Dislocations: Theory and Characteristics | Metals

In this article we will discuss about:- 1. Theory of Dislocations 2. Role and Significance of Dislocations 3. Characteristics 4. Properties.

Theory of Dislocations:

Dislocations are defined as the irregularities in the structure of metals. These arise from misplacement of bonds of the atoms in a part of the plane of a crystal and are considered to be weak centres. They are instrumental in affecting the breaking stress and plastic and chemical properties of crystals. The importance of dislocations lies primarily in the fact that they can move.

It is believed that dislocations originate mainly when a crystal is stressed, but some may be produced during the solidification of the metal, due to impurity atoms and thermal vibrations. In good crystals the normal density of dislocation lines is around 10⁸/cm² whereas in deformed crystals it may be as high as 10¹²/cm².

In addition to the grain boundaries, each grain may also possess small angle boundaries separating crystallines with only a small mis-orientation with respect to each other to yield sub-grains. Precipitates or second phase particles in the grain form interphase boundaries. All these boundaries are the preferred sites where dislocations are generated because the existing mis-arrangement in the atomic structure takes the shape of dislocations on the application of stress.

Some Salient Points in Relation to Theory of Dislocation:

1. Climb:

An edge dislocation can glide or slip in a direction perpendicular to its length. However, it may move vertically by a process known as climb. Climb needs a mass transport by diffusion. Since movement by climb is diffusion-controlled, motion is much slower than in glide and less likely except at high temperatures.

2. Cross Slip:

A cross slip is a process whereby a screw dislocation glides into another slip plane having a slip direction in common with the original slip plane (Fig. 3.23). In F.C.C., crystal the cross slip plane is a closed packed plane and is suitably stressed.

3. Jogs in Dislocations:

Refer to Fig. 3.24. Where the dislocation jumps from one plane to another it is known as Jog. A jog in a dislocation may be regarded as a short length of dislocation not lying in the same plane as the main dislocation but having the same Burger’s vector.

4. Partial and Perfect Dislocations:

In ‘partial dislocations’ the original dislocation dissociates into two portions which move together as a unit. The Burger’s vector for each partial dislocation may then be a fraction of the lattice spacing. This type of dislocation is always accompanied by a surface imperfection or a stacking fault. A dislocation in which Burger’s vector is an identity period in the lattice is known as full or perfect dislocation.

Role and Significance of Dislocations:

a. The edge dislocation plays the role of the mechanism for the simplest mode of mechanical deformation, slip. The screw dislocation plays an important role in crystal growth. Both are important in describing the cold-worked state and its elimination by annealing process.

b. It is necessary to point out regarding the role of dislocation that-

(i) The passage of dislocation through a crystal lattice requires far less than the theoretical shear stress;

(ii) The movement of the dislocation through the lattice produces a slip or slip band at the free surface.

Characteristics of Dislocation:

a. With regard to mechanical properties of metals, several characteristics of dislocations are important. These include strain fields that exist around dislocations, which are influential in determining the mobility of the dislocations as well as their ability to multiply.

b. When metals undergo plastic deformation, some fraction of the deformation energy (approx. 5%) is retained internally; the remainder is dissipated as heat. The major portion of this stored energy is as strain energy associated with dislocations.

i. Consider the edge dislocation represented in Fig. 3.25. Some atomic lattice distortion exists around the dislocation line because of the presence of the extra half-plane of atoms. As a consequence, there are regions in which compressive, tensile and shear lattice strains are imposed on the neighbouring atoms.

For example – atoms immediately above and adjacent to the dislocation line are squeezed together. As a result, these atoms may be thought of experiencing a compressive strain relative to atoms positioned in the perfect crystal and far removed from the dislocation (illustrated in Fig. 3.25.). Directly below the half plane, the effect is just opposite, lattice atoms sustain an imposed tensile strain, which is as shown. Shear strain also exist in the vicinity of the edge dislocation.

ii. For “screw dislocation”, lattice strains are pure shear only. These lattice distortions may be considered to be strain fields that radiate from the dislocation line. The strain extend into the surrounding atoms, and their magnitude decreases with radial distance from the dislocation.

c. The strain fields surrounding dislocations in close proximity to one another may interact such that forces are imposed on each dislocation by the combined interaction of all its neighbouring dislocations.

