Three dimensional concentration contours around a growing crystal

Laser schlieren technique is employed to investigate the three-dimensional concentration field around a KDP crystal growing from its aqueous solution. The convective field is set-up in the growth chamber by inserting a KDP seed into its supersaturated solution followed by slow cooling of the solution. The projection data in the form of two-dimensional schlieren images have been recorded from four different view angles by turning the crystal growth chamber. Since a circular growth chamber is employed in the present experiments, the entire width of the growth chamber for a given view angle could not be covered. Hence a single view provides only partial data, corresponding to the area localized in the vicinity of the growing crystal. The integrated values of concentration are obtained by analyzing the light intensity data of the schlieren images. Subsequently, the concentration fields at various horizontal planes above the crystal are reconstructed using the convolution back projection (CBP) algorithm. Owing to limitations in the optical system, the projection data required for tomographic inversion is often incomplete. Specifically, the number of view angles is small, and in addition, the entire field of view may not be scanned. The applicability of the inversion algorithms can then be ensured only when additional tests are conducted to validate the result obtained. Validation with numerically simulated data is reported in this work. The focus of the present study is to examine the symmetry of the concentration field in the vicinity of the growing crystal in the initial stages (diffusion-dominated growth) and in the stable growth regime (recognized by the presence of a steady convective plume rising from the crystal surface). Of interest is the relationship between the morphology of the crystal with the solutal concentration field around it, during the growth process.