Eutectic Colony Formation: A Stability Analysis

Experiments have widely shown that a steady-state lamellar eutectic solidification front is destabilized on a scale much larger than the lamellar spacing by the rejection of a dilute ternary impurity and forms two-phase cells commonly referred to as `eutectic colonies'. We extend the stability analysis of Datye and Langer for a binary eutectic to include the effect of a ternary impurity. We find that the expressions for the critical onset velocity and morphological instability wavelength are analogous to those for the classic Mullins-Sekerka instability of a monophase planar interface, albeit with an effective surface tension that depends on the geometry of the lamellar interface and, non-trivially, on interlamellar diffusion. A qualitatively new aspect of this instability is the occurence of oscillatory modes due to the interplay between the destabilizing effect of the ternary impurity and the dynamical feedback of the local change in lamellar spacing on the front motion. In a transient regime, these modes lead to the formation of large scale oscillatory microstructures for which there is recent experimental evidence in a transparent organic system. Moreover, it is shown that the eutectic front dynamics on a scale larger than the lamellar spacing can be formulated as an effective monophase interface free boundary problem with a modified Gibbs-Thomson condition that is coupled to a slow evolution equation for the lamellar spacing. This formulation provides additional physical insights into the nature of the instability and a simple means to calculate an approximate stability spectrum. Finally, we investigate the influence of the ternary impurity on a short wavelength oscillatory instability that is already present at off-eutectic compositions in binary eutectics.Comment: 26 pages RevTex, 14 figures (28 EPS files); some minor changes; references adde

Eutectic colony formation: A phase field study

Eutectic two-phase cells, also known as eutectic colonies, are commonly observed during the solidification of ternary alloys when the composition is close to a binary eutectic valley. In analogy with the solidification cells formed in dilute binary alloys, colony formation is triggered by a morphological instability of a macroscopically planar eutectic solidification front due to the rejection by both solid phases of a ternary impurity that diffuses in the liquid. Here we develop a phase-field model of a binary eutectic with a dilute ternary impurity and we investigate by dynamical simulations both the initial linear regime of this instability, and the subsequent highly nonlinear evolution of the interface that leads to fully developed two-phase cells with a spacing much larger than the lamellar spacing. We find a good overall agreement with our recent linear stability analysis [M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a destabilization of the front by long-wavelength modes that may be stationary or oscillatory. A fine comparison, however, reveals that the assumption commonly attributed to Cahn that lamella grow perpendicular to the envelope of the solidification front is weakly violated in the phase-field simulations. We show that, even though weak, this violation has an important quantitative effect on the stability properties of the eutectic front. We also investigate the dynamics of fully developed colonies and find that the large-scale envelope of the composite eutectic front does not converge to a steady state, but exhibits cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.

Relationship between casting modulus and grain size in cast A356 aluminium alloys

Microstructure of Al-Si alloy castings depends most generally on melt preparation and on the cooling rate imposed by the thermal modulus of the component. In the case of Al-Si alloys, emphasis is put during melt preparation on refinement of pro-eutectic (Al) grains and on modification of the Al-Si eutectic. Thermal analysis has been used since long to check melt preparation before casting, i.e. by analysis of the cooling curve during solidification of a sample cast in an instrumented cup. The conclusions drawn from such analysis are however valid for the particular cooling conditions of the cups. It thus appeared of interest to investigate how these conclusions could extrapolate to predict microstructure in complicated cast parts showing local changes in the solidification conditions. For that purpose, thermal analysis cups and instrumented sand and die castings with different thermal moduli and thus cooling rates have been made, and the whole set of cooling curves thus recorded has been analysed. A statistical analysis of the characteristic features of the cooling curves related to grain refinement in sand and die castings allowed determining the most significant parameters and expressing the cube of grain size as a polynomial of these parameters. After introduction of a further parameter quantifying melt refining an excellent correlation, with a R2 factor of 0.99 was obtained

Characterization of the Effect of Melt Treatments on Melt Quality in Al-7wt %Si-Mg Alloys

The effects of degassing, holding time and melt additions (Sr, Sr + Ti, Ti, B and B + Sr) on the quality of A356 melts were examined. A total of 120 reduced pressure test samples were collected. Pores in these samples were analyzed via digital image processing to determine the number density of pores as well as the statistical distribution of their sizes. Results showed that in all cases, degassing with argon reduced the number of defects regardless of the additions made to the melts. Moreover, all additions were found to degrade melt quality. The lowest number density of pores in all melts was achieved in melts with no additions that were degassed. In both degassed and non-degassed melts, Sr additions degraded the melt quality significantly. The mechanisms of melt quality improvement or degradation with different melt treatments are discussed in the paper

The usage of computer-aided cooling curve thermal analysis to optimise eutectic refiner and modifier in Al-Si alloys

Bismuth, antimony and strontium concentrations were optimised to alter the eutectic Al-Si phase in a commercial Al-Si-Cu-Mg alloy by way of computer-aided cooling curve thermal analysis. The results show that the eutectic growth temperature shifted to lower temperatures for all three inoculants. However, addition of Sr resulted in more depression of growth temperature compared with Bi and Sb. No further significant changes were observed with increasing the concentrations to more than 1, 0.5 and 0.04 wt% of Bi, Sb and Sr, respectively. The recalescence of these concentrations, meanwhile, showed a significant increase of magnitude. A good correlation was found between the results of thermal and microstructural analysis. For Bi and Sb, the eutectic depression temperature can be used as an individual criterion to gauge optimal levels of content in the refinement of Si, whereas for Sr, both depression temperature and recalescence magnitude must be considered. Based on the observed depression in eutectic growth temperature and recalescence, it can be concluded that the optimal concentrations to refine the eutectic Al-Si phase with Bi and Sb and to modify it with Sr at the given solidification conditions were 1, 0.5 and 0.04 wt%, respectively