Burger's Vectors

BURGER'S VECTORS

The dislocation lines are expressed by a burger vector It indicates the amount and direction of shift in lattice on slip plane. The figure 1.39 shows a perfect crystal and a crystal with a positive edge dislocation.

Consider a point starting from P in (fig. 1.39 (a)) which moves in a particular direction as shown and it completes atomic distances in the form of a circuit called "burger circuit" or "burger loop".

If the same circuit is drawn starting from P in fig. (1.39 (b)) then the circuit would not complete, this is because of the presence of a dislocation.

If we wish to arrive at starting point P from Q, then we must move an extra distance 'b' as shown in figure (b). The vector connects end point with starting point. This is burger's vector of the dislocation.

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 of different orientations separate the general pattern of atoms and exhibits a boundary, the defect caused is called grain boundary. (Fig. 1.41)

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 ⊥) arranged one above other in an array or series (figure 1.42.)

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 θ is very small, then tan θ = 0

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. 1.43,). The defect caused is called twin boundary.

Stacking Faults

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

Explanation

Fig. 1.44(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. 1.44 (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.