The mathematically perfect crystal is an exceedingly useful concept. In actual crystals, however, imperfections or defects are always present and their nature and effects are often very important in understanding the properties of crystals.
This is because some properties of materials such as stiffness, density and electrical conductivity which are termed structure-insensitive, are not affected much by the presence of defects in crystals while many of the properties of greatest technical importance such as mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength, which are termed structure sensitive are greatly affected by the relatively minor changes in crystal structure caused by defects.
Ordinary materials, however, contain imperfections of various kinds that produce both useful properties and also such undesirable effects as causing the strength to decrease below that of a perfect crystal.
The structural imperfections can be classified on the basis of their geometry and, the common types of crystallographic defects in solid materials are summarized as:
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1. Point defects or zero dimensional defects:
(i) Vacancies (Schottky defect)
(ii) Interstitialcies (Frenkel defect)
(iii) Compositional defect-
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(a) Substitutional impurity
(b) Interstitial impurity
(iv) Electronic defect
2. Line defects or one dimensional defect:
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(i) Edge dislocation
(ii) Screw dislocation
3. Surface defects or two dimensional defects:
(i) External surface defects
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(ii) Internal surface defects-
(a) Gain boundaries
(b) Twin boundaries
(c) Tilt boundaries
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(d) Stacking fault
4. Volume defects or three dimensional defects.
Thermal Vibrations:
No crystal is perfectly rigid, since it can be deformed by finite forces. Hence, it is possible to displace atoms from their ideal sites with a finite expenditure of energy due to thermal vibrations. The frequency of vibration is almost independent of temperature, but the amplitude increases with increasing temperature.
When the vibration becomes strong enough the atoms may break the bonds between them and this corresponds to the solid actually melting and becoming liquid, the corresponding temperature is melting temperature. Since the atoms interact with one another, they tend to vibrate in synchronism; that is, groups of atoms tend, to move in the same direction, somewhat as waves on the ocean.
Because the energy of a particular type of wave can be measured in units known as phonons, the thermal energy of the entire solid specimen is represented quite simply by a certain collection of phonons, each one of which is pictured as a special kind of ‘particle’. The thermal vibration of atoms of a solid as it is does not seriously disturb the perfection of the crystal. Every atom is on the average, in its proper position. Each atom, therefore, has requisite number of nearest neighbours at proper spacing.
Type # 1. Point Defects:
Point imperfection is lattice error at isolated lattice points. As the name implies, there are imperfect point-like regions in the crystal and, therefore, they may be referred to as zero-dimensional imperfections. A point defect extends its influence only a few atom diameters beyond its lattice position. A point imperfection comes about, as a rule, because of the absence of a matrix atom, the presence of an impurity atom on a matrix atom in the wrong place.
The most common point defects in a crystal of a pure element are described below:
i. Vacancies (Schottky Defect):
A vacancy is the simplest point defect in crystal. This refers to a missing atom or vacant atomic site. If the missing atom is transferred to the surface of the crystal, the defect is known as Schottky defect. Such defects may arise either from imperfect packing during the original crystallisation or from thermal vibrations of the atoms at high temperature.
In the latter case, when the thermal energy due to vibration is increased there is an increased probability that individual atoms will jump out of their positions of lowest energy. For most crystals, this thermal energy is of the order of 1 eV per vacancy. Vacancies may be single or two; or more and may condense into a di-vacancy or tri-vacancy [Fig. 3.1 (a)].
ii. Interstitialcies (Frenkel Defect):
In a close-packed arrangement of atoms if the atomic packing factor is low, an extra atom may be lodged within the crystal structure. This is known as interstitials. An atom can enter the interstitial void or space between the regularly positioned atoms only when it is substantially smaller than the parent atom [Fig. 3.1 (a)], otherwise it will produce atomic distortion. Interstitialcies may also be single interstitial, di-interstitials and tri-interstitials. The combination of interstitial atom and vacancy constitutes a Frenkel defect.
Schottky and Frenkel Defects in Ionic Solids:
In nonmetallic crystals, the formation of a vacancy involves a local readjustment of charge in the surrounding crystal such that charge neutrality is maintained in the crystal as a whole. Thus, if in an ionic crystal there is a vacancy in a positive-ion site; charge neutrality may be achieved by creating a vacancy in neighbouring negative-ion site. Such a pair of vacant sites is called Schottky defect [Fig. 3.1 (b)].
