Birefringence of CaCO₃and Electronic Polarizabilities of the Constituent Ions

Prospects for Fluoride Carbonate Nonlinear Optical Crystals in the UV and Deep-UV Regions

“…3 crystal (in centrosymmetric R3̅ c symmetry) and reveal that the calculated results (n o = 1.6835, n e = 1.4914, Δn = 0.1921) are in a good agreement with the experimental values (n o = 1.658, n e = 1.486, Δn = 0.172) 45. …”

“…This computational procedure ensures that our first-principles studies are self-consistent without adjusting any parameter from experiments. To prove the correctness of our computational method on carbonates, we calculate the refractive indices and birefringence of the CaCO 3 crystal (in centrosymmetric R 3̅ c symmetry) and reveal that the calculated results ( n o = 1.6835, n e = 1.4914, Δ n = 0.1921) are in a good agreement with the experimental values ( n o = 1.658, n e = 1.486, Δ n = 0.172) …”

Ba4M(CO3)2(BO3)2 (M=Ba, Sr): two borate-carbonates synthesized by open high temperature solution method

“…Analogous to the BO 3 triangles, the CO 3 groups possess a similar planar triangle, which are also beneficial for good optical properties, such as moderate birefringence or bulk NLO coefficients with the coparallel alignment [36][37][38][39][40]. For example, CaCO 3 has a large birefringence since the coparallel alignments of the CO 3 groups lead to the large anisotropic polarizability [41]. For series of alkali-alkaline earth metal carbonate fluoride, ABCO 3 F (A = K, Rb, Cs; B = Ca, Sr, Ba), the coplanar and parallel arrangements of the CO 3 groups lead to a large secondharmonic generation (SHG) response [42].…”

Reinvestigation and Characterization of the Magnesium Borate Fluoride Mg5(BO3)F

“…Each B1O 3 triangle shares vertices with one Mg1O 5 F octahedron, one Mg2O 5 F octahedron, five Mg3O 6 octahedra and edges with one Mg1O 5 F octahedron, while each B2O 3 triangle shares vertices with four Mg1O 5 F octahedra, one Mg2O 5 F octahedron, two Mg3O 6 octahedra and edges with one Mg2O 5 F octahedron (Figure S3, Supporting Information). According to the reference,34 the anisotropy of polarizability of planar BO 3 groups indicates that some borates are likely to be good candidates for future birefringent materials if their BO 3 groups are in suitable configuration, as for CO 3 in CaCO 3 35. So this configuration of BO 3 groups in Mg 5 (BO 3 ) 3 F is in an unfavorable manner for birefringent materials.…”

“…According to the reference, [34] the anisotropy of polarizability of planar BO 3 groups indicates that some borates are likely to be good candidates for future birefringent materials if their BO 3 groups are in suitable configuration, as for CO 3 in CaCO 3 . [35] So this configuration of BO 3 groups in Mg 5 (BO 3 ) 3 F is in an unfavorable manner for birefringent materials.…”