Download Metallic and Ionic Structures and Bonding Ionic compounds are

Metallic and Ionic Structures and Bonding
Ionic compounds are formed between elements having an electronegativity difference of
about 2.0 or greater. Simple ionic compounds are characterized by high melting points and very
low conductivities in their solid forms. When molten, however, conductivities are very high.
Ionic compounds formed between s- and p-block
elements involve ions with rare gas
configurations. Both experimental (x-ray
diffraction) and computational determinations of
electron densities in these structures indicate that
the electron density is very low at some point
between the nuclei of the cation and anion. From
this it is inferred that there is minimal overlap of
the cation and anion valence orbitals. The notion
that the ions can be viewed as spheres in close
contact is derived in part from these
observations. The figure shows an electron
density map for a portion of the face of the unit
cell of sodium chloride.
Covalent compounds have highly directional interactions with a (relatively) small number
of adjacent (overlap of orbitals with defined directions). Furthermore interactions with adjacent
molecules in solids are weak as they involve only dipole-dipole and/or Van der Waals
interactions. In metals each atom tends to have a much larger number of nearest neighbor
atoms, determined only by the way in which the atoms are “packed” in the array. In many cases
the arrangement is either cubic closest packed (ccp) or hexagonal closest packed (hcp), both of
which result in twelve nearest neighbors. The unit cell of the former is termed face-centered
cubic. Some structures are based upon less efficient packing (more free space) such as the
body centered cubic structure. Drawings of these are shown below.
Two layers of
closest
packed
spheres.
Face centered cubic cell
Body centered cell
Regardless of solid-state structure the electronic structures of metals involve molecular
orbitals that extend throughout the solid. The number of orbitals is so large that it is useful to
view metals have having a band structure. Because there are typically either vacancies in the
lower energy band or overlap of filled and vacant bands metals are good conductors. Many
simple ionic compounds can be viewed as having structures determined by ccp or hcp packing
of large spheres (anions) with voids in the structure occupied by smaller spheres (cations).
Other structures are related to the body centered cubic structure in which the atoms at the
corner of the cube are replaced by anions and the atom at the center is replaced by a cation.
Because there is no significant overlap of orbitals between anions, or between anion and cation,
ionic substances do not conduct.
The unit cell is the smallest unit that repeated in each direction will make up the infinite
array of a solid. For the ccp arrangement the unit cell is known as the face-centered cubic (fcc)
cell. It is shown above in exploded form. In the actual fcc cell comprised of a single type of
atom, the spheres will be in contact with one another and the cell dimension will be determined
by the diagonal which will be four times the radius of the atom. This only one of three cubic
lattice structures and one of fourteen basic lattice shapes. The entire group of fourteen is
shown on the next page.
In a cubic salt, which can be considered as a ccp
arrangement of large spheres (usually anions) with smaller
spheres (usually cations) occupying voids, the cell dimension
will frequently be determined by the contact between the anion
and cation along the edge of the cell, which is then equal to the
sum of the diameters of the anion and the cation. Note that the
empirical formula of a salt can be determined by examining the
contents of the unit cell and its density can be calculated based
upon the contents of the unit cell and its dimensions. For a
cubic cell the all sides are equivalent. In considering the
contents of a unit cell it is important to recognize that only those
atoms (ions) that are fully in the cell contribute totally to the cell.
NaCl structure
Those sitting in the sides contribute only one half to the cell
(and one half to the adjacent cell). Atoms or ions residing on
edges contribute only one fourth to the cell under consideration (and one fourth each to three
contiguous cells. Finally, atoms or ions residing at the corners of a cell contribute only one
eighth to the cell (and one eighth to each of seven other contiguous cells that meet at the
corner). This can be illustrated by the fcc structure adopted by sodium chloride and many other
The fourteen Bravais lattices divided into six systems according to their macroscopic symmetry.
The symbols at the top of the page refer to primitive (P), body-centered (I), centered on one face
(C), face-centered (F) and rhombohedral (R).
1:1 salts. Consideration of the anions (large spheres) indicates that there are six in faces,
which contribute one half each for a contribution of three, and that there are eight on the
corners, which contribute one eighth each for a contribution of 4 anions to the cell. Alternatively,
using the cations one observes that there is one cation that is entirely in the cell and twelve on
edges, which contribute one quarter each for a contribution of three cations. Thus the total
cations equals the total anions, as it must, and there are four formula units per cell.
