Optical imaging and three dimensional reconstruction of the concentration field around a crystal growing from an aqueous solution: A review

Abstract

Investigation of transport phenomena around a crystal growing from its aqueous solution has been a subject of intensive research over the last few decades. It involves the characterization of convection patterns and an understanding of their influence on the growth mechanisms of a crystal from a fundamental viewpoint. In this context, laser-based measurement techniques have proved to be a useful tool. Optical techniques are ideal for mapping the properties of the solution during a crystal growth experiment because they are non-intrusive and inertia-free. It is possible to generate images of the convective field by exploiting changes in the refractive index that accompany changes in the density of the medium. The recorded images can be interpreted as path integrals in the direction of line-of-sight. Local properties can be subsequently reconstructed by using the principles of tomography. The work reported in the present review article summarizes the principal findings of the authors' previous works on the applications of optical imaging techniques and tomography to determine the three-dimensional distribution of concentration field around a growing crystal and its effects on the overall growth mechanisms.The convective field around the growing crystal from an aqueous supersaturated solution has first been mapped using three refractive index-based optical techniques. These are interferometry, schlieren and shadowgraph. The crystal material chosen for experiments is potassium-di-hydrogen-phosphate (KDP). Images recorded by the three techniques have been compared in terms of ease of instrumentation, quality of images and the possibility of quantitative analysis. The study shows that interferometry is best suited when density gradients in the fluid medium are small. For high density gradients, shadowgraph images contain the greatest amount of information. As a balance between ease of analysis and sensitivity to density gradients, schlieren emerges as the best option in the present context.Schlieren imaging is employed to record the projection data of concentration field around the growing crystal. Three-dimensional distribution of concentration field and its gradients in the growth chamber are reconstructed using the principles of tomography. Projection data has been recorded from four view angles namely, 0, 45, 90 and 135o by turning the growth chamber. Since the width of the schlieren images is limited by the size of the optical windows, the projection data represents only partial information about the convective field in the growth chamber for a given view angle. A suitable extrapolation scheme has been employed to generate the full information from the schlieren images. The suitability of the overall reconstruction approach has been validated using a simulated convective field, where full as well as partial data are available. The accuracy of reconstruction with respect to the effects of varying levels of noise superimposed on the projection data has been discussed. A new algorithm based on the principles of proper orthogonal decomposition has been proposed for the reconstruction of time-dependent concentration fields.Crystal growth experiments have been conducted in the diffusion-dominated and convection-dominated regimes of the growth process. The three dimensional distribution of solutal concentration shows a strong correlation with the topography of the growing crystal. The reconstructed concentration fields reveal symmetry of the flow field away from the growing crystal. The concentration gradient fields reveal the effect of size of the growing crystal on the strength and orientation of buoyancy-induced convection currents in the growth chamber.