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Andrew Jarvis
science forum beginner

Joined: 29 Jun 2005
Posts: 2

Posted: Wed Jun 29, 2005 11:06 am    Post subject: Cubic lattices

Can anyone explain the differences between simple, face-centred and
body-centred cubic lattices?

I can find dozens of references to them but no definition of what they are.

Regards,
AJ
Chip Eastham
science forum Guru

Joined: 01 May 2005
Posts: 412

Posted: Wed Jun 29, 2005 2:56 pm    Post subject: Re: Cubic lattices

Andrew Jarvis wrote:
 Quote: Can anyone explain the differences between simple, face-centred and body-centred cubic lattices? I can find dozens of references to them but no definition of what they are. Regards, AJ

For the simple cubic lattice, consider points in R^3 whose coordinates
are integers.

face of each cube in this lattice, eg. points with one integer
coordinate and two coordinates that differ from an integer by 1/2.

For the body-centered cubic lattice, start once again with the simple
cubic lattice and add points whose coordinates are all different from
an integer by 1/2.

Note that if the points from both the face-centered and body-centered
cubic lattices are combined, one returns to a simple cubic lattice with
nearest neighbor spacings half of what appears in the all integer
coordinate lattice.

regards, chip

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