Solutions to exercises
Solution 1.1 – Notation for structure elements and structure
defects
1. The following expression relates the effective charge Q e of a structure element or defect to the real charge Q r of the ionic species that occupies a site
and to the charge Q n of the species that normally occupies the site:
Q
Q Q
e
r
n
=
−
2. Listed below are the structure elements and defects written in the KrögerVink notation and with the values given for Q e , Q r , and Q n :
Structure elements
Q r Q n Q e Notation
a. Sodium vacancy in NaCl
0 + 1 − 1
V ′
Na
b. Fluoride (F
–
) in normal position in CaF 2
− 1 − 1
0
F
#
F
c. Bromine vacancy in NaBr
0 − 1 + 1
V
•
Br
d. Magnesium cation (Mg
2+
)
in normal position in MgO
+ 2 + 2
0 Mg
#
Mg
e. Interstitial silver cation (Ag
+
) in AgBr
+ 1
0 + 1
Ag
•
i
f. Oxygen vacancy in TiO 2
0 − 2 + 2
V
••
O
g. Oxygen vacancy with one trapped electron
in ZrO 2
− 1 − 2 + 1
V
•
O
h. Interstitial oxide ion with two trapped
electron holes
0
0
0
O
#
i
3. Listed below are the structure elements and defects written in the KrögerVink notation and with the values given for Q e , Q r , and Q n :
Structure elements
Q r Q n Q e Notation
a. Na
+
cation in substitution position
of Mg
2+
in MgO
+ 1 + 2 − 1 Na ′
Mg
b. Oxide ion O
2–
in substitution position
of F
–
in SrF 2
− 2 − 1 − 1
O ′
F
c. Al
3+
ion in interstitial position in CaO
+ 3
0 + 3
Al
3•
i
d. Gd
3+
ion in substitution position in CeO 2 + 3 + 4 − 1
Gd ′
Ce