X-ray diffraction pattern is obtained from FCC polycrystalline aluminium (lattice parameter = 0.405 nm) using Cr-K📷 radiation of wavelength 0.2 nm. The maximum number of peaks that can be observed in the pattern is ___________ .I have seen people answering such topics on the basis of range of sin theta values that I can have at max.What should be my intuition in such questions?
Starting point of solving that question is the Bragg equation:
lambda=2*dhkl*sin(thetahkl). It is just the point you mentioned above. But there is no necessity to explicitly calculate the theta values. It is just sufficient to introduce the max value of sin(theta) as: sin(theta)
Sum FCC crystals Miller indices are either all even or all odd, (considering 0 even)
for FCC Miller indices will be e.g.(h k l) (111), (200), (220), (311), (222), (400), (331), (420) so on.
now you can calculate using Bragg Law λ=2 d sinθ -------1
and d=a/square root(h*h+k*k+l*l)------2
use eq 1 and 2 together.
and use h k l values given above.
you have a=lattice parameter and λ=wavelength
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