L7- Point defects + dislocation density

Examples of point defects intrinsic

Intrinsic defects:

• Vacancies

• self-interstitials

What are the ranges of defects and changes in microstructure plastic deformation produces?

• point defects

• changes in grain shape, orientation and/or distribution

• increase in dislocation density

Point defects in ionic crystals:

• Frenkel defect

• Schottky defect

• occur in pairs in ionic materials to maintain charge neutrality

Examples of point defects extrinsic

• solid solution atoms

•   substitution

•   interstitial

  *point defects are associated with strain field

Equation for equilibrium concentration of vacancies:

N = no. atoms

 n_eq = no. vacancies at equilibrium

 ΔH _f= Energy of formation of 1 vacancy site

Where can point defects be absorbed ?

1. grain boundaries

2. surfaces

3. dislocations

Point defect properties:

• mobile, particularly interstitials

• can also form aggregates in the case of vacancies these would result in voids

Properties of substitutional solutes:

•low diffusivity, solute atoms fixed

•atoms randomly distributed

•dislocations sample solute atoms

•resistance to flow function of atom size mismatch + solute concentration

Properties of interstitial solutes:

•high diffusivity, solute atoms concentrate

•segregate to  dislocations

•low concentration of solute has disproportionate effect in pinning dislocations

Effect of impurities on lattice :

• generates σ by distorting lattice

• σ creates barrier to dislocation motion

What does strengthening due to substitutional solutes depend on?

1. size difference between solute + matrix atoms

2. solute concentration

Substitutional solutes formulae

• a – lattice parameter

  c – concentration

  θ– lattice mismatch

What does strengthening due to interstitial solutes depend on?

1. tetragonal stress fields that inhibit the mobility of both edge and screw dislocations

2. Segregation of solutes to dislocations

Why do interstitial solutes have high diffusivity

• Interstitial solutes, such as C, O, N, and H, have high diffusivity due to their small atomic mass and ability to occupy small gaps in the lattice.

• solutes strengthen materials by segregating to dislocations, reducing energy by filling space in the tensile region, but needing ↑ stress to free the dislocation from the solute/ forcing it to diffuse with the solute atom.

Disadv of work hardening as a strengthening mechanism:

• loss in ductility

• necking + loss of ability to resist cracking

How to tell if an interaction is favourable ?

• If dislocation burgers vector, b decreases

• ⇒ decrease in E = ½ Gb²

• so favourable (Frank’s Rule)

Why do most materials work harden?

1.Dislocations are bound to encounter each other

2.These encounters produce sessile debris

3.This debris makes deformation harder

Stress to operate Frank Reed source

Force between screw dislocations

l = distance between 2 dislocations

Taylor’s model of dislocation hardening assumptions:

• yield strength increases with increasing density of obstacles

• density of obstacles increases with increasing dislocation density

• dislocation density increases with plastic strain

Taylor’s model equation:

x = glide distance / distance moved by dislocations

ρ = dislocation density