Biomedical Engineering Reference
In-Depth Information
nucleation occurs at high supersaturation, it is possible to explain the above results.
In fact, for measurements based on the phase-shift method, the growth rate data in
the low supersaturation range (while highly variable) does not lie on the expected
curve extrapolated from that in the high supersaturation range.
The effects of adding zinc or magnesium ions to the pseudo-body fluid have also
been investigated for growth rate measurements of the
c
-face [
71
,
72
]. Although
both elements are essential for organisms, they are thought to be impurities for
HAP growth [
73
-
75
]. AFM observations of
c
-face growth in a system containing
0.03-1.5 mM of magnesium ions or 0.3-7.5
M of zinc ions added to pseudo-body
fluid with
revealed that they strongly inhibit the growth of the two-
dimensional nucleus. The effect of zinc ions in particular is more pronounced than
that of magnesium ions. The effects of magnesium and zinc ions on
D
22:0
from data
on growth rate measurements are carried out at various levels of supersaturation
with their concentrations fixed at 0.06 mM and 0.75
M, respectively. Liu et al. has
formalized the growth rate for heterogeneous nucleation mode when impurities are
present [
76
]:
.1
C
/
g
1=6
exp
0
2
f=
˚
3.k
B
T/
2
ln
.1
C
/
ı
1=3
(3.18)
R
D
C
2
ˇ
2=3
.1
C
/
1=3
f
ln
ŒR=Œ
2=3
.1
C
/
1=3
f
ln
.1
C
/
g
1=6
D
ln
ˇ
f
0
2
f =3.k
B
T/
2
g
ln
C
2
C
ln
ı
1=3
:
1=
ln
.1
C
/
C
ln
(3.19)
In (
3.18
),
C
2
is a constant, and
0
is the edge free energy of a two-dimensional
nucleus in a system in which impurities are absent. In (
3.19
),
f
and
are physical
quantities unique to heterogeneous nucleation: the former is the ratio of the radii
of the critical two-dimensional nucleus to that of the impurity particles, and the
latter is the contact angle between the two-dimensional nucleus and the impurity
particles. Both
f
and
ı
,
(
3.18
) coincides with (
3.16
), which indicates homogeneous nucleation. The function
i
D
0
f
1=2
(
i
D
impurity type) relates
ı
have a range of
0<f;ı
6
1
,andwhen
f
D
ı
D
1
0
to
i
, the edge-free energy in the
presence of impurities. Finally,
,
and
f
Mg
D
0.8 and
f
Zn
D
1.1 were obtained. On the basis of the permissible range for
f
and the measurement error for
0
D
3:3k
B
T;
Mg
D
3:0k
B
T;
and
Zn
D
3:4k
B
T
,
f
Zn
can be regarded to be 1.0, meaning that the
addition of zinc does not affect
. Although the difference between the measured
and that obtained in a pure solution was somewhat larger than the measurement
error for magnesium, it is difficult to determine conclusively whether this difference
alone affects
. Therefore, the rate of reduction in the growth rate and the rate of
change in
in
the presence of magnesium. The result led to the conclusion that, in the case of
magnesium, the difference between the
ˇ
were carefully estimated against various combinations of
f
and
ı
values is not significant.
Therefore, while zinc and magnesium reduce the face growth rate by reducing
the step velocity of the formed two-dimensional nucleus, it is thought that they do
