Determination of empirical optical parameters





It is our aim to predict refractive indices at l = 589 nm derived from the chemical compositions of minerals and inorganic compounds. To achieve this important goal, we will calculate and evaluate individual electronic polarizabilities for cations and anions using the Lorenz-Lorentz, Gladstone-Dale and Drude relationships. Cation polarizabilities will be calculated for various cation valences and coordination numbers. Functions will be derived and tested for describing the dependency of cation polarizabilities on their coordination numbers. Correction algorithms will be developed for anion polarizabilities as a function of the volume occupied by them. Cation and anion polarizabilities will be refined based on our database of 2000 entries compiled from literature and from own measurements. Initial refinements, based just on the Lorenz-Lorentz approach, yielded a preliminary data set of cation polarizabilities. From this set of polarizabilities we identified several classes of compounds and some individual compounds showing unusually high deviations between observed (derived from measured refractive indices) and calculated (derived from our initial set of parameters) total polarizabilities. Therefore, a systematic evaluation of these classes, and redeterminations of the optical parameters or crystal structures will be necessary to get optimized polarizabilities.

The refined polarizabilities then can be used to calculate mean refractive indices by applying the additivity rule for elements in combination with the Lorenz-Lorentz or Drude relationship or a relationship combining the two approaches. The same approach will be done based on the Gladstone-Dale concept which is established in mineralogy but being incompatible with the Lorenz-Lorentz relationship. Finally, the results from the different approaches will be evaluated as well as systematic deviations between calculated and observed total polarizabilities. The large experimental data set will be compared to values computed by atomistic models based on density functional theory. This will lead to a deeper understanding of the limitations of current DFT based models, but more importantly, will allow us to test predictions in more detail, as the atomistic models allow a systematic investigation of correlations between structural and optical parameters in arbitrarily small increments. 

A special focus will be on the following topics, all performed at l=589 nm.

·        Validity of the Lorentz factor b = 4p/3 in function (1) in its generalized application for compounds in all crystal systems. It has been frequently discussed in the literature whether this factor can be applied for all compounds. A definitive conclusion will be given by evaluating all 2000 data sets compiled by us with various Lorentz factors.

·        Derivation of individual cation and anion polarizabilities based on the Lorenz-Lorentz and Drude relationship

·        Derivation of “refractive energies” based on the Gladstone-Dale concept. A set of parameters will be derived for metal pnictides, chalcogenides, and halides, and on the other hand for individual cations and anions. Since this is the approach most popular in mineral science to predict and compare refractive indices of inorganic compounds, it will be very important to evaluate this approach because it is formally not compatible with the polarizability concept based on the Lorenz-Lorentz relationship as explained in section 1.

·        Derivation of correction algorithms for anion polarizabilities, including polarizabilities for hydroxyls and water molecules.

·        Derivation of functions similar to equ. (15) for the description of the polarizabilities of cations with different coordination numbers for the Lorenz-Lorentz and the Gladstone-Dale concept.

·        Evaluation of systematic deviations for ion conductors, compounds with corner- and edge-linked structures, compounds with steric strain, compounds containing hydroxyls, compounds with strong hydrogen bonds.

·        For the first time attempts will be made to determine polarizabilities and refractive energies for HxOy species (H2O, H3O+, H7O4-, H4O44-, H3O2-).

·        Reorganization of the compatibility concept introduced by Mandarino [29]. This concept is widely established in mineralogy and should be reevaluated based on the results achieved here.

·        Predicting details of chemical compositions by optical constants. This is a special goal in this investigation which will be especially useful to distinguish between elements of the same kind having different valences. Because the H2O molecule has a relatively high polarizability, it might also be possible to evaluate the H2O content of hydrates using nD measurements.



Fischer, Reinhard X., Burianek, Manfred & Shannon, Robert D., 2020. Determination of the H2O content in minerals, especially zeolites, from their refractive indices based on mean electronic polarizabilities of cations. European Journal of Mineralogy, 32(1): 27-40, 

Shannon, Robert D., Kabanova, N.A. & Fischer, Reinhard X., 2019. Empirical Electronic Polarizabilities: Deviations from the Additivity Rule. II. Structures Exhibiting Ion Conductivity. Crystal Research and Technology, Early View: Paper 1900037, , First Published 23 May 2019.

Fischer, Reinhard X., Burianek, Manfred & Shannon, Robert D., 2018. POLARIO, a computer program for calculating refractive indices from chemical compositions. American Mineralogist,103(8):1345-1348, download pdf.

Burianek, Manfred; Teck, M., Niekamp, Carolin, Birkenstock, Johannes, Spieß, Iris; Medenbach, O., Fischer, L.A., Wolff, P.E., Neumann, J. & Fischer, Reinhard X.. 2016. Crystal growth, crystal structure, optical properties and phase transition of BaCaBO3F. Crystal Growth & Design, 16(8): 4411-4420, Publication Date (Web): June 24, 2016

Burianek, Manfred, Birkenstock, Johannes, Mair, P., Kahlenberg, V., Medenbach, O., Shannon, Robert D.& Fischer, Reinhard X. 2016. High-pressure synthesis, long-term stability of single crystals of diboron trioxide, B2O3, and an empirical electronic polarizability of [3]B3+. Physics and Chemistry of Minerals, 43(7): 527-534, First Online: 28 April 2016.

Shannon, Robert D. & Fischer, Reinhard X. 2016. Empirical electronic polarizabilities of ions for the determination of refractive indices. I. Oxides and oxysalts. American Mineralogist, 101(10): 2288-2300, doi:10.2138/am-2016-5730, download web.