Imperfections or Defects in Crystals

IMPERFECTIONS IN CRYSTALS

In an ideal crystal (perfect crystal), the atomic arrangement is perfectly regular and continuous throughout.

But in real crystals due to some reasons the regular orientation of atoms may be disturbed at a point, along a line or in a region.

Definition

The disturbance occurred in the regular orientation of atoms is called crystal defect or imperfection.

The imperfections or defects are always present in the actual crystal and their effects are often very important in understanding the properties of crystals.

Some properties of crystal defects are structure sensitive i.e., properties such as mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength are greatly affected by the relatively minor changes in crystal structure caused by the imperfections.

Some other of properties crystals structure-insensitive i.e., properties such as stiffness and density are not affected by the presence of imperfections.

Classification of crystal imperfections (or Defects)

Crystalline imperfections are classified on the basis of their geometry as follows:

1. Point Defects

(a) Vacancies

(b) Interstitials

(c) Impurities

2. Line Defects

(a) Edge dislocation

(b) Screw dislocation

3. Surface Defects

(a) Grain boundaries

(b) Tilt boundaries

(c) Twin boundaries

(d) Stacking faults

4. Volume Defects

Cracks

Point Defects

Point defects are crystalline irregularities of atomic dimensions. They are imperfect points like regions in the crystal. One or two atomic diametre is the typical size of a point imperfection.

i. Point defects take place due to imperfect packing of bas atoms during crystallisation.

ii. They produce distortion inside the crystal structures.

iii. They produce strain only in its surroundings but they tions do not affect the regularity in other parts of the crystal.

Types of point defects

The different types of point defects are

(a) Vacancies

(b) Interstitial

(c) Impurities

(a) Vacancies

A vacancy is the simplest point defect in a crystal. It refers to a missing atom or vacant atomic site.

Whenever one or more atoms are missing from a normally occupied position as shown in fig 1.42, the defect caused is known as vacancy.

Vacancies may be single as shown in figure 1.42 or two or more of them.

These defects may arise due to imperfect packing during original crystallisation and thermal vibrations of the atoms at high temperatures.

The atoms surrounding the vacancies are displaced inwards thereby distorting the regularity of arrangement. There are different kinds of vacancies like Frenkel defect, Schottky defect, Colour center, etc.

Schottky defect

It refers to the missing of a pair of positive and negative ions in an ionic crystal.

Here, two oppositely charged ions are missing from an ionic crystal, therefore a cation-anion divacancy is created, (fig. 1.43) This is known as schottky defect or schottky imperfection or iron pair vacancies. Since a pair is missing, electrical neutrality is maintained.

Frenkel Defect

A vacancy associated with interstitial impurity is called Frenkel defect.

Here a missing atom (responsible for vacancy) occupies interstitial position (responsible for interstitial defect) (fig 1.44.)

This defect always occurs in ionic crystal. If a positive ion moves into an interstitial site in an ionic crystal, a cation vacancy is created in normal ion site, this vacancy-interstitial pair is known as Frenkel defect.

i. Frenkel defect does not change the overall electrical neutrality of the crystal.

ii. The presence of these defects in ionic crystals causes an increase in electrical conductivity.

(b) Interstitial defect

When an extra atom occupies interstitial space (i.e., voids) within the crystal structure without removing parent atom, the defect is called interstitial defect.

An atom can enter into interstitial space or void only if it is smaller than the parent atom otherwise it will produce atomic distortion or strain because interstitial atom tends to push the surrounding atoms further apart.

Types of interstitial defect

Interstitial defect has two types

(i) Self interstitial

(ii) Foreign interstitial

(i) Self interstitial

If an atom from same crystal occupies interstitial site, then it is called self interstitial. (Fig. 1.45 (a))

(ii) Foreign interstitial

If an impurity atom (foreign atom) occupies interstitial site, then it is called foreign interstitial. (Fig. 1.45(b))

(c) Impurities

When the foreign atoms (impurities) are added to crystal lattices, they are known as impurities. The defect is called impurity defect.

The impurity atom may fit in the structure in two ways giving rise to two kinds of impurity defects. They are

i. Substitutional impurity defect

ii. Interstitial impurity defect

i. Substitutional impurity defect

A substitutional impurity refers to a foreign atom that replaces a parent atom in the lattice (figure 1.46.)

Substitutional impurities change the electrical properties enormously.

Example

1. n-type and p-type semiconductors have substitutional impurities from th group and IIIrd group elements.

A controlled addition of impurity to a very pure semiconductor is the basis of producing many electronic devices like diode and transistors.

