1. Lattice Defects

2. INTRODUCTION
Crystals will have a regular periodic arrangement of atoms.
Any deviation from this periodicity is known as defects or imperfections in crystals.
Definition: The deviation from the perfect periodicity of atomic arrays in crystals is known as crystal defects.

3. The crystal defects affect their properties such as mechanical strength, ductility, crystal growth, dielectric strength, magnetic hysteresis, conductivity, etc.
A perfect crystal, with every atom of the same type in correct position, does not exist.
Thus, all crystals have some defects. The defects in crystals may be confined to a point, line, surface and volume.

4. The basic classes of crystal defects are:
1. Point defects
(Zero-dimensional defects)
2. Line defects
(One-dimensional defects)
3. Surface defects
(Two-dimensional defects)
4. Volume defects
(Three-dimensional defects)

5. 1. Point Defects The point defects are one-dimensional defects
When an atom is missing or an atom is in an irregular place in the lattice structure, the corresponding defects are known as point defects.
A point defect produces strain in a small volume of the crystal surrounding the crystal, but does not affect the perfections distant parts of the crystal.

6. Point defects are of four types: (1) Vacancies
In general, point defects occur in metallic and ionic crystals.
Point defects are of four types:
(1) Vacancies
(2) Interstitial defects
(3) Substitutional defects
(4) Electronic defects

7. 1.1. Vacancies
Vacancies are simplest point defects in a crystal which refers to a missing atom at its site.
Definition: The defects due to the missing atoms at their lattice sites are called vacancies.
A crystal lattice with vacancy defect is shown in figure.

8. Vacancy defects are mainly due to the imperfect packing during the formation of crystal or due to thermal vibrations of atoms at high temperature.
At high temperature atoms are frequently and regularly change their positions leaving empty lattice sites behind their positions.
For most crystals, the thermal energy is of the order of 1 eV per vacancy.

9. The number of vacancies per unit volume of the crystal depends upon temperature.
In most cases, diffusion (mass transport by atomic motion) can only occur because of vacancies.
In case of ionic crystals, there are two types of point defects related to vacancies.
They are: (A) Schottky defects and
(B) Frenkel defects

10. Schottky defects
It is special case of vacancy defects in ionic crystals.
Definition: When a pair of vacancies is produced at one positive ion site and one negative ion site due to absence of positive and negative ions, then this type of defect is call the Schottky defect.
In ionic crystals, there are two types of possible vacancies, namely cation (+ve ion) vacancies and anion (–ve ion) vacancies.

11. When a +ve ion from the interior of the lattice moves out of the crystal to its surface, then a +ve vacancy is formed at its site.
The formation of +ve ion vacancy results in excess negative charge inside the crystal.
To maintain charge neutrality, a –ve ion moves to the crystal surface creating a –ve ion vacancy at its site.

12. NaCl, CsCl etc., exhibits Schottky defect
The formation of vacancies is illustrated in the following figure.

13. Frenkel defects
It is special case of vacancy and interstitial defects in ionic crystals.
Definition: When a pair of vacancies is produced at one positive ion site and one negative ion site by replacing positive and negative ions, then this type of defect is call the Frenkel defect.

14. Consider the periodic distribution of +ve and –ve ions in an ionic crystal.
When a +ve ion leave its site and settles in the interstitial position then it creates a vacancy in its position.
Thus, a vacancy and interstitial defects are created. This pair of defects is known as Frankel defect.
In case of Frankel defect also charge neutrality is maintained.

15. AgBr, AgCl, ZnS etc., exhibits Frankel defects
The formation of Frankel defects is described in the following figure.

16. 1.2. Interstitial defects
Definition: When an impurity atom tries to settle in the interstitial space between the parent atoms of the crystal without displacing, then such a defect is known as interstitial defect.
Interstitial impurities are much smaller than the atoms in the bulk matrix.
The formation of interstitial impurity defect is shown figure.

17. Formation of interstitial impurity defect is shown figure.
Example:
Carbon atoms are interstitial impurity atoms that are added to Iron to make Steel. In steel, Carbon atoms with radius of nm are well fitted in the interstitial spaces between the larger Iron atoms of radius nm.

18. 1.3. Substitutional defects
Definition: When an impurity atom occupies the one of the positions of the parent atoms of the crystal, then such a defect is known as substitutional defect.
A substitutional impurity atom is an atom of a different type than the bulk atoms.
Usually, substitutional atoms are close in size (within approximately 15%) to the bulk atom.

