Measurement of resistivity

In this section we shall consistently refer to resistivity, rather than to its reciprocal, conductivity. The choice is arbitrary, and commercial instruments are sometimes calibrated in units of resistance and sometimes in units of conductance.1 Unless otherwise stated, when we refer to resistivity we shall mean volume resistivity pv (Am), the resistance between opposite faces of a unit cube. A surface resistivity ps is often used to characterise current flow over a surface, as with an antistatic coating, and is defined as the resistance between opposite edges of a unit square. We note first that the resistance across a square is independent of the size of the square and that the unit of surface resistivity is simply the ohm (Q), occasionally written rather superfluously as ohm per square. Secondly, a conducting surface must in reality be a layer with a finite thickness t, and we have only an effective surface resistivity, which is related to the true volume resistivity of the layer by 

In a similar way resistivities of homogeneous thin sheet or film materials are often quoted as effective surface resistivities. 

Experimental determinations of resistivity have used several different arrangements of the electrical connections to the sample, variously termed electrodes, terminals or probes, as illustrated in Fig. 5.19. The simplest volume resistivity measurements use two electrodes, a 2-terminal method, in two basic arrangements. One is a rectangular or cylindrical block with electrodes on the ends, Fig. 5.19(a). The other is like that used for measurements of relative permittivity where electrodes are applied to either side of a thin disc, Fig. 5.20. The latter is more appropriate to high-resistivity materials. In both cases the volume resistivity is related to the measured resistance R between the electrodes by 

1 The unit of conductance, the reciprocal ohm (fi-1), is often called the Siemen (S). 

Concentric ring electrodes are the easiest to use for measurement of surface resistivity. The resistance R between them is the sum of the resistances of the elemental annuli in series  

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A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

Electrical—Thermal Conductivities. Electrical conductivities of alloys (Table 5) are often expressed as a percentage relative to an International Annealed Copper Standard (lACS), ie, units of % lACS, where the value of 100 % lACS is assigned to pure copper having a measured resistivity value of 0.017241 Q mm /m. The measurement of resistivity and its conversion to % lACS is covered under ASTM B193 (8). 

The header cable between anode bed and rectifier must be particularly well insulated. For this reason cables with double plastic sheathing of type NYY-O are used. The cable sheath must not be damaged during installation because the copper core at the defects will be anodically attacked in a very short time and the connection to the rectifier broken. Damage to the cable sheath is not so serious if a multicored cable is used. Usually not all the core insulation is damaged so that the operation of the anode bed is not interrupted. In addition, measurement of resistance and detection of defects is easier. 

The chlorine atom has two further useful influences on the properties of the polymer. Firstly the polymer shows improved resistance to oil compared with all-hydrocarbon rubbers. The rubbers also have a measure of resistance to burning which may be further improved by use of fire retardants. These features together with a somewhat better heat resistance than the diene hydrocarbon rubbers have resulted in the extensive use of these rubbers over many years. 

Viscosity is a measurement of resistance to flow. Although the unit of absolute viscosity is poise, its measurement is difficult. Instead, kinematic (flowing) viscosity is determined by measuring the time for a given flow through a capillary tube of specific diameter and length. The unit of kinematic viscosity is the stoke. However, in general practice, centistoke is used. Poise is related to stoke by the equation ... 

The addition of 0-2% palladium to titanium decreases the corrosion rate in boiling 5% sulphuric acid by a factor of 500, and in boiling 5% hydrochloric acid by a factor of 1 500, in relation to the rates obtained with unalloyed titanium. The addition of palladium in these quantities thus provides an adequate measure of resistance to relatively weak concentrations of the acids mentioned. ... 

The coil (wound on a light metal former) can be suspended by a fine strip of phosphor bronze between the pole pieces. Attached to this suspension is a small mirror which reflects on to a scale a beam of light which is focused upon it. An instrument of this kind is known as a D Arsonval galvanometer and is used in potentiometer circuits and various methods of measurement of resistance. 

Measurement of resistivity The most usual method of measuring soil resistivity is by the four-electrode Wenner method. Figure 10.48 indicates the basic circuit. The mean resistivity is given by... 

