341Electromagnetic Techniques for Material IdentificationFIGURE22.Spread bands obtained when 1000 samples eachof two steels of different composition (Unified NumberingSystem G10150 carbon steel and free machining steel) werecomparator bridge tested at identical instrument settings.Free machining steelCarbon steelPermeability(relative scale)Magnetic flux density(relative scale)
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The resistivity of metals has been studiedfor many years and resistivity values formost materials are readily available. Thereason that this parameter has not beenwidely used for metal identification orsorting, however, is the difficulty indetermining the resistivity without speciallaboratory techniques.Resistivity testing is also called potentialdrop testingand can be used fordiscontinuity detection.Conductivity measurements are oftenmade with eddy current devices. Thesetechniques determine the conductivity orresistivity indirectly by measuring itseffect on a coil in a high frequencyalternating current test circuit.Consequently surface roughness, surfacecurvature and trace impurities cansignificantly affect the results. Anotherdrawback is the requirement for astandard sample to compare with theunknown.Instruments are now available thatpermit measuring resistivity directly. Theadvantages of direct measurement are thatmeasurements can be made on bulkmaterial in its manufactured state, that noreference standards are required and thatresistivity values do not requireintermediate calculation.Principles of ResistivityTestsA typical instrument consists of two parts:a four-point probe and an electronicspackage to supply current, determine thevoltage drop and convert it to a resistivityvalue. The four-point probe has beenwidely used for studying semiconductormaterials; the relationship between probegeometry, voltage drop and sampleresistivity has been established for manycommon cases. Although this relationshipcannot be solved in closed form for asample of arbitrary geometry, twoimportant cases lead to very simplesolutions. Using the notation of Fig. 23Iis the current through the sample, Sisthe distance (in meter) between theprobes, Vis the voltage detected acrossthe inner probe and Wis the thickness (inmeter) of the sample. For samples oflength and width several times the overallprobe spacing, the resistivity ρfor sheetswith thickness W< 0.5 Sis:(6)and(7)for sheets with W> 3S. Resistivity ρisusually expressed in microohm centimeteror microohm meter. Note that for thinsheets resistivity ρis determinedindependently of the probe spacing. Forthick sheets the determination isindependent of thickness. An importantimplication of Eq. 7 is that the resistivitycan be determined for massive sampleslike ingots or bars, provided only thatρπ==26 2SVISVI. 8ρπ=()=VWIVWIln24 53.
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