Analysis of diffusive cellular patterns in directional solidification of bulk samples
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I.
INTRODUCTION
A defined situation in directional solidification is given when a crucible is drawn through a constant temperature gradient at a uniform rate. A propagating solid-liquid interface develops with a variety of patterns, depending on the growth conditions. For a given temperature gradient and alloy composition, the planar interface in binary alloys is destabilized beyond a certain threshold for the solidification velocity and the onset and development of cellular patterns at the interface is observed. The characterization and controlling of such microstructures and their transitions evolving during the solidification process at the interface is of practical interest, since the material properties and quality of the solidified sample are closely connected with them.[1] In this article, we are concerned with cellular growth of a bulk sample of the binary transparent organic alloy succinonitrile-acetone in dilute solution. The material properties of the alloy are well documented,[2] and the transparency facilitates direct observation of the solid-liquid interface patterns. In addition, it is known that succinonitrile-acetone freezes in a non-faceting manner like metals and could therefore serve as a model system for metallic crystal growth.[3] Cellular growth is of specific scientific interest, since diffusion lengths are of comparable size to cell distances, thus interactions between the cells are expected to significantly influence the pattern formation. Furthermore, bulk geometry has been chosen since wall effects are not negligible in quasitwo-dimensional geometries.[4] Microgravity environment on LASZLO STURZ, Research Scientist, GERHARD ZIMMERMANN and STEPHAN REX, Program Managers, and MICHAEL MATHES, Research Scientists, are with Access e.V. Materials and Processes, 52072 Aachen, Germany. Contact e-mail: [email protected] BERND KAUERAUF, formerly Research Scientist with Access e.V. Materials and Processes, is a Software Developer with SAP AG Company, 69190 Waldorf, Germany. Manuscript submitted July 17, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS A
a Space Shuttle mission with a residual g-level better than 104 g has provided growth conditions dominated by diffusion processes with negligible or very low interactions between the cellular morphologies and a residual buoyancy driven convection flow. Such flow cannot be avoided in earth-bound experiments. The interaction between flow and growth morphologies is complicated and not yet fully understood, while diffusive growth models are better established. Several approaches to predict primary spacings between cells exist for the latter, assuming different cell shapes, temperature and solute fields, or boundary conditions.[5–11] On the other hand, only a few experimental results on diffusive cellular growth of bulk samples exist.[12,13,14] The experiments carried out in the MOMO (MOrphological transitions and MOdel substances) program including the results presented here therefore serve as benchmarks for the testing and further develop
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