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Coordination of water molecules with Na+ cations in a beryl channel as determined by polarized IR spectroscopy

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Subtle variations of frequencies in the infrared (IR) absorption spectra of beryl have been predicted based on the coordination between extra-framework cations and water molecules in two orientations (referred to as type I and type II) trapped within the channel. In this study, the polarized IR spectra of hydrated synthetic beryl and natural beryl were measured to clarify the relationships between the frequencies of the absorption bands and the coordination states of type II water. Na+ was assumed to be the predominant cation coordinated to type II water in our samples, as determined by chemical analyses. These measurements revealed a clear quantitative linear relationship in absorbance between bands at 3,602 and 1,619 and at 3,589 and 1,631 cm−1. On the basis of experimental and theoretical studies, we assigned these pairs of bands to the ν1 and ν2 modes of doubly coordinated type II H2O and to singly coordinated type II H2O, respectively. These assignments were supported by IR measurements of annealed natural beryl. We also conducted dehydration studies of natural beryl, in which two observed dehydration peaks, at 600 and 750°C, suggested the dehydration of type I and type II water, respectively.

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The authors thank H. Masuda, S. Yamashita, and T. Nogi for supporting analyses of water and chemical composition and for giving suggestions for the interpretation of the obtained results. We also thank S. Nakashima and N. Aikawa for their critical comments, as well as G. D. Bromiley, an anonymous reviewer and the editor, M. Matsui for improving our manuscript and for valuable discussion. This work was supported by the 21st Century COE Program Establishment of an International Research Center for Solid Earth Science at the Institute for Study of the Earth’s Interior, Okayama University, Japan.

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Correspondence to J. Fukuda.



To calculate the approximate frequencies of the ν1, ν2, and ν3 modes of H2O by the G, F matrixes method with force constants based on the Urey–Bradley force field, the dimensions of H2O are assumed as follows:

  • r 1 = r 2 = 1 Å, ϕ = 104°, m O = 16, m H = 1

  • K = 7.8 mdyn/Å, H = 0.69 mdyn/Å, F = 0.1 mdyn/Å

where r 1 and r 2 are the equilibrium distances between oxygen and hydrogen, ϕ is the bond angle for H–O–H, and m O and m H are the atomic weights of oxygen and hydrogen, respectively. A schematic of a water molecule with these variables labeled is shown in Fig. 9. Additionally, in the above list of parameters, K, H, and F are the force constants for O–H stretching, for H–O–H bending, and for repulsion between H–H, respectively. K, H and F are standard values derived from Wilson et al. (1955). Adopting internal symmetry coordinates of H2O as

$$ S_{1} = (\Updelta r_{1} + \Updelta r_{2} )/{\sqrt 2 },\,S_{1} = \Updelta \phi ,\,S_{3} = (\Updelta r_{1} - \Updelta r_{2} )/{\sqrt 2 } $$

and assuming reduced F and G matrices as

$$ {\mathbf{F}} = {\left[ {\begin{array}{*{20}c} {{K + 2s^{2} F}} & {{{\sqrt 2 }ts(F^{\prime } + F)r_{0} }} & {0} \\ {{{\sqrt 2 }ts(F^{\prime } + F)r}} & {{(H - s^{2} F^{\prime } + t^{2} F)r^{2}_{0} }} & {0} \\ {0} & {0} & {{K + 2t^{2} F^{\prime } }} \\ \end{array} } \right]} $$
$$ {\mathbf{G}} = {\left[ {\begin{array}{*{20}c} {{(1 + \cos \phi )/m_{O} + 1/m_{H} }} & {{ - {\sqrt 2 }\sin \phi /(m_{O} r_{0} )}} & {0} \\ {{ - {\sqrt 2 }\sin \phi /(m_{O} r_{0} )}} & {{2(1 - \cos \phi )/(m_{O} r^{2}_{0} ) + 2/(m_{H} r^{2}_{0} )}} & {0} \\ {0} & {0} & {{(1 - \cos \phi )/m_{O} + 1/m_{H} }} \\ \end{array} } \right]} $$

where \( s = r_{0} (1 - \cos \phi )/q_{0} \), \( t = r_{0} \sin \phi /q_{0} \), and \( F^{\prime } = - 0.1F \), the frequencies of ν1, ν2, and ν3 modes can be approximately calculated by solving the secular equation

$$ {\left| {{\mathbf{GF}} - \lambda {\mathbf{E}}} \right|} = 0. $$

By fixing the values of K and H and varying F around the standard value, the ν1, ν2, and ν3 modes were calculated as shown in Fig. 10. Increasing F caused an increase in ν1 and a decrease in ν2. By contrast, ν3 remained at an almost constant frequency regardless of F. We explain below why the reverse shift observed in this study must result from deviation of the parameter F.