Example:

Consider two edge dislocations that have the same sign and the identical slip plane, as represented in Fig. 3.26 (i). The compressive and tensile strain fields for both lie on the same side of the slip plane; the strain field interaction is such that there exists between these two isolated dislocations a mutual repulsive force that tends to move them apart.

On the other hand, two dislocations of opposite sign and having the same slip plane will be attracted to one another, as indicated in Fig. 3.26 (ii), and dislocation annihilation will occur when they meet. That is, the two extra half-planes of atoms will align and become a complete plane.

Dislocation interactions are possible between the edge, screw, and/or mixed dislocations, and for a variety of orientations. These strain fields and associated forces are important in strengthening mechanism of metals.

d. The number of dislocations increases dramatically during plastic deformation. The dislocation density in a metal that has been highly deformed may be as high as 10¹⁰/ mm². One important source of these new dislocations is existing dislocations, which multiply; furthermore grain boundaries, as well as internal detects and surface irregularities such as scratches and nicks, which act as stress concentrations, may serve as dislocation formation sites during deformation.

Slip Systems:

The movement of dislocations on all crystallographic planes of atoms and in all crystallographic direction is not with the same degree of ease. Ordinarily there is a preferred plane, and in that plane there are specific directions along which dislocation motion occurs. This plane is called “slip plane”; it follows that the direction of movement is called the “slip-direction”. This combination of slip plane and the slip direction is termed the slip system.

The slip system depends on the crystal structure of the metal and is such that the atomic distortion that accompanies the motion of a dislocation is a minimum.

For a particular structure, the “slip plane” is the plane that has the most dense atomic packing-that is, has the greatest planar density. The “slip direction” corresponds to the direction, in this plane, that is most closely packed with atoms that is, has the highest linear density.

Example:

Consider the F.C.C. crystal structure, a unit cell of which is shown in Fig. 3.27 (i). There is a set of planes, the (111) family, all of which are closely packed. A (111)-type plane is indicated in the unit cell; in Fig. 3.27 (ii), this plane is positioned within the plane of the page, in which atoms are now represented as touching nearest neighbours.

Slip occurs along <110>-type directions within the {111} planes, as indicated by arrows in Fig. 3.27. Hence (111) <110> represents the slip plane and direction combination, or the slip system for F.C.C. Fig. 3.27 (ii) demonstrates that a given slip plane may contain more than a single slip direction.

Thus several slip systems may exist for a particular crystal structure; the number of independent slip system represents the different possible combinations of slip planes and directions. For example, for face-centred cubic, there are 12 slip systems- four unique (111) planes and, within each plane, three independent <110> directions.

For B.C.C. and H.C.P. crystals structures, the possible slip systems are listed in the following table:

Properties of Dislocations:

a. In a crystal dislocations are usually present as a result of accidents during growth of the crystal from the melt or as a result of prior mechanical deformation of the crystal.

b. Unlike point imperfections, they are not thermodynamically stable, as the enthalpy of the crystal increases much more rapidly with their presence than the entropy.

c. Many of them can be removed by heating the crystal to high temperatures, where the thermal energy will allow them to mutually cancel each other or to move out of the crystal through the surface.

d. In a crystal, the density of dislocations is measured by counting the number of points at which they intersect at random cross-section of the crystal. These points, called etch pits, can be seen under the microscope, after chemical etching of a pre-polished surface.

e. Dislocations can interact with point imperfections, if there is a decrease in the total energy (sum of energy of dislocation and energy of the point imperfection).

f. As is evident from the compressive and the tensile strains around an edge dislocation or the shear strains around a screw dislocation, dislocations have distortional energy associated with them. As a first approximation, we take these strains to be elastic strains.

The elastic strain energy U per unit length of a dislocation of Burger’s vector b is given by-

U ≈ Cb²/2 …(3.5)

Where, C = Shear modulus of the crystal.