19. The formation of substitutional impurity defect is shown figure.
Example: Zinc atoms are substitutional impurity atoms that are added to Copper to make Brass. In brass, Zinc atoms with radius of nm have replaced some of the Copper sites of radius nm.

20. 1.4. Electronic defects
These defects are special case of point defects.
Errors in charge distribution in solids are called electronic defects.
These defects are produced when the composition of an ionic crystal does not correspond to the exact stoichiometric formula.

21. Stoichiometry is a state for ionic compounds where there is the exact ratio of cations to anions as prescribed by the chemical formula.
For example:
NaCl is stoichiometric if the ratio of Na+ ions to Cl ions is exactly 1:1
A compound is non-stoichiometric if there is any deviation from the exact ratio.s
The non-stoichiometric composition is caused by an excess of metal ions.

22. Example-1
Consider deviation from the stoichiometric formula in compound ZnO.
When a stoichiometric compound ZnO is heated in the presence of zinc vapour, a non- stoichiometric compound ZnyO is produced.
In ZnO, where y > 1, the excess cations occupy interstitial spaces.

23. During the process of heating, two electrons are released from each zinc atom and stays around an interstitial cation as shown in figure.

24. 2. Line Defects
These are also called as linear defects or dislocations.
These are one-dimensional defects
Definition:
“Dislocations are areas where the atoms are out of position in the crystal structure”
(OR)
“A dislocation is a one-dimensional defect around which some of the atoms are misaligned”.

25. Thus, dislocations refer to a linear disturbance of the atomic arrangement in a crystal.
Dislocations are generated in crystals due to growth accidents, thermal stress, phase transformation etc.
They can be observed in crystalline materials with the help of electron microscope.

26. They are two basic types of dislocations:
Edge dislocations and
Screw dislocations.
Most of the dislocations found in crystals are neither pure edge nor pure screw dislocations, but contain components of both these types. They are called mixed dislocations.

27. 2.1. Edge dislocations
If one of the vertical planes does not extended to the full length, but ends in between, within the crystal, then such a defect is known as edge dislocation.
In perfect crystal, atoms are arranged in both vertical and horizontal planes as shown in Fig .
From the figure it is clear that the atoms are in perfect equilibrium in their positions and all bond lengths are in equilibrium state.

28. If one of the vertical planes does not extend to the full length, but ends in between within the crystal as shown in Fig. it is called edge dislocation.
Because of dislocation, (i) just above the discontinuity, the atoms are squeezed and are in state of compression and (ii) just below the discontinuity; the atoms are pulled apart and are in state of tension.

29. The distorted configuration spreads all along the edge into the crystal.
Thus, the maximum distortion is centered around the edge of the incomplete plane.
This distortion represents a line imperfection and is called an edge dislocation.
Edge dislocations are symbolically represented by ┴ or ┬.

30. When the incomplete plane starts from the top of the crystal, then it is called positive edge dislocation and is represented by “┴” (see Fig. a)
When the incomplete plane starts from the bottom of the crystal, then it is called negative edge dislocation and is represented by “┬” (see Fig. b).

31. 2.2. Screw dislocations
The screw dislocations are also known as Burger dislocations.
These dislocations arise due to the displacement of atoms in one part of a crystal relative to the other part
[forming a spiral ramp around the dislocation line].

32. Consider a perfect crystal having regular periodic arrangement of atoms. When one face of the crystal is cut midway along AB, and applying a shear stress parallel to the cutting plane P.

33. Let the crystal on the right side of the cut be shifted (sheared) relative to that on the left side by an amount of ‘b’, as shown in figure.
From the figure one can see that the shift has occurred for the length of one atomic spacing in the predominant part of the crystal and reached the line OO1.
Away from the line OO1, the crystal structure is undisturbed and shows an ordered atomic arrangement.

34. Along the cut boundary, the atoms get displaced and two regions will be in mismatched condition
i.e., dislocation of atoms take place around the edge line AB known as dislocation line.
From the top surface, the dislocation of atoms will be in the form of screw or spiral around AB.
Hence, this dislocation is known as screw dislocation.

35. Burger Vector
The magnitude and direction of the lattice distortion associated with a dislocation is called Burger vector.
Dislocations are quantitatively described by the Burger vector, and is donated by ‘b’
The magnitude of Burger vector is found by drawing a closed circuit around the dislocation line. This circuit is called Burger’s circuit.

