Instabilities and pattern formation in inorganic crystallization
The morphological stability - instability transition of a growing crystal interface is its fundamental property and is followed by pattern formation and other self-organization synergistic phenomena. This transition occurs in all crystallization systems, in systems with other phase transitions and has analogies in numerous other dissipative systems related to materials science. Equally important, these phenomena essentially determine the real structure, i.e., perfection of the grown crystals.
A crystal interface may be either rough or smooth. For rough, non-singular interfaces that grow normally and are characterized by fast incorporation kinetics, stabilization is provided by the nearly isotropic surface energy and the stability limits are not affected by liquid flow direction. This type of stability and the ensuing dissipative structures have been extensively studied, both theoretically and experimentally. On the contrary, for smooth crystal faces that grow layerwise the stability loss occurs as step bunching. The further development of these step bunches may cause striations and trapping of inclusions. Only qualitative observations have to date been recorded on this type of stability.
In contrast to the insensitivity of rough surfaces to small variation of orientation, the orientational dependence of the growth rate of a stepped interface is very strong and contains points of singularity. This ultimately causes orders of magnitude higher stability of faceted shapes and stepped surfaces. Step bunching during layer growth is affected by supersaturation, vicinal face orientation, and impurities amounts of the ppm level. As another consequence of the strong anisotropy of growth kinetics, the stabilization and destabilization strongly depends on the liquid flow direction. If the solution or melt flow in the same direction as the growth steps move, this liquid flow is stabilizing. If these streams are antiparallel, the liquid flow is destabilizing. This effect was discovered in qualitative experiments on the prismatic face of NH4H2PO4 (ADP) crystals and is currently theoretically understood.
In stagnant solutions or melts, step motion is qualitatively equivalent to the liquid flowing up the step staircase and thus stabilization should occur. This self-stabilization has been theoretically predicted for both solution and melt growth. It can be experimentally observed if the solution flow velocity in the vicinity of the growing face is less than the velocity of the steps. For a typical solution growth system, step velocity is within the range of a few µm/s. Hence, the stability of stepped interfaces should be studied with flow velocities ranging from a high limit of 30 cm/s to as low as 0.1 µm/s. However, at normal gravity the typical velocities of buoyancy-driven convection are 10-50 µm/s, an order of magnitude higher than the step velocities. Thus, for a comprehensive study of the step train stability or, more general, of morpological stability and pattern formation on interfaces growing layerwise, experiments under both terrestrial and low gravity conditions are required.
Note that the available observations of step bunches correspond to the later stages of the step bunch evolution. Quantitative insight into the early stages of the instability and its further development, especially based on well staged experiments on growth from condensed phases, is still missing. Hence, the purpose of the proposed experimental and theoretical work is to quantitatively investigate, for the first time, the onset, initial stages, and development of morphological instabilities on stepped vicinal crystal faces in a condensed phase.
As a model material we chose NH4H2PO4 (ADP). Its crystals grow from aqueous solutions and belong to the KDP-ADP family, widely used for optical frequency multiplication. This system has been thoroughly studied in relation to the fast growth of large (~ 50 cm) KDP single crystals for the laser fusion facilities in the USA (Lawrence Livermore National Laboratory), Japan, and France.
To evaluate the initial stages of instability, we propose to develop and employ phase shifting and Michelson interferometry, combined with atomic force microscopy and Fourier process imaging. This will allow us to map the surface morphology and step behavior from the angstrom to µm levels, thus also tracing the subsequent stages of instability development.
During the first phase of the project, the flow-through growth cell, the phase shifting interferometer and image processing set-up will be constructed. Data collection and processing will allow fine-tuning of the equipment to obtain the first data on macroscopic surface behavior. In parallel, AFM experiments will be performed to visualize microscopic surface features. During Phase 2, a new, combined interferometric and AFM set-up will be built to correlate the macroscopic and microscopic scales and to calibrate them with respect to one another. Systematic investigations of the step waves on the surface as a function of the average step density, solution flow, and growth rate will comprise Phase 3. Phase 4, proceeding in parallel, will include the development of a theoretical description of the phenomena coherent with the experimental data. The theoretical insight gained will be used to modify the experimental variables for a fuller data set. Phase 5 will include analysis of the surface behavior at the minimal flow rates possible at terrestrial conditions. The general street address is Dept. of Chemical Engineering, University of Houston, 4800 Calhoun Ave., Houston, TX 77204-4004 The fax number is (713) 743-4323.