Page 24 - Modern physical chemistry

1.11 Stability Conditions

~---p---~
I I I I I I

Q-7--~-:--9 I
II O-LL~ I-l.-O
~J..TI-O-I-/+¥ I II

I ~i-,-k~-l.~ I
I I I I IY A I I I I
11 I ~ i<~I-d.-:ir T" ~
V"l7-~'1 -U I I

: 6--,-~--}-d OisNa+
I I I I I I ~ (1-
is
~---6---~ FIGURE 1.11 Unit cube from
an NaCl crystal.

as a scatterer. The X rays then react primarily to the face-cantered cubic lattice on which
the anions are located. In KCI, on the other hand, the cation and the anion are isoelec-
tronic. The X rays are scattered strongly by both and each K+ is seen as a CI-, each CI-
as a K+. Although the K+ and CI- ions are arranged as the cations and anions are in NaCI,
the crystal appears to be simple cubic.
The NaCllattice has been found in other alkali halides except CsCI, CsBr, and Csl.
In each of these cesium halide crystals, the center of a unit cube is occupied by one of
the ions and the comers by the other, as figure 1.12 shows. The center may be associ-
ated with anyone of the comers by convention to form the basis, the point lattice being
simple cubic.
In the zinc blende form for ZnS, one species of ion forms a face-cantered cubic lattice,
while the other species appears at the centers of alternate cubelets, as figure 1.13 illus-
trates. Four anions are arranged tetrahedrally around each cation; four cations are
arranged tetrahedrally about each anion. The same configuration exists in the diamond
crystal, with all particles carbon atoms.
The wurtzite form for ZnS also employs tetrahedral arrangements about each ion.
However, the longer range order is hexagonal, as figure 1.14 shows.
In graphite, the carbon atoms are bound covalently in condensed benzene-ring layers.
Each layer is offset with respect to its neighbors as figure 1.15 indicates; the net result
is a hexagonal lattice. The fourth valence electron of each carbon atom is delocalized
over its layer and to a slight extent from layer to layer. As a consequence, the bonding
between layers is very weak, compared to that within a layer.

1. 11 Stability Conditions

The atoms, molecules, oppositely charged ions, or cations and valence electrons of
a substance attract each other. The resulting interaction causes the material to condense
and freeze if the temperature is low enough and the pressure adequate.
The consequent array tends to be most stable when it is as compact as properties of
the constituent particles allow. When the particles are equivalent and spherically sym-
metric, they pack as marbles do. Six units then surround a given one in a plane, while
three contact it from above and three from below. If the centers of the three upper ones
lie over the centers of those below, the arrangement is a hexagonal close-packed one; if