Environmental Engineering Reference
In-Depth Information
In a similar way,
Z
(h k l)
for any surface of a bcc structure is determined with the
consideration of the next-nearest
CN
[140],
Z
(h k l)
= 2
h
+(
h
+
k
+
l
) for
h
+
k
+
l
being even
(4.7-a)
Z
(h k l)
= 4
h
+2(
h+k
+
l
) for
h
+
k
+
l
being odd and
h
-
k
-
l
≥ 0
(4.7-b)
Z
(h k l)
= 2(
h+k
+
l
)+2(
h+k
+
l
) for
h
+
k
+
l
being odd and -
h+k
+
l
> 0
(4.7-c)
where the 2
nd
item of the right-hand side of Eq. (4.7) denotes the broken bond number of the
next-nearest neighbors.
For sc crystals,
Z
(h k l)
values of the nearest and the next-nearest atoms are 1 and 4 for
(100) surface as well as 2 and 5 for (110) surface, respectively. For diamond structure
crystals,
Z
(h k l)
values of the nearest and the next-nearest atoms are 1 and 6 for (110) surface.
For several surfaces of a hcp structure,
Z
(h k i l)
is obtained by [141],
Z
(h k i l)
= 4(
h+k
)+3
l
for (0001)
(4.8-a)
Z
(h k i l)
= 4(
h+k
)+(8
h
+4
k
)/3 for (10
1
0)
(4.8-b)
where the 1
st
item of the right-hand side of Eq. (4.8) denotes the average number of basal
broken bonds while the 2
nd
item is that of non-basal broken bonds.
Table 8.
A
S
, Z
S
and Z
B
values for different surfaces
and structures where a and c are lattice constants
Structure
Surface
A
S
Z
S
Z
B
3
1/2
a
2
/4
a
2
/2
2
1/2
a
2
/2
Fcc
(111)
(100)
(110)
9
8
6
12
12
12
2
1/2
a
2
/2
a
2
3
1/2
a
2
Z
S
= 6,
Z
′
S
= 4
Z
S
= 4,
Z
′
S
= 4
Z
S
= 2,
Z
′
S
= 0
Z
B
= 8,
Z
′
B
= 6
Z
B
= 8,
Z
′
B
= 6
Z
B
= 8,
Z
′
B
= 6
Bcc
(110)
(100)
(111)
3
1/2
a
2
/2
(8/3)
1/2
a
2
Hcp
(0001)
(10
−
9
16/3
12
12
1
0)
2
1/2
a
2
/4
Z
S
= 3,
Z
′
S
= 6
Z
B
= 4,
Z
′
B
= 12
Diamond
(110)
a
2
2
1/2
a
2
SC
(100)
(110)
Z
S
= 5,
Z
′
S
= 8
Z
S
= 4,
Z
′
S
= 7
Z
B
= 6,
Z
′
B
= 12
Z
B
= 6,
Z
′
B
= 12
For bcc, the
CN
of surface and bulk metals are divided into the nearest and the next-nearest bonds.
CN
is
determined by Eqs. (4.6) to (4.8). For hcp metals, an ideal
c/a
ratio (1.633) is assumed.
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