Alloy Solidification

We saw in Chapter 12 that binary and multicomponent systems do not solidify congru-ently. As a result, the final solid will not be compositionally homogeneous. Consequently, a number of solidification methods have been devised in an attempt to control the final microstructure on both a micro- and macroscale. We briefly explore some of the techniques in this chapter along with some exotic methods that are now employed in order to control the composition of the final product at the atomic scale. 

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Figure 9.2. Constitutional supercooling in alloy solidification (a) phase diagram (b) solute-enriched layer ahead of the solid/liquid interface (c) condition for a stable interface (d) condition...

Europium(III) reduction, 14 640 Eutectic alloys, solidification of, 16 173 Eutectic temperature, of sodium... 

Stability of Liquid/Solid Interface during Binary Alloy Solidification... 

Consider again the alloy solidification described in Section 20.1.3 and illustrated in Fig. 20.4. Here, the concentration spike in the liquid in front of the interface shown in Fig. 20.46 may cause the liquid in that region to be undercooled. The liquidus temperature for a liquid of composition cL is given according to the phase diagram in Fig. 20.4a by the relationship... 

R.F. Sekerka. A time-dependent theory of stability of a planar interface during dilute binary alloy solidification. In H.S. Peiser, editor, Crystal Growth, pages 691-702. Pergamon Press, Oxford, 1967. 

Two types of transformations can be very broadly distinguished. The first is the formation of a solid solution, in which solute atoms are inserted into vacancies (lattice sites or interstitial sites) or substitute for a solvent atom on a particular sublattice. Many types of synthetic processes can result in this type of transformation, including ion-exchange reactions, intercalation reactions, alloy solidification processes, and the high-temperature ceramic method. Of these, ion exchange, intercalation, and other so-called soft chemical (chimie douce) reactions produce no stmctural changes except, perhaps, an expansion or contraction of the lattice to accommodate the new species. They are said to be under topotactic, or topochemical, control. 

The alloy solidification experiments that have been performed on Spacelab missions generally fall into four categories 1) interfacial stability 2) evolution... 

Space experiments have validated many of the theories and models that form the basis of our knowledge of alloy solidification and have begun to demonstrate the range of their applicability. Several lessons learned from materials experiments in space have been put to practice. 

In recent years the conventional modeling framework has also been adopted for the description of multicomponent transport phenomena during metal alloy solidification [109, 110, 12]. 

C. Beckermann, and R. Viskanta, Mathematical Modeling of Transport Phenomena During Alloy Solidification, Appl. Mech. Rev., (46) 1-27,1993. 

F. Vodak, R. Cemy, and P. Prikryl, A Model of Binary Alloy Solidification with Convection in the Melt, Int. J. Heat Mass Transfer, (35) 1787-1791,1992. 

C. Y. Wang, and C. Beckermann, A Multiphase Micro-Macroscopic Model of Solute Diffusion in Dendritic Alloy Solidification, in MicrolMacro Scale Phenomena in Solidification, eds. C. Beckermann et al., ASME HTD, (218) 43-57, American Society of Mechanical Engineers, New York, 1992. 

C. Beckermann and C. Y. Wang, Multi-Phase/Scale Modeling of Transport Phenomena in Alloy Solidification, in C. L. Tien (ed.), Annual Review of Heat Transfer, Vol. VI, pp. 115-198, Begell House, New York, 1995. 

Microstructure after casting of Rodent consists of grains/dendrites sizes up to a few hundred micrometers. Inside the grains are imiformly distributed second phase precipitations that originated during alloy solidification as a result of a superfusion on growing dendrites boimdaries (Fig. la). 

Cha] Cha, P.-R., Yeon, D.-H., Yoon, J.-K., Phase-field Model for Multicomponent Alloy Solidification , J. Cryst. Growth, 274, 281-293 (2005) (Phase Relations, Morphology, Theory, 40)... 

Reflectivity depends on the solder surface appearance and therefore, the time solder alloy solidification characteristics. Good reflectivity will be observed when a tin-lead or eutectic lead-free alloy is used resulting in eutectic solidification. 

Although a number of models have been proposed based on the variable domain method, the single-region method remains the most popular. This is because of its ease of implementation and, unlike the variable domain method it can be readily extended to multidimensional problems. In addition, alloy solidification models can be conveniently developed using the single-region method. 

Chiang KC, Tsai HL (1992) Interaction between shrinkage-induced fluid flow and natural convection during alloy solidification. Int 1 Heat Mass Transf 35(7) 1771-1778... 

Wang CY, Beckermann C (1993) A multiphase solute diffusion model for dendritic alloy solidification. Metall Trans A 24 2787—2802... 

Wang CY, Beckermann C (1995) Computer simulations of nriciDstractural development in dendritic alloy solidification with convection. In Voller VR, Marsh SP, Fl-Kaddah N (eds) Materials processing in the computer age - II. The Minerals, Materials Society, Warrendale, PA, pp 129-143... 

Beckermann C, Ni J (1996) Simulation of sedimentation in globuUtic alloy solidification. Int J Heat Mass Transf 23(3) 315-324. 

Zabaras N, Ruan Y (1990) Moving and deforming finite-element simulation of two-dimensional Stefan problems. Commun Appl Numer Meth 6 495-506, Ruan Y, Liu JC, Ricmond O (1993) A deforming finite element method for analysis of alloy solidification problems. Finite Elem Anal Des 12 49-63... 

Beckermann C, Viskanta R (1993) Mathematical modeling of transport phenomena during alloy solidification. Appl Mech Rev 46(1) 1-27... 

Nudeation events are found in many aspects of materials processing besides the solidification of a melt. A nudeation event is required for precipitates to form in precipitation-hardened alloys, for the decomposition of immisdble systems, for new grains to form in a casting, for graphite flakes to form in cast iron, phase selection in alloy solidification and in crystal growth, etc. Understanding of the nudeation process is key to being able to control it in order to achieve the desired result in a process. 

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