spacing between three dimentional lattice planes


by abhaymv
Tags: crystallography, reciprocal lattice
abhaymv
abhaymv is offline
#1
Apr10-11, 07:58 AM
P: 9
What, exactly,does spacing between three dimentional lattice planes mean?Does it refer to the formula

d=2*pi/(translation vector)?

*I am an engineering undergraduate and this word is in my syllabus in topic crystallography.I was wondering what it meant?


Also, can someone tell me in simple words what reciprocal lattice means?When I go to wikipedia they go complicated including vectors.But I dont think it is needed in my study.
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johng23
johng23 is offline
#2
Apr13-11, 10:59 PM
P: 292
You probably already know some of this but I'll just lay it out so it's clear what we're talking about.

A crystal can be described as a basis of atoms, repeated on each point of an infinite mathematical lattice. The simplest 3-D lattice would be a cubic array (repeated through all of space), and the simplest basis would be a single atom. In crystallography we generally want to use this framework not to describe points in a crystal, but directions or planes.

So we can use this formalism to describe a plane hkl in a crystal, but it's not a single plane, it's an entire set of parallel planes with a specific orientation with respect to the crystal. And each plane in this set will be separated from the next by a perpendicular distance which is characteristic of that set of planes. That's the spacing you are asking about.


The reciprocal lattice is a second lattice you can construct for any normal ("real space") lattice you can think of. While the real lattice is associated with the actual position of atoms, the reciprocal lattice is more abstract. Each point in that lattice represents one of the sets of planes I was talking about above, and the distance from the origin to the point is the interplanar spacing that you asked about. If you're familiar with fourier transforms, then I can tell you that it's the fourier transform of the real lattice. Its most common application is in explaining x-ray diffraction from crystals.

If the reciprocal lattice seems abstract, don't worry. It takes a while to really grasp.
abhaymv
abhaymv is offline
#3
Apr16-11, 02:03 AM
P: 9
Thank you for the explanation. :)
I think I understand, but the reciprocal lattice is, as you said, a little hard to understand(and visualize).


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