Site-occupancy scheme in disordered Ca₃RE₂(BO₃)₄: a dependence on rare-earth (RE) ionic radius

The structures of polycrystalline Ca₃RE₂(BO₃)₄ (RE = La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Y; space group Pnma) orthoborates were determined using powder X-ray diffraction. Trends in the unit-cell dimensions and yet unreported trends in other structural properties (interatomic distances and the fractional occupation of three Ca/RE sites) for these compounds are demonstrated as a function of RE ionic radius. The unit-cell volume and a unit-cell parameter present a linear dependence, while the b and c unit-cell parameters change in a nonlinear manner. For the whole series, the RE atoms are present at all three cationic sites (labelled as M1, M2 and M3), but the fractional occupancies depend on the RE ionic radius. The small rare-earth atoms tend to enter mainly the M3 site; for the larger rare earths, the occupancy of this site decreases sharply. The occupancy of the M1 site by RE atoms is around 0.5 and tends to increase with increasing RE ionic radius. The M2 site is the least preferentially occupied by RE ions, but the occupancy discernibly increases with rising radius as well. These findings are assembled with properties of isostructural strontium and barium borates, allowing prediction of occupancy schemes for not yet investigated compounds from the A₃RE₂(BO₃)₄ (A = Ca, Ba, Sr).