Solidification kinetics

For an alloy droplet, the post-recalescence solidification involves segregated solidification and eutectic solidification. 619 Droplet cooling in the region (1),(2) and (6) can be calculated directly with the above-described heat transfer model. The nucleation temperature (the achievable undercooling) and the solid fraction evolution during recalescence and post-recalescence solidification need to be determined additionally on the basis of the rapid solidification kinetics. 154 156 ... 

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. 

The solidification kinetics and compositional fluctuations in the melt will decide over the crystallization pathway which can be followed by all of the melt. If local gradients in temperature or composition exist in the system the crystallization pathway can be locally inhomogeneous and create different metastable solids at different locations in the macroscopic solidified blocks. 

Rousset, P., Rappaz, M. and Minner, E. (1998). Polymorphism and solidification kinetics of the binary system pos-sos. Journal of the American Oil Chemists Society, 75(7) 857-864. 

In some countries recognition has been accorded to the method of estimating the viscous-plastic properties and solidification kinetics of reactoplasts, among them aminoplasts, on the Kanavets-type plastometer [17] with the working unit of the cylinder—cylinder type. 

A comprehensive model for solidification would necessarily require fully-coupled, three-dimensional fluid flow, heat transfer, and solidification kinetics. For operations like drop forming and enrobing, the geometry is free form, and so finite element modeling would seem the best approach. 

The main purpose of this section is to give an account of general peculiarities of the microscopic scenarios of the supercooled liquid solidification and to show that formation of the polycluster glasses is a commonplace case. A more detailed consideration of the supercooled liquid structure, its thermodynamics and solidification kinetics is given in Sect. 6.10. 

G.J. Galvin, J.W Mayer, PS. Peercy, Solidification kinetics of pulsed laser melted silicon based on thermodynamic considerations. Appl. Phys. Lett. 46,644-646 (1985)... 

To confirm that the matrix is amorphous following primary solidification, isothermal dsc experiments can be performed. The character of the isothermal transformation kinetics makes it possible to distinguish a microcrystalline stmcture from an amorphous stmcture assuming that the rate of heat released, dH/dt in an exothermic transformation is proportional to the transformation rate, dxjdt where H is the enthalpy and x(t) is the transformed volume fraction at time t. If microcrystals do exist in a grain growth process, the isothermal calorimetric signal dUldt s proportional to, where ris... 

We will be looking at kinetics in Chapter 6. But before we can do this we need to know what we mean by driving forces and how we calculate them. In this chapter we show that driving forces can be expressed in terms of simple thermodynamic quantities, and we illustrate this by calculating driving forces for some typical processes like solidification, changes in crystal structure, and precipitate coarsening. 

In chemicals like salol the molecules are elongated (non-spherical) and a lot of energy is needed to rotate the randomly arranged liquid molecules into the specific orientations that they take up in the crystalline solid. Then q is large, is small, and the interface is very sluggish. There is plenty of time for latent heat to flow away from the interface, and its temperature is hardly affected. The solidification of salol is therefore interface controlled the process is governed almost entirely by the kinetics of molecular diffusion at the interface. 

In spite of this dominance of heat flow, the solidification speed of pure metals still obeys eqn. (6.15), and depends on temperature as shown in Fig. 6.6. But measurements of v(T) are almost impossible for metals. When the undercooling at the interface is big enough to measure easily (T, -T 1°C) then the velocity of the interface is so large (as much as 1 m s 0 that one does not have enough time to measure its temperature. However, as we shall see in a later case study, the kinetics of eqn. (6.15) have allowed the development of a whole new range of glassy metals with new and exciting properties. 

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. 

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. 

A. Classen, C. Misbah, H. Miiller-Krumbhaar, Y. Saito. Kinetics in directional solidification. Phys Rev A 45 6920, 1991. 

A thermal stability study was first carried out to determine the following information (1) the solidification temperature as a function of the concentration of the sulfonate (2) the enthalpy of decomposition by DTA (3) the autocatalytic nature of the decomposition by Dewar flask (4) kinetic data for decomposition by Dewar flask (5) the time to maximum rate by ARC, and (6) the heat generation as a function of temperature, also by ARC. In addition, the enthalpy of dilution was determined for various potential water leak rates. These data were useful in defining emergency response times. 

---