A solid-liquid interface propagating under non-equilibrium conditions can appear as a spatiotemporal macroscopic structure. In solidified alloys, dendritic microstructures resulting from such growth processes are common. The main driving forces for dendritic growth are thermal and chemical diffusion, combining to determine the morphology and velocity field of the phase front. Unfortunately, an analytical solution to the problem is unavailable, even in the case of a single one-way diffusion process, due to the form of the kinetic and thermodynamic boundary conditions. These would have to account for a crystallographically induced surface-tension anisotropy resulting in a non-linear integral representation for the recasted diffusion equation. Numerical simulations have been compared with experimental observations on optically transparent model systems to extract physical information on the growth mechanism [1]. The transparent systems give information on the interface dynamics from phase contrast light microscopy, but do not in general include optically opaque alloying elements to reveal phase specific information on segregation. The validity of diffusion postulates is difficult to judge when extracted from simulations where thermal and chemical diffusion are both present and experimentally indistinguishable. Further complications arise from the interaction (through diffusion) between interfacial features, locally dependent upon factors like convective currents, etc. It would be a significant improvement if experiments were devised that could provide simultaneous information on segregation, dynamics and phasefront morphology.

Direct beam X-ray imaging of dendritic growth in real alloys turns out to be a promising method. Binary alloys of PbSn have been studied during solidification at beamline ID22 using a specially designed furnace to control the growth process and a high-resolution fast-readout FRELON [2] camera. Details on experiment and equipment are given elsewhere [3].

Figure 92 shows equiaxed dendritic growth in a Sn-52%wtPb alloy. Once above a critical size Pb nuclei develop morphological instabilities; features, with crystallographic growth directions corresponding to the highest expansion rate wrt. atomic attachment are energetically favourable ( in fcc Pb the six {100} directions). The diffusion process is mainly thermal, although Sn diffusion builds up with the increasing interfacial size. Pb crystals can survive at temperatures higher than that of the liquidus at this composition, resulting in a thermal supercooling in the liquid. As the liquid temperature falls below the liquidus slope, nucleation occurs ahead of the growing dendrites.

Figure 93 shows directional dendritic growth for an alloy composition Sn-10%wtPb. The parallel primary ß-Sn dendrites originate from the same nuclei. Initially the diffusion process is thermal, but chemical diffusion becomes dominant as excess Pb builds up in the liquid surrounding the pure ß-Sn solid. When interfacial features come close, growth directions most parallel to the thermal gradient survive and develop secondary and then tertiary branches, the latter growing parallel to the primary stalk. Pb trapped in between dendrites solidifies in an eutectic microstructure. The substantial Pb concentration building up ahead of the progressing interface gives rise to a constitutional type of supercooling.

The difference in absorption of Sn and Pb resulted in clearly visible segregation in both liquid and solid phases. Collected images have not been compared with simulations due to inadequate spatial and temporal resolution. More transparent alloys combined with the fast readout abilities (~50 ms) of the FRELON should be sufficient to extract quantitative physics regarding diffusion fields from comparison of experiment with numerical simulations.

References
[1] A. Karma, W.-J. Rappel, Phys. Rev. Lett., 77, 4050 (1996).
[2] J.-C. Labiche, J. Segura-Puchades, D. van Brusel, J.P. Moy, ESRF Newsletter, 25, 41 (1996).

Publication
[3] R.H. Mathiesen (a), L. Arnberg (b), F. Mo (a), T. Weitkamp (c), A. Snigirev (c), Phys. Rev. Lett., 83, 5062 (1999).

(a) Dept. of Physics, NTNU (Norway)
(b) Dept. of Mat. Techn., NTNU, (Norway)
(c) ESRF