An ideal crystal is one which has the same unit cell containing the same lattice points across the whole of the crystal. At absolute zero, crystals tend to have perfectly ordered arrangement of ions and there are no crystal imperfections in solids.
With the increase in temperature, the chance that a lattice site may be unoccupied by an ion increases. This produces a defect i.e. crystal imperfections in solids. Since the number of crystal defects depends on the temperature, they are sometimes called thermodynamic defects. The number of defects produced per cm3, n, is given as:
n = Ne-W/2RT
where N is the number of sites per cm3 which could be left vacant, W is the work required to produce a defect, R is the gas constant and T, the absolute temperature.
Types of Crystal Imperfections in Solids
Defects in crystals may be divided into two subheads:
- Stoichiometric crystal defects
- Non-stoichiometric crystal defects
Stoichiometric Crystal Defects
In stoichiometric compounds, irregularity in the arrangement of the ions in a lattice can occur due to a vacancy at a cation and an anion site or by the migration of an ion to some other interstitial site. Two types of such defects are common. These are:
This defect occurs when some of the lattice points are not occupied. The points which are unoccupied are known as lattice vacancies or holes. The defect of this type tends to be formed in compounds with high coordination numbers, and where the positive and negative ions are of similar size, e.g. NaCl and CsCl are good examples of ionic solids in which Schottky defect appears.
This defect occurs when an ion occupies and interstitial position between the lattice points. A hole may exist in the lattice because an ion occupies an interstitial position rather than its correct lattice site. Examples of this defect are ZnS and AgBr.
In silver bromide, AgBr, some of the AC ions are usually missing from their regular positions and occupy positions in between the other ions in the lattice. Zinc sulphide, ZnS, is another example in which Frenkel defect arises. Zn2+ ions get entrapped in the interstitial space leaving holes in this lattice.
The Frankel defect is usually favored by the compounds
- with low coordination numbers
- having ions of different sizes and
- having highly polarizing action and an easily polarizable anion.
In compounds with low coordination number the attractive forces are lesser which can be overcome easily so that the cation can easily move into the interstitial site.
Schottky and Frenkel defects in crystals lead to the following results:
- The closeness of similar charges brought about by the Frenkel defect leads to an increase in the dielectric constant of the crystals. The density of the medium however remains unchanged.
- The result of both types of defects is that the crystal is able to conduct electricity to a small extent, by an ionic mechanism. When an electric field is applied to a crystal having stoichiometric defects, a nearby ion moves from its lattice site to occupy a hole. This results in the generation of a new hole and thus another ion moves into it, and so on. Thus the ion migrates from one end to the other, causing the electricity to flow across the whole of the crystal.
- Density of the crystal as well as the lattice or the stability of the crystal are lowered due to presence of holes.
Non-stoichiometric Crystal Defects
Non-stoichiometric compounds are those where the ratio of the number of atoms of A+ to the number of atoms of does not correspond to a simple whole number as suggested by the formula. Non-stoichiometric compounds do not follow the law of constant composition. This makes the structure irregular in some way, i.e., it contains defects, which are in addition to the normal thermodynamic (Schottky and Frenkel) defects.
Non-stoichiometric crystal defects, evidently, are of two types depending upon whether positive charge is in excess or negative charge is in excess. These are known as metal excess defect and metal deficiency defects, respectively.
Metal Excess Defects
In metal excess defects, positive charge is in excess. Such defects may occur in two ways:
(i) A negative ion may be missing from its lattice site leaving a ‘hole’ which is occupied by an extra electron to maintain the electrical balance. There is evidently an excess of positive (metal) ions, although the crystal, as a whole is neutral.
This defect is somewhat similar to Schottky defect but differs in having only one hole and not a pair as in the latter case.
This type of defect is not very common. For example, when NaCl is treated with sodium vapour, a yellow non-stoichiometric form of NaCl is obtained in which there is excess of sodium ions. In such a case, the extra positive charge due to extra sodium ion is balanced by the presence of free electron in the lattice.
(ii) The metal excess defect may also appear in another way. An extra positive ion may also occupy an interstitial position in the lattice and to maintain electrical neutrality, an electron is also present in the interstitial space.