36. Consider a perfect crystal as shown in Fig.
In fig. starting from the point P, we go up by 6 steps, then move towards right by 5 steps, and move down by 6 steps, and finally move towards left by 5 steps to reach the point P and the Burger circuit gets closed.

37. The magnitude and direction of the step is called Burger Vector.
Consider the case of edge dislocated crystal shown in Fig.
When the same operation is performed on the crystal, we end upto at point Q instead of the starting point P.
Now, we have to move an extra step to return to point P in order to close the Burger circuit.
The magnitude and direction of the step is called Burger Vector.
Burger vector = = b
Note:
The Burger vector is perpendicular to the edge dislocation.

38. Consider the Berger circuit in a crystal that contains screw dislocation.
In the perfect crystal, starting from P, if we trace the Burger circuit, the circuit is closed path PMNOP as shown in Fig.

39. In case of a crystal with a screw dislocation shown in Fig
In case of a crystal with a screw dislocation shown in Fig. (b), the circuit would not be completed and requires an extra step b = FA, parallel to the dislocation axis to close the circuit. This additional vector b is called Burger vector.
Note:
The Burger vector is parallel to the screw dislocation.

40. 3. Surface Defects These are two-dimensional defects
The regions of distortions that lie about a surface having a thickness of few atomic diameters are known as surface defects.
Surface defects are two-dimensional defects that separate two regions of the crystal.
Surface imperfections are metastable imperfections.
If the crystal is heated close to its melting point, many of the surface imperfections disappear.

41. 2. Grain boundaries 3. Twin boundaries 4. Staking faults
Surface defects are of four types
1. External surfaces
2. Grain boundaries
3. Twin boundaries
4. Staking faults

42. 3.1. External surfaces The surface of a crystal itself is a defect.
The surface atoms have formed bonds with neighbours only on one side, whereas the atoms inside the crystal formed bonds with neighbours on either side of them.

43. Since the surface atoms are not bonded to the maximum number of nearest neighbours, they are in a state of higher energy than the atoms in the interior of the crystal. This gives rise to a surface energy.
The crystal tends to minimize the total surface area in order to reduce the surface energy, but it is not possible because solids are mechanically rigid.

44. 3.2. Grain Boundaries
The most important defect in crystalline samples is the grain boundary.
Grain boundaries are 2D defects in the  crystal structure.
A grain boundary is the interface between two grains, or crystallites in a polycrystalline material.
They tend to decrease the electrical and thermal conductivity of the material.

45. Grain boundaries are illustrated in Fig (a).
Grain boundaries disrupt the motion of dislocations through a material , Fig (b)
So reducing crystallite size is a common way to improve mechanical strength.

46. 3.3. Twin Boundaries This is another planar surface defect
A region in which mirror image of structure exists across a boundary is known as twin boundary.
They are formed during plastic deformation and recrystallization.
They may be produced by shear deformation.

47. The atomic arrangement on one side of a twin boundary is a mirror reflection of the arrangement on the other side as shown in Figure.

48. At one boundary, orientation of atomic arrangement changes, whereas at the other boundary it is restored back.
Hence, one side of a twin boundary is a mirror reflection of the other side.
The region between the pair of boundaries is called twinned region.
Twin boundaries are identified under an optical microscope.

49. 3.4. Staking Faults
Stacking faults are planar surface imperfections caused by fault in the stacking sequence of atomic layers in crystals.
In FCC crystal we have three different stacking layers ABC (Fig. a), while in HCP stacking we have only two different layers BC (Fig. b).

50. Hence, when FCC crystal grows we have the stackings as
…….. ABCABCABCABC ………..
While growing, if the plane A is missing then we get the sequence

51. Thus, the sequence is interrupted and a stacking fault is produced.
Therefore, we find that the stacking in the missing region becomes HCP.
The stacking faults are usually produced during the growth of the crystals.
Note: Stacking faults are observed in FCC metals

52. 3.5. Volume defects Volume defects are two-dimensional defects
Volume defects such as cracks may arise in crystals during the process of crystal growth.
While growing, any possible small electrostatic dissimilarity between the stacking layers may result in crack.

53. A large vacancy may arise due to missing of clusters of atoms which is a volume defect.
Inclusion of foreign particles or non- crystalline regions of dimensions of at least 10-30Å also belong to the category of volume defects.
Using optical microscopes, presence of volume defects can be detected.
Interferometric techniques can also be applied to study the volume defects.

54. The End