What Type of Lattice Does This Crystal Have Based on X-ray Diffraction Data?

In summary, the conversation discusses the determination of the type of lattice and the lattice parameter of a crystal based on a set of diffraction lines obtained with CuKα radiation. The conversation also mentions the use of Bragg's Law and a table of Bravais Lattice selection conditions to determine which peaks are expected to be absent in P-, I-, and F-lattices. The conversation concludes with the discovery of a key ratio that rules out the I-lattice and provides information about the other lattice parameters. However, it is noted that this method may not be able to guarantee the absence of other angles in the crystal.
  • #1
kharngod
1
0

Homework Statement


On a crystal (cubic) a set of diffraction lines (θ) was obtained with CuKα (1.54 Å) radiation:
13.70, 15.89, 22.75, 26.91, 28.25, 33.15, 36.62, 37.60 and 41.95 degrees. Using
the following table to determine which peaks are expected to be absent in a cubic
P-, I-, and F-lattice, what type of lattice does this crystal have and what is the lattice parameter
of this crystal?
*Table of Bravais Lattice selection conditions*

Homework Equations


Bragg's Law:
2d*sin(theta) = n*lambda

d = a/Sqrt(h^2 + k^2 + l^2)
where h, k, l are integers related to the plane you are reflecting off, n is an integer number of wavelengths and a is the lattice parameter (size of the cubic unit cell)

The Attempt at a Solution


In a spreadsheet i threw together ratios of the sines of all the thetas (squared) and looked for things that were (within some error due to rounding) numbers which could be whole number ratios, but I'm not sure how to go from here to constraining the selection criteria since n and the sum of the squares of h, k and l vary from theta to theta.

It seems like all the list of 'working' thetas gives me will end up being is ratios of sine squares, but unless I'm misunderstanding the question, even if I could find a nice whole number ratio of two sines, since it looks like I have 6 free parameters in a ratio I don't have enough information. Also with only two decimal places the angles don't give 'clear' ratios in many of the cases, even if they should be whole number ratios.

I think I cracked it, I was looking at the nice large whole number ratios (like 8) but the more informative ones are the small ones it seems when you consider the very few ways you can make a ratio of 4/3, and 3 guarantees n = 1 for that theta, and thus the sum of the squares is 3, which can only be if h,k,l are all equal to 1, and that gave me a 'key' to the rest of the problem as well as ruling out the I-lattice.

Although it seems that in this form, you could never guarantee it isn't just a cubic P-lattice unless you were told that it includes such and such angles and no-others.
 
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  • #2
Otherwise you can't rule out the possibility that all the other angles were just too small for the resolution.
 

FAQ: What Type of Lattice Does This Crystal Have Based on X-ray Diffraction Data?

1. What is X-ray diffraction?

X-ray diffraction is a technique used to study the atomic and molecular structure of materials. It involves shining a beam of X-rays onto a sample and analyzing the diffraction pattern produced by the interaction of the X-rays with the atoms in the sample.

2. How does X-ray diffraction work?

X-rays are electromagnetic waves with a very short wavelength, which allows them to interact with the atomic structure of materials. When X-rays hit a sample, they are scattered in different directions by the atoms in the sample. The resulting diffraction pattern can be analyzed to determine the arrangement of atoms in the sample.

3. What is Bragg's Law?

Bragg's Law is a mathematical equation that describes the relationship between the angle of incidence of X-rays, the distance between atomic planes in a crystal, and the wavelength of the X-rays. It is used to determine the spacing between atoms in a crystal lattice from the diffraction pattern produced by X-ray diffraction.

4. How is Bragg's Law used in X-ray diffraction?

Bragg's Law is used to calculate the diffraction angle of X-rays when they interact with a crystal. By measuring the angle of diffraction and the wavelength of the X-rays, the distance between atomic planes in the crystal can be determined. This information can then be used to determine the atomic and molecular structure of the sample.

5. What are the applications of X-ray diffraction?

X-ray diffraction has a wide range of applications in various fields, such as materials science, chemistry, and biology. It is commonly used to determine the crystal structure of materials, identify unknown substances, and study the composition and properties of molecules. X-ray diffraction is also used in the development of new materials, pharmaceuticals, and electronics.

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