All diffractometers (and spectrometers) have their resolutions. You will not get any peak that has less width than the resolution width even if the signal has no width like a delta function. So the resolution width is the minimum width. Now if you sample gives signal of finite width then the observed width will be the width of a convolution of the instrumental profile with the profile of the sample peak. If then all all Gaussian then then thesquare of resultant or observed width will be the addition of the squares of the widths of instrumental and sample profiles. For a powder diffractometer the instrumental resolution can be calculated from the optics of the instruments. For a simple diffractometer you can use Caglioti function for the calculation.
A bit more concrete, the target dimension of your x-ray tube, your applied slits, the sollers used etc. all these factors will affect your peak broadening, even for an ideal sample. In order to determine grain size or lattice defect concentration, first you have to extract this part of peak broadening which is coming from your instrument and has nothing to do with your sample.
it is also due to the beam spread when it is incident on your sample, this causes a small difference in the incident angle as the beam is diverging, hence there is data recorded from the detector for a set of incident angles and not just the position displayed in the diffractometer, also, the X-ray source it self is not monochromatic
The factors that contribute to the instrumental broadening of a powder diffractometer are : Bragg angle \theta, three collimation angles \alpha1, \alpha2, \alpha3 and the mosicity of the monochromator crystal \eta0 and \monocromator Bragg angle \theta0. The three collimation angles are: (1) collimation before the monochromator \alpha1, (2) collimation angle after the monocrromator \alpha2, (3) collimation angle before the detector \alpha3. Normally \alpha2 is kept 0 (neutron powder diffractometer). You can then calculate the instrumental broadening \Delta 2theta by the simplified Caglioti formula:
(\Delta 2 theta)^2=\alpha1^2(1-2\tantheta/\tantheta0)^2+4\eta0^2(1-\tantheta/\tantheta0)^2+\alpha3^2
Generally, polymer has broadening XRD peaks, especial amorphous polymer.
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