The perfectly regular crystal structures that have been considered upto now are called ideal crystals in which atoms are arranged in a regular way. In actual crystals, however, imperfections or defects are always present and their nature and effects are very important in understanding the properties of crystals. These imperfections affect the properties of crystals such as mechanical strength, chemical reactions, electrical properties etc., to a great extent.
Imperfections are found in all crystals unless some special means are used to reduce them to a low level.
The crystallographic defects are classified as follows:
1. Point Defects or Zero Dimensional Defects:
ADVERTISEMENTS:
(i) Vacancy
(ii) Schottky imperfections
(iii) Interstitialcy
(iv) Frenkel defect
ADVERTISEMENTS:
(v) Compositional defects
(a) Substitutional impurity.
(b) Interstitial impurity.
(vi) Electronic defects.
ADVERTISEMENTS:
2. Line Defects or One Dimensional Defects:
(i) Edge dislocation.
(ii) Screw dislocation.
3. Surface Defects or Plane Defects or Two Dimensional Defects:
ADVERTISEMENTS:
(i) Grain boundaries.
(ii) Tilt boundaries.
(iii) Twin boundaries.
(iv) Stacking fault.
ADVERTISEMENTS:
4. Volume defects or three dimensional defects.
1. Point Defects:
Point defects are imperfect point like regions in a crystal. The typical size of a point defect is one or two atomic diameters.
These defects are completely local in effect, e.g., a vacant lattice site.
Point imperfections are always present in crystals and their presence results in a decrease in the free energy.
The point defects may be created as follows:
(i) By thermal fluctuations
(ii) By quenching (quick cooling) from a higher temperature.
(iii) By severe deformation of the crystal lattice; e.g., by hammering or rolling. While the lattice still retains its general crystalline nature, numerous detects are introduced.
(iv) By external bombardment by atoms or high-energy particles; e.g., from the beam of the cyclotron or the neutrons in a nuclear reactor. The first particle collides with the lattice atoms and displaces them, thereby forming a detect. The number produced in this manner is not dependent on temperature but depends only on the nature of the crystal and on the bombarding particles.
The various point defects are discussed below:
1. Vacancy:
A vacancy is the simplest point defect and involves a missing atom within a metal. These detects may come up as a result of imperfect packing during the original crystallisation. They may also arise from thermal vibrations of the atoms at high temperatures.
2. Schottky Imperfections:
These are closely related to vacancies but are found in compounds which must maintain a charge balance. They involve vacancies of pair of ions of opposite charges. This type is dominant in alkali halides.
3. Interstitialcy:
It is the addition of an extra atom within a crystal structure particularly if the atomic packing factor is low. This results in atomic distortion. The foreign atom may form added alloying agent or simply an impurity. The vacancy and interstitialcy are therefore, inverse phenomena.
4. Frenkel Defect:
An ion dislodged from the lattice into an interstitial site is called Frenkel defect. The interstitialicies and Frenkel defects are less in number than vacancies and Schottky defects, because additional energy is required to force the atom into the new position.
Close-packed structures have fewer interstitialicies and Frenkel defects than vacancies and Schottky defects, as additional energy is required to force the atoms in their new positions.
When an ionic crystal does not correspond to exact stoichiometric formula defect structures are produced. Such defect structures have an appreciable concentration of point imperfections.
The presence of a point imperfection introduces distortions in the crystals. If the imperfection is a vacancy, the bonds that the missing atom would have formed with its neighbours are not there. In the case of an impurity atom, as a result of the size difference, elastic strains are created in the region of the crystal immediately surrounding the impurity atom.
The elastic strains are present irrespective of whether the impurity atom is larger or smaller than the parent atom. A large atom introduces compressive stresses and corresponding strains around it, while a smaller atom creates a tensile stress- strain field. Similarly, an interstitial atom produces strains around the void it is occupying.
All these factors tend to increase the enthalpy or the potential energy of the crystal. The work required to be done for creating a point imperfection is called the enthalpy of formation (∆ Hf) of the point imperfection. It is expressed in kJ/mole or eV/point imperfection.
The enthalpy of formation of vacancies in a few crystals is listed below:
Owing to the fact that a point imperfection is distinguishable from the parent atom, the configurationally entropy of a crystal increases from zero for a perfect crystal to positive values with increasing concentration of the point imperfection.
It has been observed that point imperfection of various types can interact with one another and lower the total energy. For example – a solute atom that is larger than the parent atom can have smaller distortion energy, if it stays close to a vacancy. This reduction in energy is called the binding energy between the two point imperfections. It is typically in the range of 10-20 percent of enthalpy of formation of imperfections.
