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Development of refractive index matching cell for three-dimensional reconstruction of the concentration field around a growing crystal

Kenta Murayama 2Atul Srivastava 1Katsuo Tsukamoto 2

1. Indian Institute of Technology Bombay (IITBOMBAY), Powai, Mumbai 400076, India
2. Graduate school of Scienece, Sendai 980-8578, Japan


Growth of a crystal from its aqueous solution is accompanied by the distribution of three-dimensional concentration gradients in the growth chamber. Under the influence of gravity, beyond a critical size of the growing crystal and the solution supersaturation level, gradients in the concentration field are responsible for the evolution of buoyancy-induced convection currents in the vicinity of the growing crystal [1]. The characteristic of the flow field thus generated is an important factor for crystal quality. Therefore, mapping of convection patterns is essential to understand the physical mechanism of crystal growth. In this regard, optical techniques are ideal since they are non-intrusive and inertia-free [2, 3]. However, the optical techniques provide only the two-dimensional information in the form of path-integrated concentration field along the direction of the propagation of the light beam. In order to retrieve the concentration field distribution in the third dimension, principles of tomography have been employed by various researchers in the recent past [4].

     It has been experimentally as well as theoretically established that the resolution of tomography reconstruction strongly depends on the number of projection angles employed for recording the two-dimensional data of the field of interest. The literature on the three-dimensional reconstruction of concentration field around a growing crystal has revealed that researchers in the past have employed a maximum of only 4 projection data (recorded from 0, 45, 90 and 135 o viewing angles) for tomography reconstructions due to inherent curvature effects of cylindrical growth cells. Strong curvature effects of cylindrical growth cells lead to unwanted refraction and reflection errors as the light beam passes through the growth chamber and adversely affect the quality of the projection data. In order to circumvent this limitation, researchers have approximated the cylindrical growth cells by octagonal cells, thus restricting the number of views to a maximum of four.  In view of this lacunae in the literature, we implemented the principle of refractive index matching to minimize the curvature effects of a cylindrical crystal growth cell so as to record the maximum number of projection data from any view angle in the span of 0 to 360 o . The present work is concerned with the details of the development and application of refractive index matching crystal growth cell for three-dimensional reconstruction of concentration field around a crystal growing from its aqueous solution. The crystal growth chamber, made of quartz, is cylindrical in shape with 4 mm inner diameter and a height of 20 mm. Thickness of the walls of the growth chamber is 0.5 mm. The cylindrical growth cell is placed inside an outer square chamber, also made of quartz, with dimensions 20 mm. The annulus region between the inner growth cell and outer square chamber is filled with refractive index matching liquid whose index of refraction is close to that of the cylindrical cell. The experiments have been performed in free convection regime of the growth process with Sodium Chlorate (NaClO3) being the crystal material. A microscopic Mach-Zehnder interferometer has been employed for recording the projection data of concentration field. It is inferred that by using the cylindrical growth cell with the refractive index matching method, the projection data can be recorded from any arbitrary view angle within a span of 0 to 360 o . With larger number of projection data available, it is, therefore, expected to improve the spatial resolution of three-dimensional distribution of the concentration field. Detailed investigation of the three-dimensional reconstruction of the concentration field using the principles of tomography with varying number of projection data would be presented in the conference.

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Related papers

Presentation: Poster at 17th International Conference on Crystal Growth and Epitaxy - ICCGE-17, General Session 6, by Atul Srivastava
See On-line Journal of 17th International Conference on Crystal Growth and Epitaxy - ICCGE-17

Submitted: 2013-04-14 12:06
Revised:   2013-04-14 12:44