Objectives:
Reference: §18.1 - 18.17; 19.1 - 19.8 of The Science and Engineering of Materials, 3rd Edition, Askeland, PWS Publishing Co.
Definitions and Concepts:
There are many applications for which the electrical characteristics of a material are more important than its mechanical properties. Transmission wires must have low resistance as well as reasonable strength. Ceramic insulators and the polymer insulation must isolate high voltages (good dielectrics). Semiconductor devices must be hardened against surges like lightning. Also, anywhere there are moving charges, a magnetic field will also be present. Magnetic fields are essential to the operation of motors, generators, transformers, and computer disks. I will attempt to summarize below some of the topics presented in the textbook.
Electrical conductivity is given by
The charge q is a constant for a given
material. Charge carriers may be electrons (and holes insemiconductors)
or ions. n is the number of charge carriers and 
is
the mobility. Example 18-2 (page 599) shows how this equation is used for
a copper wire.
The Pauli exclusion principle is a statement about what we see - in any atom, no two electrons may have the same quantum numbers. This means that it is possible for not more than two electrons to have the same energy, since they can still differ in spin (½ vs - ½). This is also true when atoms come together to form a solid. Since any two atoms could (unless something else prevented it) each have 2 electrons of the same energy for a total of 4, the Pauli exclusion principle requires that the energy level broaden slightly (see the middle diagram of Figure 18-3, page 600). Suppose there are N atoms in a solid; therefore, there will be N 2s levels (just to pick one of the energy levels). Thus, if the exclusion principle were inoperative, there would be 2N electrons with the same energy. So the energies broaden into a band of energies as shown in the right hand diagram of Figure 18-3.
In metals, the band containing the valence electrons is known as the valence band. These electrons are poorly bound to any particular atoms. When an electric field is applied, they acquire energy, move into the conduction band, and are called the "Fermi sea of electrons." The energies represented by the valence band overlap those for the conduction band, so the electrons have little difficulty in making this transition.
In semiconductors, there is a definite gap (in energy) between the valence band and the conduction band. Thus, the resistivities of semiconductors are much higher than that for metals. Insulators have much larger gaps and therefore very large resistivities. Since conductivity is the reciprocal of resistivity, you can see this effect by studying Table 18-1 (page 597). You'll see that the conductivities of the metals are on the order of 105, whereas the semiconductors silicon (Si) and germanium (Ge) have much smaller conductivities. And the insulators (alumina, epoxy, glass) have extremely small conductivities. In fact, to get them to conduct electricity one has to apply an electric field which essentially destroys the material!
Resistivity is dependent on temperature according to
where a is the temperature resistivity
coefficient (see Table 18-3, page 604) and
is the resistivity at room temperature. Lattice defects also increase the
resistivity, since they cause additional electron scatter:
See Figure 18-10, page 605.
The critical temperature is the temperature below which a material becomes superconducting; i.e., its resistivity becomes zero. Another effect is that magnetic fields are excluded from the superconductor, which explains magnetic levitation. As the external magnetic field is increases, the critical temperature decreases in Type I superconductors; thus, there is a critical magnetic field Hc above which the material cannot exclude the field and superconduction is suppressed. Type II superconductors go through three stages from completely superconductive to mixed state to normal conduction (as the external field is increased). Type II superconductors also revert to normal conductivity if the current density is too high. Prior to 1986, critical temperatures were quite low, requiring liquid helium to effect the cooling. But superconducting ceramics have been discovered that have critical temperatures around 100 K; some researchers have been predicting that room-temperature superconductors would soon be created.
Here's a good low-tech summary of applications... and here's some information on organic superconductors.
Pure semiconductors have a small enough energy gap between the valence and conduction bands so that some electrons have sufficient thermal energy to cross the gap. Holes (essentially positive charges by default) are left behind. Nearby electrons move to fill the holes, leaving other holes behind. This is known as "hole conduction." The conductivity is a combination of the electron and hole mobilities:
The number of electrons that can cross the gap, and therefore the conductivity, is given by the Arrhenius relation:
Both the electron's spin and its orbital motion produce a magnetic field. In addition, the spin of the nucleus produces a magnetic field (or magnetic moment). Since the spins of the electrons in afull energy level are opposed, there is no net magnetic moment arising from, for example, the 1s level in sodium. Valence electrons in an atom usually come from the unfilled levels. While one would expect these spins (which are not cancelled out by other electrons) to produce a net magnetic moment, that does not usually happen since the valence electrons from nearby atoms cancel out any effect. But there are elements for which an inner (non-valence) energy level is unfilled.
Materials can be classified as diamagnetic, paramagnetic, ferromagnetic, ferrimagnetic, or antiferromagnetic. Please study section 19-4 page 651 for an explanation of these.
Domains are regions in a ferromagnetic material where all of the dipoles are aligned resulting in a net magnetic field. In an unmagnetized ferromagnetic material, these domains are oriented randomly and the net field is zero. The domains are quite small, usually about 50 micrometers wide. When subjected to an external field, domains that are aligned with the external field grow at the expense of unaligned domains. When the field is removed, the material remains magnetized because the domain walls prevent regrowth to form the original random orientation. Of course, one can assist demagnetization by raising the temperature (see section 19-7, page 659) or by supplying energy by striking the material (e.g., with a hammer). The use of a field that changes direction frequently (such as that produced by 60 Hz current) causes the domains to shift back and forth. This happens constantly in the core of a transformer. Figure 19-8 (page 655) illustrates the hysteresis curves that result for different magnetic materials. Furthermore, eddy currents are induced by the changing magnetic field. For transformers, if the core is not constructed so that these currents remain small, the core will heat and may melt.