Biomedical Engineering Reference
In-Depth Information
occurred [
35
]. Using surface observations conducted, and after performing detailed
measurement of the slope of the growth hillock formed by spiral steps, together
with face growth rate data, they indirectly calculated the step velocity. It disagreed
with the linear dependence on supersaturation predicted by the BCF model. They
explained this contradiction by arguing that the step velocity increased non-linearly
due to two-dimensional nucleation occurring at the terraces between steps.
With spiral growth, the original BCF model described the face growth rate on
the basis of the behavior of the growth steps at a single growth center on the
crystal surface. However, there are multiple growth centers on a crystal surface,
and the ones that control the growth rate undergo changes as a result of alterations
in their relative activity that are associated with supersaturation. Efforts to resolve
this problem and conduct measurements near the theoretically assumed growth
conditions were carried out vigorously from the late 1980s to the early 1990s using
in situ optical interferometry. This method was applied to ADP and KDP crystals
[
36
,
37
] and subsequently led to studies on Ba(NO
3
)
2
[
38
] and on K-Alum [
39
].
The use of interferometry for studying various soluble inorganic crystals has clar-
ified many phenomena. For example, observations of KDP and K-Alum confirmed
the nonlinear dependence of the step velocity on supersaturation, which was the
similar with that reported by van Erk et al. for the garnet crystal. However, it was
shown that this nonlinear dependence is not due to two-dimensional nucleation at
the terraces but rather to a decrease in velocity caused by adsorption of impurities on
the step front at low supersaturation and a rapid increase in velocity caused by less
adsorption of impurities with an increase in supersaturation. It was also showed that
step behavior, which differs from that predicted by the BCF model, greatly affects
the dependence of the face growth rate on the supersaturation. For example, even
when spiral growth occurs on a crystal surface, the relationship between the growth
rate and supersaturation could suggest growth by two-dimensional nucleation.
These findings revealed the danger inherent in the simplistic fitting of growth rate
data to a model.
The rate-limiting process of growth has also been investigated using interfer-
ometry. In early research on KDP and ADP, surface diffusion was thought to be
unimportant, as it was for research on Ba(NO
3
)
2
and K-Alum. For crystal growth in
an aqueous solution system, the consensus was that surface diffusion did not play
a major role, and even if it were present, the diffusion length would be minimal.
Vekilov et al. investigated the previously unobserved faces of ADP crystals and,
after performing detailed comparison of data using growth models, concluded that
growth progressed via surface diffusion and that a surface kinetic process including
surface diffusion was rate-limiting [
40
]. It is currently understood that, even in the
same crystal, the optimal growth model depends on the relative importance of each
elemental process for each crystal face.
Observations using interferometry of two-dimensional nucleation of ADP have
been performed [
41
]. The observations and subsequent quantitative analysis re-
vealed that impurities reduce the activation energy needed for nucleation at low
supersaturation and are active sites for heterogeneous nucleation. Homogeneous
nucleation takes place only at high supersaturation. This has been verified by the
