GC Problem? please help

[YourDentition]

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HI I'm having a hard time understanding equivalent number of atom in a crystal lattice structure. I would appreciate if someone could explain what a lattic structure is and how do we determine number of equivalent units in a Simple Cubic, Body centered cubic and Face centered cubic, structures.

Thanks a ton.

 

[ethanyoo726]

All you have to know for the DATs:

Simple Cubic: 1 atom per unit cell.
Body Centered: 2 atoms per unit cell.
Face Centered: 4 atoms per unit cell.

Here are explanations that you really don't have to know for the DATs:

Simple Cubic:

Has one lattice point at each CORNER of the cube, so each atom at the lattice points is shared equally between 8 adjacent CUBES. So [(1/8) * 8] = 1, for 1 atom per unit cell.

Body Centered:

Has one lattice point at the center of the unit cell, in addition to the 8 corner points. So [(1/8) * 8] + 1 = 2 atoms per unit cell.

Face Centered:

Has lattice points on each FACE/SIDE of the unit cell. Each face, lattice points contributes only 1/2 to adjacent cubes. Also has 8 corner points. So [(1/8 for each corner) * 8 corners] + [(1/2 for each face) * 6 faces] = 4. So 4 atoms per unit cell.

Again, the explanation is something beyond DATs. It still takes me a while to wrap my head around the calculations. Just know the atoms per unit cell and you'll be fine.

Hope this helps.

 

[failedmagician]

All you have to know for the DATs:

Simple Cubic: 1 atom per unit cell.
Body Centered: 2 atoms per unit cell.
Face Centered: 4 atoms per unit cell.

I had a feeling this is all I had to know. So, I memorzied this a while back. Thanks!