5.1 Basic Considerations 81
Figure 5.1 Combination of prisms with different surface energy. To minimize surface energy,
combinations of two prisms will occur in the way as indicated as (a) and (d). The two other
combinations (b) and (c) lead to higher surface energy; therefore, they do not occur.
a
c
a
c
γ γ
>
a
c
γ γ
<
(a)
(b)
(c)
(d)
a
Box 5.2 Formation of Rods and Plates
The configuration (a) shown in Figure 5.1 has a surface energy of
u
ac
a
a
c
surf A
− =
+
8
2
2
γ
γ
(5.3)
and the arrangement indicated as (b)
u
ac
a
a
c
surf B
− =
+
6
4
2
γ
γ .
(5.4)
Comparing formulae (5.3) and (5.4) and keeping in mind a < c one can compare
the surface energies of the arrangements (a) and (b); this leads to
8
2
6
4
1
2
2
γ
γ
γ
γ
γ
γ
a
c
a
c
a
c
ac
a
ac
a
c
a
+
<
+
⇒
<
or
γ
γ
a
c
a
c
< .
(5.5a)
Equation (5.5a) is equivalent to Eq. (5.2). For the configurations (c) and (d) one
obtains analogously:
γ
γ
a
c
a
c
> .
(5.5b)
Agglomeration of particles of a compound fulfilling condition (5.5a) will grow
as rods, those fulfilling the condition (5.5b) as platelets.