This is closely related to vacancies. On the other hand, if the charge neutrality is maintained by having a positive ion in an interstitial position, the pair constitutes a Frenkel defect (Fig. 3.1 (b) closely related to interstitialcies). Moreover, a missing atom in a metal lattice also constitutes a Schottky defect, when the atom is transferred to the surface of a crystal.
Close-packed structures have fewer interstitialcies and Frenkel defects than vacancies and Schottky defect, as additional energy is required to force the atoms in their new positions.
Concentration of Schottky Defects:
If Ev is the energy required to take an atom from a lattice site inside the crystal to a lattice site on the surface (called the enthalpy of formation of the point imperfection), n Ev is the increase in energy associated with the generation of n isolated vacant sites. The total number of ways in which we can pick up n-atoms from the crystal consisting of N atoms is given by-
Since disorder increases due to the creation of n vacancies the corresponding increase in entropy is given by-
This is the turn produces a change in free energy F,
Using Stirling approximation-
log x ! ≅ x log x – x
We have, F = nEv – kBT [N log N – (N – n) log (N-n) – n log n]
Free energy in thermal equilibrium at constant volume must be minimum with respect to changes in n; i.e.,
The equilibrium concentration of vacancies decreases as the temperature decreases.
In ionic crystals, the formation of paired vacancies is most favoured and the number of pairs can be related to the total number of atoms present in the crystal.
The different ways in which n separated pairs can be formed are:
Increase in entropy is given by-
With corresponding change in free energy-
where, Ep is the energy of formation of a pair.
Using Stirling approximation, the free energy is-
F = nEp – 2kBT [N log N – (N – n) log (N – n) – n log n]
Differentiating the above equation with respect to n, we get-
At equilibrium, the free energy is constant, so that-
provided n << N. In NaCl crystal Ep = 2.02 eV and at room temperature-
It is interesting to conclude from – (i) and (ii) that a certain amount of defect is always present at all temperatures above absolute zero and that the number of defects present in a crystal increases exponentially as its temperature rises. It may be added, however, that these calculations are not very rigorous; these have ignored for example, the tendency of the vacancies to pair up or to move together, although not necessarily adjacent to each other. This tendency of vacancies is due to their having effective charges- a cation vacancy has a negative charge and an anion vacancy has a positive charge.
Concentration of Frenkel Defects:
Proceeding in the same way as in the case of Schottky defect, we can calculate the number of Frenkel defects in equilibrium at a temperature T. Let in a perfect crystal, Ei be the energy required to displace an atom from a regular lattice site to an interstitial position, Ni be the interstitial atoms and N be the number of atoms.
Now the total number of ways in which n Frenkel defect can be formed is given by-
The corresponding increase in entropy due to the creation of Frenkel defect is given by-
Which in turn produces a change in free energy-
Using Stirling’s approximation and substituting the value of a logarithmic term in the expression for free energy and then differentiating with respect to n, we get-
showing that n should be proportional to [NNi]1/2.
This is the expression for the equilibrium concentration of Frenkel defects at the temperature T. Like (i), this also predicts that certain amount of defects is always present at all temperatures above absolute zero, and that the number of defects present in a crystal increases exponentially as its temperature rises; the exponential factor in this case being a function of different energy than it was in (i).
Again, the treatment has not been very rigorous; it ignores, in particular, the possible interaction among the interstitial atoms, the tendency of which is to cluster atoms in the same way as the vacancies are combined to form voids.
One may now note that both the kinds of defects must be present in all solids at all temperatures. But there is always a tendency for one type of defect to predominate since their energies of formation are usually unequal.
In pure alkali halides, for example, it is believed from ionic conductivity studies and density measurements (production of Schottky defects obviously lowers the density of the crystal, whereas that of Frenkel defects does not) that the Schottky defects below 700°K are the Frenkel defects. In metals, it appears that the energy favours the formation of Schottky defects, although Frenkel defects undoubtedly are also formed.
iii. Compositional Defects:
Compositional defects arise from impurity atom during original crystallization. Impurity atom considered as defects in a perfect lattice are responsible for the functioning of most semiconductor devices. They occurs on a lattice point as a substitutional impurity or as an interstitial impurity and the resulting phase is known as solid solution.
