Optical rotation in biaxial, achiral and ferroelectric NaNO2-crystal at 296K.

Volume 8, Issue 1, February 2023     |     PP. 1-15      |     PDF (1704 K)    |     Pub. Date: January 25, 2023
DOI: 10.54647/chemistry150294    89 Downloads     161195 Views  

Author(s)

M. Karppinen, Institution of Chemistry, University of Uppsala, Box 531, Uppsala S-75121 Sweden.

Abstract
NaNO2 crystal is biaxial, achiral and ferroelectric ionic solid at room temperature. It belongs to the symmetry class mm2. The magnitude and sense of optical rotation with opposite signs are determined in the two optic axis directions, OA1 and OA2, of the crystal model at four wavelengths. The handedness of the crystal structure is in correlation with the optical rotation character of the dominant components of plane polarized light, when it propagates in the directions of both OAs. The directions of the involved OAs are derived from the known refractive indices in the principal axis directions and they deviate with the same angle from the bisector axis, at any one wavelength, in the mm2 symmetry. Cross products of the wave vector in the propagation direction of light and the electric moments in the other two principal axis directions of the quadric around the NO2‒ ion generate two axial vectors of second rank. The dominating vector of them accommodates the position of Z-axis of the indicatrix, which is experimentally observed and lies parallel with the crystallographic b-axis. The magnitude of the refractive index in the direction of OA is extracted in polar coordinates from the contributions arising from the principal axis directions of the crystal. The magnitudes of two orthogonal polar vectors, Θ’OA and Θ’ZZ, in the directions of optic axes and the optic normal, respectively, in the quadric of the second electric moments, are iterated to topological equivalence with the net charges of N and O atoms as variables, until the ratio of them reached the inverted ratio of the corresponding refractive indices in the quadric of the optical indicatrix. Both quadrics are representation surfaces of second rank and geometrically three axial ellipsoids. The magnitude and sense of the dominant component of the circularly polarized light in the direction of OA reveal the sense of optical rotation character of crystal. When a plane polarized light travels in the OA1 direction of the absolute crystal structure with a right-handed system of coordinate axes of NaNO2 crystal, a clockwise rotation of +17.2 ° mm ‒ 1 is observable. The crystal is dextrorotatory. When a plane polarized light propagates in the direction of OA2, the crystal turns left-handed and rotates the plane of light anticlockwise ‒17.2 ° mm ‒ 1 and now the crystal is levorotatory when seen against the light source by an observer.

Keywords
NaNO2, optical rotation, biaxial, achiral, refractive indices,second electric and axial vectors.

Cite this paper
M. Karppinen, Optical rotation in biaxial, achiral and ferroelectric NaNO2-crystal at 296K. , SCIREA Journal of Chemistry. Volume 8, Issue 1, February 2023 | PP. 1-15. 10.54647/chemistry150294

References

[ 1 ] Kaminsky, W., Thomas, P.A. and Glazer A.M. (2002). Z. Kristallogr. 217, 1-7.
[ 2 ] Kobayashi, J., Uesu, Y. (1983). J. Appl. Crystallogr. 16, 204-211.
[ 3 ] Kobayashi, J., Uesu, Y., Takehara, H. (1983). J. Appl. Crystallogr. 16, 212-219.
[ 4 ] Claborn, K., Isborn, C., Kaminsky, W. and Kahr B. (2008). Angew. Chem. Int. Ed. 47, 5706-5717.(Internet: Optical Rotation of Achiral Compounds – Academia.edu).
[ 5 ] Born, M., Phys. (1915). Z., 16, 251.
[ 6 ] Reijnhart, R., Dissertation, (1970). Technische Hogeschool, Delft (1970). (Internet: P1966-3184.pdf).
[ 7 ] Devarajan, V. and Glazer, A. M. (1986). Acta Cryst. A42, 560-569.
[ 8 ] Ramachandran, G.N. (1951). Proc. Indian Acad. Sci. A33, 217 - 227.
[ 9 ] Ramachandran, G.N. (1951). Proc. Indian Acad. Sci. A33, 309 - 315.
[ 10 ] Ramachandran, G.N. (1951). Proc. Indian Acad. Sci. A34, 127 - 135.
[ 11 ] Glazer, A.M. and Stadnicka, K. (1986). J. Appl. Crystallogr, 19, 108-122.
[ 12 ] Nesse, W.D. (1986). Introduction to Optical Mineralogy, Oxford University Press.
[ 13 ] Axe, J.D. (1968). Phys. Rev. 167, 573.
[ 14 ] Ravindran, P., Delin, A., Johansson, B. and Eriksson, O. (1999). Phys. Rev. B 59, 1776.
[ 15 ] Fresnel, A. (1824). Bull. Soc. Philomath. Paris. pp. 147-158.
[ 16 ] Ziegler, G.E. (1931). Phys. Rev. 38, 1040.
[ 17 ] Carpenter, G.B. (1952). Acta Cryst. 5, 132.
[ 18 ] Kay, M.I. and Frazer, B.C. (1961). Acta Cryst. 14, 56.
[ 19 ] Gohda, T., Ichikawa, M., Gustafsson, T. and Olovsson, I. (1996). J. Korean. Phys. Soc. 29, S551-S554.
[ 20 ] Sawada, S., Nomura, S., Fuji, S. and Yoshida, I. (1958). Phys. Rev. Lett. 1, 320.
[ 21 ] Mitsui, T. Iio, K. Hanazaki, B. and Nakamura, T. (1985). Jpn. J. of Appl. Phys. 24, 272 (On line.).
[ 22 ] Dmitriev, V.G., Gurzadyan, G.G. and Nikogosyan, David N. (2013). Handbook of Nonlinear Optical Crystals, 3th Revised Edition, Springer-Verlag.(Internet: Refractive Indices in biaxial NaNO2 crystal).
[ 23 ] Farrugia, L.J. (1997). ORTEP-3 for Windows, J. Appl. Crystallogr. 30, 565.
[ 24 ] Chern, Mao-Jin. and Phillips, R.A. (1970). J. Op. Soc. Am., 60,1230-1232.
[ 25 ] Chern, Mao-Jin., Dissertation, (1972) University of Minnesota, (1972). (Internet: A study of optical activity and Raman scattering in the sodium-nitrite crystals).
[ 26 ] Buckingham, A.D. (1959). Q. Rev. Chem.Soc. 13, 183.
[ 27 ] Buckingham, A.D. (1970). Physical Chemistry. An Advanced Treatise. Vol. IV, p.349.
[ 28 ] Karppinen, M. (2015). Acta Crystallogr. Sect. B 71, 334-341.
[ 29 ] Nye, J.F. (1972). Physical Properties of Crystals. Oxford: Clarendon Press.