# (111) plane in BCC

Hello, as i mentioned i am studying about crystal structure recently, i am facing another problem. In the book it says that :

(111) plane in BCC does not cut the center atom.

But i do some geometry and i come about that the perpendicular distance from the center of that atom to the (111) plane is 2/3 of the radius of atom. So from my point of view it should cut the atom (since the distance is less than the radius of the atom).

Can anyone help me to find out my mistakes?

## Replies

• Ramani Aswath
Which crystal are you considering?
• u_know_who
well, it is said in the post that it is BCC crystal structure.
• Ramani Aswath
Is the article (or book) referring to any particular material or just generally about BCC structure? The central ion need not have the same radius as the corner ones. This could cause the difference.
• u_know_who
bioramani
Is the article (or book) referring to any particular material or just generally about BCC structure? The central ion need not have the same radius as the corner ones. This could cause the difference.
I can't agree with you regarding this : "The central ion need not have the same radius as the corner ones." Reason? You determine the lattice parameter of BCC crystal a = 4/sqrt(3) * R considering the central atom is the same radius of other atoms.

Someone told me that if a plane cut through the center of the atom then we have to consider that atom, otherwise we have not to bother about it. If i consider his suggestion then well it seems agree with the book.

But what is the reason behind that?

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