Environmental Engineering Reference
In-Depth Information
Determination of
γ
lv0
(T
m
) Values
Table 13 gives the comparison between the predicted γ
lv0
(
T
m
) values for 48 liquid metals
in terms of Eq. (5.6-a) and the corresponding available mean values of experimental results
γ
e
lv0
(
T
m
) [171,178,189]. These experimental data are mainly obtained by the maximum bubble
pressure technique for low-melting-point oxidizable metals like Na, the sessile drop technique
for moderate-melting-point metals like Cu, and the drop weight technique employed at the
extremity of a pendant wire with electron bombardment heating for refractory metals like W
[178].
It is found that φ = |γ
lv0
(
T
m
)-γ
e
lv0
(
T
m
)|/γ
e
lv0
(
T
m
) for 40 elements from Cu to Ba (see table
13) is smaller than 10%. Note that although γ
e
lv0
(
T
m
) = 867 mJ/m
2
was proposed for Al [171],
several measurements suggested that the most data for γ
e
lv0
(
T
m
) of Al pertain to oxygen-
saturated material and that for pure Al could be about 1070 mJ/m
2
[187,192]. If this result is
taken, φ for Al will only be 3.6%. For the divalent metals Mg, Zn and Cd, the predictions are
evidently smaller than γ
e
lv0
(
T
m
). According to Miedema and Boom [189], these three metals
have exceptionally stable free atomic configuration, which is close to that of rare gas. Thus,
smaller γ
lv0
(
T
m
) values in terms of Eq. (5.6-a) may be reasonable. Although φ values of Ta,
Nb, Li, Be, and La range from 13% to 22%, the causes are unknown.
The above data imply that Eq. (5.6-a) is suitable not only for transition metals, but for all
metals although the deviations from transition metals are slightly larger than those for other
metals.
γ
lv0
(
T
m
) values of transition metals increase along an isoelectronic row where a heavier
element has a larger γ
lv0
(
T
m
) value. This is because the
d
level of a heavier element is higher
in energy and the corresponding
d
wave functions with stronger bonding are more extended.
Two exceptions are Pd and Zr. For Pd, the full-filled
d
orbital drops the system energy in
terms of Hund′s rule, which makes that its
H
v
value only approaches that of Ni. Since
V
m
and
T
m
values of Pd are obviously larger than those of Ni, γ
lv0
(
T
m
) of Pd is thus smaller than that
of Ni in terms of Eq. (5.6-a); For Zr, its
H
v
and
V
m
values approach those of Hf while its
T
m
value is obviously smaller than that of Hf, γ
lv0
(
T
m
) of Zr is thus larger than that of Hf in terms
of Eq. (5.6-a). The reason of larger
H
v
value of Zr is unclear.
Table 13. Comparisons of
γ
lv0
for liquid metals between
γ
lv0
(T
m
) of Eq. (5.6-a) and the
experimental results
γ
e
lv0
(T
m
) [171,178,189], as well as
comparisons of
γ′
lv0
between
γ′
lv0
(T
m
) of Eq. (5.7) and the corresponding experimental
or estimated results
γ′
e
lv0
(T
m
) [171,178,189-190]
γ
lv0
(
T
m
)
γ
e
lv0
(
T
m
)
-
γ′
lv0
(
T
m
)
γ′
e
lv0
(
T
m
)
H
v
(kJ/g-atom)
T
m
(K)
ρ
L
(kg/m
3
)
d
ρ
L
/d
T
(kg/m
3
-K)
(mJ/m
2
)
(mJ/m
2
-K)
Cu
*
1352
1355, 1310
0.21
0.19, 0.23
300
1358
8000
-0.801
Ag
*
925
910, 925
0.18
0.17, 0.21
255
1234
9346
-0.907
Au
*
1211
1138, 1145
0.18
0.19, 0.20
330
1338
17360
-1.500
Ni
*
1810
1838, 1796
0.33
0.42, 0.35
378
1728
7905
-1.160
Pd
1467
1475, 1482
0.25
0.28, 0.28
380
1828
10490
-1.266
Pt
*
1896
1746, 1860
0.31
0.29, 0.31
490
2045
19000
-2.900
Co
*
1779
1830, 1881
0.30
0.37, 0.34
375
1768
7760
-0.988
Search WWH ::
Custom Search