Chapter 3: Problem 1
What is the difference between atomic structure and crystal structure?
Chapter 3: Problem 1
What is the difference between atomic structure and crystal structure?
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Get started for freeMolybdenum has a BCC crystal structure, an atomic radius of \(0.1363 \mathrm{nm},\) and an atomic weight of \(95.94 \mathrm{g} / \mathrm{mol}\). Compute and compare its theoretical density with the experimental value found inside the front cover.
Below are listed the atomic weight, density, and atomic radius for three hypothetical alloys. For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your determination. A simple cubic unit cell is shown in Figure 3.23 $$\begin{array}{lccc} \hline & \text {Atomic} & & \text {Atomic} \\ & \text {Weight} & \text {Density} & \text {Radius} \\ \text {Alloy} & \text { (g/mol) } & \left(\mathrm{g} / \mathrm{cm}^{3}\right) & (\boldsymbol{n m}) \\ \hline \mathrm{A} & 43.1 & 6.40 & 0.122 \\ \mathrm{B} & 184.4 & 12.30 & 0.146 \\ \mathrm{C} & 91.6 & 9.60 & 0.137 \\ \hline \end{array}$$
Convert the [110] and \([00 \overline{1}]\) directions into the four-index Miller-Bravais scheme for hexagonal unit cells.
Using the Molecule Definition Utility found in both "Metallic Crystal Structures and Crystallography" and "Ceramic Crystal Structures" modules of \(V M S E,\) located on the book's web site [www.wiley.com/college/callister (Student Companion Site)], generate (and print out) a three-dimensional unit cell for \(\beta\) tin given the following: (1) the unit cell is tetragonal with \(a=0.583 \mathrm{nm}\) and \(c=0.318\) \(\mathrm{nm},\) and (2) \(\mathrm{Sn}\) atoms are located at the following point coordinates: $$\begin{array}{ll} 000 & 011 \\ 100 & \frac{1}{2} 0 \frac{3}{4} \\ 110 & \frac{1}{2} 1 \frac{3}{4} \\ 010 & 1 \frac{1}{2} \frac{1}{4} \\ 001 & 0 \frac{1}{2} \frac{1}{4} \\ 101 & \frac{1}{2} \frac{1}{2} \frac{1}{2} \\ 111 \end{array}$$
Show for the body-centered cubic crystal structure that the unit cell edge length \(a\) and the atomic radius \(R\) are related through \(a=4 R / \sqrt{3.\)
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