How Does Crystal Structure Affect X-Ray Diffraction Angles?

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In summary, the Bragg Equation is a fundamental equation in X-ray crystallography that relates the wavelength of X-rays, the angle of incidence, and the spacing of crystal lattice planes. It is used to determine the atomic structure of materials and has been crucial in scientific discoveries. The assumptions made in the Bragg Equation include a perfect crystal lattice, monochromatic X-rays, and specific incident angle. This equation can also be applied to other types of waves, but may require modifications.
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Dante Tufano
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1. Consider a cubic crystal as shown in the figure below. As this single crystal is rotated in an x-ray spectrometer, many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in the figure.

http://capa.sci.geneseo.edu/p223library/p223Graphics/Gtype02/crystal.GIF

Suppose the wavelength of the x-rays is l = 3.14 nm. Find the angle (with respect to the surface plane AA) of the n = 1 intensity maxima resulting from scattering from planes with spacing d1.

Homework Equations



n*λ=2*d1*sinθ

The Attempt at a Solution



So I found the value of d1 using the geometry of the diagram. I tried using the equation to find θ, and got a value of about .065 radians. However, this is apparently wrong. Any ideas on why this isn't right?
 
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There could be a few reasons why your answer is not correct. First, make sure that you are using the correct units for the wavelength. In this case, it should be in meters, so you may need to convert from nanometers to meters. Additionally, make sure that you are using the correct value for n. In this case, n = 1, so make sure you are not accidentally using a different value. Finally, double check your calculations to make sure there are no errors. If you are still having trouble, try using a calculator or software to double check your answer.
 

1. What is the Bragg Equation?

The Bragg Equation is a fundamental equation in X-ray crystallography that describes the relationship between the wavelength of X-rays, the angle of incidence, and the spacing of crystal lattice planes. It is expressed as nλ = 2d sinθ, where n is the order of diffraction, λ is the wavelength of X-rays, d is the spacing of crystal lattice planes, and θ is the angle of incidence.

2. How is the Bragg Equation used in X-ray crystallography?

The Bragg Equation is used to determine the spacing of crystal lattice planes, which in turn provides information about the atomic structure of a material. By measuring the angle of incidence and the wavelength of X-rays, scientists can use the Bragg Equation to calculate the spacing of crystal lattice planes and determine the arrangement of atoms in a crystal.

3. What is the significance of the Bragg Equation in science?

The Bragg Equation is a crucial tool in X-ray crystallography, a technique used to study the atomic and molecular structure of materials. It has been instrumental in numerous scientific discoveries, including the discovery of the double helix structure of DNA by Watson and Crick. It is also used in various fields such as materials science, chemistry, and biology to analyze the structure of crystals and molecules.

4. What are the assumptions made in the Bragg Equation?

The Bragg Equation assumes that the crystal is a perfect, periodic arrangement of atoms and that the X-rays are monochromatic (have a single wavelength). It also assumes that the incident X-rays are perfectly parallel and that the crystal is oriented in such a way that the X-rays strike the crystal at a specific angle.

5. Can the Bragg Equation be applied to other types of waves?

Yes, the Bragg Equation can be applied to any type of wave that exhibits diffraction, such as electrons and neutrons. However, the equation may need to be modified to account for the different properties of these waves.

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