Exercises
Exercise 1.1 – Notation for structure elements and structure defects
1. Give the expression that relates the effective charge Q e of a structure element
or structure defect to the real charge Q r of the ionic species occupying a site
and to the charge Q n of the species that normally occupies the site.
2. Use Kröger-Vink notation to express:
a. a sodium vacancy in NaCl,
b. a fluorine anion in its normal position in CaF 2 ,
c. a bromine vacancy in NaBr,
d. a magnesium cation in its normal position in MgO,
e. an interstitial silver cation in AgBr,
f. an oxygen vacancy in TiO 2 ,
g. an oxygen vacancy that has trapped an electron in ZrO 2 ,
h. an interstitial oxide ion that has trapped two holes.
Give the values of Q e , Q r , and Q n .
3. Use Kröger-Vink notation to express the structure defect that corresponds to:
a. a Na
+
cation substituted for Mg
2+
in MgO,
b. an oxide ion O
2−
substituted for F
−
in SrF 2 ,
c. a Al
3+
ion in an interstitial position in CaO,
d. a Gd
3+
ion substituted for Ce
4+
in CeO 2 .
Give the values for Q e , Q r , and Q n .
4. Use Kröger-Vink notation to express the following associated defect pairs:
a. a Gd
3+
ion in a substitution position in CeO 2 and an oxygen vacancy,
b. a chlorine vacancy and a sodium vacancy in NaCl.
Give the values of Q e , Q r , and Q n .