91Ó°ÊÓ

Calculate the fraction of atom sites that are vacant for copper at its melting temperature of \(1084^{\circ} \mathrm{C}(1357 \mathrm{K}) .\) Assume an energy for vacancy formation of \(0.90 \mathrm{eV} /\) atom.

Calculate the number of vacancies per cubic meter in gold at \(900^{\circ} \mathrm{C}\). The energy for vacancy formation is 0.98 eVlatom. Furthermore, the density and atomic weight for Au are \(18.63 \mathrm{g} / \mathrm{cm}^{3}\) (at \(\left.900^{\circ} \mathrm{C}\right)\) and \(196.9 \mathrm{g} / \mathrm{mol}\), respectively

For both \(\mathrm{FCC}\) and \(\mathrm{BCC}\) crystal structures there are two different types of interstitial sites. In each case, one site is larger than the other, and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at \(0 \frac{1}{2} \frac{1}{4}\) positions - that is, lying on \\{100\\} faces, and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both \(\mathrm{FCC}\) and \(\mathrm{BCC}\) crystal structures, compute the radius \(r\) of an impurity atom that will just fit into one of these sites in terms of the atomic radius \(R\) of the host atom.

Calculate the composition, in weight percent, of an alloy that contains \(105 \mathrm{kg}\) of iron, \(0.2 \mathrm{kg}\) of carbon, and \(1.0 \mathrm{kg}\) of chromium.

What is the composition, in atom percent, of an alloy that contains \(44.5 \mathrm{lb}_{\mathrm{m}}\) of silver \(83.7 \mathrm{lb}_{\mathrm{m}}\) of gold, and \(5.3 \mathrm{lb}_{\mathrm{m}}\) of \(\mathrm{Cu}\) ?

What is the composition, in atom percent, of an alloy that consists of 5.5 wt\% \(\mathrm{Pb}\) and \(94.5 \mathrm{wt} \% \mathrm{sn} ?\)

Determine the approximate density of a Ti-6Al-4V titanium alloy that has a composition of \(90 \mathrm{wt} \% \mathrm{Ti}, 6 \mathrm{wt} \% \mathrm{Al}\), and \(4 \mathrm{wt} \% \mathrm{V}\)

Some hypothetical alloy is composed of 25 wt \(\%\) of metal \(A\) and 75 wt \(\%\) of metal \(B\) If the densities of metals \(A\) and \(B\) are 6.17 and \(8.00 \mathrm{g} / \mathrm{cm}^{3},\) respectively, whereas their respective atomic weights are 171.3 and \(162.0 \mathrm{g} / \mathrm{mol}\) determine whether the crystal structure for this alloy is simple cubic, face-centered cubic, or body-centered cubic. Assume a unit cell edge length of \(0.332 \mathrm{nm}\) .

Germanium forms a substitutional solid solution with silicon. Compute the weight percent of germanium that must be added to silicon to yield an alloy that contains \(2.43 \times 10^{21} \mathrm{Ge}\) atoms per cubic centimeter. The densities of pure Ge and \(\mathrm{Si}\) are 5.32 and \(2.33 \mathrm{g} / \mathrm{cm}^{3}\) respectively .

For an FCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (111) plane? Why? (Note: You may want to consult the solution to Problem 3.53 at the end of Chapter \(3 .\) ) .