Course notes
9
positive, negative, or neutral. The symbols used for the sign of the charge are
given in table 1.
Table 1 – Symbols used to indicate sign of effective charge.
Sign
> 0
= 0
< 0
Symbol
•
#
′
For example, let us write the structure element for a cation vacancy M
+
in MX.
The corresponding site is a M site, the effective charge is Q e = 0 − 1 = − 1, and
the structure element is V ′
M . The structure element for the impurity D
2+
that is
substituted for M
+
in MX is denoted D
•
M .
We find
2 normal structure elements that describe the perfect crystal (i.e., M
#
M and
X
#
X ) and
2 structure defects (or point defects) that encompass all the other structure
elements in the real crystal and that coexist with the normal structure elements.
1.2 – Reactions and equilibria
1.2.1 – Atomic disorder and electronic disorder
For thermodynamic reasons, atomic-defect pairs, which are qualified as intrinsic
disorder, are the dominant type of disorder in ionic crystals. We typically identify
2 Schottky disorder, which is characterized by the formation of cationic and
anionic vacancies. In MX, this is the pair V ′
M + V
•
X .
2 Frenkel disorder, which is
• Cationic when it involves the formation of cationic vacancies and interstitial cations. In MX, an example of this is the pair V ′
M + M
•
i .
• Anionic disorder when anionic vacancies and interstitial anions appear. In MX, an example of this is the pair V
•
X + X ′
i .
Each of these types of disorder gives rise to a chemical equilibrium involving
the defects with an equilibrium constant K.
Moreover, ionic crystals always contain intrinsic electronic disorder, which
involves the equilibrium in the crystal between free electrons e ′ and holes h
•
.
9
positive, negative, or neutral. The symbols used for the sign of the charge are
given in table 1.
Table 1 – Symbols used to indicate sign of effective charge.
Sign
> 0
= 0
< 0
Symbol
•
#
′
For example, let us write the structure element for a cation vacancy M
+
in MX.
The corresponding site is a M site, the effective charge is Q e = 0 − 1 = − 1, and
the structure element is V ′
M . The structure element for the impurity D
2+
that is
substituted for M
+
in MX is denoted D
•
M .
We find
2 normal structure elements that describe the perfect crystal (i.e., M
#
M and
X
#
X ) and
2 structure defects (or point defects) that encompass all the other structure
elements in the real crystal and that coexist with the normal structure elements.
1.2 – Reactions and equilibria
1.2.1 – Atomic disorder and electronic disorder
For thermodynamic reasons, atomic-defect pairs, which are qualified as intrinsic
disorder, are the dominant type of disorder in ionic crystals. We typically identify
2 Schottky disorder, which is characterized by the formation of cationic and
anionic vacancies. In MX, this is the pair V ′
M + V
•
X .
2 Frenkel disorder, which is
• Cationic when it involves the formation of cationic vacancies and interstitial cations. In MX, an example of this is the pair V ′
M + M
•
i .
• Anionic disorder when anionic vacancies and interstitial anions appear. In MX, an example of this is the pair V
•
X + X ′
i .
Each of these types of disorder gives rise to a chemical equilibrium involving
the defects with an equilibrium constant K.
Moreover, ionic crystals always contain intrinsic electronic disorder, which
involves the equilibrium in the crystal between free electrons e ′ and holes h
•
.