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The theoretical analysis of growth habits of sodium fluorosilicate ice-analogues crystals grown from solution and gel

Mariusz J. Krasiński 1Jolanta Prywer 2

1. Technical University of Łódź, Center of Mathematics and Physics (CNMF), Wólczańska 219, Łódź 93005, Poland
2. Technical University of Łódź, Institute of Physics, Wólczańska 219, Łódź 93005, Poland

Abstract

The sodium fluorosilicate (Na2SiF6) crystals have recently received much attention because of their application as ice-analogues [1,2]. The refractive index of sodium fluorosilicate is very close to that of ice at visual wavelengths and its crystals replicate the variety of growth habits of atmospheric ice crystals. The shapes of ice crystals can significantly affect the radiative transfer in ice clouds and in this way influence the climate evolution. Hence, it is important to accurately represent cirrus cloud and their single-scattering properties in climate models and in remote sensing applications [3]. Proper interpretation of scattering data requires laboratory experiment with artificial clouds and ice-analogous crystals are cheaper alternative to difficult experiments on real ice. It is however vital for scattering experiments to obtain all typical for atmospheric ice habits and to know relation between growth conditions of sodium fluorosilicate and final shape of its crystals.

In this work we present results of theoretical analysis of growth habitsin base of relative growth rates of individual surfaces of sodium fluorosilicates growing in solution and gel. The theoretical considerations are compared with experimental data concerning growth rates of particular faces.

Experimental data were taken from two types of experiment. In the first one, the saturation was obtained by the controlled evaporation of solute from initially undersaturated solution. In the second method, the crystals were grown in terametohoxysilane gel and supersaturation was obtained by temperature decrease. During experiments in solution the growth rates and evolution of aspect ratio were continuously measured (see [4] for more information). Among variety of habits obtained during experiments (hexagonal columns, plates, sectored plates, simple or six-armed stars, stellar dendrites and radiating dendrites) it seems that only hexagonal columns and plates, grown as well from solution and gel, are single crystals. Additionally, these habits are most common for atmospheric ice crystals. Thus, the theoretical analysis was performed for these two kinds of habits.


Fig. 1. Hexagonal columns (a,b) and plates (c,d), grown from solution and gel. Kinetic conditions corresponding to the growth of single crystals of these two characteristic habits of sodium fluorosilicate crystals (e). Scale bar is 100 μm.

These two kinds of habits which are under theoretical considerations are composed of basal and prism forms in the case of hexagonal columns (Fig. 1a, 1b) and, additionally of pyramidal form in the case of hexagonal plates (Fig.1c, 1d). In order to explain these different habits, we use an idea of the critical growth rate Rcrithkl, which is defined as the normal growth rate of the (hkl) face at which a given size of this face is preserved. Taking into account the measured in situ growth rates and the analytical expression that relates the critical growth rate Rcrithklwith the growth rates of each face, we obtained the kinetic conditions corresponding to growth of different habits of sodium fluorosilicate crystal, which are schematically presented in Fig. 1e. The experimental data and theoretical analysis demonstrates that the crystals of hexagonal columns and plates grow with appropriate relative growth rates within the dashed regions only. The theoretical approach in connection with experimental data allows us also to derive the kinetic conditions corresponding to the appearance of the pyramidal form, which is characteristic for hexagonal plates only.

  1. Z. Ulanowski, E. Hesse, P.H. Kaye & A.J. Baran. Light scattering by complex ice-analogue crystals. J. Quantit. Spectr. Rad. Transf. 100 (1-3), pp.382-392 (2006)
  2. Z. Ulanowski, E. Hesse, P. H. Kaye, A. J. Baran, R. Chandrasekhar Scattering of light from atmospheric ice analogues. J. Quantit. Spectr. Rad. Transf. 79-80C (2003) 1091
  3. A.J. Baran, On the scattering and absorption properties of cirrus cloud, J. Quantit. Spectr. Rad. Transf. 89 (2004) 17
  4. M.J. Krasiński, K.R. Krasińska, Z. Ulanowski, Investigation of growth kinetics and crystal morphology of sodium fluorosilicate ice-analogue crystals in solution and in gel, This conference

 

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Related papers

Presentation: Poster at Joint Fith International Conference on Solid State Crystals & Eighth Polish Conference on Crystal Growth, by Mariusz J. Krasiński
See On-line Journal of Joint Fith International Conference on Solid State Crystals & Eighth Polish Conference on Crystal Growth

Submitted: 2007-01-15 14:01
Revised:   2009-06-07 00:44