Environmental Engineering Reference
In-Depth Information
γ
lv0
(
T
m
) values of
sp
metals except that of Be are smaller than those of
d
metals due to the
bond nature of
s
and
p
electrons, which are more mobile than the localized
d
electrons.
Moreover, in contrast to the transition metals, γ
lv0
(
T
m
) values of
sp
metals decrease along an
isoelectronic row. This arises because the outmost
n
′
s
electrons (the number of period
n
′ = 2-
6) are progressively bound more loosely as they are screened from the nucleus by the
increasing number of filled inner shells in the ionic core.
To find the similarity between Eq. (5.6-a) and Eq. (5.1), the prefactor
c
5
′ in Eq. (5.1) can
be determined by rearranging Eq. (5.6-a) at
T
=
T
m
[181],
γ
lv0
(
T
m
) =
c
5
H
v
/
V
m
2/3
(5.8)
with
c
5
= (
m
′-
T
m
S
/
H
v
)/(λ
N
a
1/3
).
(5.9)
Eq. (5.9) has determined
c
5
′ value in Eq. (5.1) although Eq. (5.8) differs from Eq. (5.1) a
little due to the difference of
H
v
and
H
v
′, or
c
5
=
c
5
′
H
′
v
/
H
v
.
3.2
Re
W
Os
Ru
2.4
Ir
Ta
Tc
Nb
Rh
Mo
Pt
V
Ni
Zr
Na,Ba,Sr
Co
Hf
1.6
Be
Pd
Fe
U
Cr
Ti
Au
Cu
Ag
Mn
Al
Th
Y
Ce
0.8
Sc&La
Nd
G
Pr
Tl,Li,Pb,Zn
Ca
Mg
Cd
Cs,Rb,K
0.0
0.00E+000
6.00E+008
1.20E+009
1.80E+009
H
v
/
V
2/3
(J/m
2
)
Figure 7. The plot of γ
lv0
(
T
m
) against
H
v
/
V
2/3
for liquid metals in terms of Eq. (5.8) where the solid line
is linearly regressed.
Figure 7 gives a plot of γ
lv0
(
T
m
) against
H
v
/
V
2/3
for considered liquid metals in terms of
Eq. (5.8) with a linearly regressed slope of
c
5
= 0.174 × 10
-8
mol
1/3
where the correlation
coefficient of the fit
is 0.998. All elements can thus be estimated by the same
c
5
value, which
implies that
T
m
/
H
v
is almost a constant (since
S
value has been taken as a constant according
to Lindemann′s criterion,
m
′ ≈ 0.19 and λ ≈ 1.08) in terms of Eq. (5.9), which also confirms
the correctness of Eq. (5.8). It is known that
H
v
∝
H
m
[176], and
T
m
/
H
m
= 1/
S
m
where
H
m
and
S
m
are the melting enthalpy and melting entropy. Since
S
m
is almost a constant for metallic
elements,
c
value as a constant is reasonable. In terms of the
H
′
v
data listed in table 1 of Ref.
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