Anybody have time to answer a simple question?
Stephanie Wukovitz
sebab at ucla.edu
Wed Dec 13 22:35:34 EST 1995
In article <4amoae$1r1s at mercury.cc.uottawa.ca>, Stuart Reid
<g567621 at danis.uottawa.ca> wrote:
> I was hoping somebody could tell me why a unit cell cannot be
simultaneously A and B-centered, but not C-centered.
> Any (correct) answer appreciated.
> - a Confused Physical-Biochem Student
OK, you can think of this as being a result of the fact that there is no
way to orient such a (nonexistent)
cell such that it "looks" like part of a primitive lattice. More specificallyr:
Here's an argument to show that you can't have the "lattice" you propose:
Assume you can. You are then allowed the translations (0,0,1),(0,1,0),
(1,0,0),(-1,0,0), etc., translations by
multiples of a unit cell. You are also permitted (0,1/2,1/2), (1/2,0,1/2)
and so forth (the centering on two faces)
You may *not* have the translation (1/2,1/2,0), which represents centering
on a third face.
However, (0,1/2,1/2) + (1/2,0,1/2) + (-1,0,0) = (1/2,1/2,0). This is
centering on the third face, which we said
was not allowed! Therefore we do not have a lattice.
Hope this helps!
--
Stephanie Wukovitz
steph at newton.mbi.ucla.edu
UCLA Dept. of Biomathematics/Molecular Biology Institute (Yeates lab)
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