The birefringence of the new Ba2Na3[B3O6](2)F (BNBF) (P6(3)/m) and Ba-7(BO3)(4-y)F2+3y (P6(3)) phases has been investigated. Coefficients of the Sellmeier equations have been determined. Parallel [B3O6](3-) rings in the Ba2Na3[B3O6](2)F structure generate the major anisotropic polarizabilities and produce large birefringence Delta n = 0.1097 - 0.0428 from 350 nm to 5 mu m, comparable to that of commercial birefringent crystal alpha-BaB2O4. A new flux for growing a high quality BNBF crystal has been proposed. In the measured wavelength range from 266 nm to 1.7 mu m noncentrosymmetric phase Ba-7(BO3)(4-y)F2+3y (y = 0.49) exhibits low birefringence Delta n = 0.0111 - 0.0037 which can be accounted for non-coplanar arrangement of the anionic groups in the structure. Low birefringence prevents the use of this crystal for nonlinear optical applications, since phase-matching conditions for second harmonic generation can not be reached. (C) 2017 Elsevier Ltd. All rights reserved.