A substitutional impurity is created when a foreign atom substitutes for a parent atom in the lattice [Fig. 3.2(a)]. 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 [Fig. 3.2(b)]. In steel, carbon atoms occupy the interstitial positions in the iron lattice.
iv. Electronic Defects:
Errors in charge distribution in solids are termed electronic defects. This does not imply that deviations from smooth uniformity of charge within the volume of a unit cell are defects. Far from it, the charge distribution is actually non-uniform. However, departures from the normal regularity of charge distribution or energy are electronic defects.
Deviations of special distribution of charge commonly accompany the geometrical or structural crystal defects just discussed. For example, an impurity atom may have a charge quite different from that of the host atoms and hence may produce a local electronic charge deviation.
In addition to these, the electron in a geometrically perfect lattice may themselves move in such a way as to produce local fluctuations in charge. Furthermore, the electrons may absorb varying amounts of thermal energy so that their motion through the lattices is altered.
These so-called electronic imperfections are primarily necessary to explain electrical conductivity and related phenomenon in solids. Perhaps the most prominent 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.
Production of Point Defects:
In addition to point defects formed by thermal fluctuations, point defects may be created by other means also. One method of producing an excess number of point defects at a given temperature is by quenching (quick cooling) from a higher temperature.
Another method of creating excess defects is by severe deformation of the crystal lattice, for example, by hammering or rolling. While the lattice will retain its general crystalline nature, numerous defects are introduced.
A third method of creating excess point defects is by external bombardment by atoms or high-energy particles, for example, from the ion beam of the accelerator or the neutrons in a nuclear reactor. The first particle collides with the lattice atoms and displaces them, thereby forming a point defect. 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.
Type # 2. Line Defects or Dislocations:
As the name implies, line defects are those which extend along some direction in a crystal. 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. Note that 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 emphasizes that it is only the termination of the displacement which introduces the defect. It is obvious that this defect is centered along a line which is also the boundary between the slipped and un-slipped regions of the crystal. This defect is commonly called a dislocation and boundary as the dislocation line.
Virtually all crystalline materials contain some dislocations that were introduced during solidification, during plastic deformation, during segregation of solute atoms, and as a consequence of thermal stresses that result from rapid cooling.
It has been found that there are two basic types of dislocations- edge dislocation (or Taylor-Orowan dislocation), and screw dislocation (or Burgers dislocation). We now describe the geometry of these two types of dislocations.
i. Edge Dislocation:
The geometry of edge dislocation may be understood in terms of a slip process occurring with reference to Figs. 3.8 (a) and 3.8 (b). Fig. 3.8 (a) shows the external character of a simple cubic crystal after it has undergone the following operation- Let the upper half is pushed sideways, keeping the right side rigid, such that the line A’B’, which initially coincide with AB, is shifted by an amount ‘b’ as is indicated and is known as Burgers vector.
The vector ‘b’ giving both the magnitude and direction of the displacement. Fig. 3.8 (b) shows the square network of lines drawn (through atoms) on the front face BCD of the crystal after the operation. It obviously follows that the slip process introduces an extra line of atoms somewhere in the middle of the upper half of the network, which corresponds to the extra plane of atoms in the crystal.
This extra plane of atoms terminates along an ‘edge’ in a plane between the slipped and the un-slipped regions. Realize that this ‘edge’ is also the boundary along which the displacement of the slipped region over the un-slipped region is terminated, and hence constitutes a dislocation in the crystal.
This is the edge dislocation as it is centered along the edge, and the edge is the dislocation line. Dislocation line runs indefinitely in the slip plane in a direction normal to the slip direction. According to Fig. 3.8, it is perpendicular to the paper through the point E, i.e., EF is the dislocation line.
The edge dislocations containing the extra plane of atoms lying above the slip plane are conventionally called the positive edge dislocations, and those containing that lying below the slip plane the negative edge dislocations.
The positive edge dislocation is represented by the symbol ‘⊥’ and negative edge dislocation by ‘⊤’ where the horizontal line in the symbol represents the slip plane and the vertical line the incomplete atomic plane. These symbols also indicate the position of the dislocation line. Fig. 3.8 (c) shows the atomic view in an edge dislocation.
ii. Screw Dislocation:
The geometry of screw dislocations may be understood in terms of a slip process of a different kind that occurs with reference to Fig. 3.9 (a) and 3.9 (b). Fig. 3.9 (a) shows the external character of simple cubic crystal after it has undergone the following operation- Let the crystal on one side be displaced (i.e. sheared) relative to that on the other side by an amount b parallel to the cut.
