Rare-earth chromium borates RCr₃(BO₃)₄, where R = La-Er, obtained as a result of spontaneous solutionmelt crystallization and belonging to two polytypic modifications (R32 (D ⁷₃ ) and C2/c (C ⁶_2h ) space groups) are studied by infrared spectroscopy with the factor group analysis of vibrations. Borates with R = La-Nd are shown to crystallize in the monoclinic C2/c space group. Borates with R = Sm-Er in the 1:1 ratio of batch and solvent form rhombohedral (R32 space group) and monoclinic (C2/c space group) phases at the 2.3:1 ratio, except EuCr₃(BO₃)₄ and GdCr₃(BO₃)₄ that have the rhombohedral structure under all crystallization conditions. Both rhombohedral and monoclinic polytypes may contain oppositely ordered layers. Y-, Tm-, Yb-, Lu-chromium borates are not formed.

Rare-earth aluminum borates RAl₃(BO₃)₄ (R = Y, Nd-Yb) obtained by spontaneous high-temperature flux crystallization form two polytype modifications described by the space groups R32 (D ⁷₃ ) and C2/c (C ⁶_2h ). They differ in the symmetry versions in mutual arrangement of layers. These borates have been investigated by mid- and far-IR spectroscopy in combination with factor-group analysis of the vibrations of BO ³⁻₃ ions; translational motions of Al³⁺, R³⁺ (Y, Nd-Yb), and BO ³⁻₃ ions; and BO ³⁻₃ rotations. Rare-earth aluminum borates are assigned to different space groups according to their IR spectra. Borates with large rare-earth Nd and Pr cations are crystallized into the space group C2/c (C ⁶_2h ), while borates with smaller (Y, Sm-Yb) ions are crystallized into the space group R32 (D ⁷₃ ). The rhombohedral structure of the latter compounds includes monoclinically ordered domains, as is evidenced by the presence of monoclinic-phase bands in the IR spectrum. NdAl₃(BO₃)₄ and SmAl₃(BO₃)₄ can form both monoclinic and rhombohedral polytypes. The IR spectrum of the monoclinic SmAl₃(BO₃)₄ phase contains bands due to the rhombohedral phase, while the IR spectrum of NdAl₃(BO₃)₄ (which is described by the space group R32) contains bands due to the monoclinic polytype. The presence of domains with another arrangement of layers in the polytype structure is a characteristic sign that corresponds to the order-disorder theory; this theory explains the structure of polytypes.