Electrical Resistance in Solids

The Drude model is a crude model, but it contains the accepted mechanism for electrical resistance in solids, which is the effect of collisions with the cores of the crystal. There are a number of more sophisticated theories than the Drude theory. However, the results of these theories are similar in their general form to Eq. (28.4-9). The major differences are in the interpretation of the quantities r, and m One problem with the Drude theory is that the conductivities of most common metals are found experimentally to be approximately inversely proportional to the temperature, instead of being inversely proportional to the square root of the temperature, as in Eq. (28.4-11). One can rationalize this by arguing that the mean free path should decrease as the temperature rises, because of the increased vibrational amplitude of the cores, making them into targets with larger effective sizes at higher temperature. 

Superconductivity is a phenomenon characterized by sudden and complete disappearance of electrical resistance in a substance when it is cooled below a certain tempeSrature, called the critical transition temperature, T. Superconductivity was discovered in 1911 by measuring the resistance of solid mercury (Hg) on cooling with a sharp discontinuity in resistance at about 4.2 K (see Fig. 1). In addition to the total loss... 

The electrical resistance of solid bismuth is greater than that of liquid bismuth, the ratio of liquid to solid resistivity being approximately 0.5-0.8 for most metals this ratio is 2.0. The linear dependence of resistivity on temperature does not hold for temperatures below 10 K. High thermoelectric effects are produced when bismuth is coupled with certain other metals. Of all metals, it is the most diamagnetic and the increase in resistivity in a magnetic... 

Colver, G. M., Use of Electrical Resistivity in the Diagnostics of Powder Dynamics, International Powder and Bulk Solids Conference/Exhibition, Chicago, Illinois, May 12-14, 1981, pp. 89-96. 

FIGURE 24.19 Relative change of the electrical resistance in VN (a) and CrN (b) coatings as a function of helium ion irradiation dose. (From Guglya, A. et ah, Radiat. Eff. Defects Solids, 162(9), 643, 2007. With permission from Taylor Francis Group.)... 

The electric resistivity in the solid solution system TiB2-ZrB2 was studied by Rahman et al. [273]. Billehaug and 0ye [274] present a study of several transition metal diborides for cathode materials in Hall-Herould cells and come to the conclusion that TiB2 should be an excellent candidate because of its stability against the... 

Opekar F, Stulik K (1999) Electrochemical sensors with solid polymer electrolytes. Anal Chim Acta 385 151-162 Opekar F, Svozil D (1995) Electric resistance in a Nation membrane exposed to air after a step change in the relative humidity. J Electroanal Chem 385 269-271 Osada Y, De Rossi DE (eds) (2000) Polymer sensors and actuators. Springer, Berlin... 

Best estimates of the experimental values for the electrical resistivity in the liquid, Pl> solid, and of dpJdT for the R s at their melting points, are shown in table 9. Similar values for the thermoelectric power, Q Q, dQJdT, and (<2l Gs) displayed in table 10. Considerable difficulties have been encountered in containing these highly reactive liquid metals, and in maintaining their purity while their electronic properties are measured. For discussions of the ways these difficulties have been addressed, the reader is referred to the literature references cited. 

The electrical resistivity in units of micro-ohm-centimeters, p.S2 cm for most elemental solids the resistivity is of order 1-100 in these units, except for some good insulators which have resistivities 10 (k), 10 (M) or 10 (G) times higher. 

Selenium exhibits both photovoltaic action, where light is converted directly into electricity, and photoconductive action, where the electrical resistance decreases with increased illumination. These properties make selenium useful in the production of photocells and exposure meters for photographic use, as well as solar cells. Selenium is also able to convert a.c. electricity to d.c., and is extensively used in rectifiers. Below its melting point selenium is a p-type semiconductor and is finding many uses in electronic and solid-state applications. 

See 2-3.1. Electrical conduction through solids takes place both through the bulk material and over the surface. In most cases surfaces have different physical and chemical properties than the bulk, for example due to contamination or moisture. Volume and surface resistivity can be separately measured for solid materials such as antistatic plastic sheet. Powders represent a special case since although both surface and bulk conduction occur, their contributions cannot be individually measured and the volume or bulk resistivity of a powder includes surface effects. 

The doping of Ceo with alkali metals creates carriers at the Fermi level in the tiu-derived band and decreases the electrical resistivity p of pristine solid Ceo by several orders of magnitude. As x in Ma C6o increases, the resistivity p(.-r) approaches a minimum at x = 3.0 0.05 [9, 112], corresponding to a half-filled flu-derived conduction band. Then, upon further increase in x from 3 to 6, p x) again increases, as is shown in Fig. 11 for various alkali metal dopants... 

Fig. 5. Electrical resistance as a function of the temperature at the indicated magnetic fields for a single microbundle of carbon nanotubes. The solid line is a fit using the two-band model for graphite (see inset) with an overlap A = 3.7 meV and a Fermi level right in the middle of the overlap (after Langer et at. l9 ).

Instruments based on the contact principle can further be divided into two classes mechanical thermometers and electrical thermometers. Mechanical thermometers are based on the thermal expansion of a gas, a liquid, or a solid material. They are simple, robust, and do not normally require power to operate. Electrical resistance thermometers utilize the connection between the electrical resistance and the sensor temperature. Thermocouples are based on the phenomenon, where a temperature-dependent voltage is created in a circuit of two different metals. Semiconductor thermometers have a diode or transistor probe, or a more advanced integrated circuit, where the voltage of the semiconductor junctions is temperature dependent. All electrical meters are easy to incorporate with modern data acquisition systems. A summary of contact thermometer properties is shown in Table 12.3. 

Thermal conductivity can be as low as one-eighth that of solid metal in the case of steel 7 W/m°C. The electrical resistance (specific) of copper, zinc and silver is about twice that of the cast metal, and of aluminium as much as five times, depending on spraying conditions. Adhesion in tension should... 

Nonstoichiometry is relatively common among mixed metal oxides, in which more than one metal is present. In 1986 it was discovered that certain compounds of this type showed the phenomenon of superconductivity on cooling to about 100 K, their electrical resistance drops to zero (Figure 20.9). A typical formula here is YBa2Cu30 where x varies from 6.5 to 7.2, depending on the method of preparation of the solid. 

Note that "b" in this diagram is the same as that in 3.1.8. Because edge and volume defects propagate throughout the lattice, they affect the physical properties of the solid, whereas it is the point defects that affect the chemical properties of the solid. These latter properties include electrical and resistive, optical and reactivity properties of solids. Thus, we can now classify directs in solids as ... 

Apart from use in metallurgical research and measurements, solid electrolytes have also been put to use as heating elements in electrical resistance furnaces. In order to prevent electrolysis from occurring, alternating currents must be used. In contrast to metallic heating elements, they may be used in air at around 2000 °C. In view of the fact that their conductivity must be very low at room temperature, there is a need for them either to be kept continuously warm, or to be preheated with an auxiliary heating element. 

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