5. Compositional Defects:
These defects arise from impurity atom during original crystallisation. Impurity atoms considered as defects in a perfect lattice are responsible for the functioning of most semiconductor devices. They occur on a lattice point as a substitutional impurity or as interstitial impurity and the resulting phase is known solid solution.
A substitutional impurity is created when a foreign atom substitutes for a parent atom in the lattice. In brass, zinc is a substitutional atom in the copper lattice.
An interstitial impurity is a small sized atom occupying an interstice or space between the regularly positioned atoms. In steel, carbon atoms occupy the interstitial position in the iron lattice.
6. Electronic Defects:
Electronic detects are the errors in charge distribution in solids.
The so-called electronic imperfections are primarily necessary to explain electrical conductivity and related phenomenon in solids. An important example of this is the creation of positive and negative charge carriers. This effect is responsible for the operation of p-n junctions and transistors.
2. Line Defects (Dislocations):
A linear disturbance of the atomic arrangement, which can move very easily on the slip plane through the crystal is known as dislocation. The dislocation may be caused during growth of crystals from a melt or from a vapour or they may occur during a slip.
The line defects, as the name implies, extend along some direction in an otherwise perfect crystal. One such defect can therefore be considered as the boundary between the two regions of a surface which are perfect themselves but out of register with each other.
In case of crystals it arises when one part of the crystal shifts or slips relative to the rest of the crystal such that displacement terminates within the crystal. However, if the displacement does not terminate within the crystal, but continues throughout the crystal instead, it may not introduce any defect in the crystal.
This defect is created along a line which is also the boundary between the slipped and unslipped regions of the crystal. The defect is commonly called a “dislocation” and the boundary as the “dislocation line”.
Two basic types of dislocations are:
1. Edge dislocation (or Taylor-Orowan dislocation).
2. Screw dislocation (or Burger’s dislocation).
These are usually two extreme types of dislocations. Any particular dislocation is usually a mixture of these two extreme types. These may be regarded as the components of a general dislocation.
1. Edge Dislocations:
Refer to Fig. 3.13 [(a), (b)].
An edge dislocation may be described as an extra plane of atoms within a crystal structure. It is accompanied by zones of compression and of tension so that there is a net increase in energy along a dislocation.
The displacement distance for atoms around the dislocation is called the ‘Burger vector’. This vector is at right angle to the edge dislocation.
Burger’s vector (b) is determined by drawing a rectangle in the region being investigated by connecting an equal number of atoms on opposite sides, as shown in the Fig. 3.13. If a certain region contains an edge dislocation, the circuit will fail to close. The dotted line PP’ given in the Fig. 3.13 is the Burger’s vector.
The edge dislocations are represented by the symbols ⊥ and T denoting the insertion of extra plane from the top and bottom side of the crystal respectively. These two configurations are called positive and negative edge dislocations. These symbols also indicate the position of the dislocation line.
Fig. 3.13 (c) shows the atomic view in an edge dislocation.
2. Screw Dislocation:
Refer Fig. 3.14. [(a), (b)]
Screw dislocation may originate from partial slipping of a section of crystal plane.
In this type of dislocation shear stresses are associated with adjacent atoms and extra energy is involved, along the dislocation. The successive atom planes are transformed into the surface of the helix of screw by this dislocation which accounts for its name as screw dislocation.
A screw dislocation has its displacement of Burger’s vector parallel to the linear defect but there is distortion of the plane.
When the screw dislocation is present in a crystal, the complete planes of atoms normal to the dislocation no longer exist. Rather all the atoms lie on a single surface which spirals from one end of the crystal to the other with dislocation line as the axis of spiral.
The displacement of the atom from their original positions in the perfect crystal is described by the equation:
Where, r = The displacement along the dislocation line, and
θ = The angle measured from some axis perpendicular to the dislocation line.
It may be noted that as θ increases by 2π, the displacement increases by the factor b; thus, b is, in this respect, the measure of the strength of dislocation.
d. A screw dislocation does not exhibit climb motion.
The following effects of a screw dislocation are of great importance:
(i) Plastic deformation is possible under low stress, without breaking the continuity of the lattice.
(ii) The force required to form and move a screw dislocation is probably somewhat greater than that required to initiate an edge dislocation.
(iii) Screw dislocation causes distortion of lattice for a considerable distance from the centre of the line and takes the form of spiral distortion of the planes. Dislocations of both types (combinations of edge and screw) are closely associated with crystallization as well as deformation.
