Growth thickness-dependent

A very recent application of the two-dimensional model has been to the crystallization of a random copolymer [171]. The units trying to attach to the growth face are either crystallizable A s or non-crystallizable B s with a Poisson probability based on the comonomer concentration in the melt. This means that the on rate becomes thickness dependent with the effect of a depletion of crystallizable material with increasing thickness. This leads to a maximum lamellar thickness and further to a melting point depression much larger than that obtained by the Flory [172] equilibrium treatment. 

If the growth front is frozen, the crystallization at the growth front depends crucially on the commensurability between the thickness of the growth front and the length of crystallizing chains. For details, see Ref. 49. A collection of polydisperse chains gets effectively fractionated at the growth front. 

Figure 5.7. Optical microscope image of a thin film (thickness 2 p.m) of a-p-NPNN grown on a glass substrate (1.6 x 1.0 mm, crossed polarizers). Reprinted from Journal of Crystal Growth, Vol. 209, J. Caro, J. Fraxedas and A. Figueras, Thickness-dependent spherulitic growth observed in thin films of the molecular organic radical p-nitrophenyl nitronyl nitroxide, 146-158, Copyright (2000), with permission from Elsevier.

The observed non-linear radial growth of the spherulites can be described in terms of a thickness-dependent growth law given by the expression ... 

Two other factors could contribute to the observed departure of the growth thickness at long times from that predicted by equation 17. First, homogeneous nucleation in the melt and the subsequent growth of precipitates will act as sinks for solute atoms, just as film growth does. The exact location in the melt where homogeneous nucleation will occur depends on the melt compositional and thermal profiles (96). The precipitates are less dense than the melt and will rise to the top of the melt. Such precipitates... 

Fig. 11 Craze in commercial polystyrene showing the characteristic steps nucleation through void formation in a pre-craze zone, growth of the fibrillar structure of the widening craze by drawing-in of new matrix material in the process zone, and final breakdown of the fibrillar matter transforming a craze into a crack (the crack front is more advanced in the center of the specimen, shielded by a curtain of unbroken fibrils marked by the arrow). The fibril thickness depends—of course—on the molecular variables, the strain rate-stress-temperature regime of the crazing sample and on its treatment (preparation, annealing) and geometry (solid, thin film) for PS typical values of between 2.5 and 30 nm are found [1,60,61]...

Yip et al [29] reported the following 00.2 FWHMs 516, 275 and 478 arc sec for layers 0.2, 0.57 and 1.4 pm thick, respectively. For all three layers, twist mosaicity did not change much (10.1 reflection of 1692, 1728 and 1982 arc sec, respectively). The results of these authors seem to be typical the tilt mosaicity decreases up to a certain thickness (dependent on different growth conditions), and then it starts to increase. 

In general, crystal growth is more complex than the system outlined above due to the behaviour of the To (temperature at the bottom of the solidified wafer), which in general is not constant, the temperature dependence of the material characteristics, and the often turbulent flow in the liquid silicon melt. The variable growth speed results in thickness dependent material characteristics due to processes like velocity dependent effective segregation of metallic impurities. 

The above mechanism was consistent with several experimental observations. MgO was known to be preferentially formed on the surface of Al-Mg alloys under many circumstances, as described earlier, either because of cation demixing in spinel, to form periclase, or due to rapid diffusion of Mg in the solid state and subsequent surface segregation. The single crystal oxidation product clearly precluded any mechanism that involved repeated nucleation of corundum (alumina) grains, which in any event is known to he difficult at temperatures below 1200°C. Finally, the presence of a film of molten alloy at a distance of about 1 pm from the surface accounted for the relative absence of a growth rate dependence on composite thickness (a rather slow decrease is actually observed). 

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