Planes of simple cubic structure and X-ray diffraction experiment

Click For Summary

Discussion Overview

The discussion revolves around the use of specific plane indices in X-ray diffraction experiments related to simple cubic structures. Participants explore the implications of these indices for calculating interplanar distances and the relationship between diffraction patterns and crystal structures.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the choice of plane indices used in a textbook for calculating interplanar distances in cubic structures.
  • Another participant suggests that a simple cubic lattice would include additional reflections, such as (100), and questions whether the first plane should be (110) instead of (111).
  • A participant emphasizes the importance of knowing the planes that generate diffraction to compare with experimentally obtained patterns.
  • There is a suggestion that different operations with the values of sin²(θ) may be necessary to match the diffraction pattern with a structure.
  • One participant notes that if the structure is unknown, consulting databases may be necessary, and mentions the potential to reconstruct the structure from a complete 3-D diffraction pattern.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate plane indices for cubic structures and the necessity of knowing these planes for diffraction analysis. The discussion remains unresolved regarding the correct indices and methods for analysis.

Contextual Notes

There are limitations related to the assumptions about crystal structures and the specific indices used in calculations. The discussion also highlights the dependence on experimental data and the potential for multiple interpretations of diffraction patterns.

Marketo
Messages
10
Reaction score
0
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
 
Physics news on Phys.org
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 \Sigmaexp(2\pii(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(\pii(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).
 
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
 
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.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
6K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
10K
  • · Replies 1 ·
Replies
1
Views
11K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
7
Views
6K
Replies
1
Views
2K