Defects VIII - Dislocation Motion and Generation

8/9/2019 Defects VIII - Dislocation Motion and Generation

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3.4 Dislocation motionand generation

Hartmut S. Leipner: Defects in crystals

! Slip of crystals

! Velocity of dislocations

! Peierls energy

! Frank–Read source

! Cross slip of screw dislocations

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hsl 2009 – Defects in crystals – 3.4 Dislocation motion

Concept of slip

! Glide – conservative motion of dislocation in the surface which contains both its line and Burgers vector

! Climb – nonconservative motion out of the glide surface normal to the

Burgers vector ! Glide of many dislocations results in slip, the manifestation of plastic

deformation of crystals! Slip planes are normally the planes with highest density of atoms,

direction of slip the direction of closest spacing

! Slip plane + slip direction: slip system

Examples:

hcp (0001) basal planes, directions1210

fcc {111}110 –

–

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Resolved shear stress

Geometry of slip

Shear stress resolved on the slipplane in the slip direction:

Schmid factor m = cos ! cos !

Min. stress required for the onset of slip:

critical resolved shear stress

[Hull, Bacon 1992] SlipSalami

F

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!

Dislocations of opposite sense glidein opposite directions! For dislocation glide, a shear stress

must act on the slip plane in the

direction of the Burgers vector

!

The direction of the motion isgiven by the Peach–Koehler

formula, F d = (! ·b)"#

Direction of dislocation glide

[Hull, Bacon 1992] Glide direction

b

b

b

b

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Measurement of the dislocation glide velocity

Etch pits LiF modified

Dislocation etch pits on a LiF crystal. The crystal has been etched threetimes. The movement of dislocation B under two subsequent stress pulsesis indicated by the pits. Dislocations A did not move.

[Gilman, Johnston 1957/Hull, Bacon 1992]

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In situ observation of dislocation glide

Disloc_TEMmpgMisfit loop

Thermal activation of dislocation glide by heating of the specimeninside the transmission electron microscope to a temperature of 680 °C

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Velocity of dislocations

! Different velocities for different types of dislocations

! Critical stress for the onset of glide (CRSS)

! Strongly material dependent

! Strong dependence on purity of materials (doping)

! Speed of sound upper limit for dislocation velocity

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Velocity of dislocations

Stress dependence of dislocation velocity in LiF[Gilman, Johnston 1959/Hull, Bacon 1992]

Dislocation velocity LiF

Stress (MPa)

D i

s l o c a t i o n v e l o c i t y ( c m / s ) Velocity of (110)[110] shear waves

–

3·105 cm/s

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Dislocation velocity in III–V compounds

Dislocation velocities in undopedGaAs and InP

[Sumino 1992]

Dislocation velocity GaAs InP

m Q/eV

GaAs 1.6…1.8 1.3…1.4

InP 1.4…1.8 1.6…1.7

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Peierls model of the dislocation core

Displacement of atoms u at an edgedislocation. The lower panel shows thedisplacement difference !u across theslip plane (disregistry).

[Hull, Bacon 1992]

!u = u(B)!

u(A)dislocation width w: disregistrygreater than one half of itsmaximum value

Peierls model

ub

!u/b

x

x

y

w

u

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Peierls barrier

! Disregistry core energy, resistance to dislocation movement

! Simple approach (Peierls–Nabarro model): sinusoidal force relationbetween planes A, B

! Calculation of the dislocation core energy per unit length as a functionof the dislocation position

!

Maximum: Peierls energy

! Peierls stress: resolved shear stress required to move a dislocation in theperfect crystal

! Direct consequence of the lattice periodicity

! ! P depends on the core structure

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Peierls potential

E

x

Peierls valleys

(dislocation equilibriumposition at 0 K)

Closed packeddirection

h

E P

Dislocation positionat finite temperature

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Double-kink nucleation

S 11-91 double kink

! Thermally activated process of double-kink nucleation at T > 0

! Minimum spacing XY required, typically 20b

Kink jump frequency

Kink diffusivity

Kink velocity Dislocation velocity

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Frank–Read source

S18-90 Frank Read source

! Radius of curvature depends on resolved shear

! Critical bow out for R = L/2 ( L = AB) ! ! Gb/ L

! Further steps are the formation of a kidney-shaped loop and the annihilation of

dislocation segments with the same Burgers vector but opposite line sense.

A

B

A

B

A

B

A

B B

A A

B

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Dislocation source in deformed silicon

TEM weak-beam image of dislocations in deformed silicon. The lengthof the Frank–Read source amounts to 2 µm.

[George, Rabier 1987]

Frank Read source in Si

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Cross slip

! In principle, screws can glide on any slip plane! In praxi, closed packed planes preferred

! Screw can switch from one plane to another: cross slip

[Hull, Bacon 1992] Xslip1

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hsl 2009 – Defects in crystals – 3.4 Dislocation motionJogs

Jogs and kinks

[Hull, Bacon 1992]

Kinks and jogs

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Intersection of edge dislocations

[Read 1953/Hull, Bacon 1992] Jog1

The formation of the jog after the

cutting of edge dislocations with b1 ! b2

can be envisaged by considering the

displacement of the plane PAB produced

by the dislocation XY.

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Formation of kinks by dislocation intersection

Intersection of edge dislocations with b1 || b2

[Hull, Bacon 1992] Jog2

" Jogs (kinks) in pure edge dislocationsdo not affect the glide motion.

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Intersection of screw dislocations

Generation of jogs by the intersection of an edge dislocation with a right-handed screw

(left) and by the intersection of two screw dislocations (right).

(a) (b)

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hsl 2009 – Defects in crystals – 3.4 Dislocation motion Jog5

The jog PP’ is a short edge segment and can only glide in the

PP’R’R plane. The movement of the screw to A’B’ requires the

climb of the jog along PQ.

[Hull, Bacon 1992]

Motion of a jog on a screw dislocation

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Influence of jog height – Superjogs

! Elementary jogs produce

point defects pd (vacancy

jogs/interstitial jog)

! Superjogs: Dislocation

segments XM, NY can

move independently

! Intermediate jog: Segments

NP and MO cannot pass,

formation of a stable

dislocation dipole

[Gilman, Johnston 1962/Hull, Bacon 1992] Jog7

pd

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Glide of a jogged screw dislocation producing trails of point defects

Jog6

Jog dragging

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Defects VIII - Dislocation Motion and Generation