Planes of simple cubic structure and X-ray diffraction experiment

In summary, the conversation discusses the problem of using planes indices to calculate the interplanar distance in the book of Dr. Ronald Askeland. The first plane listed, (111), may be a typo and should possibly be (110) for a BCC structure. The conversation also touches on the necessity of knowing the planes of each structure for diffraction and using different operations to match diffraction patterns with structures. It is also mentioned that databases can be consulted to determine the structure if the diffraction pattern is unknown.
  • #1
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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
 
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  • #2
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 [tex]\Sigma[/tex]exp(2[tex]\pi[/tex]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([tex]\pi[/tex]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).
 
  • #3
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
 
  • #4
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.
 

FAQ: Planes of simple cubic structure and X-ray diffraction experiment

What is a simple cubic structure?

A simple cubic structure is a type of crystal structure where the atoms or ions are arranged in a cubic lattice with one atom at each corner of the cube. This structure is the most basic and simplest form of crystal structure and is often found in metals and alkali halides.

How is the X-ray diffraction experiment used to study planes of a simple cubic structure?

X-ray diffraction is a technique used to analyze the arrangement of atoms in a crystal. In this experiment, a beam of X-rays is directed at a crystal, and the resulting diffraction pattern can be used to determine the spacing between planes of atoms in the crystal lattice. Using this information, the structure of the crystal can be determined.

What factors affect the diffraction pattern in a simple cubic structure?

The diffraction pattern in a simple cubic structure is affected by several factors, such as the wavelength of the X-rays, the angle of incidence of the X-rays, and the spacing between the planes of atoms in the crystal lattice. Other factors, such as the crystal size and orientation, can also play a role in the diffraction pattern.

What information can be obtained from the diffraction pattern in a simple cubic structure?

The diffraction pattern in a simple cubic structure can provide information about the spacing between planes of atoms, the crystal lattice parameters, and the arrangement of atoms in the crystal. It can also be used to identify the type of crystal and its orientation.

What are some real-world applications of studying the planes of a simple cubic structure using X-ray diffraction?

X-ray diffraction is an essential tool in materials science and is used in various industries, such as pharmaceuticals, electronics, and construction. It can be used to analyze the structure of materials, identify unknown substances, and develop new materials with specific properties. X-ray diffraction is also used in the study of geological samples to understand the composition and formation of crystals in rocks and minerals.

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