Equilibrium cooling

In some crystalhzation apphcations it is desirable to increase the solids content of the shiny within the body above the natural consis-tencw, which is that developed by equilibrium cooling of the incoming feed solution to the final temperature. This can be done by withdrawing a stream of mother liquor from the baffle zone, thereby thickening the shiny within the growing zone of the crystallizer. This mother liquor is also available for removal of fine ciystals for size control of the product. 

So, for this binary solution of components A and B, which mix perfectly at all compositions, there is a two-phase region at which both solid and liquid phases can coexist. The uppermost boundary between the liquid and liquid + solid phase regions in Figure 2.3f is known as the liquidus, or the point at which solid first begins to form when a melt of constant composition is cooled under equilibrium conditions. Similarly, the lower phase boundary between the solid and liquid + solid phase regions is known as the solidus, or the point at which solidification is complete upon further equilibrium cooling at a fixed composition. 

When anstenite is cooled nnder more rapid conditions, a compound called bainite is produced. Bainite is a noneqnilibrinm prodnct that is similar to pearlite, but consists of a dispersion of very small FesC particles between the ferrite plates. Bainite formation is favored at a high degree of snpercooling from the austenite phase, whereas pearlite forms at low degrees of supercoohng, or more equilibrium cooling. 

The solution to equations 12-14 for the growth of a pseudobinary compound, A JB C, can be expressed in analytical form (94) for the three common temperature programs ramp or equilibrium cooling, step cooling, and supercooling. The expressions for thickness as a function of time are given by ... 

ABC ternary system forms three binary eutectics and a ternary eutectic as shown below. Discuss equilibrium cooling paths for the overall compositions p, q and r indicated in the diagram. Discuss also the change in microstructure that should occur during cooling. 

Equilibrium cooling or ramp cooling is a linear growth cooling from the equilibrium temperature. The temperature of the solution is lowered at a rate a, (K min-1) from the liquidus temperature (7 ) to the end temperature (Tg), while in contact with substrate. In this case, the kinetics of growth is limited by diffusion. 

The left part of the Fig. 9.4 presents the growth by equilibrium cooling on mc-substrates and the resulting epitaxial layer and the right, with y°y° technique. 

Fig. 9.4. LPE growth on multicrystalline silicon substrate at INL [23] with equilibrium cooling (left) or yoyo technique (right). Before growth (950° with Sn), substrate roughness is about 2-3 pm. From top to bottom are cross section view, surface view and schematic temperature profile...

The constitution and transformation characteristics of NiAl bronze materials have been described in detail elsewhere (Ref 16-18, 20, 22-30). An as-cast Cu-9Al-5Ni-4Fe alloy solidifies as a single-phase p solid solution. The sequence of transformations during subsequent equilibrium cooling is summarizedinFig. 8.2(a),... 

Fig. 8.2 (a) Sequence of transformations during equilibrium cooling of a Cu-9AI-5Ni-4Fe alloy, (b) Typical... 

Thus, during equilibrium cooling, the composition of the solid will mn down the solidus line, ri to S2 to S3, and so on, and the composition of the liquid in equilibrium with the solid runs down the liquidus from Zi to I2 to I3, and so on, as the liquid cools. The composition of the solid phase when all of the liquid has solidified will be equal to that of the original liquid phase. Not only does the composition of the solid and liquid phases change continuously as the temperature falls through the two-phase region, but the number of small crystals present also increases. When temperature T4 is reached, the microstructure of the solid consists of crystallites or grains... 

Differentiation of interstitial aluminate and ferrite elite and belite lose sharp regularity Equilibrium cooling to complete crystallization through 1250°C (Brown, 1948)... 

However, if the molecules are cooled, the population of thermally excited vib-rot states falls drastically and the spectrum simplifies. Thus, at 77 K, 69% of UFs is in its lowest vibrational state, and this increases to 85% at 55 K. However, the vapor pressure is untenably low at such temperatures (7 x 10 Pa at 77 K), and equilibrium cooling is out of the question. Still by cooling in a nonequilibrium expansion nozzle, uranium vapor concentration can be kept at a useful level and LIS is possible. None of this changes the fact that molecular LIS was abandoned in favor of AVLIS. 

Fig.1 Typical microstructure of a 95Sn-3.5Ag solder resulting from non-equilibrium cooling showing primary dendrites of Sn-rich solid solution and interdendritic space filled with acicular AgsSn in a Sn-rich solid solution matrix.

Some of the consequences of nonequilibrium solidification for isomorphous alloys will now be discussed by considering a 35 wt% Ni-65 wt% Cn alloy, the same composition that was used for equilibrium cooling in the previons section. The portion of the phase diagram near this composition is shown in Figme 9.5 in addition, microstructures and associated phase compositions at varions temperatures upon cooling are noted in the circular insets. To simplify this discussion, it will be assumed that diffusion rates in the liquid phase are sufficiently rapid snch that equilibrium is maintained in the liquid. 

At point d ( 1220°C) and for equilibrium cooling rates, solidification should be completed. However, for this nonequilibrium situation, there is still an appreciable... 

---