Partial Dislocations

Lauren Ayers

22.71

Outline• Partial Dislocations

– Why Partials?

– Stacking Faults

• Lomer-Cottrel Lock

• Force on a Dislocation

• Line Tension Model

• Dislocation Density

Partial Dislocations

b1

Single unit dislocation can break down into two Shockley partials

Partial Dislocations

b2

Single unit dislocation can break down into two Shockley partials b3

Why Partials?• Frank’s Rule:

|b1|2>|b2|2+|b3|2

• Energy of a dislocation is proportional to |b|2

• Partial dislocations decrease strain energy of the lattice

Stacking Faults

• Movement of partial dislocations generate discontinuity in stacking planes, ex: ABCAXCABC

• Two separated partials have smaller energy than a full dislocation

• Reduction in elastic energy proportional to:

• Equilibrium splitting distance

What does this mean?• Wide vs. narrow ribbon affects cross slip

– Cu, s = 2nm: high constriction energy barrier

– Al, s= 4 A: cross slip occurs more easily

Lomer-Cottrel Lock (LC)

• 2 Dislocations on primary slip planes combine

• Formed by:

• Slip by bLC creates a high energy stacking fault

• No {111} plane which the LC can move as an edge dislocation

• “Lock”: Once the state is formed, hard to leave

• Acts as a barrier against other dislocations

Force on a Dislocation

• Climb: “Non-conservative”

• Glide: “Conservative”

Line Tension Model

• Assume:

– Line tension η (total elastic energy per length) independent of line direction ξ

– Dislocations do not interact with each other elastically

• Local model

• From dF, derive critical external stress:

Dislocation Density• Total length of all dislocations in a unit volume of

material

• 1/m2 or m/m3

Thanks!