Download Ionic solids 2.9 Characteristic structures of ionic solids

Ionic solids
2.9 Characteristic structures of ionic solids
Geometries of Crystal Lattices (Section 2.9)
There are a few very common crystal structures adopted by large numbers of compounds. A few
of them are shown below. For simple binary compounds which are predominantly ionic, the
structure which is observed can often be predicted based on the stoichiometry (1:1, 1:2, etc.) and
on the relative sizes of the ions. Anions tend to be larger than cations so, in an ideal structure,
there is contact between adjacent anions, while the cations are in contact with the neighbouring
anions, but there is no cation - cation contact.
Structures where the cations is large enough to push apart the anions can occur, but structures
where the cation would be "loose" in their sites are undesirable. Therefore it is possible to
calculate ranges over which a particular structure is likely based on the ratio of cation to anion
radius. This illustrated below for three common 1:1 structures.
Rock Salt (Sodium Chloride) This structure is based on cubic close-packed anions with cations
in all the octahedral holes, that is, the cations a 6-coordinate.
Other structures
The other simple structures described in class are:

Wurtzite - another form of zinc sulphide based on hexagonally close packed sulphide
ions with zinc ions in one half of the tetrahedral holes, just like the zinc blende structure.
The same ideal radius ratio applies.

Flourite and Antifluorite - The fluorite typified by CaF2 structure is based on a facecentred cubic flouride arrangement with calcium ions in all the tetrahedral holes, and the
anifluorite structure typified by K2O has the reverse arrangement.
Rutile - The compound from which the name comes is TiO2. The ion Ti4+ cannot exist in
a truly ionic compound: there will always be significant covalency because the ion would
be very small and highly charged, strongly polarizing the counter anions. The structure is
not based on cubic or hexagonal close packing. The cations are 6-coordinate and the
anions are 3-coordinate.
Perovskite - This is an example of a more complicated structure for compounds of the
form ABX3. The named mineral is CaTiO3. It was used as an example of how to deduce
the formula of an ionic compound from a picture of the unit cell.


2.10 The rationalization of structures
SolidsRationalization of Structures (Section 2.10)
Ionic Radii and the Ideal Radius Ratios
table Bonding Configurations in Ionic solids.
In reality an ideal fit of a cation into the close packed anion arrangement almost never occurs
. Now consider what would be the consequence of placing a cation that is (a) larger than the
ideal, (b) smaller than the ideal, into the cation sites.
Example: The following compounds have similar empirical formulas. Use the radius ratio
rules and the table of ionic radii in the appendix to explain why they have different structures.
(a) NaCl (b) ZnS (c) CsCl
Radius Ratio rules.
The discussion of tetrahedral, octahedral, and cubic holes in the previous section suggests that
the structure of an ionic solid depends on the relative size of the ions that form the solid. The
relative size of these ions is given by the radius ratio, which is the radius of the positive ion
divided by the radius of the negative ion.
The relationship between the coordination number of the positive ions in ionic solids and the
radius ratio of the ions is given in the table below. As the radius ratio increases, the number of
negative ions that can pack around each positive ion increases. When the radius ratio is between
0.225 and 0.414, positive ions tend to pack in tetrahedral holes between planes of negative ions
in a cubic or hexagonal closest-packed structure. When the radius ratio is between 0.414 and
0.732, the positive ions tend to pack in octahedral holes between planes of negative ions in a
closest-packed structure.
Radius Ratio Rules
Radius
Ratio
Coordination Holes in Which
Number
Positive Ions Pack
0.225 - 0.414
4
tetrahedral holes
0.414 - 0.732
6
octahedral holes
0.732 - 1
8
cubic holes
1
12
closest-packed structure
The table above suggests that tetrahedral holes aren't used until the positive ion is large enough
to touch all four of the negative ions that form this hole. As the radius ratio increases from 0.225
to 0.414, the positive ion distorts the structure of the negative ions toward a structure that purists
might describe as closely-packed.
As soon as the positive ion is large enough to touch all six negative ions in an octahedral hole,
the positive ions start to pack in octahedral holes. These holes are used until the positive ion is so
large that it can't fit into even a distorted octahedral hole.
Eventually a point is reached at which the positive ion can no longer fit into either the tetrahedral
or octahedral holes in a closest-packed crystal. When the radius ratio is between about 0.732 and
1, ionic solids tend to crystallize in a simple cubic array of negative ions with positive ions
occupying some or all of the cubic holes between these planes. When the radius ratio is about 1,
the positive ions can be incorporated directly into the positions of the closest-packed structure.
Coordination numbers for cations and anions are the same when there are equal numbers of
ions
e.g. NaCl.
MX : Rock-salt (NaCl) r+ / r- = 0.52 Octahedral, 6 Coordination
The relative sizes of the anions and cations required for a perfect fit of the cation into the
octahedral sites in a close packed anion array can be determined by simple geometry:The basic
premise for making predictions is that it is acceptable if the smaller ion (usually the cation) is too
big for the hole in the close packed array of larger ions (usually the anions) so that the anions are
forced apart. However, the smaller ion must not be a loose fit in its site. In this way, for 1:1
compounds we predict that:




