DEFECTS IN CRYSTALS
Introduction to crystal imperfections:
So far we have seen only ideal crystals. In ideal crystal, the atomic arrangement is perfectly regular and continues through out. But real crystals never perfect.
In the crystals, lattice distortion and various imperfections, irregularities (or) defects are generally present in them. With this defect, the mechanical, electrical and magnetic properties are affected, particularly in metals and alloys.
Imperfections or defect:
To describe any deviation from the perfect periodic array of atoms in the crystal.
Crystalline imperfections can be classified on the basis of their geometry under four main divisions, namely,
Vacancies
Interstitialcies
1) Point defects (Zero-Dimensional Defect):
Impurities
Electronic defects
Edge Dislocation
2) Edge dislocation (One-Dimensional Defect):
Screw Dislocation
Grain boundaries
Tilt boundaries
3) Surface Defects (Two-Dimensional Defect)
Twin boundaries
Stacking faults
Ferromagnetic Domain walls
Cracks
4) Volume Defects (Three-Dimensional Defect)
Air bubbles or Voids.
POINT DEFECTS:
Point imperfections are also called zero dimensional defects.
In a crystal lattice, point defect is a vacant lattice site.
The point defect in a crystal increases its internal energy as compared to that of the perfect crystal.
They change the electrical resistance of a crystal.
If a point defect is a vacancy, then there is no bonding. Hence the value of the mechanical strength at that point is reduced.
Point defects are created during crystal growth and application of thermal energy, mechanical stress or electric field.
Vacancies:
Vacancies are simply empty atom sites.
Vacancies may be single or two or tri vacancy.
Vacancy may occur as a result of imperfect packing during the original crystallization or they may arises from thermal vibrations of atoms at elevated temperatures, because as thermal energy is increased there is a higher probability that individual atoms will jump out their position of lowest energy.
A) Perfect crystal B) Vacancy Defect
Schottky defect:
“A schottky defect is the combination of one cation vacancy and anion vacancy``
Ion vacancies are called schottky defects.
A pair of one cation and one anion can be missing from an ionic crystal as shown in fig.
Vacancies are created by movements of an anion and one cation from positions inside the crystal to positions on the surface of the crystal, a schottky defect is said to have been formed.
The concentration of schottky defects decreases the density of the crystal.
This type of point defect is dominant in alkali halides.
Frenkel defect:
“An ion displaced from the lattice into an interstitial site is called Frenkel defect``
A frenkel defect is the combination of one cation vacancy and one cation interstitial defect.
The concentration of frenkel defects does not change the density of the crystal.
The point imperfections in silver halides and calcium fluoride are of the frenkel defects.
Frenkel and schottky defects together are called “Intrinsic defects”.
Interstitialcies:
“In the ideal crystal, the vacant positions are occupied by the extra atoms”.
Interstitialcies produces atomic distortion or strain because interstitial atom tends to push the surrounding atoms further apart, unless the interstitial atom is smaller than the rest of the atoms in the crystal.
Impurities:
A controlled addition of impurity to a very pure semiconductor crystal is the basis of producing many electronic devices like diodes and transistors.
Addition of pentavalent and trivalent impurity atoms in silicon or germanium crystal increases its electrical conductivity.
Basically impurities are two types,
Substitution impurity
Interstitial impurity
Substitution impurity:
Refers to a foreign atom that substitutes for or replace a parent atom in the lattice. In the case of semiconductor technology aluminum and phosphorous doped in silicon are substitution impurities in the crystal.
Interstitial impurity:
Is a small sized atom occupying the void space in the parent crystal, without dislodging any of the parent atoms from their sites as shown in fig.
Electronic defects:
Errors in charge distribution in solids are called electronic defects. These are produced, when the composition of an ionic crystal does not correspond to the exact stoicheometric formula.
E.g.: Let us consider deviations from the stoichemetric formula in compounds Zno& Feo.
Znyo: In Znyo, where y>1,
The excess cations occupy interstitial voids. While heating the compound in zinc vapor, two electrons are released from each zinc atom and stays around an interstitial cation in fig
In Fexo, where x>1, vacant cations are present by heating 2 electrons required by O atom is denoted by 2 Fe ions, which become Fe (ferric) ions shown in fig.
