These rates are not necessarily fixed or constant but they can vary by orders of magnitude depending on local lattice gradients (curvature, GNDs), on local stored energy, and on local content of solutes and precipitates etc. The GB mobility (in case of the growth rate, is particularly sensitive).

It is thus maybe more valid to speak of fixed upper bounds,  which would be here maybe the self-diffusion coefficient as both types of processes require re-organisation of the local atomic motifes which relates to the diffusion coefficient.

 I attach a text which maybe helpful.

Good luck.

Dear Sir Dierk Raabe, your explanation is very logical and useful to me. Thank you so much for your time and effort.