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value is expected since when the atomic distance is larger than
h
, the bond energy decreases
dramatically. Thus, Eq. (4.9) can be rewritten as [162],
γ
lv
(
D
)/γ
lv0
≈ γ
sv
(
D
)/γ
sv0
≈ 1-4
h
/
D
.
(4.14)
2.0
Be (0001)
1.5
1.0
Al (110)
Mg (0001)
0.5
Na (110)
0.0
0.0
0.1
0.2
0.3
0.4
0.5
1/
D
(nm
-1
)
Figure 5. γ
sv
(
D
) as a function of 1/
D
in terms of Eq. (4.12) (solid lines) and Eq. (4.14) (segment lines)
for nanocrystals Be, Mg, Na and Al with different facets. The symbols ■, ▲ and ● denote the
experimental results for Be and Mg (0001) [163], the theoretical values for Na (110) [164] and Al (110)
[165]. Note that the experiments on γ
sv
(
D
) and crystal equilibrium shapes with certain facets were
performed at
T
≈
T
m
. The equilibrium shape of a crystal follows Wulff construction [167].
1.8
Au (110)
Au (100)
1.2
Au (111)
0.6
0.0
0.1
0.2
0.3
1/
D
(nm
-1
)
Figure 6. γ
sv
(
D
) as a function of 1/
D
for nanocrystals Au with different facets in terms of Eq. (4.12)
(solid lines) and Eq. (4.14) (segment lines). The symbols ■, ▲and ● denote the calculated results for
(111), (100) and (110) facets in terms of a modified embedded-atom-method potential, respectively
[166].
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