Table 3.1 Atomic Radii and Crystal Structures for 16...

Table 3.1 Atomic Radii and Crystal Structures for 16 Metals Crystal Atomic Radius$^b$ Crystal Atomic Radius Metal Structure$^a$ (nm) Metal Structure (nm) Aluminum FCC 0.1431 Molybdenum BCC 0.1363 Cadmium HCP 0.1490 Nickel FCC 0.1246 Chromium BCC 0.1249 Platinum FCC 0.1387 Cobalt HCP 0.1253 Silver FCC 0.1445 Copper FCC 0.1278 Tantalum BCC 0.1430 Gold FCC 0.1442 Titanium ($alpha$) HCP 0.1445 Iron ($alpha$) BCC 0.1241 Tungsten BCC 0.1371 Lead FCC 0.1750 Zinc HCP 0.1332 $^a$FCC = face-centered cubic; HCP = hexagonal close-packed; BCC = body-centered cubic. $^b$A nanometer (nm) equals $10^{-9}$ m; to convert from nanometers to angstrom units ($AA$), multiply the nanometer value by 10. Copyright © 2012 John Wiley & Sons, Inc. All rights reserved.

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Using the data for silver in Table 3.1, compute the interplanar spacings in nm for the (a) (110) and (b) (221) sets of planes. Table 3.1 Atomic Radii and Crystal Structures for 16 Metals Crystal Structurea Atomic Radiusb (nm) Metal Aluminum FCC 0.1431 Molybdenum BCC 0.1363 Cadmium HCP 0.1490 Nickel FCC 0.1246 Chromium BCC 0.1249 Platinum FCC 0.1387 Cobalt Copper Gold HCP 0.1253 Silver FCC 0.1445 Tantalum BCC 0.1430 Titanium HCP 0.1445 Iron Lead 0.1241 Tungsten BCC 0.1371 FCC 0.1750 Zinc HCP 0.1332 aFCC = face-centered cubic; HCP = hexagonal close-packed; BCC = body-centered cubic To compute the interplanar spacings in nm for the (110) set of planes, we need to find the atomic radius of silver in Table 3.1. The atomic radius of silver is 0.1445 nm. The interplanar spacing for the (110) set of planes can be calculated using the formula: d = a / sqrt(h^2 + k^2 + l^2) where d is the interplanar spacing, a is the lattice constant, and h, k, and l are the Miller indices of the planes. For the (110) set of planes, the Miller indices are h = 1, k = 1, and l = 0. Substituting the values into the formula, we get: d = 0.1445 / sqrt(1^2 + 1^2 + 0^2) d = 0.1445 / sqrt(2) d = 0.1445 / 1.414 d ≈ 0.102 nm Therefore, the interplanar spacing for the (110) set of planes in silver is approximately 0.102 nm. To compute the interplanar spacings in nm for the (221) set of planes, we use the same formula. For the (221) set of planes, the Miller indices are h = 2, k = 2, and l = 1. Substituting the values into the formula, we get: d = 0.1445 / sqrt(2^2 + 2^2 + 1^2) d = 0.1445 / sqrt(9) d = 0.1445 / 3 d ≈ 0.048 nm Therefore, the interplanar spacing for the (221) set of planes in silver is approximately 0.048 nm.

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