In the ccp arrangement of spheres there are three types of
voids (holes), trigonal (three nearest neighbors), tetrahedral (four
nearest neighbors) and octahedral (six nearest neighbors). The
latter two are most commonly occupied and it is important to know
that there are two tetrahedral holes per sphere and one octahedral
hole per sphere making up the ccp array. This can be determined
by examination of the fcc unit cell, which contains a total of four
spheres. As the top drawing to the right indicates there is one
complete octahedral hole in the center of the unit cell and 1/4 of
an octahedral hole along each edge of the cell (1 + 12/4 = 4
holes/cell or one hole per sphere. The bottom drawing shows
one of the eight tetrahedral holes that are fully contained within
the unit cell (each tetrahedral hole is formed by a corner sphere
and the three adjacent spheres that sit on the faces. In the
simple cubic arrangement the cation occupying the cubic hole
would have eight neighbors. For the larger spheres making up
the ccp array to remain just in contact the maximum radius that
the smaller sphere can have will be 0.155 of the large radius of
the large sphere for the trigonal hole, 0.225 for the tetrahedral
hole and 0.414 for the octahedral hole. This leads to the
definition of a radius ratio r+/r- for ions.
In the simple cubic structure there is one cubic hole per unit cell or one hole per sphere.
The radius ratio is 0.73.
Now realize that the maximum electrostatic energy results when two opposite charges
interact through the shortest distance and when a charge of one type interacts with the greatest
possible number of opposite charges. Therefore, under ideal circumstances cations will occupy
holes that minimize the distance between the cation and its anion and that maximize the number
of nearest neighbors. In general a cation will not occupy a hole that is too small since the ion will
not be centered in the hole. On the other hand a cation that is too large for a hole will only result
in separation of the anions. Based upon this we can conclude that combinations of anions and
cations with r+/r- of <0.22 should have the cation in the trigonal holes, those with ratios in the
range 0.22-0.4 should have the cations in tetrahedral holes and those with ratios 0.4-0.73
should have the cations in octahedral holes. Those with r+/r- >0.73 should adopt the simple
cubic structure in which the ions would have eight neighbors.
Some examples of structures that result from occupancy of tetrahedral holes the ccp lattice are
shown below.
Zinc sulfide (zinc blende)
Platinum sulfide
Calcium fluoride (fluorite)
Lead oxide
Note the different ways in which partial occupancy of tetrahedral holes occurs in the ZnS, PtS
and PbO lattices, whereas all of the tetrahedral holes are occupied in the fluorite structure. In
representing these structures the cations make up the fcc lattice in the fluorite, PbO and PtS
structures. A non-closest packed structure is found in cesium chloride and related salts.
Cesium chloride
The energy of interaction between an anion and cation (ion pair) can be calculated on
the basis of an electrostatic interaction between charges operating through a distance equal to
the sum of the ionic radii. Electron-electron repulsions between the valence electrons of the
cation and anion help to maintain an equilibrium internuclear distance. In the electrostatic
model, the energy is proportional to the product of the ion charges Z+Z- and inversely
proportional to the sum of the ionic radii, r+ + r-. When this energy is calculated for a mole of
sodium chloride ion pairs, the energy calculated is 589 kJ mol-1. This is only about 75% of the
experimentally determined lattice energy for sodium chloride, which is 770 kJ mol-1. The
difference results from extended interactions between cations and anions that are not nearest
neighbors. Summation of the interactions, nearest neighbors and beyond, results in an infinite
series that converges to a value of 1.74756. There are similar constants for other structures.
The simple cubic structure, which is found for cesium chloride has a constant of 1.76267 and
that for ZnS (zinc blende) of 1.63805. Lattice energies can be estimated based upon
consideration of several factors. The most important are: the product of the charge on the ions,
the type of structure, and the internuclear distance between the cation and anion (sum of the ion
radii). The energy is proportional to the first two and inversely proportional to the latter. So for a
given structure, the energy goes up as the charge on the ions increase and their size decreases.
The effects ion size and charge on properties is well illustrated by the data in the
following table.
Salt
m.p./K
density
ro
unit cell/Å
U/kJ mol-1
NaF
1268
2.558
2.31
4.63
928
NaCl
1073
2.165
2.76
5.64
770
NaBr
1020
3.20
2.94
5.94
736
MgO
3073
3.58
2.1
4.21
3791
2.46
*
2526
MgCl2
981
2.32
.*does not have fcc (sodium chloride) structure