full of electrons cannot conduct electricity, because there is no state of nearby energy to which the electrons can jump. Materials in which all bands are full (i.e. the Fermi energy is between two bands) are insulators. In some cases, however, the band theory breaks down and materials that are predicted to be conductors by band theory turn out to be insulators. * https://en.wikipedia.org/wiki/ File:Metals_and_insulators,_quantum_difference_from_band_structure.ogv
- 17. *Metals are good conductors because they have unfilled space in the valence energy band. *In the absence of an electric field, there exist electrons traveling in all directions and many different velocities up to the Fermi velocity (the velocity of electrons at the Fermi energy). *When an electric field is applied, a slight imbalance develops and mobile electrons flow. Electrons in this band can be accelerated by the field because there are plenty of nearby unfilled states in the band. *Resistance comes about in metal because of the scattering of electrons from defects in the lattice or by phonons.
- 18. Like balls in a Newton's cradle, electrons in a metal quickly transfer energy from one terminal to another, despite their own negligible movement.
- 19. *Conductivity in metal is a measure of a material’s ability to transmit heat, or electricity (or sound). The reciprocal of conductivity is resistance, or the ability to reduce the flow of those. *An understanding of a material’s tendency to conduct may be a critical factor in the selection of that material for a given application. Clearly, some materials are chosen because they readily conduct electricity (as wire, for example) or heat (like fins or tubes in a radiator or heat exchanger). For other applications (like insulation), materials are selected because they specifically do not conduct very well.
- 20. *Pure metals will tend to provide the best conductivity. In most metals, the existence of impurities restricts the flow of electrons. Compared to pure metals, then, elements which are added as alloying agents could be considered “impurities”. So alloys tend to offer less electrical conductivity than pure metal. If different properties provided by alloying are required (for additional hardness or strength, for example) it is important to choose the alloy additions that do not significantly affect conductivity if that is also important. *Metals conduct electricity by allowing free electrons to move between the atoms. These electrons are not associated with a single atom or covalent bond. Since like charges repel each other, the movement of one free electron within the lattice dislodges those in the next atom, and the process repeats – moving in the direction of the current, toward the positively charged end.
- 21. What is an Electrical Conductor? *In electrical engineering, a conductor (or electrical conductor) is defined as an object or type of material that allows the flow of charge in one or more directions. Materials made of metal are common electrical conductors, as metals have high conductance and low resistance. *Electrical conductors allow electrons to flow between the atoms of that material with drift velocity in the conduction band. *Electrical conductors may be metals, metal alloys, electrolytes, or some non-metals like graphite and a conductive polymer. These materials allow electricity (i.e. the flow of charge) to pass through them easily.
- 22. How Does a Conductor Conduct Current? *The substance of the electrical conductor atom must have no energy gap between its valence band and conduction band. *The outer electrons in the valence band are loosely attached to the atom. When an electron gets excited due to electromotive force or thermal effect, it moves from its valence band to the conduction band. *The conduction band is the band where this electron gets its freedom to move anywhere in the conductor. The conductor is formed of atoms. Thus as a whole, the conduction band is in the abundance of electrons. *In other words, it can be said that the metallic bonds are present in the conductors. These metallic bonds are based on the structure of positive metal ions. An electron cloud surrounds these structures.
- 23. *When a potential difference occurs in the conductor across two points, the electrons get sufficient energy to flow from lower potency to higher potency in this conduction band against a small resistance offered by this conductor material. Electricity or current flows in the opposite direction of the flow of the electrons.
- 24. How an Electron Flows through a Conductor? *Electrons do not move or flow in a straight line. In a conductor, the electrons are in to and fro motion or random velocity i.e. is called Drift Velocity (Vd) or average velocity. Due to this Drift Velocity, the electrons collide every moment with atoms or another electron in the conduction band of the conductor. *Drift velocity is quite small, as there are so many free electrons. We can estimate the density of free electrons in a conductor, thus we can calculate the drift velocity for a given current. The larger the density, the lower the velocity required for a given current. In the Conductor, the flow of the electrons is against the Electric Field (E).
