Environmental Engineering Reference
In-Depth Information
[189], it is found that
H
′
v
/
H
v
is nearly a constant (≈ 1.09) for transition metals. Thus,
c
5
=
c
5
′
H
′
v
/
H
v
= 0.174 × 10
-8
mol
1/3
where
c
5
′ = 0.16 × 10
-8
mol
1/3
as determined [171,176]. In
contrary to Eq. (5.1), which is considered to be only suitable for transition metals
[171,176,189], both transition and non-transition metals are involved in figure 7. This
improvement is only induced by the substitute of
H
′
v
by
H
v
(
T
m
).
H
v
(
T
m
) describes the atom
bonding of stable liquid and can be exactly measured while
H
′
v
can be obtained only by
extension of experimental results. In addition, since the difference between 0 K and
T
m
for
transition metals are larger than that for non-transition metals, which leads to larger difference
between
H
v
(
T
m
) and
H
′
v
for transition metals than for non-transition metals. This results in
smaller suitability range of Eq. (5.1) than that of Eq. (5.8).
In terms of Eq. (5.6-a), the introduction of
S
drops the value of γ
lv0
(
T
). At
T
m
, the
decreasing extents range from 8% (for La and Ce) to 20% (for Mg and Sr).
Determination of
γ′
lv0
(T
m
) Values
Table 13 also shows the comparison between γ′
lv0
(
T
m
) values of Eq. (5.7) and the
available experimental or estimated results γ′
e
lv0
(
T
m
) [171,178,189-190]. A good agreement is
also shown, which indicates that Eq. (5.7) provides a satisfactory description for γ′
lv0
(
T
m
).
Eq. (5.7) at
T
=
T
m
can be written as,
-γ′
lv0
(
T
m
) = (
p
-2
q
/3)γ
lv0
(
T
m
)/
T
m
.
(5.10)
In terms of the expressions for
c
and
p
,
p
=
m
′/(
c
λ
N
a
1/3
) ≈ 0.19. Taking the mean value of
-0.17 for
q
= (
d
ρ
L
/
dT
)[
T
m
/ρ
L
(
T
m
)], there is the slope β =
p
-2
q
/3 ≈ 0.30.
The relation between -γ′
lv0
(
T
m
) and γ
lv0
(
T
m
)/
T
m
for the Fourth, Fifth and Sixth periods are
plotted in figure 8 in terms of Eq. (5.10) with the given slope β = 0.30 where -γ′
lv0
(
T
m
)
functions increase almost linearly with increasing γ
lv0
(
T
m
)/
T
m
for the A family metals in the
same period and the sequence is nearly the same as that in the Periodic table of the Elements
although some deviations appears. It is understandable since their outmost electric
configurations of
s
+
d
electrons undergo nearly the same situation from the leftmost (IA
metals) of one to the rightmost (VIIIA metals) of ten in these periods. The exceptions can be
discussed as follows: (i) In the Fourth Period (from K to Ni), the anomalies of Mn and Cr are
present where their 3
d
orbital is half-filled; (ii) Similarly, the appearance of the full 4
d
orbital
also results in the anomaly of Pd of the Fifth Period (from Rb to Pd). On the contrary, the
occurrence of half full 4
d
orbital in Mo does not change the sequence; half full 5
d
orbital of
Re in the Sixth Period (from Cs to Pt) also does not change it. These may be explained as the
following: In terms of Hund′s rule, the half and the full fillings of orbital usually lead to the
drop of the system energy and the effect of full filling is more effective. For example, the
H
v
values of Cr and Mn are evidently smaller than the neighbor elements V and Fe as shown in
table 13. It is also applicable to Pd in comparison with Rh (Ag is not involved because it is B
family metal). While the increase of electronic shell decreases the effect of electric
configuration, the
H
v
value of Mo (Re) is thus in between those of Nb (W) and Tc (Os). Since
γ
lv
(
T
m
) is proportional to the total energetic level of the system
H
v
in terms of Eq. (5.7), the
abnormity only happens in Cr, Mn and Pd.
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