Fig. 9
figure 9

Schematic of an H2O molecule showing the parameters used for the calculations in the Appendix

Fig. 10
figure 10

Frequency shifts of ν1, ν3 (upper), and ν2 modes (lower) of H2O calculated from Eq. 4 by fixing the values of K and H and varying F around the standard value

Some related parameters for Na(H2O)+ and Na(H2O)2 + complexes that were reported in the theoretical study of Bauschlicher et al. (1991) are listed in Table 2. These data indicate that the O–H bond distance and H–O–H bond angle remain almost constant regardless of the coordination number of H2O, whereas the distance between Na and O, r (Na–O), is elongated, ν1 increases by 8 cm−1, and ν2 decreases by 3 cm−1 when H2O becomes doubly coordinated to Na+. Although the results of Bauschlicher et al. (1991) are based on models of freely moving Na(H2O)+ and Na(H2O)2 +, we assumed that the calculation could be applied without major modification to our case of a beryl channel. On the basis of this assumption, the frequency differences of Δν1 = +13 cm−1 (3,589 → 3,602 cm−1) and Δν2 = −12 cm−1 (1,631 → 1,619 cm−1), depending on whether the type II H2O was singly or double coordinated, obtained in our study were qualitatively consistent with the calculations of Bauschlicher et al. (1991). However, our frequency differences were a little higher than the calculated differences. Since the parameters of singly and doubly coordinated H2O were assumed to be almost constant in the beryl channel, the parameters K and H must not have caused the relatively high observed frequency differences. By contrast, parameter F could possibly have caused the frequency differences, because F can be modified by slight changes in the H2O parameters. A potential function V of repulsion between two unbound atoms is generally defined as

$$ V(q) = a/q^{n} $$

where a is a constant, n is an index between 9 and 12, and q is the distance between the two unbound atoms. When the H–H distance deviates as Δq from the equilibrium distance, q 0, the change in VVq)] is expressed as

$$ \Updelta V(\Updelta q) = V(q_{0} + \Updelta q) - V(q_{0} ) = - F^{\prime } q_{0} \Updelta q + F\Updelta q^{2} /2 $$

where \( F = an(n + 1)/q^{{n + 2}}_{0} \) and F′ = −0.1F because n + 1 is approximately 10. ΔVq) is the energy change to be added to the F matrix. The parameter F is highly enhanced to the tenth power of q 0. Even if the H2O parameters in our studies were too slightly modified to effect a change in K and H, F would have been effectively enhanced by even a subtle change in q 0. The effective change of F due to such a negligible change in q 0 could have caused the reverse shift of ν1 and ν2 shown in Fig. 10. The F for singly or doubly coordinated type II H2O enclosed in the beryl channel must have been modified to a greater extent than that for the free Na(H2O)+ and Na(H2O)2 + calculated by Bauschlicher et al. (1991).

Table 2 Selected parameters for Na(H2O)+ and Na(H2O)2 + coordination as reported by Bauschlicher et al. (1991)

In Fig. 10, the frequency of the ν3 mode was fairly constant with varying F values. This result means that the difference in frequency between the ν1 and ν3 modes can possibly change with varying F values. The measured IR frequency difference between the ν1 and ν3 modes of a free H2O molecule is generally 100 cm−1 (3,657 cm−1 for the ν1 mode and 3,756 cm−1 for the ν3 mode; Eisenberg and Kauzman 1969). The absolute frequencies calculated from the simple parameters differ from the measured frequencies. This variance between the frequencies probably occurred because insufficient parameters were used in the calculations. Nevertheless, the tendencies of the ν1, ν2, and ν3 frequency changes controlled by F values were still reliable and could explain the frequency modification of H2O observed in the channel in this study. As approximately calculated in Fig. 10, the frequency difference could have been changed under the special condition such that an H2O molecule is located in the channel, i.e., K and H remained constant but F was effectively changed. We suggest that the deviation of frequency difference between the ν1 and ν3 modes of H2O in the channel from the generally accepted difference was caused by varying F values.

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Fukuda, J., Shinoda, K. Coordination of water molecules with Na+ cations in a beryl channel as determined by polarized IR spectroscopy. Phys Chem Minerals 35, 347–357 (2008).

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