Crystal transverse cross section

As one can gather from Eq. (14.17), during crystal pulling from the variable cross section crucible, several possibilities emerge to control the volatile activator in crystal. The direct path is variation of C(q. Besides, C(S) depends on the crystal pulling rate and the relation of the values of crystal transverse cross section vs. free melt surface ds l(d — ds ). In the variable cross section crucible, the value of this relation can be easily varied, the volatile activator concentration for ingots of various diameters being kept constant and made the same. 

When the radiation incident on the crystal was horizontally (H) polarized (the E vector oscillating in the plane of k and L) and the angle a was constant, the pattern observed depended on the radiation power P, i.e. on the intensity of the electric field. At low power the transmitted beam was uniform over its transverse cross section, and its divergence was small. As the power was increased, the angular divergence 0 of the beam increased sharply and the beam took on a complex structure rings appeared in the plane of the screen, which was perpendicular to k. They increased in number as the... 

In its ultimate form, the problem of controlled continuous pulling boils down to the production of a single crystal that has a transverse cross section that is unchanging with height, and grows with a constant axial rate. (In the first approximation, we shall consider that the melt should crystallize only on the growing crystal evaporation of substances from the free surface of the melt can be... 

So, it might be very desirable that one of the parameters (transverse cross section or axial speed) should be kept constant independently of each other, which is feasible only in the event that the adjustment is done by way of variation of a third parameter, which exercises an influence on these parameters, to be more precise, on the crystallization rate in general. Since the latter is determinable by the difference between heat removal from the crystallization front through the growing crystal and the heat influx from the melt to the crystallization front, this parameter would be either temperature in the crystal or that in the melt. 

These difficulties can be avoided by employing a technique of crystal puUirig from the melt that has a variable geometry of the free surface [4, 5]. As a matter of fact, this implies the use of crucibles with a variable transverse cross section. 

One may attempt to derive the ideal shear strength So of the van der Waals solid normal to the chain axis from the value of the lateral surface free energy, a. This value is well known for common polymers such as PE or polystyrene (PS) (Hoffman et al, 1976) or else can be calculated from the Thomas-Stavely (1952) relationship a = /a Ahf)y, where a is the chain cross-section in the crystalline phase, Ahf is the heat of fusion, and y is a constant equal to 0.12. If one now assumes that a displacement between adjacent molecules by Si within the crystal is sufficient for lattice destruction then the ultimate transverse stress per chain will be given by So = cr/31. The values so obtained are shown in Table 2.1 for various polymers. In some cases (nylon, polyoxymethylene, polyoxyethylene (POE)) the agreement with experiment is fair. In the others, deviations are more evident. In order to understand better the discrepancy between the experimentally observed and the theoretically derived compressive strength one has to consider more thoroughly the micromorphology of polymer solids and the phenomena caused by the applied stress before lattice destruction occurs. 

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