Nonequilibrium solidification

The phases present in products can differ from those predicted from equilibrium diagrams. Nonequilibrium metastable phases form at solidification rates experienced in commercial ingots. Because of the low rate of diffusion of iron in alurninum, equilibrium conditions can only be established by long heat treatments and are very slowly approached at temperatures below about 550 °C. Small additions of other elements, particularly manganese, can also modify the phase relations. 

G.E. Jellison, Jr., Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R.F. Wood and G.E. Jellison, Jr., Melting Model of Pulsed Laser Processing R.F. Wood and F.W. Young, Jr., Nonequilibrium Solidification Following Pulsed Laser Melting... 

At F4, solidification is completed. It is thus seen that nonequilibrium freezing is characterised by... 

In summary, the solidification begins with the formation of numerous solid nuclei and the growth of these nuclei follows. Each nucleus has a gradient of composition from its centre to the periphery. This nonequilibrium effect is referred to as coring. 

Figure 4.6 (a) Portion of a binary-phase diagram illustrating equilibrium solidification (b) nonequilibrium (rapid) solidification, which results in a chemical composition gradient in the crystals, a condition known as coring. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)... 

The second limiting case approximates conventional metallurgical casting processes in which the cooling rate is on the order of 10-3 to 10° K/s. As a result, the solidification rate is several orders of magnitude too fast to maintain equilibrium. The most widely used classical treatment of nonequilibrium solidification is by Erich Scheil (Scheil, 1942), who was at the Max-Planck-Institute for Metals Research in Stuttgart. The model assumes negligible solute diffusion in the solid phase, complete diffusion in the liquid phase, and equilibrium at the solid-liquid interface. In this case, Eq. 4.16 can be rewritten as... 

R. F. Wood and F. W. Young, Jr., Nonequilibrium Solidification Following Pulsed Laser Melting... 

The aim of fusion and controlled solidification of a catalytic material is the generation of a metastable catalytic material. The thermodynamic instability can be caused by a nonequilibrium composition, by a non-equilibrium morphology, or by a combination of both. In the case of the SLP catalysts the desired effect is to avoid the formation of solidification in order to maintain a structureless state of the active material. 

We also list three other alloy phase types of current interest that are not treated here in detail. Quasicrystals are alloy phases partially or completely lacking translational symmetry (see Quasicrystals) they form both equilibrium and nonequilibrium alloy phases. Metallic glasses lack crystalline symmetry entirely they are always metastable and generally require gas-phase deposition or rapid solidification to be retained, although in some cases their equilibration kinetics are so slow that they can be prepared in bulk from the melt (bulk metallic glasses). 

The main feature of the nonequilibrium behavior of solutions dnring cryocrystallization is the appearance of amorphous solids. Generally vitrification of the liquid system depends on the rate of structural relaxation processes, which are substantially determined by the viscosity of the solution. At higher cooling rates and reduced temperatures, the cluster structure of the solution cannot follow the changes, predetermined by the equilibrium behavior of the system, so that even after solidification, the structure of the amorphous solid is very similar to the structure of the solution at low temperatnres. According to modem concepts, the amorphous state can be considered as a kind of snpercooled liqnid with an extremely high viscosity coefficient. 

Nonequilibrium Treatment of Solidification. In the following, as examples of nonequilibrium treatments of solidification in a binary system, a kinetic-diffusion controlled dendritic crystal growth and a buoyancy-influenced dendritic crystal growth are examined. 

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