Growing crystals

Plasmas are used extensively to melt materials for a variety of purposes. In many cases, the materials are introduced as a powder into the gas stream in a plasma torch. The molten droplets can be used to grow crystals of refractory materials such as niobium (166). 

For example, consider the cross sections of a growing crystal as in Fig. 18-58. The polygons shown in the figure represent varying stages in the growth of the crystal. The faces marked A are slow-growing... 

Gillman, The Ait and Science of Growing Crystals, Wiley, New York, 1963. 

We saw in Chapter 6 that diffusive transformations (like the growth of metal crystals from the liquid during solidification, or the growth of one solid phase at the expense of another during a polymorphic change) involve a mechanism in which atoms are attached to the surfaces of the growing crystals. This means that diffusive transformations can only take place if crystals of the new phase are already present. But how do these crystals - or nuclei - form in the first place ... 

We now apply the thermodynamic and kinetic theory of Chapters 5-8 to four problems making rain getting fine-grained castings growing crystals for semiconductors and making amorphous metals. 

When a metal is cast, heat is conducted out of it through the walls of the mould. The mould walls are the coldest part of the system, so solidification starts there. In the Al-Si casting alloy, for example, primary (Al) crystals form on the mould wall and grow inwards. Their composition differs from that of the liquid it is purer, and contains less silicon. This means that silicon is rejected at the surface of the growing crystals, and the liquid grows richer in silicon that is why the liquid composition moves along the liquidus line. 

The rejected silicon accumulates in a layer just ahead of the growing crystals, and lowers the melting point of the liquid there. That slows down the solidification, because more heat has to be removed to get the liquid in this layer to freeze. But suppose a protrusion or bump on the solid (Al) pokes through the layer (Fig. A1.33). It finds itself in liquid which is not enriched with silicon, and can solidify. So the bump, if it forms, is unstable and grows rapidly. Then the (Al) will grow, not as a sphere, but in a branched shape called a dendrite. Many alloys show primary dendrites (Fig. A1.34) and the eutectic, if it forms, fills in the gaps between the branches. 

The first x-ray structure of a porin was determined by the group of Georg Schulz and Wolfram Welte at Ereiburg University, Germany, who succeeded in growing crystals of a porin from Rhodobacter capsulatus that diffracted to 1.8 A resolution. Since then the x-ray structures of several other porin molecules have been determined and found to be very similar to the R. capsulatus porin despite having no significant sequence identity. 

One of the more important uses of OM is the study of crystallization growth rates. K. Cermak constructed an interference microscope with which measurements can be taken to 50° (Ref 31). This app allows for study of the decompn of the solution concentrated in close proximity to the growing crystal of material such as Amm nitrate or K chlorate. In connection with this technique, Stein and Powers (Ref 30) derived equations for growth rate data which allow for correct prediction of the effects of surface nucleation, surface truncation in thin films, and truncation by neighboring spherulites... 

The rate equations determine the rate of change of the probability of a particular configuration, a, within an ensemble of growing crystals. They must include the rate constants for adding or subtracting units, which are assumed to obey microscopic reversibility. The net flux between configurations a and a which occur with probability P(a) and P(a ) respectively, and differ by one unit is ... 

Near room temperature most gases become less soluble in water as the temperature is raised. The lower solubility of gases in warm water is responsible for the tiny bubbles that appear when cool water from the faucet is left to stand in a warm room. The bubbles consist of air that dissolved when the water was cooler it comes out of solution as the temperature rises. In contrast, most ionic and molecular solids are more soluble in warm water than in cold (Fig. 8.22). We make use of this characteristic in the laboratory to dissolve a substance and to grow crystals by letting a saturated solution cool slowly. However, a few solids containing ions that are extensively hydrated in water, such as lithium carbonate, are less soluble at high temperatures than at low. A small number of compounds show a mixed behavior. For example, the solubility of sodium sulfate decahydrate increases up to 32°C but then decreases as the temperature is raised further. 

The powdered raw material TiB, is deposited in a hot gas onto the molten surface of the crystal being grown. An arc is used instead of a combustion heat source. The growing crystal is shielded from air with Ar. 

The growing crystal, or boule, is a cylinder supported by its vertical axis. The top of the crystal is kept molten by impinging a flame upon it. Fine adjustment of the head is not critical because the diameter of the boule can change to accommodate variations in heat input. 

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