Module 5: Schlieren and Shadowgraph
  Lecture 32: Results and discussion related to crystal growth (part 2)
 

Figure 5.30 shows the concentration profiles reconstructed over five horizontal planes above the growing crystal. The location is just above the crystal while y/H = 0.90 represents a plane close to the top of the recorded schlieren image. The reconstructions correspond to the images presented in Figure 5.26. The outer circle represents the periphery of the beaker in which the crystal growth process is conducted. For a given time instant the images become progressively darker away from the crystal revealing the presence of supersaturated solution in the far field. At later times, as well as away from the crystal, the solution closer to the walls of the beaker is seen to be supersaturated, and the field is close to axisymmetric since the concentration contours here are circular. There is a significant departure from axisymmetry in the initial phase of crystal growth, as well as for longer times near the crystal itself. The second factor is explained by the fact that the crystal itself has a pyramidal structure and lacks circular symmetry. In the initial stages of growth, solutal transport is dictated by molecular diffusion from the solution to the crystal surface. Consequently, the lack of symmetry in the crystal morphology is felt on planes away from the crystal itself. At later times, a weak convection plume introduces the symmetry pattern of the beaker in the solute distribution. Hence, a degree of regularity is seen in the concentration contours, particularly on planes away from the crystal.

There are several interesting features to be noticed in Figure 5.30.

  1. At the central core of the reconstructed cross-section, the dark shade indicates the presence of a supersaturated solution. The surrounding region is bright, indicative of solution depleted of salt. Thus, the deposition of the salt on the crystal is seen to occur on the periphery of the crystal. This is a region of bright light intensity (Figure 5.26) and hence high concentration gradients. The relationship between high gradients and preferential growth rates of the crystal faces is brought out in Section Influence of Ramp Rate and Crystal Rotation on Convection Patterns.
  2. The concentration contours near the crystal show significant departure from symmetry during the initial stages of the growth process as well as during the transition phase . The transition referred here is the appearance of a convection plume that is gradually set up around the crystal, resulting in the partial unsteadiness in fluid motion. The loss of symmetry in the reconstruction can be traced to the unsteadiness as well. Symmetry is partly restored on planes above hours, indicating the influence of uniform solute concentration in the bulk of the solution. For t=70 hours, the convection plume is steady and the reconstructions are better structured closer to the crystal as well (for example,).
  3. The spacing of contours in the central region is smaller for the convection regime, when compared to diffusion. Thus, convection increases the concentration gradients near the crystal, increases the salt deposition rate and hence the overall increase in crystal size (Figure 5.29). This is possibly the most suitable transport regime for crystal growth.