Environmental Engineering Reference
In-Depth Information
Note that Tc and the lanthanide elements are not involved in figure 8 because γ′
lv0
(
T
m
)
value of Tc is absent while those of the lanthanide elements are abnormally small possibly
due to the effect of
f
electrons on γ′
lv0
(
T
m
) value. Since the
s
+
d
electrons of most lanthanide
elements remain constant, their γ′
lv
(
T
m
) values hardly change as shown in table 13, and the
corresponding β values thus approach zero. In other words,
f
electrons hardly work as valence
electrons.
When elements with empty or full filled electrons of second outmost sub-shell are
considered, only the outermost electron layer (
s
electron layer) is valence electrons, two
groups of elements exist, namely
s
= 1 (IA and IB metals) and
s
= 2 (IIA and IIB metals).
There still exists a linear correlation between γ′
lv0
(
T
m
) and γ
lv0
(
T
m
)/
T
m
as shown in figure 9.
When figure 8 and figure 9 are compared, the β value of metals in groups IIA an IIB with
s
=
2 is similar to that of Eq. (5.10). However, the β value of metals in groups IA an IB with
s
= 1
is 30% smaller than that when the period number
n
′ remains constant.
Fe
(a)
Ti
Ni
Mn
Co
2
V
Ca
Cr
Sc
K
0
Ru
(b)
Pd
Nb
Rh
2
Mo
Zr
Sr
Y
Rb
0
(c)
Pt
W
Os
Ta
2
Ir
Re
Hf
Ba
Cs
0
0
4
8
12
γ
lv
(
T
m
)/
T
m
(
×
10
-4
J/m
2
-K)
Figure 8. -γ′
lv0
(
T
m
) as a function of γ
lv0
(
T
m
)/
T
m
for (a) the fourth (7), (b) the fifth (∀) and (c) the sixth
(Β) periods A family metals where the solid lines are determined by Eq. (5.10).
As shown in figures 8 and 9, all elements with the sub-shell of (
n
′-1)
d
are located on the
right of the figure while all elements with the sub-shell of (
n
′-1)
p
are found on the left of the
figure. When the sub-shell is (
n
′-1)
s
, the elements are located in the middle or right of the
figure. In addition, as
n
′ increases, -γ′
lv0
(
T
m
) values decreases linearly. Thus, the electron
orbital movements and valence electron contributions of sub-shells are different for different
orbitals and different
n
values as temperature increases. From thermodynamic point of view,
the difference of β between figure 9a and figure 8 is induced by different
p
values in Eq.
(5.10) since the corresponding
H
v
/
T
m
value is systematically larger than that of the transition
metals.
Search WWH ::
Custom Search