Applications of Point defects:
Addition of copper atoms in gold increases, the “ductility” of gold so that it can be drawn into wires for marking ornaments.
In copper lattice the low melting point Tin atoms behave as substitional impurity atoms and increase the “bearing properties”.
Addition of trivalent Ge and Si semiconductors increases their “electrical conductivity” enormously even through some local strains are produced.
Impurity defects produce the “diffusion” and phase transformation processes.
LINE DEFECTS:
Line defects are called dislocations these are one – dimensional imperfections in the geometrical sense.
Dislocations arise in crystals as a result of
Growth accidents (During crystallization)
Thermal stresses
External stresses
Phase transforms.
In line defects two basic types of dislocations are,
Edge dislocation
Screw dislocation
Edge dislocation:
An edge dislocation is created in the crystal any extra plane that does not extend up to the base of the crystal.
In a perfect crystal all the atoms are present at equilibrium positions; there fore distance between any two adjacent atoms any where in the crystal will be equal to equilibrium value. But in an edge dislocated crystal just above the edge of incomplete plane, the atoms are squeezed and are in a state of compression. The distance between neighboring atoms will be lesser than the equilibrium value. Just below the edge of the incomplete plane, the atoms are pulled apart and are in a state of tension. The distance between neighboring atoms. While greater than the equilibrium value.
In the first case the dislocation (PQ) is said to be positive and is represented by the symbol, ( ) in the later case it (PQ) is said to be negative and is represented by the symbol “T”.
Burger’s vector:
In fig (a) take a point move x times the atomic distance in the positive x direction and then move y times the atomic distance in the positive y direction and then move x times the distance in the negative X- direction and then move y times the atomic. Distance in the negative Y- direction. After this movement we can arrive at the original starting point P. The circuit is a closed one called “burger circuit”.
Then come to the fig(b) in that if we draw the burgers circuit as explained above the circuit would not be completed since the end point Q and starting point P are not located at the same place. From Q if we must move an extra distance b as shown in fig(b).
There fore Vector b= PQ
Burger’s Vector = PQ=b.
Screw dislocation:
Screw dislocation results from the a displacement of the atoms in one part of a crystal relative to the rest of the crystal, forming a spiral ramp around the dislocation line as shown in fig.
In the fig EF indicates the dislocation line.
Fig shows what happens when one part of the crystal is displaced relative to the rest of the crystal and displacement terminals with in the crystal. The row of atoms marking the termination of the displacement is the dislocation.
Normally the real dislocations occurred in the crystals are the mixtures of edge and screw dislocations and take the shape of curves or loops called dislocation loops.
Effect of dislocations on the properties of solids:
Screw dislocation is useful in explaining crystal growth.
During annealing of cold worked metal recovery is brought about by the movements of dislocations due to vacancy diffusion.
When the dissociation movement is stopped by some obstacles like grain boundaries then the tensile strength and hardness are increased in a close worked metal.
If there are too much of dislocations in different slip planes, then the strength of the material is reduced. Finally it may lead to the fracture (or) crack production in the material.
In the case of high temperature superconductors, the presence of dislocations create holes (or) vacancies which will increase the value of superconducting transition temperature.
Differences between Edge Dislocation and Screw Dislocation:
EDGE DISLOCATION
1) In the case of edge dislocation, an edge of an atomic plane is formed internal to the crystal.
2) An edge dislocation lies perpendicular to its Burger vector.
3) An edge dislocation glides or slips in the direction of burgers vector. This vertical movement of dislocation which occurs during diffusion of atoms or vacancies is called climb.
4) An edge dislocation involves an extra row of atoms either above (+ve sign) or below (-ve sign) the slip plane. Symbols “┴” or “┬”.
5) The forces required to form and move an edge dislocation are smaller in their values.
6) Speed of movement of an edge dislocation is greater.
7) The edge dislocation is particularly useful in explaining slip in plastic flow during mechanical working.
