COMPARISON OF THE THREE TECHNIQUES

The knowledge of transport phenomena in the growth of crystals from their aqueous solution in the free convection regime is important for understanding the fundamental mechanisms involved and for fixing process parameters. As opposed to forced convection, the free convection technique has its own importance, for example in protein crystal growth where it is the only choice because of its delicate structure and the ease of managing defects. The creation of a homogeneous concentration field in the boundary-layer adjacent to the solution-crystal interface and uniform distribution of solute in the bulk solution are two major requirements. Refractive index-based optical techniques can be used to examine the nature of convection patterns as a function of time and hence the quality of the grown crystal.

A comparison of the images of the three techniques shows interferograms to be most vivid, since fringes deform and get displaced in relationship to the local velocity field. Thus, they offer the most direct information about concentration distribution as well as the underlying flow field in the solution. Schlieren and shadowgraph images reveal regions of high concentration gradients in the form of heightened brightness, though the former shows greater sensitivity. A review of Equations 1, 3 and 5 shows that interferograms are easy to analyze, schlieren requires integration of the intensity field, (Lecture 29) while shadowgraph requires the solution of a Poisson equation to recover the local concentration.

The three optical techniques under discussion yield images that are integrated values of the concentration field in the direction of propagation of the light beam.  Thus, if the spatial extent of the disturbed zone in the solution is small, the information contained in the image is small. In the context of interferometry, the consequence could be the appearance of too few fringes in the infinite fringe setting and small fringe deformation in the wedge fringe setting. In schlieren and shadowgraph, weak disturbances show up as small changes in intensity and hence contrast. The difficulty can be alleviated in schlieren by using large focal length optics so that small deflections are amplified.  In shadowgraph, image quality can be improved by moving the screen away from the test cell. Additional difficulties with interferometry are the need for maintaining identical experimental conditions in the crystal growth and the compensation chambers, careful balancing of the test and the reference beams, and limitations arising from fact that quantitative information is localized at the fringes. This discussion shows that configuring the interferometer as the instrument for on-line process control poses the greatest challenge, schlieren and shadowgraph being relatively simpler. Based on the above discussion, schlieren may be considered as an optimum while comparing the ease of analysis with the difficulty of instrumentation.