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.

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Niobium forms a substitutional solid solution with vanadium. Compute the number of niobium atoms per cubic centimeter for a niobium-vanadium alloy that contains 24 wt\% \(\mathrm{Nb}\) and \(76 \mathrm{wt} \% \mathrm{V}\). The densities of pure niobium and vanadium are 8.57 and 6.10 \(\mathrm{g} / \mathrm{cm}^{3},\) respectively .

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For an ASTM grain size of \(6,\) approximately how many grains would there be per square inch at (a) a magnification of \(100,\) and (b) without any magnification?

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

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