Point-dipole theory and optical birefringence of calcite-type carbonates

Abstract

A critical survey of the literature has revealed that recent structure determinations and optical data are available for only three calcite-type carbonates: calcite, rhodochrosite and magnesite. For these structures, the limitations of the pointdipole approximation are discussed.The point-dipole model was introduced by Bragg (1924) to explain quantitatively the birefringence of calcite and aragonite with respect to the crystal structures. In this approach optical anisotropy arises from differences in dipole-dipole coupling along different crystallographic directions. This source of anisotropy is connected with the Lorentz-factor tensor. In addition, however, optical anisotropy may arise from an intrinsic anisotropy in the constituent ions. In this case electronic polarizability tensors should be considered.In order to investigate the relation between atomic arrangement and double refraction, the crystals of carbonates have been used repeatedly. The latest studies are those given by Isherwood &James (1976) andPohl (1978). In his paper Pohl (1978) has developed a method to determine the electronic polarizabilities of ions from structural and optical data by a least-squares fit. The method is based on Bragg's (1924) model of point dipoles and on an exact calculation of Lorentz-factor tensors. This model satisfactorily accounts for the double refraction of aragonite-type carbonates. In the present paper we discuss the application of the method to calcite-type carbonates.Structural parameters of only three calcite-type carbonates have been determined: calcite (Chessin, Hamilton & Post, 1965), rhodochrosite (Brown & Forsyth, 1967) and magnesite (Oh, Morikawa, Iwai & Aoki, 1973). Optical constants are given by Winchell & Winchell (1964). Application of Pohl's (1978) method yields the electronic polariz- Bragg's (1924) ideas, the birefringence arises from the oxygens within the isolated COl-groups: the stronger the birefringence the stronger the influence of the O z-ions on each other. Strengthening of the oxygen interaction can take place in two ways. Firstly, the distance between the carbon and oxygen can be diminished. Secondly, the polarizability of the oxygen ion can be increased. Since the C-O distance is fixed according to the structure determination, only an increased polarizability of the 0 2-ion remains. However, this results in an increased mean refractivity which in return is compensated by a smaller polarizability of the cation, thus explaining the above results.To overcome the shortcomings encountered with the Bragg model of point dipoles, two improvements may be considered. Firstly, the point dipoles can be positioned outside the atomic centers, because the outer electrons responsible for the optical effects may have a center of gravity distinct from that determined by X-rays. Secondly, an intrinsic anisotropy can be allocated to the polarizability of the ions. Both of these improvements involve the introcluction of at least one extra parameter. Thus the number of adjustable parameters will exce...

Refinement of the structure of Ikaite, CaCO3 - 6H2O

“…This interaction can be considered using the computer program DIPSUM of Pohl (1978). For that purpose, the C-atom is assumed to be non-polarizable, and the polarizabilities of Ca and oxygen atoms of the carbonate group are assumed to be 0.42 and 1.43 Â 3 , respectively (Pohl, 1979), and the polarizability of the water molecules is estimated to be 1.47 Â 3 (by means of the Lorentz-Lorenz formula applied to water (Pohl, 1982). The calculated values are listed in Table 4.…”

Anisotropic bond polarizabilities in birefringent crystals

“…In the past carbonate minerals repeatedly served as model compounds for investigating structural sources of optical anisotropy (Lawless & Devries, 1964;Lo, 1973;Pohl & Rath, 1979 For an analysis of the optical anisotropy we used the materials listed in Tables 4 and 5. As a first step we attempted to describe za X of different compounds with as few parameters as possible.…”

“…Especially successful examples of its application are the calculation of elastooptical coefficients in a-sulfur (Bounds & Munn, 1979) and the description of optical activity in various crystals (Devarajan & Glazer, 1986). However, the point-dipole approximation yields negative values for the polarizability of the Mg 2÷ ion (Pohl & Rath, 1979) and the polarizability of the same ion varies even in similar crystals (Lo, 1973).…”