Environmental Engineering Reference
In-Depth Information
The Determination of Nucleus-liquid Interface Energy
γ
sl
(
D
n
,
T
n
)
As above-mentioned, several improved expressions for
g
m
(
T
) function have been
proposed through considering Δ
C
p
function below
T
m
and read as [72-74],
7
H
T
(
T
−
T
)
a
m
,
(2.23-a)
g
(
T
)
=
m
m
T
(
T
+
6
T
)
m
m
2
H
T
(
T
−
T
)
,
(2.23-b)
g
b
m
(
T
)
=
m
m
T
(
T
+
T
)
m
m
H
T
(
T
−
T
)
c
m
(2.23-c)
g
(
T
)
=
m
m
T
2
m
where superscripts of
a
,
b
and
c
stand for metallic elements, ionic crystals and
semiconductors, respectively. Eq. (2.23) predicts a steepest variation near
T
m
, and a much
weaker temperature-dependence near the ideal glass transition temperature or isentropic
temperature
T
k
, which can be determined in terms of the relationship of d
g
m
(
T
)/d
T
= 0 [89].
With these
g
m
(
T
) functions, the respective
H
m
(
T
) functions can also be determined in terms of
H
m
(
T
) =
g
m
(
T
)-
T
d
g
m
(
T
)/d
T
(Helmholtz function),
a
m
2
2
H
(
T
)
=
49
H
T
/(
T
+
6
T
)
,
(2.24-a)
m
m
b
m
2
2
H
(
T
)
=
4
H
T
/(
T
+
T
)
,
(2.24-b)
m
m
c
m
2
H
(
T
)
=
H
(
T
/
T
)
.
(2.24-c)
m
m
Because
g
m
(
T
) determined by Δ
C
p
while Δ
C
′
p
between crystal and glass approaches to
zero when
T
≤
T
k
, the liquid must transform to glass [89]. Thus, Eq. (2.24) is valid only at
T
>
T
k
where
c
k
T
=
. Noted that
T
>
T
k
is
satisfied in undercooling experiments. Combining Eq. (2.13) and Eq. (2.24), the temperature-
dependent γ
sl0
(
T
) functions can be expressed as,
a
k
b
T
/
2
T
=
(
7
−
1
T
/
6
,
T
=
(
2
−
1
T
and
m
m
k
m
2
hH
S
7
T
a
sl
2
γ
(
T
)
=
m
vib
(
)
,
(2.25-a)
0
3
RV
T
+
6
T
m
2
hH
S
2
T
b
sl
2
γ
(
T
)
=
m
vib
(
)
,
(2.25-b)
0
3
RV
T
+
T
m
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