Dear Jean,

x-ray applications  always suffer from low net x-ray flux at the detector. So it is obvious that the strongest  fluorescence line is taken for the XRD  measurements. For the case of Cu anode the flux ratio of Cu K-beta (1+3) to K-alpha(1+2) is about 0,14.

Unfortunately not only the K-alpha radiation contributes to the XRD pattern but also the bremskontinuum  of the x-ray spectrum.

The bremskontinuum will lead to a continuous background of the diffractograms.  So also here it it advantageous to use K-alpha because of its higher flux compared to K-beta.

Some more aspects (e.g. different anode material and K-beta blocking)  of this topic are given in the answers of a similar question here on RG some time ago. 

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

Thanks a lot Dear Mr. Gerhard Martens