Equilibrium, thermal growth

The addition of heat shifts the equilibrium concentrations away from the products and back towards the reactants, the monomers. This is one reason why processing these types of polymers is often more difficult than processing products of chain growth mechanisms. The thermal degradation process can be dramatically accelerated by the presence of the low molecular weight condensation products such as water. Polyester, as an example, can depolymerize rapidly if processed in the presence of absorbed or entrained water. 

Another very complicated problem where the approach to equilibrium with time after a quenching experiment is described by an asymptotic law is the owth of wetting layers, in a situation where thermal equilibrium would require the surface to be coated with a macroscopically thick film, but is initially nonwet. For a short-range surface potoitial as discussed in section 3.5, analytical theories predict for a non-conserved density a growth of the thicknm of the layer according to a law f(t) oc In t, and this has in fact been observed by simulations . In the case where the surface potential decays with stance z from the surface as z, the prediction for the thickness l(t) is for the nonconserved case and... 

Under most circumstances the equilibrium shape of silicon crystals is octahedral, ie, the slowest-growing faces are (111). However, external conditions can radically alter that shape. For example, when growth is from the vapor, concentration gradients in the gas stream may affect the shape, and when growth is from the melt, the shape is primarily determined by thermal gradients in the melt. 

A major complication in the analysis of convection and segregation in melt crystal growth is the need for simultaneous calculation of the melt-crystal interface shape with the temperature, velocity, and pressure fields. For low growth rates, for which the assumption of local thermal equilibrium is valid, the shape of the solidification interface dDbI is given by the shape of the liquidus curve Tm(c) for the binary phase diagram ... 

In addition, the structure and properties of point defects at low temperatures and at high temperatures may be different (29). The observation of extrinsic-type dislocation loops in dislocation-free, float-zone Si indicate that self-interstitials must have been present in appreciable concentrations at high temperature during or after crystal growth (30, 31). However, it is unclear whether these self-interstitials were present at thermal equilibrium or were introduced during crystal growth by nonequilibrium processes. 

The buildup of the H2 concentration, for any given depth x, starts with all its time derivatives zero at t = 0, increases gradually, and after a depth-dependent induction time becomes linear in t. The unbounded growth can be truncated by allowing the molecules either to dissociate or to diffuse. Dissociation will of course modify the development of the H° distribution molecular diffusion will not. As regards dissociation, there are to date no time-dependent solutions for this problem available presumably if the molecules are immobile, they would show an approach to a flat thermal-equilibrium distribution, which would extend to deeper depths at longer times. The case of diffusion without dissociation will be taken up in the paragraphs to follow. 

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