Hi I have 2 questions about the structure factor and the corresponding diffraction pattern. Suppose you have the following structure factor: S=f_A+f_Be^{i\frac{\Pi}{2}\left(h+k\right)}, and you take h=1 and k=0 then you get S = f_A+ i f_B. Is this imaginary peak a valid solution? Also if you would take f_B = 0 do you then get diffraction peaks with the same intensity or no diffraction at all?
yes the structure factor can be complex. Remember that we are adding waves, and as such the phase of each individual wave is encoded by a complex number. The total wave (amplitude and phase) is given by the sum over all the individual waves. However, the standard X-ray detector detects the intensity of a scattered wave, so you need to take the absolute value squared of the total amplitude.
Thank you, my first question is all clear now. But how about the case when f_B = 0? Do you then get different diffraction peaks with the same intensity? Or just 1 peak since S then no longer depends on h and k.
When f_B=0 the B-atoms do not scatter any x-rays so they don’t contribute in the measured spectrum. As the structure factor in this case does not cause some peaks to disappear, you get peaks whenever the Laue condition is met (i.e., at all reciprocal lattice vectors)
I also have a question about the structure factor. Suppose the following lattice/basis is given (found in the lecture notes):
Here a conventional unit cell is defined, as stated. But one could also think of a primitive unit cell:
\vec{a_1}=\frac{a}{2}(\hat{x}+\hat{y}),
\vec{a_2}=\frac{a}{2}(\hat{x}+\hat{z})
\vec{a_3}=\frac{a}{2}(\hat{y}+\hat{z})
And a basis: (0,0,0). Could this also be used to calculate the structure factor? If I calculated the above correctly I end up with a different structure factor as given in the lecture notes.
In this case the structure factor is 1 because you only have an atom at the origin. The challenge with using a non-conventional unit cell is that the Miller planes corresponding to certain Miller indices are hard to identify (see exercise on this)
Okay thank you. So it would (for the usual purposes in this course) be more convenient to define a conventional unit cell with a corresponding basis and use these to calculate the structure factor. And this is because the given Miller planes are defined with respect to a conventional unit cell?
Thank you for explaining