Planes of simple cubic structure and X-ray diffraction experiment

[Marketo]

In the book of the Dr. Ronald Askeland the problem about x-ray diffraction use the next planes indices to calculate the interplanar distance, but I don't understand why to use such planes indices? Are these planes all of planes in a cubic structure?

(111)
(200)
(211)
(220)
(310)
(222)
(321)
(400)

Thanks for your attentions an suggestions

 

[johng23]

A simple cubic lattice would include other reflections as well, most obviously 100. Are you sure the first plane isn't supposed to be (110)? Because otherwise that looks like the BCC structure. You need to calculate the structure factor $$\Sigma$$exp(2$$\pi$$i(hx+ky+lz) where x,y,z are the fractional locations of the atoms in the unit cell. So for BCC you would have atoms at 000 and 1/2 1/2 1/2 in the unit cell, giving you 1+exp($$\pi$$i(h+k+l)). This is zero when h+k+l is odd, so those reflections are absent. What you are left with are the planes you listed, in order of increasing (h^2+k^2+l^2).

 

[Marketo]

Hey Johng23!

is it necessary to know the planes of each structure that generate diffraction to compare with the h^2+k^2+j^2 experimentally
pattern obtained by diffraction angules?

I Also think is necessary to try different kind of operations with all of the obtained values of sin²(teta) to get a diffraction pattern that reasonably match with a structure

Am I right?, suggestion will be appreciated

 

[johng23]

I'm not sure what you mean with the second part of your question. As far as the first part, if it's textbook question you can probably assume that the structure will either be cubic, hcp, bcc, fcc, or diamond. Experimentally, if you really have no idea what the structure is, it is necessary to consult databases that people have developed. Although if you really had the full diffraction pattern in 3-D, you should be able to reconstruct the real structure since the two are essentially Fourier transforms of each other. I'm not an expert on the various techniques people use to analyze XRD data; I'm sure there are a lot of methods for extracting information.