Disc shaped nuclei

A theoretical treatment, similar to that given above for spherical nuclei, may be provided for disc-shaped nuclei of only one or two molecules thickness (5jc) on reactant surfaces. For these... 

Thus, the larger the under cooling, the smaller the value of AG (and the more rapid the nucleation) and the value of r (the smaller the size of the critical nucleus) required to initiate crystallization. Other models for the nucleus give similar equations. For example, for disc shaped nuclei... 

Schematic vfew of the formation of disc-shaped nuclei on a crystal (ri) dew parallel to the surface and (b) view normal to the surface.

The current associated with the growth of an isolated disc shaped nucleus is therefore expected to increase linearly with time. In practice, of course, it is extremely difficult to observe the growth of a single nucleus, so that it is necessary to take into account the way in which the growth centres are formed. The limiting cases of Equation (9.21) and (9.22) are useful here. If the nucleation of growth centres is essentially instantaneous, the net current density corresponding to a number density of Nq of isolated centres is... 

The theory can also be modified to allow for different nucleus geometries, e.g. disc-shaped caps, without substantially affecting the overall result. If the substrate is allowed to have curvature, or if the formation of nuclei in cavities on the surface is considere< it is found that the barrier to nucleation is reduced even further. ... 

The s electrons are spherically distributed about the chorine nucleus, and the px and py electrons lie in a disc perpendicular to the z axis with the Cl nucleus at its center. Now let us suppose instead that the chlorine atom has full sp3 hybridization and uses one of these hybrid orbitals to form the bond. The remaining three pairs of electrons will lie in the three equivalent hybrid orbitals, which have approximately the shape shown in Fig. 3-17. It is easily seen that electrons in such an orbital are much more concentrated below the xy plane than above it, and hence there will be an orbital dipole moment which can be represented by a vector of magnitude v pointing along the axis of the orbital. There is, then, a dipole moment contribution in the bond direction of — v cos 71°, or a total from the three such orbitals of — 3v cos 71°, namely ... 

Atomic nuclei can be stretched like cigars (prolate shape) or compressed like discs (oblate shape). The deformation is described by the electric quadrupole moment Q (prolate Q>0 oblate Q<0). The principal interaction is, of course, the normal electrostatic (Coulomb) force on the charged nucleus (monopole interaction). The differential interaction, which depends... 

Atomic nuclei can be stretched like cigars (prolate shape) or compressed like discs (oblate shape). The deformation is described by the electric quadrii-pole moment Q (prolate Q > 0 oblate Q < 0). The principal interaction is, of course, the normal electrostatic (Coulomb) force on the charged nucleus monopole interaction). The differential interaction, which depends on the structure of the nucleus and on the valuation of the field across its finite extension, is of course very much smaller quadrupole interaction). It gives rise to an electric hyperfine structure. The energy contribution depends on the direction of the nuclear spin in relation to the electric field gradient. For the electric hyperfine interaction one obtains... 

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