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# Crystal Defects

The regular arrangement of constituent particles in a crystalline solid is not perfect. So, any deviation from a perfectly ordered structure is a defect or imperfection in a crystal. It can arise due to the presence of impurity or absorbance of heat from surroundings.

There are three types of defects present in crystals which are given below.

### Point Defect

The defect which arises due to the irregularity in the arrangement of atoms or ions is called point defect. It may be classified into the following three types.

1. Chronometric defects
2. Non- Chronometric defects
3. Impurity defects

### Line Defect

When the deviation from the perfect arrangement is present in the entire row of lattice points, then the defect is known as line defect. These are commonly called as dislocation. This can be further divided into two types, the edge dislocation and the screw dislocation.

### Planar Defect

This is the interface between the homogeneous regions of the material. It includes the grain boundaries and stacking faults.

## Line Defects

Line defects are dislocations. Dislocations are areas where the atoms are out of position in the crystal lattice and cause the crystal defects. They are generated and displaced by applying stress. The motion of dislocations allows slip - plastic deformation to occur.

The two main types of dislocations are the edge dislocation and the screw dislocation.

1. Edge Dislocation

The edge defect exists due to the presence of an extra half plane of atoms in the crystal lattice. This dislocation is a line defect because distortion is present only in the immediate vicinity of the dislocation line. This area is called dislocation core or area. Dislocation lines are along the top of extra half plane. This type of dislocation can distort the perfect crystal with a small stress. This dislocation moves parallel to the direction of stress.

The dislocation movement can be explained with the movement of a caterpillar. As the caterpillar needs a large amount of force to move his whole body at once. Instead of moving the whole body at once, it moves a small portion and creates a hump. The hump then moves forward and moves all of the body forward by a small amount.

As shown in the figure above, the dislocation moves similarly a small amount at once. The first figure shows dislocation in the top half of the crystal is slipping one plane at a time as it moves to the right from its position in image and second shows its position in image and the third is the final image in which the dislocation is completed.

In the process of slipping a plane at once, the dislocation is spread across the crystal. Due to this movement, the top half of the crystal moves with respect to the bottom half of the crystal. This movement needs a very small amount of force. The magnitude and the direction of distortion in crystal lattice is given by the burger vector B. In edge dislocation, burger vector is perpendicular to dislocation line.

As shown in the figure above, the dislocation moves similarly a small amount at a time. The first figure shows dislocation in the top half of the crystal is slipping one plane at a time as it moves to the right from its position in the image and second shows its position in image and the third is the final image in which the dislocation is completed.

In the process of slipping a plane at once, the dislocation spreads across the crystal. Due to this movement, the top half of the crystal moves with respect to the bottom half of the crystal. This movement needs a very small amount of force. The magnitude and the direction of distortion in a crystal lattice is given by burger vector B. In edge dislocation, burger vector is perpendicular to the dislocation line.

The direction depends on the plane of dislocation. The magnitude is given by this equation:

$\left \| b \right \|$=$\frac{a}{2}\sqrt{h^2+k^2+l^2}$

In this equation, a is the unit cell length of the crystal, ||b|| is the magnitude of Burgers, vector h, k, and l are the components of Burgers vector.

### 2. Screw Dislocation

This is the second type of line defect which can't be easily envisioned. The movement of screw dislocation is a result of shear stress but the defect moves in perpendicular direction of the stress of the atom displacement. This can be explained with a metal block shown in the figure below by applying shear stress.

If a shear stress is applied to the block of metal as shown in figure (a). The plane of atoms of top side will not move from their original position as shown in figure (b). The atoms of the bottom side have moved to their new position in the lattice and have re-established metallic bonds. The middle side atoms are in the process of moving. In this, only a small portion of the bonds are broke at a time. This movement requires a much smaller force than breaking all the bonds across the middle plane and edge dislocation. The atoms will continue the movement with increasing shear stress.

The stresses caused by a screw dislocation are less complex than those of an edge dislocation. The stress of screw dislocation is represented by the equation given below;

$T_r$ = $\frac{-\mu b}{2\pi r}$

Where $\mu$ is the shear modulus of the material, b is the Burgers vector, and r is a radial coordinate. FCC and BCC metals have many dense planes, so, dislocations move easier and these materials have high ductility because the essential stress for dislocation increases with increasing the space between the plane and the dislocation which moves along the dense plane.

The material with the ionic and covalent bonding is more brittle than metal as the slip is difficult due to less density.

## Planar Defects

A planar defect is distortion in a perfect crystal across the plane. The two main types of defects are Stacking & grain boundary.

Stacking Fault

A distortion in the long-range stacking sequence can produce two other types of crystal defects.

1. a stacking fault and
2. a twin region

A change in the stacking sequence over a few atomic planes produces a stacking fault. It arises with the interruption of one or two layer stacking sequence of atom plane while the changes over many atomic spacing give the twin region. It's specially found in closed packed structure like FCC and HCP. Both structures differ only in stacking order and have close packed atomic planes with six fold symmetry. The atoms form equilateral triangles. In both structures, the first two layers arrange themselves identically, and are said to have an AB arrangement. If the third layer is placed, so that, its atoms are directly above the first layer, then the stacking will be ABA which is a hcp arrangement as shown in the figure above. So, the arrangements will be ABABAB type.

The another possible arrangement for first layer that the atoms are not situated just above the first layer and they are in the line with the first layer and arranged in ABC type which is a FCC Structure. So, HCP structure switches to FCC structure or ABABAB type changes to ABCABCABC type which shows the presence of stacking fault. In the FCC arrangement the pattern is ABCABCABC but due to stacking fault the pattern would become ABCABCAB_ABCABC.

If it continues over some number of atomic planes, it will produce a next stacking fault which is the twin of the first one. For above example if the stacking pattern is ABABABAB switches to ABCABCABC for a period of time before switching back to prior state, a pair of twin stacking faults is produced. The blue region in the stacking sequence shows the [ABCABCACBACBABCABC] twin plane.

(b) Grain boundary-This is another type of planar defect which is found in poly crystals. Single crystal is found in specially controlled growth conditions. Solids are made of a number of small crystallizes which are also known as Grains. The size range of grains is up to nanometers to millimeters. The orientations of atomic planes rotate with respect to their neighboring grains. All the grains are separated by boundaries which are called Grain boundaries and the atoms in this region are not in perfect arrangement. In the crystallization process of solid, these boundaries give the uneven growth to the solid.

These boundaries are important as they develop the opaque property in the material and also affect the mechanical properties. They limit the lengths and the movement of dislocations. It means more grain boundary surface area or small grain give more strength than a larger grain. Grain's size can be controlled by temperature cooling. Rapid cooling gives the small grains while slow cooling produces larger grains. This is the reason for the low strength, hardness and ductility of large grains at room temperature.

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