Bragg Reflection = Standing Waves

In summary, the conversation revolves around understanding Bragg reflection in solid state physics. The individual has a solid grasp on most of the complex subjects but is struggling with this fundamental phenomenon. They mention Kittel's explanation of standing waves at the first brillouin zone with k=½G, but are unsure why this is the case. They inquire about an equation that could help them understand why the wavefunctions are composed of equal parts of waves traveling in opposite directions at k=½G. The other person suggests looking at Bragg diffraction in Kittel, where Bragg's condition for diffraction can also be expressed as k=1/2G for X-rays and electrons.
  • #1
DrBrainDead
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Homework Statement


I've got my exam in solid state physics tomorrow, and although I've understood most of the most complex subjects now, I feel I'm missing the understanding on one fundamental phenomena; Bragg reflection..

Throughout Kittel it's mentioned, that when we're at the first brillouin zone with k=½G, then we have standing waves. I don't think it's mentioned anywhere why though?

Is there some equation from which I can easily realize, that when k=½G then the wavefunctions are made up of equal parts of waves traveling to the right and left?
 
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  • #2
If you look in Kittel at Bragg diffraction you will see that Bragg's condition for diffraction can be also put in the same form: k=1/2 G where k is the wave-vector of the X-ray.
For electrons, k is the wave-vector of the electron wave.
 

What is Bragg Reflection and how does it relate to standing waves?

Bragg Reflection is a phenomenon in which X-rays are diffracted off of the regular atomic structure of a crystal at a specific angle, resulting in constructive interference. This is similar to how standing waves are formed when two waves with the same frequency and amplitude travel in opposite directions and overlap, resulting in areas of high and low amplitude. In both cases, the waves are reflected and amplified due to their specific wavelengths and the regularity of the medium they are interacting with.

What is the Bragg equation and how is it used to calculate the angle of reflection?

The Bragg equation, also known as the Bragg law, is a mathematical formula that relates the wavelength of the X-ray, the spacing of the atomic planes in the crystal, and the angle of reflection. It is given by nλ = 2d sinθ, where n is an integer representing the order of the reflection, λ is the wavelength of the X-ray, d is the spacing of the atomic planes, and θ is the angle of reflection. This equation can be rearranged to solve for θ, allowing scientists to determine the angle at which Bragg Reflection will occur for a specific crystal and X-ray wavelength.

What are the applications of Bragg Reflection and standing waves in scientific research?

Bragg Reflection and standing waves are commonly used in X-ray crystallography to determine the atomic structure of crystals. By analyzing the diffraction pattern created by Bragg Reflection, scientists can determine the positions of the atoms within the crystal and their arrangement. This technique has been used to study the structures of proteins, DNA, and other molecules, providing valuable insights into their functions and interactions. Bragg Reflection is also used in other fields such as materials science, where it is used to analyze the structure and properties of various materials.

What factors affect the intensity of Bragg Reflection and standing waves?

The intensity of Bragg Reflection and standing waves is influenced by several factors, including the wavelength of the X-ray, the spacing of the atomic planes in the crystal, and the orientation of the crystal relative to the incident X-ray beam. The intensity is also affected by the number of atoms in the crystal and their scattering properties. Additionally, the beam width and the quality of the crystal can also impact the intensity of the reflection and the formation of standing waves.

What are the limitations and challenges of using Bragg Reflection and standing waves in scientific research?

One of the main limitations of using Bragg Reflection and standing waves is that it requires a high-quality crystal with a regular and well-defined atomic structure. This can be challenging to obtain for certain materials, making it difficult to use this technique for their analysis. Additionally, the analysis of the diffraction pattern can be complex and time-consuming, requiring specialized equipment and expertise. Another limitation is that Bragg Reflection only works for X-rays with a specific wavelength, limiting its use for certain applications. Finally, the equipment used for Bragg Reflection experiments can be expensive and not readily available, making it less accessible for some researchers.

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