SCREW DISLOCATION
In the case of screw dislocation only a distortion of the lattice planes in the immediate vicinity is produced
A screw dislocation lies parallel to its burgers vector.
A screw dislocation glides in the direction perpendicular to the burgers vector. There is no dislocation climb.
In the screw dislocation the distortion follows a helical or screw path and both right hand and left hand senses are possible.
The forces required to form and move a screw dislocation are greater in their values
Speed of movement of a screw dislocation is lesser.
Screw dislocation is especially useful in explaining crystal growth as well slip in plastic deformation.
SURFACE DEFECTS:
Surface imperfections which are two dimensional in the mathematical sense refer to regions of distortions that lie about a surface having a thickness of a few atomic diameters. These are also called plane defects. Surface defects are also involved with the movement of dislocations. It can classify into two types:
External surface imperfections and
Internal surface imperfections.
External surface imperfections:
The external surface of a crystal is an imperfection in itself, as the atomic bonds do not extend beyond the surface. Although we may visualize and external surface as simply thermions of the crystal structure, the atoms on that surface cannot be compared with the atoms within the crystal.
Internal surface imperfections:
Internal surface imperfections arise from a change in the stacking of atomic planes across a boundary. The change may be one of the orientation (or) of the stacking sequence in the planes.
Some important internal surface imperfections are given below:
Grain boundaries.
Tilt boundaries.
Twin boundaries.
Stacking faults and
Ferromagnetic domain walls.
Grain boundaries: During solidification (or) during re crystallization of polycrystalline crystals, new crystals are randomly oriented with respect to one another.
When two crystals are impinge; the atoms that are caught in between the two crystals are being pulled by each of the crystals to join its own configuration. They can join neither crystal due to the opposing forces and therefore take up a compromise position the thickness of this region is only a few atomic diameters, because of the opposing forces from neighboring crystals are felt by the intervening atoms only at such short distances. The boundary region is called a “Grain boundary”.
So, if we take a piece of iron (or) copper, it is not in a single crystalline form, but pt consists of many small interlocking crystals (or) grains crystal having random orientation. The boundary between two adjacent grains therefore must have a structure that somehow conforms to the structures and orientations of both grains.
Lower angular miss orientation is of the order of few degrees but less than 10 powers 0 i.e.
High angle boundaries have miss orientation of the order of (or) even greater than this amount.
Tilt boundaries:
Tilt boundary may be regarded as an array of edge dislocations ( ). It is also a class of low angle boundaries. By rotation of an axis in the boundary it is possible to bring the axis of two bordering grains into coincidence, i.e. tilt boundary, shown in figure.
Tan =b/h (or) =b/h
Tan ~ = low angle boundaries (or) angle of miss orientation
B= length of burgers vector,
h= vertical length of two neighboring edge dislocations.
Twin boundaries:
Surface imperfections which separate two orientations that are mirror images of one another are called twin boundaries.
Twin boundaries occur in pairs, such that the orientation change introduced by one boundary is restored by other, as in fig:
Stacking faults:-
The stacking fault is a discrepancy in the packing sequence of the layers of atoms.
E.g. : In the FCC stacking sequence can be written as ABC, ABC…………….. and ……….. BC, BC……….. Which belongs to HCP structure instead of ……… ABC, ABC……………,.
Above figure shows the stacking fault in a FCC metal.
So we may conclude that stacking may arise when there is only small dissimilarity (electrostatic ally) between the stacking sequence of closed-packed planes in FCC and HCP metals.
Ferromagnetic domain walls:
When two ferromagnetic regions differ from one another only in the direction of magnetism, the boundary between them is an imperfection and is called a Ferromagnetic domain wall.
These domain walls determine the magnetic properties of ferromagnetic materials. Domain in a small region in a ferromagnetic properties of a material and is completely magnetized by spin exchange, interaction.
VOLUME DEFECTS:
Volume defects such as cracks may arise when there is only small electrostatic dissimilarity between stacking sequence of closed packed plane in metals.
Further when atoms are missing and a large vacancy arises which is also a volume imperfection.
Other particle inclusions, large voids (or) non-crystalline region with the dimensions of at least to be also called Volume imperfections.
