Solidification fronts

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... 

In this section we discuss the basic mechanisms of pattern formation in growth processes under the influence of a diffusion field. For simphcity we consider the sohdification of a pure material from the undercooled melt, where the latent heat L is emitted from the solidification front. Since heat diffusion is a slow and rate-limiting process, we may assume that the interface kinetics is fast enough to achieve local equihbrium at the phase boundary. Strictly speaking, we assume an infinitely fast kinetic coefficient. 

X. Feng, E. A. Brener, D. E. Temkin, Y. Saito, H. Miiller-Krumbhaar, Creep motion of a solidification front in a two-dimensional binary alloy. Phys Rev E (to appear) X. Feng, E. A. Brener, D. E. Temkin, Y. Saito, H. Muller-... 

EXAMPLE 10.5 Particle Engulfment by An Advancing Solidification Front. Experiments were conducted at 80°C in which the solidification front of naphthalene was observed to either engulf or reject dispersed particles of several solids. Table 10.6 lists the observed engulfment (E) or rejection (R) behavior for various systems as well as the surface tensions of the various substances. The surface tensions of solid and liquid naphthalene at 80°C are 26.4 and 32.8 mJ m 2, respectively. Is the surface tension criterion cited above consistent with these observations How might any inconsistencies be explained Evaluate the product (7j/2 - 7i1/2)(t2/2 -7l/2) for these systems. 

Solution The surface tension of liquid naphthalene (1) is greater than that of solid naphthalene (3). Therefore A312 is expected to be negative for all systems having 7 values greater than 7.,. This is the case for the first six compounds listed in Table 10.6. Therefore these substances are expected to display rejection by the solidification front. This is indeed observed for five of the six cases. The case of nylon-6,12, which deviates from the predicted behavior, is best understood by examining the product (73s - 711/2)(72/2 - y]12)- Values of this product for the various systems considered are listed in Table 10.6. The factor arising from the solid-liquid (3-1) naphthalene has the constant value -0.0186 for all cases, but differs when various solids are used as component 2. For nylon-6,12, the second factor becomes -0.0022, and the product of the two, 0.41 10 4 mJ m 2, is the smallest of all such products listed in the table. As the surface tension difference decreases, the sensitivity of the behavior to variations in d0 increases. ... 

Although appealing from an engineering perspective, the analyses based on linear thermoelasticity do not address the action of defects and dislocations created by microscopic yield phenomena below the CRSS and of those that are incorporated in the crystal at the solidification front. In the previous works cited (104-108), the authors assume that no defects exist at the melt-crystal interface and that the stresses on this surface are zero. Constitutive equations incorporating models for plastic deformation in the crystal due to dislocation motion have been proposed by several authors (109-111) and have been used to describe dislocation motion in the initial stages of... 

Not only can negative VDW forces be correlated with particle engulfment or rejection phenomena at solidification fronts (I), and of the phenomenon of phase separation in solutions of pairs of polymers (2), but these repulsive forces also can be applied to novel separation meth-... 

Although there are analogies between solidification and crystallization, there are also some important structural differences between the solid-melt interface (also called the solidification front) and the solid-solvent interface due to the differing concentration, viscosity, and temperature of the respective liquid phase. These may be summarized as follows ... 

The measurement of contact angles on solids in powder or particle form is a challenging task, and numerous methods have been proposed 7. In this section, three successful indirect approaches are discussed capillary penetration into columns of powders, sedimentation volume of particles, and solidification fronts of particles. These methods are indirect because they provide the solid surface tension rather than the contact angle. For the sake of completeness, various direct approaches are also summarized briefly. 

The particle is pushed along by the solidification front. This occurs when the free energy of engulfment is positive. The particle is not, however, pushed for all velocities of the solidification front. For each particle that is pushed, there is a maximum, or critical, velocity above which the particle will be engulfed by the advancing solidification front. 

The behavior of small particles at an advancing solidification front has been investigated experimentally for both vertical [ 149-154] and horizontal [140,141, 144,155-158] motion of the solidification front. 

Thermodynamically, the process of particle engulfment by the advancing solidification front can be modeled by the net free energy change of the system... 

The size of the crystalites produced will depend on the nucleation rate and crystal growth rate at the solidification front. Both are controlled by the local supersaturation. The rate expressions for homogeneous nucleation (equation (6.15)) and heterogeneous nucleation (equation... 

Fig. 1.15. Picture that shows breakdown of the solidification front in MC Si...

Second, in the fast-cooling solidification process, the m-c interface is concave to the crystal and the melt flows from the periphery to the center along the solidification front surface. Thus, the impurities in the melt and the SiC particles generated at the interface are transported to and accumulated in the... 

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