Grain size measurement by XRD
In order to figure out the relationship between grain size and pore size, I tried to use XRD measurement to determine the grain size by Scherrer equation.
t = kλ/(B cosθ)
where t is the average grain size, k is the shape factor that is in the range 0.87-1.0 (it is usually assumed to be 1), λ is the x-ray wavelength, B is the width at half the maximum intensity, and θ is the Bragg angle.
The following is the first XRD result.

As you can see, there is a sharp peak with high intensity in the XRD curve. After compared with PDF card, however, it’s confirmed that this strong peak is corresponding to (400) orientation and is from the (100) silicon substrate rather than from the membrane. Since the membrane is only 15nm thick, the X-ray is easy to go through the film and hit the substrate. That’s why the intensity of this peak is so high. After first attempt, I tried to decrease the incident angle to about 1 degree between X-ray and the membrane in order to keep the X-ray in membrane area. And the following is the second result.

In this picture, we could see three tiny peaks around 28, 47 and 56 degree. Compared with the PDF card, I found that these three peaks are from (111), (220), and (311) orientation and they are all from the membrane. However, all the intensities are very low and the signal to noise ratio is very high. Obviously the strongest peak is also too small to calculate the grain size.
So next I’m thinking maybe I could focus the incident angle on the strongest peak area, say from 26 to 30 degree approximately, to see whether I could get the peak with enough intensity.