We report measurements of all the material constants necessary to fully characterize barium borate as a nonlinear optical material. All data was taken on crystals supplied by Professor Chuangtien Chen, Fuzhou, People’s Republic of China. We have determined the crystal structure, the optical absorption, the refractive indices from the UV to the near IR, the thermo‐optic coefficients, the nonlinear optical or coefficients, the resistance to laser damage, the elastic constants, the thermal expansion, thermal conductivity and dielectric constants, and the fracture toughness. This data is used to evaluate barium borate for a variety of applications. We find that, in general, barium borate has a low acceptance angle, and that despite its higher optical nonlinearity, it is therefore not significantly more efficient than other commonly available materials, except in the UV below 250 nm. On the other hand, it has a high damage threshold, it is physically robust, it has good UV and IR transparency, and it has excellent average power capability. It permits deep UV generation, and has great potential for generating tunable visible and IR light as an optical parametric amplifier.

Optical, mechanical, and thermal properties of barium borate

Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tc = 348° ± 15°K, is a tungsten bronze‐type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024 ± 0.00002 and c = 3.91341 ± 0.00001 A at 298°K, space group P4bm, and five formulas in the unit cell. The integrated intensities of 6781 structure factors were measured with PEXRAD, 875 symmetry‐independent structure factors being significantly above background. The metal‐atom positions were determined from the three‐dimensional Patterson function and the oxygen atoms from subsequent Fourier series. The final agreement factor between measured and calculated structure factors is 0.0508. The structure consists of close‐packed slightly puckered layers of oxygen atoms separated by nearly c / 2. The Nb atoms are slightly displaced from one layer, the Ba and Sr atoms from the other and in the same sense. The oxygen atoms in the Ba and Sr layer are disordered. Neither of the two independent sites occupied by the Ba and Sr atoms is fully filled....

Ferroelectric Tungsten Bronze‐Type Crystal Structures. I. Barium Strontium Niobate Ba0.27Sr0.75Nb2O5.78

Starting from a general quantum-mechanical perturbation theory on the nonlinear optical (NLO) effect in crystals, this review gives a systematic presentation of the basic concepts and calculation methods of the ‘anionic group theory for the NLO effect of crystals’ and a brief discussion of the approximations involved. Calculations have been made for the second harmonic generation (SHG) coefficients of a few typical NLO crystals. Comparisions between these theoretical values and the experimental values made both on powdered crystals and on single crystals suffice to show the feasibility of the theoretical treatment and calculation methods. On this basis, borate ions of various structure types are classified and systematic calculations are carried out for the NLO susceptibilities of some typical borate crystals with good prospects of applications in opto-electronics. Through these calculations, a series of structural criteria serving as useful guidelines for searching and developing new NLO crystal...

The anionic group theory of the non-linear optical effect and its applications in the development of new high-quality NLO crystals in the borate series

Ferroelectric Ba(4+x)Na(2 − 2x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze‐type structure and crystallizes in the orthorhombic system, with subcell lattice constants a = 17.59182 ± 0.00001, b = 17.62560 ± 0.00005, and c = 3.994915 ± 0.000004 A at 298°K. The space group is Cmm2, and there are two formulas in the subcell. The c axis of the true cell is double that of the subcell. The integrated intensities of 6911 reflections within a reciprocal hemisphere of radius (sinθ)/λ = 1.02 A−1 were measured with PEXRAD, 1873 symmetry‐independent structure factors being significantly above background. The metal atom positions were determined from the three‐dimensional Patterson function and the oxygen atoms from metal‐phased Fourier series. The final agreement index between measured and calculated structure factors is 0.0579. The structure differs only in detail from previously determined tetragonal tungsten bronze structures. In the general formula (A1)2(A2)4C4(B1)2(B2)8O30, the B1 and B2 sites are fully occupied by Nb, the A2 sites by Ba and the A1 site by 87.0% Na and 6.5% Ba. Evidence from chemical analysis, x‐ray density calculations and the present determination suggests that the best approximation to the formula of the crystal studied is Ba4.13Na1.74Nb10O30. The Ba and O atoms at z ≃ 12 are disordered in a manner similar to the O atoms in the Ba layer in barium strontium niobate. The four crystallographically independent Nb atoms, each in octahedral coordination, are linked to O atoms by distances ranging from 1.765 ± 0.021 to 2.270 ± 0.021 A, with a mean value of 1.989 A. Ba is 10 coordinated, with Ba–O distances ranging upward from 2.671 ± 0.013 A. Na is 12 coordinated, with Na–O distances ranging from 2.660 ± 0.014 to 2.990 ± 0.015 A, with a mean of 2.788 A. The Nb‐atom displacements from the mean oxygen planes lie in the range 0.171–0.205 A; the parabolic relation with Curie temperature predicts a displacement of 0.204 A. The measured value of Ps at room temperature is 40 μC cm−2: the linear relation between displacement and polarization predicts a saturation value of 44–53 μC cm−2. All metal atoms are displaced from the oxygen planes in the sense given by the macroscopic positive polarity.

Ferroelectric Tungsten Bronze‐Type Crystal Structures. II. Barium Sodium Niobate Ba(4 + x)Na(2 − 2x)Nb10O30

The structural features of over 460 anhydrous oxoborates that are described in literature were analysed. Lewis acid strengths were calculated for all cations other than B 3+ that were found in these structures, using the valences of the cations and their determined average coordination numbers. From the observation of a restriction of the occurrence of complex polyborate anions to specific ranges of cation Lewis acid strength in existing oxoborate compounds, the Lewis base strengths of the complex polyborate anions (not of the oxygen ligands) were inferred, using the idea that is at the bottom of the valence matching principle, that in the most stable compounds the Lewis acid strength of the cation nearly equals the Lewis base strength of the anion. From this, general inherent rules for the occurrence of the miscellaneous polyborate anions with respect to the ratio cation: boron (A:B), the Lewis acid strength(s) L a of the cation(s) other than B 3+ and the cation radii were developed These rules offer the possibility for a prediction of the stoichiometry and the most probable polyborate structural group that will be adopted by a new anhydrous borate compound.

A. Perloff

Papers

The crystal structure of the high temperature form of barium borate, BaO.B2O3