2. During the production of brass alloy, zinc atoms are doped in copper lattice. Here, zinc atoms are called as substitutional impurities.

ii. Interstitial impurity

An interstitial impurity is a small small size size atom occupying the empty space (interstitial) in the parent crystal, without dislodging any of the parent atoms from their sites (Fig. 1.47)

An atom can enter into interstitial or empty space only when it is substantially smaller than parent atom.

Example. In FCC iron, the atomic radius of iron atom is 0.225 nm. The carbon atoms with atomic radius 0.078 nm can occupy empty spaces in FCC lattice as interstitial impurities.

Line Defects or Dislocations (One Dimensional Effect)

The defects due to dislocation or distortion of atoms along a line are known as line defects.

These defects are also called dislocations. In the geometrical sense, they are one dimensional defects.

In line defect, a portion of a line of atoms is missing or displaced from its regular site.

Types of line defects

There are two types of line defects.

(a) Edge dislocation and

(b) Screw dislocation

(a) Edge dislocation

An edge dislocation arises when one of the atomic planes forms only partially and does not extend through the entire crystal (fig. 1.48.)

The atomic plane AB abruptly terminates at B. It is viewed as an extra plane inserted in between a set of parallel planes.

The edge of such a plane forms a line defect and it is called an edge dislocation.

The atomic row 1 passing through point B has one atom more than row 2 adjacent to it.

Classification of edge dislocation

Edge dislocations are symbolically represented by 1 or T depending on whether the incomplete plane starts from top or bottom of the crystal.

These two configurations are referred as

i. Positive edge dislocation

ii. Negative edge dislocation

i. Positive edge dislocation

If the extra plane of atoms is above the slip plane of the crystal than the edge dislocation is called positive as shown in fig 1.49. It is denoted by the symbol 1.

ii. Negative edge dislocation

If the extra plane of atoms is below the slip plane than the edge dislocation is called negative. (Fig. 1.49) It is denoted by the symbol T.

(b) Screw dislocation

Screw dislocation is due to displacement of atoms in one part of a crystal relative to rest of the crystal. The displacement terminates within crystal. This dislocation forms a spiral ramp around dislocation line (Fig. 1.50).

In a screw dislocation, there is a line of atoms about which crystal planes are warped to give an effect similar to threads of a screw.

The row of atoms marking the termination of the displacement is the screw dislocation. EF indicates the dislocation line.

The term screw represents that one part of the crystal is moving in spiral manner about dislocation line.

If spiral motion of one part of the crystal is in clockwise direction then, dislocation is right handed, on the other hand spiral motion is in anti-clockwise direction then, dislocation is left handed.

Surface Defects (Plane Defects)

The defects on the surface of material are called surface defects or plane defects.

They are also known as two dimensional imperfections.

Surface defects are due to a change in the stacking of atomic planes on or across a boundary.

Some important internal surface defects

(i) Grain boundaries

(ii) Tilt and twist boundaries

(iii) Twin boundaries

(iv) Stacking fault

(i) Grain boundaries

Whenever the grains of different orientations separate the general pattern of atoms and exhibits a boundary, the defect caused is called grain boundary. (Fig. 1.52)

A grain boundary is formed when two growing grain surfaces meet. The shape of the grain is usually influenced by the presence of surrounding grains.

This type of defect generally takes place during the solidification of liquid metal.

(ii) Tilt and twist boundaries

Tilt boundary is another surface imperfection. It is an array of parallel edge dislocations of same sign (i.e., either T or 1) arranged one above other in an array or series (figure 1.53)

Tilt boundary is a type of low angle boundary (i.e., less than 10°).

By rotation of an axis in the boundary, it is possible to bring the axis of two bordering grains into coincidence, then

Angle of tilt, tan θ = b / D

D- Dislocation spacing

b = Length of Burger's vector

When is very small, then tan θ = θ

θ = b / D

Twist boundaries

Twist boundaries are another type of low angle boundaries. It consists of atleast two sets of parallel screw dislocations lying in the boundary. In twist boundary, the rotation is about an axis normal to the boundary.

(iii) Twin boundaries

Twin boundaries are another surface imperfections.

If the boundaries in which the atomic arrangement on one side of the boundary is somewhat a mirror image of the arrangement of atoms of the other side (fig. 1.54). The defect caused is called twin boundary.

(iv) Stacking Faults

It is a kind of surface imperfection. Whenever the stacking of atoms is not in proper sequence throughout the crystal, defect caused is called stacking fault.

Explanation

Fig. 1.55(a) shows the proper sequence of atomic planes if we read from bottom to top as A - B - C - A - B - C - A - B - C

But fig. 1.55 (b) shows the sequence of atomic planes as A - B - C - A - B - A - B - A - B - C.

The region in which the stacking fault occurs (A - B - A - B) forms a thin region of a hexagonal close packing in a FCC crystal.