Similarly, b is again a Burgers vector giving both the magnitude and the direction of the displacement. Fig. 3.9 (b) shows the network of lines drawn (through atoms) inside the structures (a) after the operation. It obviously follows from these figures that the displacement in this case terminates in the crystal along a row EF of atoms, and consequently constitutes a dislocation in the crystal. This is screw dislocation and EF is the dislocation line in the case.
We may note that this dislocation line is parallel to the slip direction. The name ‘screw’ follows from the new character of the atom planes which are transformed such that as one moves around the dislocation line in a circuit such as shown in Fig. 3.9 (b), one advances in the direction of the dislocation line by an amount equal to ‘b’ for every turn, (b may be one or more atom distance). This is at once understood if one recalls, in addition the character of motion along the grooves of a screw.
Thus, when the screw dislocation is present in a crystal, the complete planes of atoms normal to the dislocation no longer exit. Rather, all atoms lie on a single surface which spirals from one end of the crystal to the other with dislocation line as the axis of the spiral. The displacement of the atoms from their original positions in the perfect crystal is described by the equation-
r = b/2 θ (spiral ramp)
where, r is the displacement along the dislocation line, and the angle θ is measured from some axis perpendicular to the dislocation line. Note that as θ increases by 2, the displacement increases by the factor b. Thus, b is, in this respect, the measure of the strength of dislocation.
It may now be added that both the dislocation types are accompanied by the distortion in the crystal. This distortion varies with distance from the center of the dislocation, being severest in the immediate vicinity of the dislocation line. In fact, along the dislocation line the atoms may not even possess the correct number of neighbours (which is the characteristic property of the perfect crystals), while not more than a few atom-distance away from the center, the distortion is so small that the crystal is locally nearly perfect.
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. It may be realized that in case of edge dislocation the local strain is composed of dilation (with tension below the dislocation edge and compression above it). Whereas in case of screw dislocation it is composed of shear.
Burgers Vector:
An important property of a dislocation is its Burgers vector, b which indicates the extent of lattice displacement caused by the dislocation. The Burgers vector also indicates the direction in which slip will occur. An edge dislocation is represented in Fig. 3.10. It can be assumed that the edge dislocation is due to the presence of an additional half-row of atoms within the lattice.
If an atom-to-atom circuit is described within a portion of regular lattice, as shown in the lower half of Fig. 3.10, it will be a complete closed circuit, start (S) and finish (F) of the circuit meeting at the same atom. If however, a similar circuit is described around the dislocated portion of the lattice, the start and finish will not be co-incident as shown in the upper half of Fig. 3.10. The distance SF will be the Burgers vector b. In an edge dislocation, b vector is normal to the dislocation line.
As we have taken the Burgers circuit to be clockwise, the direction of the Burgers vector depends upon the direction of the circuit which can be clockwise or anticlockwise. To avoid this ambiguity, a unit vector ‘t’ is first assigned to denote the direction of the dislocation line. The direction vector is drawn tangential to the dislocation line at the point of interest.
Then a right hand screw convention is followed in tracing the circuit, i.e., we place the end of an ordinary screw on the paper and turn the head of screw clockwise, the screw tends to move into the plane of the paper. If the vector ‘t’ has a direction vertically into the plane of the paper, the Burgers circuit should be drawn clockwise.
In case of a screw dislocation, a Burgers circuit describes a helical, or screw path and b is in the same direction as the line of dislocation. Screw dislocations are symbolically represented by ͽ or ͼ depending on whether the Burgers vector and ‘t’ vector are parallel or antiparallel, where ‘t’ vector is the dislocation line. These two-cases are referred to as positive and negative screw dislocations.
Mixed Dislocations:
Most dislocation found in crystalline materials is probably neither pure edge nor pure screw, but exhibit components of both types, these are termed mixed dislocations. All three dislocation types are represented schematically in Fig. 3.11 the lattice distortion that is produced away from the two faces is mixed, having varying degrees of screw and edge character.
Comparison between an Edge Dislocation and a Screw Dislocation:
Edge:
1. These dislocation arises due to introduction or elimination of an extra row of atoms.
2. Tensile, compressive and shear stress fields may be present.
3. Region of lattice disturbances extents along an edge inside a crystal.
4. The force required to form and move edge dislocation is smaller than screw dislocation.
5. Burgers vector is always perpendicular to the dislocation line.
6. These dislocations are formed during deformation and crystallization.
7. An edge dislocation can glide and climb.
Screw:
1. A screw dislocation provided for easy crystal growth because additional atoms and unit cells can be address to step of the screw.