- 25. Properties of Electrical Conductor The main properties of electrical conductors are as follows: 1. A conductor always allows the free movement of electrons or ions. 2. The electric field inside a conductor must be zero to permit the electrons or ions to move through the conductor. 3. Charge density inside a conductor is zero i.e. the positive and negative charges cancel inside a conductor. 4. As no charge inside the conductor, only free charges can exist only on the surface of a conductor. 5. The electric field is perpendicular to the surface of that conductor.
- 26. Type of Conductors Electrical conductors can be classified based on their Ohmic Response. They are: Ohmic Conductors This type of conductors always follow Ohm’s Law (V I) ∝ V vs. I graph gives a straight line always. Example: Aluminum, Silver, Copper etc. Non-Ohmic Conductors This type of conductors never follow Ohm’s Law (V I) ∝ V vs. I graph does not give a straight line i.e. nonlinear graph. Example: LDR (Light Dependent Resistor), Diode , Filament of Bulb, Thermistors, etc.
- 27. • Ohm's Law: DV = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s) I e- A (cross sect. area) DV L Resistivity, r and Conductivity, s: -- geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity -- Resistivity is a material property & is independent of sample A I L V 1
- 28. *Which will conduct more electricity? *Analogous to flow of water in a pipe *So resistance depends on sample geometry, etc. D 2D I VA RA
- 29. R = r L/A (L and A are length and cross section of the wire) r (Ω cm) is the electrical resistivity, a material parameter. is the conductivity, the reciprocal of r. Since V= IR and R = L/As then I/A = s V/L where I/A is the current density J (A/cm2) and V/L is the electric field e (V/cm), then; Another way of stating Ohm’s law is: J = se J also equals nqv, where n is the number of charge carriers (carriers/cm3), q is the charge on each electron (1.6 x 10-19 C) and v is the average velocity (cm/s). Thus; se = nqv or s = nq (v/e) = nqm, where m is the carrier mobility (cm2 /Vs). Hence; s = nqm
- 30. The examples of conductors are given below: Solid Conductor 1. Metallic Conductor: Silver, Copper, Aluminum, Gold, etc. 2. Non Metallic Conductor: Graphite 3. Alloy Conductor: Brass, Bronze, etc. Liquid Conductor 4. Metallic Conductor: Mercury 5. Non Metallic Conductor: Saline Water, Acid Solution, etc. NB: 1. Copper Conductor is the most common material used for electrical wiring. 2. Gold Conductor is used for high-quality surface-to-surface contacts. 3. Silver is the best conductor on the Conductors list. 4. Impure Water is listed in the Conductor List but it has less conductivity.
- 31. What is the Charge of a Conductor During Carrying Electricity? *A current-carrying conductor at any instance has zero charge. This is because in any instance number of electrons (at drift velocity) is equal to the number of protons in this conductor. So the net charge is zero. *Suppose a conductor is connected across a battery, i.e. positive end and negative end are connected with a conductor. Now electrons flow through the conductor from the negative end to the positive end of the battery. This flow of electrons is possible until this battery has EMF-producing capability through a chemical reaction inside.
- 32. Effect of Temperature on a Conductor *The more effect of temperature, the more vibration in the conductor molecules. This impedes the electrons from flowing, i.e. the electrons get obstruction to flow smoothly through the conductor. Thus conductivity decreases gradually with increasing temperature. *Again, the rise of temperature breaks some bonds in the conductor molecules and releases some electrons. These electrons are less in number. As a whole, it can be said that an increase in the temperature opposition against the drifting electron increases in the conductor.
- 33. Scattering of electrons reduces conductivity
- 34. Resistivity due to thermal vibrations and Lattice Defects
- 35. Resistivity due to Cold Work and Alloying Content
- 39. Solid Solution effect on Resistivity