Tolerance factor for huntite-family compounds

85$RM_{3}$(BO$_{3}$)$_{4}$ ($R$ is the rare-earth element (Y, La–Lu) and $M$ = Al, Sc, Cr, Fe, or Ga) compounds with the huntite structure have been analyzed. The analysis of the structures has made it possible to determine critical atomic displacements during the phase transition $R$32 $\leftrightarrow$ $P$3$_{1}$21 and establish how these critical displacements can be controlled by varying the ionic radii. A tolerance factor has been derived and its threshold value below which the structure is stable in the $R$32 phase and above it, in the distorted $P$3$_1$21 phase, has been found. The formula has been tested on more than 30 huntite-family compounds and good agreement has been obtained. Therefore, it can be used with confidence to predict new compounds. At the moment, the tolerance factor has allowed us to establish previously unknown regularities in huntites.