2. Only shear stress field stress.
3. Region of lattice disturbance extends in two separate planes at right angles to each other.
4. The force required to form and move screw dislocation is larger than edge dislocation.
5. Burgers vector is parallel to the dislocation line.
6. These are also formed during deformation and crystallization.
7. A screw dislocation can slide only.
Furthermore, the nature of a dislocation (i.e., edge, screw, or mixed) is defined by the relative orientations of dislocation line and Burgers vector. For an edge, they are perpendicular (Fig. 3.8), whereas for a screw, both are parallel (Fig. 3.9); they are neither perpendicular nor parallel for a mixed dislocation.
Also even though a dislocation changes direction and nature within a crystal (e.g., from edge to mixed to screw), the Burgers vector will be the same at all points along its line. For example, all positions of the curved dislocation in Fig. 3.11 will have the Burgers vector shown. For metallic materials, the Burgers vector for a dislocation will point in a close-packed crystallographic direction and will be of magnitude equal to the interatomic spacing.
Full and Partial Dislocations:
Dislocation in real crystals can be classified as full and partial dislocation. For a partial dislocation, the Burgers vector is a function of a lattice translation. For a full dislocation, the Burgers vector is an integral multiple of a lattice translation. As the elastic strain energy of a dislocation is proportional to the square of the Burgers vector, dislocations tend to have as small as a Burgers vector as possible.
The most probable Burgers vectors of full dislocation in cubic crystals are given below:
Note that the Burgers vector in a CsCl crystal cannot be from a body corner to the body centre, as this is not a full lattice translation. If we have an edge dislocation with Burgers vector of 1/2 <111> in a CsCl crystal, the extra plane will have excess electrical charges. The crystal as a whole will not be electrically neutral and therefore, such a configuration is not stable.
Similarly, the Burgers vector in a NaCI crystal cannot be from the centre of a chlorine ion at the body corner to the centre of a sodium ion halfway along the cube edge. This restriction in ionic crystals tends to make the Burgers vectors large e.g. in the FCC crystal of Cu, the Burgers vector of a full dislocation is only 2.55Å whereas in NaCI crystal, the Burgers vector is 3.95Å.
Type # 3. Surface Imperfections:
Surface imperfections of a structural nature arise from a change in the stacking of atomic planes on or across a boundary. The change may be one of the orientation or of the stacking sequence of the planes. In geometric concept surface imperfections are two-dimensional.
There are two types of surface defects- external and internal:
i. External Surface Imperfections:
The external types is just what its name implies, the imperfections represented by a boundary. The most obvious boundary is the external surface. Although we may visualise a surface as simply a terminus of the crystal structure, we should appreciate the fact that the atoms on the surface cannot be compared with the atoms within a crystal.
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 that of internal atoms. This energy of the surface atom, for most metals, is of the order 1 J/m2.
ii. Internal Surface Imperfections:
Internal surface imperfections are manifested by such defects as grain boundaries, tilt boundaries, twin boundaries, and stacking faults.
a. Grain Boundaries (High Angle Grain Boundaries):
Grain boundaries are those surface imperfections which separate crystals or grains of different orientation in a polycrystalline aggregation during nucleation or crystallisation. 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 surrounding atoms.
As a result, a region of transition exists in which the atomic packing is imperfect. The boundary where the crystals or grains change orientation abruptly and orientation difference between neighbouring grains is more than 10-15°, the boundaries are known as high angle grain boundaries and are sketched in Fig. 3.13 (a). Although a grain boundary is two-dimensional it has a definite thickness of 2 to 10 or more atomic distances.
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 arrangements or different compositions is called an interphase boundary or commonly an interface.
b. Tilt Boundaries (Low Angle Grain Boundaries):
Tilt boundary is another surface imperfection. This is called low-angle boundary as the orientation difference between two neighbouring crystals less than 10°.
This is why the disruption in the boundary is not as drastic as in the high-angle boundary. In general, low-angle boundaries can be described by suitable arrays of dislocation. A low-angle tilt boundary is composed of edge dislocation lying one above the other in boundary [Fig. 3.13(b)]. The angle of tilt will be θ = b/D, where b is the magnitude of the Burgers vector and D is the average vertical distance between dislocations.
c. Twin Boundaries:
Another planar surface imperfection is a twin boundary. The atomic arrangement on one side of a twin boundary is a mirror reflection of the arrangement on the other side. Twin boundaries occur in pairs, such that the orientation change introduced by one boundary is restored by the other. The region between the pair of boundaries is called the twinned region.