Measurement of resistance As previously mentioned, the four-electrode resistivity meters can be used to measure resistances. For this purpose the... 

The accurate measurement of resistance can of course be carried out by means of a Wheatstone bridge, Carey Foster bridge, or a similar arrangement. 

The measurement of resistance to remote earth of a metallic structure is normally carried out with a four-electrode instrument. The connections are shown in Fig. 10.52. A current / is passed between the structure and a remote electrode. The potential difference V is measured between the structure and a second remote electrode. In this way the ohmmeter records the resistance of the structure to earth, i.e. V/I. The spacing of the electrode from the structure is important and must be such that the remote potential electrode lies on the horizontal part of the resistance/distance curve, as shown in Fig. 10.52. Generally speaking, a minimum distance of 15 m from the structure is necessary for the potential electrode to lie on the flat part of the curve, with the current electrode usually at least twice the distance of the potential electrode. 

Hardness signifies the resistance to deformation shown by materials undergoing abrasion, cutting and indentation. As strength is also a measure of resistance to deformation, the two properties are, to some extent, related but not all hard metals are strong, for hardness takes... 

Durometer hardness is defined as the measure of resistance to indentation using either a macro- or microhardness tester. To the pharmaceutical drug manufacturer, hardness is important because of its relationship to ultimate mechanical properties— particularly modulus. In general, softer compounds of the same elastomer base have better coring and reseal properties, whereas harder compounds tend to process better on high-speed filling lines. 

ISO 1853, Conducting and dissipative rubbers, vulcanized or thermoplastic -Measurement of resistivity, 1998. 

ISO 1827 1991 Rubber, vulcanized or thermoplastic - Determination of modulus in shear or adhesion to rigid plates - Quadruple shear method ISO 1853 1998 Conducting and dissipative rubbers, vulcanized or thermoplastic -Measurement of resistivity... 

Figure 1 Typical apparatus for the measurement of resistivity after M. Osofsky, Naval Research Laboratory.

Resistivity measurements are also routinely made with an ac four probe technique. The wiring would follow according to Figure 1 and the measuring currents used would be in the range 0.1 - 10 mA with frequencies of 100 Hz (9). For flux creep now known to modify susceptibility and critical current measurements care must taken with ac measurements of resistivity although for the low current densities involved the effect will not likely be observed except very close to Tc (10) or in a magnetic field. 

Since both hardness and strength are relative measures of resistance to plastic deformation, we would expect them to be proportional to each other. This is indeed the... 

From the fundamental standpoint, the primary concern in resist sensitometry is the measurement of resist response to radiation which involves... 

Air flow is a measure of the resistance that a foam presents to air passing through it. Intuitively one would expect that large pore size presents less of an impediment to flow than small cells. This is indeed true and it is this method that quantifies the effect. It is obvious by now that air flow is an important property in the context of this book. Unfortunately, the ASTM tests were designed for the measurement of resistance to air flow only. Our interests focus on the flow of other fluids, specifically water, through the foam. Nevertheless, air flow represents a quick and precise way to determine the quahty of a foam. If you are not sure of the difference between a reticulated foam and an open-cell foam, this test will differentiate them. Reticulated foams offer much less resistance to flow than open-cell foams. 

Measurements of resistance are not normally made using an applied AC voltage and, if they were, account would need to be made of the fact that the... 

The international standard for measurement of resistivity of rubbers is ISO 185317 which details one procedure only, the potentiometric or four electrode method. The principle of the method is shown in Figure 13.2 the strip test piece has metal current electrodes clamped at each end and is... 

In a null comparison measurement of resistance, the effect of an unknown resistance must be compared with the effect of a variable standard resistance under conditions as identical as possible. Therefore, the unknown and standard resistances are placed in identical circuits in such a way that the resulting voltage or current in each circuit can be compared. Then the standard is varied until the difference in voltage or current between the two circuits is zero. Several methods for performing this comparison have been devised, of which the Wheatstone bridge is by far the most common. Comparison methods for resis-... 

No attempt was made to prevent surface oxidation of the metals. The copper powder was initially free of oxide but oxidized noticeably during the experiments, which generally took about two weeks from compaction to measurement of resistivity. Optical examination was made immediately after polishing. 

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