X-Ray Diffraction Homework: Find Crystal Spacing

Instead, you can use the Debye-Scherrer equation: λ = 2dsinθwhere λ is the wavelength of the X-ray beam, d is the crystal spacing, and θ is the angle of diffraction. In this case, θ = 22 degrees and 35 degrees, and the known value of λ is 10^10m. By plugging in these values, you can solve for d, which will be the average crystal spacing in the powdered sample.
  • #1
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Homework Statement


An X Ray beam (wavelength 10^10m) is incident upon a sample of a powdered crystalline material. At a distance of 5m from the sample a flat detecting film has been placed. A pattern of 2 circles have been recorded on this film (radius 2cm and 3.5cm).

What crystal spacing does this pattern correspond to?


Homework Equations


I'm not sure but:

mλ = 2dsinθ

(The reason I am unsure as that is for solid crystals not powder)

The Attempt at a Solution



So far I ahve calculated the angles the circles are at to the beam:

tan θ = 2/5 so θ = 22 degrees

tan θ = 3.5/5 so θ = 35 degrees

Next I tried putting them both into the above equation trying to calculate d but that makes little sense to me.

Anyone able to help?
 
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  • #2
The equation you have uses the Bragg Diffraction principle which is valid for single crystal only. Since this is a powdered sample, the diffraction will be from many crystals in a random orientation. Hence, you cannot use the Bragg equation to find the crystal spacing.
 

1. How does X-ray diffraction work?

X-ray diffraction is a technique used to determine the atomic and molecular structure of a crystal. It works by directing a beam of X-rays at a crystal and measuring the angle and intensity of the scattered rays. The resulting diffraction pattern can then be used to calculate the crystal spacing and the arrangement of atoms within the crystal.

2. What is crystal spacing?

Crystal spacing, also known as lattice spacing, is the distance between adjacent planes of atoms in a crystal. It is an important characteristic of a crystal and can be determined by analyzing the diffraction pattern produced by X-ray diffraction.

3. How is crystal spacing calculated using X-ray diffraction?

To calculate crystal spacing using X-ray diffraction, the Bragg equation is used. This equation relates the incident angle, the wavelength of the X-rays, and the crystal spacing. By measuring the angle of diffracted X-rays and knowing the wavelength of the X-rays used, the crystal spacing can be calculated.

4. What factors can affect the accuracy of crystal spacing measurements using X-ray diffraction?

There are several factors that can affect the accuracy of crystal spacing measurements using X-ray diffraction. These include the quality and purity of the crystal, the intensity and wavelength of the X-ray beam, and any imperfections or defects in the crystal lattice. It is important to carefully prepare and analyze the crystal sample to minimize these potential sources of error.

5. What are some practical applications of X-ray diffraction in crystallography?

X-ray diffraction is commonly used in crystallography to determine the structure and composition of various materials, including minerals, proteins, and polymers. It is also used in fields such as materials science, geology, and pharmaceuticals to study the properties and behavior of crystals. Additionally, X-ray diffraction is an important tool in the development and quality control of new materials and products.

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