Twin boundaries are easily identified under an optical microscope. Twins which form during the process of recrystallization are called annealing twins and those which form during plastic deformation of the material are called deformation twins. Mechanical twins are produced in bee or hcp metals under conditions of rapid rate of loading and decreased temperature.
d. Stacking Faults:
A stacking fault results when in the regular stacking sequence of a crystal one plane is out of sequence, while the lattice on the either side of the fault is perfect. As an example, let us consider the stacking sequence of close-packed planes to form an ideal fcc crystal- ABCABCABC… ; and suppose, somehow or the other, this sequence has changed into the sequence ABCABABCA The ‘A’ plane of atoms after the second ‘B’ constitutes as a very thin region of hcp stacking in the fcc crystal.
The stacking faults are usually produced during the growth of the crystals. When close-packed layers grow one over the other to form a close-packed crystal, it is possible for a layer to start incorrectly; that is a C layer can start to grow, for example, instead of the B layer as required by the preceding stacking sequence.
These mechanisms favoured if the crystal grows sufficiently rapidly. The other possible mechanism which can also produce these defects is the plastic deformation of crystals. When the plastic deformation takes place, a B layer may be displaced to the site of a C layer (see Fig. 3.15) and the stacking sequences may thus change. This actually takes place by the relative motion of the two parts of a crystal.
The persistence of the faults produced by this mechanism after the forces producing the displacement are removed is due to the fact that the immediate coordination of each atom is not changed (i.e., the CN value remains at 12 regardless of the stacking sequence). The energy requirements for the production of these faults are evidently very high.
The production of stacking faults can also be described in terms of dislocations. To understand this, consider a hcp layer (designated as A-layer), and suppose that the next identical layer above it is a 6-layer; see Fig. 3.15. Next, observe that if this layer is displaced along BC, a stacking fault is produced, if it is displaced along BB (=b, the Burgers vector), a unit dislocation is produced; BC < BB. It will be evident then that a stacking fault is produced whenever a partial dislocation gets into the crystal. The crystal may be expected to behave differently in the region of stacking faults.
Surface defects are not stable in a thermodynamic sense, i.e., if the thermal energy is increased by heating a crystal close to its melting point, many of the surface defects can be removed. The grain boundary area decrease, as larger crystals grow at the expense of smaller crystals.
Type # 4. Volume Defects:
Volume defects such as cracks may arise when there is only small electrostatic dissimilarity between the stacking sequences of closed packed planes in metals. Further when cluster of atoms are missing, a large vacancy or void is got which is also a volume defect. Mosaic structure and inclusions are the defects which are distributed volume-wise.
The individual imperfections in crystals group together and form systems. Under the influence of nets of imperfections, a crystal decomposes into perfect parts mutually separated by the net, so that in small angle ranges, the individual perfect parts are mutually disoriented. Such a crystal is called mosaic.
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 crystallization. Foreign particle inclusions, large voids or non-crystalline regions which have the dimensions of the order of 20Å are also called volume imperfections.
Comparison between Slip and Twinning:
Slip:
1. It is a shear deformation that moves atoms by many interatomic distances in one crystal plane over the atoms of another crystal plane.
2. It occurs in discrete multiples of atomic spacing.
3. The orientation of the crystal above and below the slip plane is the same after and before deformation.
4. It occurs over wide planes.
5. Slip begins when shearing stress on the slip plane in the slip direction reaches a threshold value called the critical resolved shear stress.
6. It takes place in several milliseconds.
7. Slip lines do not appear during any heat treatment.
8. Slip lines disappear after grinding or other surface finishing operations.
9. Slip lines may be present in even or odd numbers.
Twinning:
1. It is that process by which a portion of the crystal takes up an orientation which makes that portion a mirror image of the parent crystal.
2. Atom movements are much less than the atomic spacing.
3. Orientation difference takes place across the twin plane.
4. Every atomic plane is involved.
5. There is no critical resolved shear stress for twinning.
6. It takes place in few microseconds.
7. Twin lines appear during the annealing operation of materials.
8. Twin lines run through the whole depth of the material and hence do not disappear or grinding etc.
9. Twin lines always occur in pairs.