AS XRD determines the cell volume and its mass, you may use the following Eq. to estimate the XRD density (proposed by Smith and Wijn):

 ρ(x) = Mw.n/(NA.(a)^3 )

where Mw is the molecular weight,  NA is the Avogadro’s number, a is the lattice constant, and n is  the number of the lattice points of each unit cell.

Then measure the bulk density (ρb= m/v). The porosity can be obtained through the following equation:

Porosity = (1-(ρb/ρ(x)) * 100

c.f. the following discussions as well:

https://www.researchgate.net/post/Anyone_can_help_me_please_How_do_calculate_the_bulk_density_of_nanoparticle

https://www.researchgate.net/post/what_is_meant_by_X-ray_density_which_is_measured_in_XRD_pattern_Is_there_any_relation_between_bulk_density_X-ray_density_and_porosity

I assume that a) the given formula is only correct for cubic phases (a³), and b) if possible, there is a huge uncertainty....

XRD by itself can not used to measure sample porosity (it only identifies crystalline phases/structures in the sample)... It can be used to determine the theoretical density of the phases present in the sample as given above or from the XRD file for the identified phase. The sample density has to be measured independently to estimate porosity.

XRD can be used to estimate particle size of powders by line broadening.

On the basis of XRD data, it is very difficult to comment on porosity. From XRD, we can calculate the crystal size rather than particle size (in particular). BET characterization plays vital role in finding the porosity. Depending on the pore size or volume, we may jump to decision. Microporous = 1 - 2 nm

Mesoporus = 2 - 50 nm

Macroporous = > 50 nm.

Hope, it helps.