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

There should no relation between grain size and peak intensity. Change in intensity could occure due to sample amount, if you put less sample in holder you will get lower intensity and if you put more sample you will get higher intensity in the same sample type. only thing that show your crystal size is the full width at half maximum (FWHM) that with increasing in crystal size, FWHM will decrease.

I hope this will be useful for you.

To the best of my knowledge, there is no relation between the intensity and grain size, but the peaks intensity is related to the texture effect (grains orientation), but the grain size affects the Full Width at Half Maxima as follows.

I also agree that change in the intensity could occur due to the sample thickness or amount.

Firstly, how the texture affects x-ray intensity ?

To understand this effect, we have to remember that, for the poly crystalline samples, there are many possible {hkl} planes expected to yielding a diffraction at Bragg’s diffraction angles with intensity variation determined by many factors such as structural factor, Lorentz factors, and multiplicity. On the other hand, for the texture sample the crystallographic orientations are not random, but have some preferred orientations. Due to the preferred orientation in these type of materials, most of its grains would have one preferred plane parallel to the sample axis and this plane will have the maximum intensity compared to the other planes in the crystal.

Secondly, how grain size affects x-ray diffraction?

According to Bragg’s law, invery small crystallites, there are not enough planes to produce complete destructive interference, so a broadened peak is observed, which mean the decrease in the crystallite size causes an increase in the width of the diffraction.On the other hand, with annealing, the grain size increase while developing texture as we will see in sample 2. Due to the large grain size, thediffraction from a large number of planes willproduce complete destructive interference and result in a sharp peak.Depending on this change in peak width due to the grain size Debye-Scherrer relates the crystallite size to the full width at half maximum (FWHM) of peaksaccording the following equation[3]: r = 0.9λ/B cos θwhere r represents the mean grain size, and B represent the Full Width at Half Maxima of the peak.