Environmental Engineering Reference
In-Depth Information
(a)
Au
Cu
Ag
1.5
Li
K
Na
Cs
β
= 0.20
Rb
0.0
(b)
Be
2
Zn
Mg
Cd
Sr
β
= 0.29
Ca
Ba
0
0
4
8
12
γ
lv
(
T
m
)/
T
m
(
×
10
-4
J/m
2
-K)
Figure 9. -
γ′
lv0
(
T
m
) as a function of
γ
lv0
(
T
m
)/
T
m
for (a) IA and IB (
,
) as well as (b) IIA and IIB (
8
) metals.
Noted that γ
lv
(
T
m
) = 359, 466, 305 mJ/m
2
for Mg, Zn and Cd based on Eq. (5.6-a) are
employed in plotting figures 7 and 9, the existences of these linear correlations imply that
these calculated values may be reasonable.
In terms of Eq. (5.7), the contribution of
S
on γ′
lv0
(
T
m
) value ranges from 36% (for metals
like Nb and Pt with larger γ
lv0
values) to 78% (for metals like Cd, Li and Sr with smaller γ
lv0
values). Neither
S
nor dρ
L
/d
T
is thus negligible.
Estimation of
γ
lv0
(T) and
γ′
lv0
(T) Functions
Figure 10a shows the comparison of γ
lv0
(
T
)/γ
lv0
(
T
m
) between the predictions of Eq. (5.6-
b), Eq. (5.3) and the available experimental results for transition metals Ni, Co, Re and W
with good agreement [168,193-195]. The experimental data for liquid Ni, Co, Re and W in
the temperature ranges of 1573~1893, 1541~1943, 2800~3600 and 3360~3700 K respectively
correspond to the undercooling of 155, 227, 659 and 320 K as well as the overheating of 165,
175, 141 and 20 K [168,193-195]. The plots in terms of Eq. (5.3) and Eq. (5.6-b) are nearly
identical for Co, Re and W. Although it seems that the difference between Eq. (5.3) and Eq.
(5.6-b) is large for Ni, its actual value is only about 1%. The agreements shown in figure 11a
not only confirm the validities of Eqs. (5.3) and (5.6-b), but also indicate that the linear
correlation between γ
lv0
(
T
) and
T
exists at
T
near
T
m
(including
T
<
T
m
and
T
≥
T
m
), namely,
Eqs. (5.3) and (5.6-b) are also applicable for supercooled liquid metals.
Figure 10b shows the comparisons of γ
lv0
(
T
)/γ
lv0
(
T
m
) between the predictions of Eq. (5.6-
b) and the available experimental results for non-transition metals Na, K, Rb and Cs [196-
197]. It is found that the differences between the predictions and the experimental data are
smaller than 5% where the experimental data encompass the largest temperature range (from
T
m
to 3.5
T
m
) to the best of our knowledge. Here, the approximately linear relation between
γ
lv0
(
T
) and
T
is present again, which implies that Eq. (5.3) is a good approximation of Eq.
(5.6-b).
Search WWH ::
Custom Search