Which theta should be taken from xrd pattern for calculating Scherrer's equation

Question

We use scherrer's equation to calculate crystalline size of a particle.

But which theta should we take from xrd pattern for this calculation.

For example

Above picture shows the diffraction pattern of nano (above) and bulk (below) silicon and it has two diffraction peaks at 69 and 76 (approx) 2theta angle. For calculating crystalline size of nano silicon which theta should we take and why?

Answer 1

Scherrer’s formula is a simple equation for the simple case of a single peak broadened only due to crystalline particle size. Application of the formula to other, more complex cases, gives only an estimate. Quoting Wikipedia:

It is important to realize that the Scherrer formula provides a lower bound on the particle size. The reason for this is that a variety of factors can contribute to the width of a diffraction peak; besides crystallite size, the most important of these are usually inhomogeneous strain and instrumental effects. If all of these other contributions to the peak width were zero, then the peak width would be determined solely by the crystallite size and the Scherrer formula would apply. If the other contributions to the width are non-zero, then the crystallite size can be larger than that predicted by the Scherrer formula, with the "extra" peak width coming from the other factors.

Scherrer formula gives an estimate, an order of magnitude. Here, calculate the particle sizes for the two peaks, and they should be close. The differences are covered by the large uncertainty of your resulting value.