- #1
baseballfan_ny
- 92
- 23
- 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
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