Download (4Mb) - Etheses - Saurashtra University

Chapter II Solution Growth….
stable equilibrium with its vapor, which is neither super-saturated nor under-
saturated, then a step in equilibrium on the crystal surface will exhibit a
constant mean direction h , inclined at an angle θ to the principle direction
given by the following expression,
tan θ = n+ n- (2.1)
Where, n+ and n- are the numbers of kinks of opposite sign per atom spacing.
The potential energy considerations suggest that at absolute zero
temperature, a step will tend to remain as straight as possible.
As the temperature increases from absolute zero, the component
molecules will start vibrating relative to one another. As the temperature
increases the vibrations become progressively stronger. Now the scenario
changes, some molecules will be able to overcome the energy that binds
them to the crystal and will jump in the space surrounding it. In this manner, a
certain vapor concentration, which is the average number of vapor molecules
per unit volume, will occur in contact with the crystal surface. With comparison
to the other molecules, the molecules positioned at the kink are more prone to
depart from the crystal and vaporize. The molecules at the kinks are bound by
three molecules. Moreover, the molecules on the straight portions of the step
are bound by four molecules and those on the flat portions of the surface by
five. The energy required for a molecule to leave the kink position such as A
in figure (2.3 a) is equal to the evaporation energy W. Two different processes
will occur simultaneously; in one some molecules will be leaving the crystal
and in the other one the molecules will be arriving at the crystal from the
58