Since the first observation of banded microstructures by Boettinger [2], several experimental studies have been carried out [3-8] to understand the formation of a banded structure. These bands were assumed to result from the repeated nucleation of the primary and the peritectic phase. A conceptual analytical model of banding in peritectic systems was first proposed by Trivedi [6] for diffusive growth in which the change in phases occurred when appropriate nucleation undercooling was reached. This model predicted that a discrete band structure under diffusive growth is possible only within a finite range of initial alloy composition in the hypoperitectic range. All earlier experimental results, which showed banded structures, had compositions outside this banding composition window. For example, in the Sn-Cd system, the banded structures were found for alloy compositions in the range 1.0 - 1.7 wt. % Cd, which are in the hyperperitectic composition. In the Pb-Bi system, finite number of bands were observed over both the hypo and hyperperitectic regions [8]. These observations clearly indicate that the observed band structures are not controlled by diffusive growth. In fact, a thorough examination of these microstructures showed that the bands were not discrete, but both the a and the b phases were continuous. Figure 3 shows the microstructure observed by successively polishing the sample of 6.0 mm. diameter. The figures are from the section near the surface to the section at the center of the sample. The microstructure which appears like discrete bands near the surface of the sample is in fact a more complex structure made up of two continuous interconnected phases in three dimensions. In particular, the microstructure consists of a large tree-like domain of primary a-phase that is embedded inside the peritectic b-phase. The formation of this structure is governed by oscillating convection present in a large diameter (6.00 mm) sample. In the Sn-Cd system, convection has been found to be the dominant mode of transport for sample diameter larger than 3 mm, so that all the experimental results in samples of 3.0 to 6.00 mm diameter indeed form tree-like oscillating structures. The observation of a continuous tree-like structure is thus important in that it shows that the widely reported structure in the literature is not made up of discrete bands and, hence, is not controlled by nucleation after the first b-band is formed.

Fig. 3. Micrographs showing the three-dimensional shape of a tree-like structure of the a-phase surrounded by the b-phase. The first figure is a section 1 mm below the surface and the last section is at the center, i.e. 3 mm below the surface of the sample. <intermediate figures are successive sections located between 1 and 3 mm from the surface. These results are for Sn - 1.3 wt. % Cd alloy directionally solidified in a 6.0 mm ID tube at V = 3 µm/s, and G = 13.5 K/mm.

        In order to establish the effect of convection, a new experimental technique was developed to directionally solidify several samples simultaneously in capillary tubes with a range of diameters from 0.2 to 6 mm, which allowed to systematically reduce the effect of convection. As the diameter of the sample was reduced, the tree-like structure diminished, and finally only a single a to b transition was observed in 0.4 mm. sample which is the result predicted by the diffusive growth model, as shown in Fig. 4.

Fig. 4. Micrographs showing the effect of ampoule size on the microstructure development in directionally solidified hyperperitectic Sn-1.56 wt. pct Cd alloys at V = 5.0 µm/s and G = 25.0 K/mm. Dark region are primary a-phases and light regions are peritectic b- phases. (a) Bulk sample which is shown in two parts, (b) d= 3.0 mm, (c) d = 1.0 mm, (d) d = 0.6 mm, and (e) d = 0.4 mm.

Fig. 5. A banded microstructure formed in a directionally solidified Sn- 0.75 wt % Cd alloy in a fine tube of 0.6 mm diameter, at V = 3 µm/s, and G= 23 K/mm. The alloy composition is within the window of band formation predicted by the diffusive model. The long sample is shown in three sections with directional solidification begining from the bottom of sample at the left and ending at the top of the sample at the right.

        In order to test the validity of discrete band formation by repeated nucleation of the primary and peritectic phases, experiments were conducted in samples of diameters 0.6 mm for compositions within the narrow composition range in the hypoperitectic region where diffusive band formation is predicted. Fig. 5 shows the formation of discrete bands, as predicted by the theory. Measurements of composition variation in the axial direction showed that the diffusive banding cycle operates below and above the peritectic temperature, as predicted by the theory [6]. This result is important in that it is the first experimental verification of the existence of nucleation-controlled discrete band formation in a purely diffusive regime, which has been theoretically predicted, but not observed experimentally.

        Experimental studies also showed that the microstructure in the diffusive regime is not unique and can depend in a complex way on velocity, composition and the nucleation. undercoolings of the two phases. For example, in 0.6 mm diameter samples, discrete bands were consistently observed. However, in thinner diameter samples, i.e. 0.4 mm and less, several new morphologies were observed which include partial bands, coupled growth and oscillatory coupled growth, as shown in Fig. 6. These widely differing microstructures resulted from the interaction of diffusion fields between the growing nuclei of the peritectic (or primary) phase and the growth of the existing primary (or peritectic) phase.

            (a)                                  (b)                      (c)

Fig. 6. Experimental observations of two-phase microstructures. (a) Discrete bands in Sn-0.9 wt % Cd alloy, V = 3.0 µm/s, G = 23 K/mm, and d= 0.6 mm. (b) Islands or partial bands in Sn-0.0.75 wt % Cd alloy, V = 4.0 µm/s, G = 23 K/mm, and d= 1.0 mm. (c) Oscillating coupled growth in Sn-0.0.75 wt % Cd alloy, V = 4.0 µm/s, G = 23 K/mm, and d= 0.4 mm.