Chemistry Reference
In-Depth Information
The Niggli symbol is limited to the coordination number of the surrounding
oppositely charged ions (6/6) and the type of infinite structure (G for German
“Gitter”
lattice). Another possibility for shortening the structure symbol is the
indication of the types of ions in curly brackets (see Fig.
10.20
): the brackets
symbolize the solid salt, the “G” (German “Gitter”) the three-dimensional structure.
The result of rigorous shortening is the symbol with the least information: the
stoichiometric symbol NaCl. Since teachers mostly work with stoichiometric
symbols, and since these even suggest an abbreviation of the substance name, the
learner cannot build up any mental model of the structure at all. The consequences
are often misconceptions concerning salt structures [
4
]: NaCl molecules, NaCl
formula units, etc.
The ratio of two different types of ions can be determined in three different
ways:
¼
1. A closest sphere packing of spheres shows two types of gaps: the octahedron
gaps (OG) and the smaller tetrahedron gaps (TG). The ratio of their numbers is:
spheres:OG:TG
1:1:2. The fraction of occupied octahedral or tetrahedral gaps
defines the ion ratio (see Table
10.4
).
2. The ratio of ions can be counted directly on an appropriate segment of the
packing of spheres, but not on the usual elementary NaCl cube: it has a ratio
of 14:13. If another layer is added to the cube, the ratio is 18:18. Only experts are
able to determine those segments.
3. The unit cell is the smallest unit of an infinite crystal structure that forms the
whole lattice by translation in all three directions in space. It does not only show
all lattice symmetries but also the ion ratio. The NaCl unit cell shows the ratio
4:4 or shortened to 1:1 (see Fig.
10.21
).
¼
The examples NaCl and ZnS show that different structures can occur with
the same ion ratio (see Fig.
10.21
) - so it is necessary to not only take the formulae
Na
+
Ions:
Li
+
Ions:
Zn
2+
Ions:
Cl
-
Ions:
O
2-
Ions:
S
2-
Ions:
12
=3
×
6
×
½ =3
8
×
=8
6
×
½ =3
4
×
=4
6
×
½ =3
1
1
×
=1
8
×
=1
8
×
=1
8
×
=1
8
8
8
Total 4
Total 4
Total 8
Total 4
Total 4
Total 4
{(Li
+
)
8
(O
2-
)
4
}
{(Na
+
)
4
(Cl
-
)
4
}
{(Zn
2+
)
4
(S
2-
)
4
}
Zn
4
S
4
, Zns
Na
4
Cl
4
, NaCl
Li
8
O
4
, Li
2
O
Fig. 10.21 Derivation of chemical symbols for ionic structures from unit cells
