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Mechanics & Stress Analysis*
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Defects & Deformation of Crystal Structures

In this notes sheet:

  1. Slip & Slip Systems

  2. Calculating Deformations

  3. Defects in Crystal Structures

  4. Strengthening


There are two types of deformation of crystalline materials: elastic and plastic. The former is fully reversible, whereas in the latter, atomic planes slip over one another to form a new, different formation. This kind of deformation is irreversible.

  • Note that the elastic deformation graph could be non-linear (e.g. rubber)

Slip & Slip Systems

The slipping of atomic planes (slip planes) happens in whatever direction requires the least energy. It is brought about by the application of an external force, resulting in shear stresses within the crystal structure.

In a perfect sample, the slip would occur over the whole plane at once, however imperfections in the crystal structure prevent this: slip is a gradual process.

Close-packed planes are the most susceptible to slip. This is because more energy is required for a non-close-packed plane to slip, as there is a greater distance for each displaced atom to move.

The number of slip systems a crystal lattice has reflects how likely slip in the structure is.

The more slip systems present, the more susceptible to slip.

This is determined as the product of close-packed directions and non-parallel close-packed planes:

Lattices with few slip systems are said to show brittle deformation, while those that have many undergo ductile deformation.

HCP Slip Systems

There are three close-packed directions per close-packed plane, however all close-packed planes are parallel. Therefore, the number of slip systems is 3, so the deformation is brittle:

FCC Slip Systems

The close-packed planes in an FCC lattice are along the diagonal-corner, and there are four:

Each plane has three close-packed directions, so the number of slip systems is 12, so the deformation is ductile.

BCC Slip Systems

There are no close-packed planes, but there are 6 nearly-close-packed planes, each with two close-packed directions:

Therefore, the number of slip systems is 12, so the deformation is ductile.

Calculating Deformation

The applied stress must be resolved in terms of the slip plane, φ, and direction, λ:

  • σ is the normal stress, given by F/A

Under the application of a shear stress, slip will occur in the most favourably orientated slip system. This is the system with the largest value of resolved shear stress:

The value of shear stress required for this slip to occur in the most favourable direction is the critical resolved shear stress:

For single crystals, slip occurs when φ = λ = 45°.

Defects in Crystal Structures

Crystals are never perfect – they are littered with defects that allow slip to occur at significantly lower values of applied stress than you would calculate from the equations above. There are three types of defects:

  1. Point Defects – defects with atomic dimensions in all three directions, e.g. a missing atom (a vacancy)

  2. Line Defects – defects in two atomic dimensions but are normal in the third direction.

  3. Area Defects – defects in only one dimension, e.g. a grain boundary

All defects distort the lattice, increasing the energy stored inside it.

Line Defects

Line defects, also known as dislocations, is when a row of atoms is added or removed. These allow lattices to slip in steps, instead of all at once. Two types of dislocations are edge and screw dislocations: