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Forum index » Science and Technology » Math » Recreational
Cubic lattices
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Andrew Jarvis
science forum beginner


Joined: 29 Jun 2005
Posts: 2

PostPosted: Wed Jun 29, 2005 11:06 am    Post subject: Cubic lattices Reply with 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
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Chip Eastham
science forum Guru


Joined: 01 May 2005
Posts: 412

PostPosted: Wed Jun 29, 2005 2:56 pm    Post subject: Re: Cubic lattices Reply with quote
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.

For the face-centered cubic lattice, add an additional point on each
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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