Determining the Bragg plane spacing from diffraction pattern

In summary, determining the Bragg plane spacing from a diffraction pattern involves analyzing the angles and intensities of the diffracted beams produced when X-rays or neutrons interact with a crystalline material. By applying Bragg's law, which relates the wavelength of the incident radiation to the angle of diffraction and the spacing between crystal planes, one can calculate the interplanar distances. This process typically includes measuring the diffraction angles and using the appropriate equations to extract the spacing information, which is essential for understanding the crystal structure and properties of the material.
  • #1
baseballfan_ny
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Homework Statement
Figure 1 shows a single 2D slice of a 3D diffraction pattern. The wavelength used is 0.975 Å and the distance between the crystal and detector is 13.7 cm.
1.1) What symmetry and symmetry axes do you see in this diffraction pattern? Please identify by specifying the type of symmetry (e.g. 3-fold rotation symmetry) and the direction of the axis (e.g. 3-fold rotation symmetry along the horizontal axis).
1.2) The diffraction pattern can be described as a 3D lattice with spots at lattice points of varying intensity. Measure the distance between adjacent lattice points along the horizontal axis?
1.3) Using Bragg’s Law to calculate, what is the repeat distance in the crystal that gives rise to the lattice spacing between diffraction spots along the horizontal axis?
Relevant Equations
Modified Bragg's Law (given, also shown below)
$$ d = \frac {\lambda} {2\sin[ \frac {(\tan^{-1}(\frac {d^*} {R}))} {2}] } $$
##d## = distance in crystal
##\lambda## = wavelength used
##d^*## = measured distance between adjacent lattice points in the diffraction pattern
##R## = distance between crystal and detector
1696503805825.png

1696504465016.png


1.1) I see 4-fold rotational symmetry about the axis going through the center of the diffraction pattern perpendicular to the plane of the page

1.2) and 1.3) This is where I'm stuck. Once I get the horizontal spacing between adjacent lattice points, ##d^*##, the repeat distance in the crystal ##d## would be relatively straightforward to calculate using the above version of Bragg's law in 1.3. However, I'm confused about measuring ##d^*## along the horizontal axis of the diffraction pattern in 1.2. The separation between any two spots in the diffraction-pattern along the horizontal axis is not uniform, so how do I measure "the distance between adjacent lattice points" along the horizontal axis if its constantly varying?

Edit: LaTeX delimiters
 
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  • #2
Not all of the spots are the same strength but the spacing looks pretty regular to me. What is the diameter of the film disc?
 

FAQ: Determining the Bragg plane spacing from diffraction pattern

What is Bragg plane spacing in the context of diffraction patterns?

Bragg plane spacing, often referred to as d-spacing, is the distance between adjacent planes in a crystal lattice. It can be determined from the diffraction pattern produced when X-rays, neutrons, or electrons are scattered by the crystal. The spacing is crucial for understanding the crystal structure and is calculated using Bragg's Law.

How is Bragg's Law used to determine the plane spacing from a diffraction pattern?

Bragg's Law relates the angle at which X-rays are diffracted by the crystal planes to the spacing between those planes. It is given by the equation \( n\lambda = 2d\sin\theta \), where \( n \) is the order of the diffraction, \( \lambda \) is the wavelength of the incident X-rays, \( d \) is the plane spacing, and \( \theta \) is the angle of incidence. By measuring the angle \( \theta \) and knowing \( \lambda \), the plane spacing \( d \) can be calculated.

What type of diffraction patterns are used to determine Bragg plane spacing?

Diffraction patterns from X-ray diffraction (XRD), neutron diffraction, and electron diffraction are commonly used to determine Bragg plane spacing. Each method involves directing a beam of X-rays, neutrons, or electrons at the crystal and analyzing the angles at which the beams are diffracted to obtain information about the crystal structure.

What equipment is needed to measure diffraction patterns and determine plane spacing?

To measure diffraction patterns and determine plane spacing, specialized equipment such as an X-ray diffractometer, neutron diffractometer, or electron diffractometer is required. These instruments are designed to precisely measure the angles and intensities of the diffracted beams, which are then used to calculate the plane spacing using Bragg's Law.

Can plane spacing be determined for all types of crystals using diffraction patterns?

Yes, plane spacing can be determined for a wide variety of crystalline materials using diffraction patterns. This includes metals, minerals, semiconductors, and complex biological molecules like proteins. The key requirement is that the material must be crystalline, as the regular arrangement of atoms in a crystal lattice is what produces the distinct diffraction pattern needed for analysis.

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