Different crystals of rare earth-doped YAB, with dopant concentrations less than 5at%, have been grown by the closed crucible flux method. Their lattice constants have been measured from the XRPD diffraction angles, given a mean value of a=9.281(3)Å and c=7.223(2)Å.From these growth processes two final crystal morphologies have been obtained: one with the {101} form higher than the {21¯0} one, and the other with the later form higher than the first. Simulations of the crystallization process explain the final external shape in terms of the relative growth rates of these forms, and it is demonstrated that although all crystal processes begin with the same morphology, a change in relative velocity produces two types of final shapes. The disappearance of the growth sector of the {001} form, during the first steps of growth process, is postulated.