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18–16The electrical resistivity of a beryllium alloy containing 5 at% of an alloyingelement is found to be 50 106ohmcm at 400 C. Determine the contributionsto resistivity due to temperature and due to impurities by finding the expected resis-tivity of pure beryllium at 400 C, the resistivity due to impurities, and the defectresistivity coefficient. What would be the electrical resistivity if the berylliumcontained 10 at% of the alloying element at 200 C?Solution:From the data in Table 18–3, the resistivity at 400 C should be:Consequently the resistance due to impurities is:Since there are 5 at% impurities present, x0.05, and the defectresistivity coefficient is:The resistivity at 200 C in an alloy containing 10 at% impurities is:18–17Is Equation 18–7 valid for the copper-zinc system? If so, calculate the defect resis-tivity coefficient for zinc in copper. (See Figure 18–11.)Solution:The conductivity and resistivity of pure copper are:For 10 wt% Zn in copper:From Figure 18–11(a), the conductivity of the Cu–10% Zn alloy at zerodeformation is about 44% that of pure copper, or¢r0.381050.1671050.213105r1s0.38105s15.98105210.4422.63105xZn11xZn210.09752110.097520.088xZn110 65.382110 65.382190 63.5420.0975s5.98105orr1s0.167105ohm#cm21.510616.110637.6106ohm#cm10610.12110.12141062 3110.02521200252 4178.9r200rrdb8.510610.052110.052178.9106ohm#cmrdbx11x2orbrdx11x2rd8.5106ohm#cm5010641.5106rdrrtrdrt141062 3110.02521400252 441.5106#CHAPTER 18Electronic Materials199
200The Science and Engineering of MaterialsInstructor’s Solution ManualThe following table includes the calculations for other compositions:wt% ZnxZnxZn(1xZn)%ssrr0001015.98 1050.167 1050100.09750.088442.63 1050.380 1050.213 105150.1460.125372.21 1050.452 1050.285 105200.1960.158331.97 1050.508 1050.341 105300.2940.208281.67 1050.599 1050.432 105These data are plotted. The slope of the graph is “b”:1.8105ohm#cmb0.41050.21050.190.0818–19GaV3is to operate as a superconductor in liquid helium (at 4 K). The Tcis 16.8 Kand Hois 350,000 oersted. What is the maximum magnetic field that can be appliedto the material?Solution:18–20Nb3Sn and GaV3are candidates for a superconductive application when the mag-netic field is 150,000 oersted. Which would require the lower temperature in orderto be superconductive?Solution:18–21A filament of Nb3Sn 0.05 mm in diameter operates in a magnetic field of 1000 oer-sted at 4 K. What is the maximum current that can be applied to the filament inorder for the material to behave as a superconductor?Solution:From Figure 18–12, the maximum current density for Nb3Sn in a field of 1000 oersted is about 2 106A/cm2.IJA12106A/cm2214210.005 cm2239.3 AT12.7 KFor GaV3:150,000350,000311T16.8224T11.42 KFor Nb3Sn:150,000250,000311T18.05224150,000Ho311T Tc224HcHo311T Tc224350,0003114 16.8224330,159 oerstedTc16.8 KHo350,000 oersted0.20.4∆r= 10−50.10.2x(1−x)
18–22Assume that most of the electrical charge transferred in MgO is caused by the diffu-sion of Mg2ions. Determine the mobility and electrical conductivity of MgO at25 C and at 1500 C. (See Table 5–1.)