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
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