Kinetics of structural change I - diffusive transformations

Most metals are melted or solidified at some stage during their manufacture and solidification provides an important as well as an interesting example of a diffusive change. We saw in Chapter 5 that the driving force for solidification was given by 

In order to predict the speed of the process we must find out how quickly individual atoms or molecules diffuse under the influence of this driving force. 

To get a driving force the cell is pushed towards the cold block, which cools the interface below T, . The solid then starts to grow into the liquid and the growth speed can be measured against a calibrated scale in the microscope eyepiece. When the interface is cooled to 35°C the speed is about 0.6 mm mimk At 30°C the speed is 2.3 mm mimk And the maximum growth speed, of 3.7 mm mim, is obtained at an interface temperature of 24°C (see Fig. 6.3). At still lower temperatures the speed decreases. Indeed, if the interface is cooled to -30°C, there is hardly any growth at all. 

We now apply this result to the layer of liquid molecules immediately next to the solid-liquid interface (layer B in Fig. 6.4). The number of liquid molecules that have enough energy to climb over the energy barrier at any instant is 

In order for these molecules to jump from liquid positions to solid positions they must be moving in the correct direction. The number of times each liquid molecule oscillates towards the solid is v/6 per second (there are six possible directions in which a molecule can move in three dimensions, only one of which is from liquid to solid). Thus the number of molecules that jump from liquid to solid per second is 

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Most kinetic growth processes produce objects with self-similar fractal properties, i.e., they look self-similar under transformation of scale such as changing the magnification of a microscope [122]. According to a review by Meakin [134], the origin of this dilational symmetry may be traced to three key elements describing the growth process I) the reactants (either monomers or clusters), 2) their trajectories (Brownian or ballistic), and 3) the relative rates of reaction and transport (diffusion or reaction-limited conditions). The effects of these elements on structure are illustrated by the computer-simulated structures shown in the 3x2 matrix in Fig. 55. 

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