Module 5: Schlieren and Shadowgraph
  Lecture 31: Results and discussion related to crystal growth (part 1)
 

Figure 5.16 shows the formation and time-evolution of fringes in the infinite and wedge fringe settings of the interferometer around the growing crystal. The first image of the transient shows the appearance of fringes due to crystal dissolution. This process increases the local density, causing the solution to descend vertically downwards. Hence, the fringe displacement is also in the downward direction (Figure 5.16(a)). Large concentration gradients in the vicinity of the dissolving crystal give rise to time-dependent fluid motion as well. A second factor contributing to unsteadiness is the change in the crystal geometry from rectangular to prismatic. As the crystal attains thermal equilibrium on one hand and its natural shape on the other, the concentration gradients gradually diminish. During a time period of 15-35 hours, the gradients were small enough to produce only a single visible fringe adjacent to the growing crystal (Figure 5.16(b)). The fringe was found to be stable with respect to time indicating uniform deposition of the solute around the growing crystal. Experiments in the wedge fringe setting of the interferometer reflect identical trends. The horizontal fringes deform vertically downwards (Figure 5.16(e-f)), and is followed by a phase when they are practically straight. Near the crystal, the solution is practically saturated, while it is supersaturated in the far field. The wedge fringes get displaced in regions of a large change in concentration with respect to the bulk of the supersaturated solution. With further cooling, the solution in the near-field becomes supersaturated with reference to the new temperature, additional salt deposits on the crystal, and the growth process is once again initiated. This leads to concentration gradients adjacent to the crystal, and a continuation of buoyancy-driven flow. In the time frame of 20-30 hours after the insertion of the KDP seed, the infinite and the wedge fringes showed considerable symmetry as well as stability in time, ensuring uniform growth on all the faces of the crystal. This time duration may be called the stable growth regime of the crystal.

With an increase in the crystal size, the influence of even mild concentration gradients is strengthened, increasing the fringe deformation. Over a longer duration of the experimental run time (> 50 hours), the solution is found to be layered (stratified) with respect to density (Figures 5.16(c-d) in the infinite fringe setting and Figures 5.16(g-h) in the wedge fringe setting). This is understandable because crystal growth takes place from a fixed volume of the solution in the growth chamber, and with time, the solution is increasingly depleted of salt. The density inversion suppresses convection to a point where the increase in the crystal size is negligible. The downward movement of these layers of constant concentration is driven by molecular diffusion, and contributes to a very slow increase in the crystal size. The appearance of straight horizontal fringes above the crystal in the infinite fringe setting, and opposed curvature of wedge fringes in the far-field can thus be taken as the limiting point where the growth process is to be terminated.