Solidification dendritic

The metal-wrap-tab solder joints on boards with FR4 and Immersion Tin as the PCB-protective coating on SACX and Sn/Cu/Ni alloys showed small voids on the cross-section with SACX alloy. This alloy also demonstrated better wetting. Twinning and solidification dendrites can be seen on both microstructures. 

Fig. 7. (a) Impurity elements are rejected into the Hquid between the dendritic solidification fronts, (b) Corresponding impurity concentration profiles. Cq, weld metal composition k, impurity partitioning coefficient in the Hquid maximum impurity soHd solubiHty eutectic composition at grain... 

Figure 14.10 shows the end profile of a sectioned stack plate with deep, irregularly shaped casting voids at the intersection of walls. Sectioning through these void zones revealed deep internal tunnel porosity (Fig. 14.11). When viewed under a low-power microscope, the contours of porous areas showed distinct solidification features (dendrites).

The rejected silicon accumulates in a layer just ahead of the growing crystals, and lowers the melting point of the liquid there. That slows down the solidification, because more heat has to be removed to get the liquid in this layer to freeze. But suppose a protrusion or bump on the solid (Al) pokes through the layer (Fig. A1.33). It finds itself in liquid which is not enriched with silicon, and can solidify. So the bump, if it forms, is unstable and grows rapidly. Then the (Al) will grow, not as a sphere, but in a branched shape called a dendrite. Many alloys show primary dendrites (Fig. A1.34) and the eutectic, if it forms, fills in the gaps between the branches. 

The thixocasting mentioned above exploits dendritic solidification of alloys a semi-solidified alloy is forged under pressure into a die the dendrites are broken up into small fragments and a sound (pore-free) product is generated at a relatively low temperature, prolonging die-life. The array of related techniques of which this is one was introduced by Flemings and Mehrabian in 1971 and Flemings (1991) has recently reviewed them in depth. 

The phase-field model and generalizations are now widely used for simulations of dendritic growth and solidification [71-76] and even hydro-dynamic flow with moving interfaces [78,79]. One can even use the phase-field model to treat the growth of faceting crystals [77]. More details will be given later. 

In our treatment of directional solidification above, only one diffusion field was treated explicitly, namely the compositional diffusion. If a simple material grows dendritically (thermal diffusion) one may worry about small amounts of impurities. This was reconsidered [132], confirming a qualitative previous result [133] that impurities may increase the dendritic growth rate. Recently some direct simulation results have been obtained with two coupled diffusion fields, one for heat and one for matter, but due to long computing times they are not yet in the state of standard applications [120,134]. 

R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physica D (55 410, 1993 R. Kobayashi. A numerical approach to three-dimensional dendritic solidification. Exp Math 5 59, 1994. 

A. Karma, W.-J. Rappel. Phase field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys Rev E 55 R3017, 1996 A. Karma, W.-J. Rappel. Quantitative phase field modeling of dendritic growth in two and three dimensions. Phys Rev E 57 4111, 1998. 

J. A. Warren, J. S. Langer. Prediction of dendritic spacings in a directional solidification experiment. Phys Rev E 47 2102, 1993. 

Figure 2. Photographs of cellular and dendritic structures in a thin-film solidification experiment of an organic alloy (succinonitrile-acetone) reported by Ref. 6.

The treatment above is the traditional derivation of the Scheil equation. However, it is not possible to derive this equation, using the same mathematical method, if the partition coefficient, k, is dependent on temperature and/or composition. The Scheil equation is applicable only to dendritic solidification and cannot, therefore, be applied to eutectic-type alloys such Al-Si-based casting alloys, or even for alloys which may be mainly dendritic in nature but contain some final eutectic product. Further, it cannot be used to predict the formation of intermetallics during solidification. 

In most Al-containing alloys, the shape of the particles was tear-drop like due to the tight surface oxide film. The typical shape was shown in Fig.l. The effect of rapid solidification on microstructures is shown in Fig. 5 for AI2CU (precursor for Raney Cu) with a small amount of Pd (11). In the case of slowly solidified (conventional) precursor, most of the added Pd was solidified as a secondary Pd rich phase shown by white dendritic structure in Fig.5 (a). On the other hand, no such secondary phase was observed in a rapidly solidified precursor as shown in Fig.5 (b). 

The phase-field simulations reproduce a wide range of microstructural phenomena such as dendrite formation in supercooled fixed-stoichiometry systems [10], dendrite formation and segregation patterns in constitutionally supercooled alloy systems [11], elastic interactions between precipitates [12], and polycrystalline solidification, impingement, and grain growth [6]. 

CELLULAR AND DENDRITIC SOLIDIFICATION 22.2.1 Formation of Cells and Dendrites... 

As a reasonable approximation, the dendritic structure may be represented by the diagram in Fig. 22.4. The solidification in the interdendritic space can be described by constructing the cell (shown dashed) and assuming that solidification proceeds in a manner similar to the plane-front solidification of a bar (as discussed in Section 22.1). Under typical casting conditions, kf k. Therefore, the segregation... 

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