Compounds with r+/r- from 0.22 to 0.41 will adopt the ZnS (blende or wurtzite)
structures.
Compounds with r+/r- from 0.41 to 0.72 will adopt the NaCl structure.
Compounds with r+/r- greater than 0.72 will adopt the CsCl structure.
I r+/r- is less than 0.22, the copounds are likely to be quite covalent.
When the actual structures are compared to what is predicted, the results are quite bad, especially
for the ZnS structure, which persists in cases where r+/r- is much larger than the presumed limit
of 0.41. Only a general trend can be detected. One difficulty is the difficulty in assigning reliable
ratii to the ions.
Structure Maps
These are plots of the electronegativity difference between the elements of which the compound
is formed, and the average principal quantum number of the elements. On such scatter diagrams
(Figures 2.22 and 2.23) quite well defined zones of one structural type are revealed. This is not
unexpected because there is a close link between ion size and the electronegativity and between
size and the period in which the ion is found.
The Bond Triangle
The covalent-ionic continuum described above is certainly an improvement over the old covalent
-versus - ionic dichotomy that existed only in the textbook and classroom, but it is still only a
one-dimensional view of a multidimensional world, and thus a view that hides more than it
reveals.
The main thing missing is any allowance for the type of bonding that occurs between more pairs
of elements than any other: metallic bonding. Intermetallic compounds are rarely even
mentioned in introductory courses, but since most of the elements are metals, there are a lot of
them, and many play an important role in metallurgy. In metallic bonding, the valence electrons
lose their association with individual atoms; they form what amounts to a mobile "electron fluid"
that fills the space between the crystal lattice positions occupied by the atoms, (now essentially
positive ions.) The more readily this electron delocalization occurs, the more "metallic" the
element.
Thus instead of the one-dimension chart shown above, we can construct a triangular diagram
whose corners represent the three extremes of "pure" covalent, ionic, and metallic bonding.
We can take this a step farther by taking into account collection of weaker binding effects known
generally as van der Waals forces. Contrary to what is often implied in introductory textbooks,
these are the major binding forces in most of the common salts that are not alkali halides; these
include NaOH, CaCl2, MgSO4. They are also significant in solids such as CuCl2 and solid SO3 in
which infinite covalently-bound chains are held together by ion-induced dipole and similar
forces.
The only way to represent this four-dimensional bonding-type space in two dimensions is to
draw a projection of a tetrahedron, each of its four corners representing the "pure" case of one
type of bonding.
Note that some of the entries on this diagram
(ice, CH4, and the two parts of NH4ClO4) are
covalently bound units, and their placement
refers to the binding between these units. Thus
the H2O molecules in ice are held together
mainly by hydrogen bonding, which is a van
der Waals force, with only a small covalent
contribution.
Note: the triangular and tetrahedral diagrams
above were adapted from those in the excellent article by William B. Jensen, "Logic, history and
the chemistry textbook", Part II, J. Chemical Education 1998: 817-828.
Recommended Questions from Shriver and Atkins:
"Exercises"
2.1, 2.2
You should be able to answer this.
2.3
Not covered, Fall 2001
2.4 - 2.12 You should be able to do these.
You should be able to recognize the new structure if you draw
diagram of 8 Unit cells of CsCl, and then delet the appropriate
ions.
2.14 - 2.17 You should be able to do these.
2.18, 2.19 May not be covered, Fall 2001.
"Problems"
2.1 - 2.4 You should be able to do these.
2.5
May not be covered, Fall 2001.
2.6
This is just geometry - you should be able to do it.
2.7
A bit too philosophical for this course.
2.8
You shoul dbe able to answer this.
2.9
May not be covered, Fall 2001.
2.13