Solid Defects

All solids contain defects, where the ideal lattice as described in terms of an infinitely repeating unit cell is broken. Defects can have a large effect on a range of properties of the material, such as the mechanical strength, electrical conductivity, corrosion and chemical reactivity.

Defects may be formed due to thermodynamic effects, and these defects are known as intrinsic defects, or due to imperfections in stoichiometry, which are not due to thermodynamics, and which are known as extrinsic defects.

Defects which are localized in space, ie. those which occur at single sites in the crystal, are known as point defects, whereas extended defects are those which penetrate through the crystal in one or more dimensions.

Intrinsic Defects

When a defect is formed, disorder is introduced into the otherwise perfect lattice. This increase in disorder leads to an increase in the entropy, S, of the system. Although the creation of a defect is generally endothermic, ie. it has a positive enthalpy, H, of formation, the overall free energy of formation is given by G = H – TS. As the temperature rises, both H and S increase. For T > 0, there will be a minimum in the free energy of formation of the defects at a non-zero defect concentration, and so the formation of defects is spontaneous.

Point defects which preserve stoichiometry

There are two main types of intrinsic defect which preserve the stoichiometry of a compound, the Schottky defect and the Frenkel defect.

The Schottky Defect

This is a defect where an ion is removed from its lattice site, leaving a vacancy. There are generally equal numbers of vacancies on cation and anion lattice points, so as to preserve charge neutrality, and so the overall stoichiometry is unchanged. The concentration of Schottky defects varies from a concentration of 10-12 molL-1 in alkali metal halides, to about 12 molL-1 in some d-metal oxides. This corresponds to one defect for every 1014 formula units in the alkali metals, up to one defects for every 10 formula units in the d-metal oxides, so there is a huge range of defect concentrations.

In general, Schottky defects are found when the metal ions are able to have more than one oxidation state.

The Frenkel Defect

This is a defect where an ion is removed from its lattice site, leaving a vacancy, and moved into an interstitial site. Ionic solids may have cation interstitial, as in silver halides, anion interstitials, as in BaF2, PbCl2, and PbBr2, and a mixture of both cation and anion interstitials, as in PbI2.

Frenkel defect formation is therefore favoured by the ready availability of interstitial sites large enough to hold the displaced ion. Open structures, such as sphalerite and wurtzite, with low coordination numbers are those in which Frenkel defect formation commonly occurs.

A Schottky Defect A Frenkel Defect

A less common form of point defect is the atom interchange defect, where a pair of atoms are simply swapped to each other’s lattice point. This is common in metal alloys.

Point defects which do not preserve stoichiometry

When a large crystal is prepared, there will always be impurities present. In some cases, as in semiconductors, the impurities are deliberately introduced. These impurities give rise to extrinsic point defects.

In cubic zirconia, ZrO2, for example, contamination by CaO leads to the replacement of some of the Zr ions by Ca ions in the fluorite structure leads to the formation of a vacancy in the fluoride ion lattice, ie. a (ZrO)2+ unit is replaced by Ca2+. The introduction of the calcium ions in this way acts to stabilize the cubic lattice.

A general range of extrinsic defects are known as colour defects: these are so called because they have an effect on the electronic absorption of the material in the infra-red, visible, and ultra-violet regions.

This category of defects include the F-center and the H-center defects.

F-center defects

These are electrons trapped in anion vacancies, and produced by the exposure of an alkali metal halide crystal to the alkali metal vapour. There is addition of metal to the system.

The F-center defect

H-center defects

These are self-trapped holes, and correspond to the removal of metal from the system. The holes are, in fact, a single negative charge spread over two anions, creating an X2 species. The formula is M1-xX, but is more properly written as (M+)1-x(X)1-2x(X2)x. The energy levels in the X2 species are well described by the usual molecular orbital diagram for a diatomic species, and electronic transitions between the energy levels in the X2 species may be observed.

The H-center Defect

Non-Stoichiometric compounds

Compounds with incomplete lattices are those compounds which exist with variable composition but which retain essentially the same structure. The continuity of the structure over the whole composition range can be seen from the fact that the position of the peaks in the X-ray diffraction pattern do not change with composition.

TiO is a metallic conductor with the rocksalt structure, and it occurs with stoichiometry in the range TiO0.7 to TiO1.25. This variation in composition is accommodated by vacancies in either the O or Ti lattice sites.

In the stoichiometric TiO, 15% of the cation and anion sites are vacant, and hence this compound has an unusually high concentration of Schottky defects. However, this is complicated by the fact that the defects tend to cluster due to interaction between vacancies and also the formation of metal-metal bonds within the defect lattice.

In general, the formation of non-stoichiometric compounds is common with d-, f-, and some p-block metals with soft anions such as S2-, and also with harder anions such as O2-. Non-stoichiometric compounds with anions such as F, Cl, SO42-, and NO3 are much less common.

Common Non-Stoichiometric compounds
d-block hydrides x in range
TiHx 1 – 2
ZrHx 1.5 – 1.6
HfHx 1.7 – 1.8
NbHx 0.64 – 1.0
d-block oxides x in range
rocksalt structure Rutile Structure
TiOx 0.7 – 1.25 1.9 – 2.0
VOx 0.9 – 1.20 1.8 – 2.0
NbOx 0.9 – 1.04
d block sulphides x in range
ZrSx 0.9 – 1.0
YSx 0.9 – 1.0