The problem statement, all variables and given/known data[/b] Solids consist of
ID: 2140346 • Letter: T
Question
The problem statement, all variables and given/known data[/b]
Solids consist of a crystalline lattice of atoms-a unit cell that has a certain configuration of atoms that is repeated over and over. The picture that I can't post here, shows a pyramidal structure of metal spheres. The base is 8 spheres by 8 spheres with a height of 8 spheres. The metals spheres represent a lattice configuration called face centered cubic (fcc). Calculate the packing fraction for this case, e.g., the amount of volume occupied by the metal spheres divided by the total volume of the pyramidal structure.
Please walk me through how to figure this out. I don't have a clue. I need the correct answer coupled with all of the steps. The person to do so will get the points.
Explanation / Answer
Let a be the A the side length of the unit cell of FCC lattice and R the diameter of the atoms.
The FCC unit cell is formed by 8 atoms:
- 8 times one eighth of an atom at the corners of the cube
- 4 times a half of an atom at the center of the of the faces.
At the faces the atoms at the corners and the center atom touch, so that the perfectly fill the face. Hence the length of the face diagonal is
D = R + 2R + R = 8R
From Pythagorean theorem you get
A
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