Crystal refraction measurements polarizability

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

Recently, Heiberg et al. [26] have studied polarizabilities of the intermolecular contacts in bis(ethylenedithiolo)tetrathiafulvalene (BEDT-TTF) and bis(ethylenedioxy)tetrathiafulvalene (BEDO-TTF) molecular crystals by polarizing microscope techniques. The principal refractive indices and the corresponding optical axes have been calculated by tensorial addition of the bond polarizabilities of all bonds in the molecules. Comparison of calculated and measured values of the relative polarizabilities showed that the polarizabilities of the molecules only cannot yield the measured indicatrix and axes angle. Thus polarizabilities with other orientations must be involved. From the crystal structure of the molecular crystals it is known that 10 and four different contacts exist between the molecules of BEDT-TTF and BEDO-TTF, respectively, with contact distances lower than van der Waals distances. Assigning of polarizabilities of these contacts can explain the measured behavior. 

Relevant properties of the sodium and potassium ions, gleaned from Chap. 2 and elsewhere (Marcus 1997) are shown in Table 5.6. The bare potassium ion is larger than the sodium one and is more polarizable, as their crystal ion radii n (valid also in solutions) and molar refractivity 7 di show. However, the K+ cations move faster in aqueous solutions as their mobilities u and diffusion coefficients D show, the K+ ions having a smaller Stokes radius, rist. The K+ cations carry along when moving less of their hydration shells that are more loosely bound, the residence times of water molecules near K+ being about one half that near Na+. Also, the hydration number h of K+ is smaller than that of Na+, as derived from the compressibility of the solutions as well as other measures. Such numbers are smaller than the coordination numbers CN in solution, which are governed only by the sizes... 

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