It may be mentioned here that both the dislocations are accompanied by the distortion in the crystal which varies with distance from the centre of the dislocation (being severest in the immediate vicinity of the dislocation line).
The region near the dislocation line where the distortion is extremely large is called the “core of the dislocation”; here the local strain is quite high. In edge dislocation the local strain is composed of dilation (with tension below the dislocation edge and compression above it), whereas in screw dislocation it is composed of shear.
3. Surface Defects:
Surface defects are the two dimensional regions in a crystal. They arise from a change in the stacking of atomic planes on or across a boundary.
They are of the following two types:
1. External defects.
2. Internal detects.
The external type is just what its name implies, the defects or imperfections represented by a boundary. The external surface of the material is an imperfection itself, because the atomic bonds do not extend beyond it. The surface atoms have neighbours on one side only, while atoms inside the crystal have neighbours on either side of them. Since these surface atoms are not entirely surrounded by others, they possess higher energy than those of internal atoms.
The energy of surface atom, for most metals is of the order of 1 J/m2.
These defects are discussed below:
Grain boundaries are those imperfections which separate crystals or grains of different orientation in polycrystalline aggregation during nucleation or crystallisation.
In materials like copper there may be crystals of various orientations. These individual crystals arc called grains. In one grain atoms are arranged with one orientation and one pattern. However, there is a transition zone between two adjacent grains which are not aligned with either grain.
As shown in Fig. 3.20, various degrees of crystallographic misalignment between adjacent grains are possible. When this orientation mismatch is slight, on the order of a few degrees, then the term small or low angle grain boundary is used. In the boundary where the crystals or grains change abruptly and orientation difference between neighbouring grains is more than 10-15°, the boundaries are known as high angle grain boundaries.
The mismatch of the orientation of adjacent grain produces a less efficient packing of the atoms at the boundary. Thus, the atoms along the boundary have a higher energy than those within the grains.
The boundary between two crystals which have different crystalline arrangement or different compositions, is called an interphase boundary or an interface.
Tilt boundary in reality is a series of aligned dislocations which tend to anchor dislocation movements normally contributing to plastic deformation. Little energy is associated with this type of boundary.
This is called low-angle boundary (Fig. 3.21) as the orientation difference between two neighbouring crystals is less than 10°.
A low-angle tilt boundary is composed of edge dislocation lying one above the other in the boundary.
The angle of tilt,
θ = b/D
Where, b = Magnitude of the Burger’s vector, and
D = Average vertical distance between dislocations.
A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror-image positions of the atoms on the other side (Fig. 3.22). The region of material between these boundaries is appropriately termed a “twin”.
Twins result from atomic displacements that are produced from applied mechanical shear forces (mechanical turns), and also during annealing heat treatments following deformation (annealing twins).
Annealing twins are typically found in crystals that have the F.C.C. crystal structure, while mechanical twins are observed in B.C.C. and H.C.P. metals.
Twinning occurs on a definite crystallographic plane and in a specific direction, both of which depend on the crystal structure.
The twins correspond to those regions having relatively straight and parallel sides and a different visual contrast than the untwined regions of the grains within which they reside.
(iv) Stacking Fault:
The energy requirements for the production of these faults are very high; the measured values at this energy are 19 x 10-7 J/m2 in copper and between 100 to 200 x 10-7 J/m2 in aluminium.
In thermodynamic sense, surface imperfections are not stable. They are present as metastable imperfections. If the thermal energy is increased by heating a crystal close to its melting point, many of surface imperfections can he removed.
The grain boundary area decreases as a polycrystalline material is heated above 0.5 Tm, where Tm is the melting point in K. Large crystals grow at the expense of small crystals. Even though the average size of a crystal increases during this grain growth, the number of crystals decreases, resulting in a net decrease in grain boundary area per unit volume of the material.
4. Volume Defects or Three Dimensional Defects:
Volume (or bulk) defects include pores, cracks, foreign inclusions, and other phases.
Cracks may arise when there is only small electrostatic dissimilarity between the stacking sequences of closed-packed planes in metals.
A large vacancy or void is obtained when cluster of atoms is missing.
Inclusions are certain regions within the crystal which are occupied by some other phase than that of the host crystal. Various known inclusions are formed mostly during crystallisation.
Bulk or volume defects are normally introduced during processing and fabrication steps.
Note:
A colour centre is lattice defect that absorbs visible light. The usual place to find colour centres is in ionic crystals.