I have the ionic compound cesium chloride and have been asked to use the equation
p(k) = (sum over j) exp(-iK.r)f(k)
to find the structure factor for x-ray diffraction from cesium and explain why it can take two values. It also asks how you would expect the intensities of the bragg reflections in the x-ray patterns of cesium, cesium chloride and cesium iodid to compare.
The Attempt at a Solution
I know that cesium chloride has a simple cubic structure with Cs at 0,0,0 and Cl at 1/2 , 1/2, 1,2
So I found the recipricol lattice vectors to be a*=(2*Pi/L)x b*=(2*Pi/L)y and c*=(2*Pi/L)z
The recipricol lattice vector is K=ha*+kb*+lc*
p(k) = f(Cs)exp(0) + f(Cl)exp(-iK.(L/2,L/2,L/2))
=f(Cs) + f(Cl)exp(-i*pi*(h+k+l))
which is =f(Cs) + f(Cl) if h+k+l is even or =f(Cs)-f(Cl) if h+k+l is odd.
I'm not sure where the -i*pi*(h+k+l) part came from? are h,k,l just 2,2,2??
for the second bit I know that the intensity is proportional to the structure factor squared...
not sure where to go from here.