Unit Cells
Previously in this class we learned about the type of crystal structure called simple cubic. This is one of a few types of structures. This worksheet will go over 2 more structures called body-centered cubic (BCC) and face-centered cubic (FCC).
Face-centered cubic (FCC)
The face-centered cubic cell is a crystal structure found in many metals. This structure has atoms located at each of the corners of the cube as well as on the center of each face of the cube. This can be seen in the figure below. In this figure, the atom centers are represented by small red spheres.
The equation that relates the cube length, a, and the atomic radius R for FCC is:
\[ a = 2R\sqrt2 \]
Body-centered cubic (BCC)
The body-centered cubic cell is another common metallic crystal structure. This structure contains atoms on all of the corners of the unit cell as well as one single atom in the center. This can be seen below, where the atom centers are represented by small blue spheres.
The equation that relates the cube length, a, and the atomic radius R for BCC is:
$$a = \frac{4R}{\sqrt{3}}$$
Recall from simple cubic:
Excersises
Practice Problems:
- Show for body-centered cubic that the unit cell edge length a and the atomic radius are related through \( a = \frac{4R}{\sqrt{3}} \)
- Calculate the atomic packing factor of FCC
- Draw the densest packed planes for FCC and BCC