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Problem: For structures consisting of identical atoms, how many atoms are contained in the simple, body-centered, and face-centered cubic unit cells? Explain how you obtained the values. 

FREE Expert Solution

We are asked how many atoms are contained in the simple, body-centered, and face-centered cubic unit cells for structures consisting of identical atoms.


A Simple cubic unit cell is composed of a cube with one atom at each of its corners



                                                  contribution
corner atoms                                 1/8

In a simple unit cell:

corner atoms = 8

# of atoms=8×18

# of atoms = 1 per 1 unit cell


There's 1 atom per simple cubic unit cell. 


A body-centered cubic (BCC) unit cell is composed of a cube with one atom at each of its corners and one atom at the center of the cube



                                                  contribution
corner atoms                                 1/8
atoms in center                             1
atoms in face of the cube            1/2 


In a BCC unit cell:

corner atoms = 8
atoms in center = 1

# of atoms=8×18+1

# of atoms = 2 per 1 unit cell


There's 2 atoms per body-centered unit cell. 


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Problem Details

For structures consisting of identical atoms, how many atoms are contained in the simple, body-centered, and face-centered cubic unit cells? Explain how you obtained the values. 

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