Although this type of defect is somewhat similar to Frenkel defect yet it differs from that in having no holes and in having interstitial electrons. This defect is much more common than the first type of metal excess defect. This type of defect is shown by such crystals which are likely to develop Frenkel defect. An interesting example is zinc oxide crystal.
- As the crystals associated with metal excess defects of the first or second type contain free electrons, they can conduct electricity to some extent because the number of defects and therefore the number of electrons are very small. Such crystals are usually termed as semiconductors.
- The crystals showing metal excess defects are generally coloured. This is due to the presence of free electrons. When these electrons are excited to higher energy levels by absorption of certain wavelengths from the visible white light, these compounds appear coloured. For example, zine oxide is white in cold but appears yellow when hot.
Metal Deficiency Defects
Theoretically metal deficiency can occur in two ways. Both need variable valency of the metal, and might therefore be expected with the transition metals.
In the first way, a positive ion may be missing from its lattice site, and the extra negative charge is balanced by an adjacent metal ion having two charges instead of one. It means that the metal may be in position to show variable valency. Thus, this defect is generally shown by compounds of transition metals, such as FeO, FeS, NiO, etc.
In the second way, an extra negative ion may find an interstitial position and the charges are balanced by means of an extra charge on an adjacent metal ion. Negative ions are usually large, and it would be expected to be difficult to fit them into interstitial positions. In fact no example of crystals containing such negative interstitial ions is known so far.
Crystals with metal deficiency defects are semiconductors. This property arises from the movement of an electron from one ion to another ion. The substances permitting this type of movement are known as P-type semiconductors.
Linear Defects Dislocations
In case of perfectly crystalline metals, the shear force (or stress) required to deform them are much higher (100-10,000 times) than actually observed. This has been explained by suggesting that the actual metallic crystals have certain imperfections or defects which help them to undergo elastic deformation under quite small loads.
Such imperfections were postulated as line defects and known as dislocations. The two main line defects, known as the edge dislocations and screw dislocations, are explained below:
This defect occurs due to the termination of the edge of an atomic plane within the crystal instead of passing all the way through. The way in which an edge dislocation moves under the shear and helps in the deformation of a crystal is shown in Figure.
Thus because of the shear, the dislocation moves across the crystal with the net result that the top half of the crystal gets displaced one lattice distance with respect to the bottom half of the crystal.
To understand it, imagine a cut in a crystal with the particles to the left of the cut pushed up through the distance of one unit cell, as shown in Figure. The unit cells now make a continuous spiral around the end of the cut, the screw axis. It means that the atomic planes around the screw axis (dislocation line) form a spiral or helical ramp. Such a displacement of atoms is known as screw dislocation.
The existence of screw dislocation would help in the further growth of the crystal because atoms can easily settle down on the step. However, when the lower terrace of the crystal is completely covered, further growth ceases. Just like the edge dislocations, the screw dislocations can also move under the influence of appropriate shear force and thus help in the deformation.
Plane Defects (Surface Imperfections)
Surface imperfections of a structural nature arise from a change in the stacking of atomic planes across a boundary. The changes may be one of the orientation or of the stacking sequence of the planes.
Grain Boundaries: Grain boundaries are those surface imperfections which separate crystals of different orientation in a poly-crystalline aggregation during nucleation or crystallization.
The shape of a grain is usually influenced by the presence of surrounding grains. The boundary atoms in two randomly oriented grains, therefore, cannot have a perfect complement of the surrounding atoms.
As a result, a region of transition exists in which the atomic packing is imperfect.
Stacking fault: A stacking fault is a surface imperfection that results from the stacking of one atomic plane out of sequence on another while the lattice on either side of the fault is perfect.
For example, the stacking sequence in an ideal face centered cubic (FCC) crystal may be described as ABC, ABC, …. A stacking fault might change the sequence to ABC, ABA, BCA ….
The stacking fault in this case is due to the A plane of atoms after the second B and may be described as a very thin region of (HCP) stacking in a (FCC) crystal. Such stacking faults may occur during crystal growth or may result from the separation of two particular dislocations.
Thanks for reading about “crystal imperfections or defects in solids”.
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