Solutions to exercises
39
Solution 1.9 – Crystallographic and thermodynamic study
of thorium dioxide ThO 2
A – Crystallographic study
1. The ideal crystalline structure for ThO 2 is shown in figure 7 (a) in perspective
and (b) in standard [001] projection.
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ò
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ò
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Figure 7 – Representation of the ideal structure of ThO 2
(a) in perspective and (b) in standard [001] projection.
For compact stacking, the Th
4+
ions are joined along a face diagonal (fig. 8),
which gives (with a the lattice parameter of ThO 2 ):
r
a
and a
r
4
2
2
4
Th
Th
4
4
=
=
#
+
+
.
a
2
4 1 02
#
=
.
a
A
2 885
=
c
Figure 8 – Representation
of the cationic sub-lattice
of ThO 2 for the case of compact
stacking of Th
4+
ions.
Under these conditions, does the face-centered-cubic lattice provide sufficient
space for the O
2−
ions to occupy the tetrahedral sites?
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