Chapter 1
Description of ionic crystals
Course notes
1.1 – Definitions
1.1.1 – The perfect crystal
The notion of the perfect crystal is based on the results of crystallography. This
discipline describes a solid by giving, in particular, the precise location of points
in space (called lattice sites) occupied by the chemical species of the crystal. To
illustrate this notion, consider the example of an ionic crystal described by the
formula MX (M
+
, X
−
). The perfect MX crystal consists of a lattice of normal
sites that are occupied, between which are unoccupied interstitial sites. We
distinguish between the normal cationic sites, all occupied by the species M
+
,
and the normal anionic sites, all occupied by the species X
−
. Figure 1(a) shows
a schematic two-dimensional representation of a perfect MX crystal. Note that
this pure stoichiometric composition does not exist, although we can approach
it near 0 K with extremely pure material.
1.1.2 – The real crystal
For a real crystal, we consider thermal motion and the presence of foreign
elements. Thermal motion is responsible for the formation of defects, which
results from the displacement of the original chemical elements [see fig. 1(b)].
For a pure real crystal, we normally identify M
+
and X
−
vacancies, which are
denoted V M and V X , respectively, interstitial species, denoted M i
+
and X i
−
,
and antistructure defects M X
+
and X M
−
, which are extremely unlikely to form
© Springer Nature Switzerland AG 2020
A. Hammou and S. Georges, Solid-State Electrochemistry,
https://doi.org/10.1007/978-3-030-39659-6_1
7
Description of ionic crystals
Course notes
1.1 – Definitions
1.1.1 – The perfect crystal
The notion of the perfect crystal is based on the results of crystallography. This
discipline describes a solid by giving, in particular, the precise location of points
in space (called lattice sites) occupied by the chemical species of the crystal. To
illustrate this notion, consider the example of an ionic crystal described by the
formula MX (M
+
, X
−
). The perfect MX crystal consists of a lattice of normal
sites that are occupied, between which are unoccupied interstitial sites. We
distinguish between the normal cationic sites, all occupied by the species M
+
,
and the normal anionic sites, all occupied by the species X
−
. Figure 1(a) shows
a schematic two-dimensional representation of a perfect MX crystal. Note that
this pure stoichiometric composition does not exist, although we can approach
it near 0 K with extremely pure material.
1.1.2 – The real crystal
For a real crystal, we consider thermal motion and the presence of foreign
elements. Thermal motion is responsible for the formation of defects, which
results from the displacement of the original chemical elements [see fig. 1(b)].
For a pure real crystal, we normally identify M
+
and X
−
vacancies, which are
denoted V M and V X , respectively, interstitial species, denoted M i
+
and X i
−
,
and antistructure defects M X
+
and X M
−
, which are extremely unlikely to form
© Springer Nature Switzerland AG 2020
A. Hammou and S. Georges, Solid-State Electrochemistry,
https://doi.org/10.1007/978-3-030-39659-6_1
7