MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 1

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• Review of grain boundary structure

• Diffusion paths in polycrystals

• Regimes of grain boundary diffusion for stationary boundaries

• Migration of a moving grain boundary diffusion source

• Regimes of grain boundary “short-circuit” diffusion for stationary and

moving boundaries

• Some grain boundary diffusion mechanisms

• Dislocation core structure and dislocation “short circuits”

• Some phenomena where short-circuits are important

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 2

• Steady-state migration of a moving boundary diffusion source

Diffusion with respect to a frame at the interface migrating at velocity v :

which has the solution

−∇⋅J = −d

dx−DL

dc

dx−νc

=0

c = c0 exp −v DL( )x[ ]

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 3

Incr

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Increasing lattice diffusional transport

• Regimes of grain boundary “short-circuit” diffusion for stationary and moving boundaries

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 4

• Mechanism of grain boundary diffusion (continued)

Dislocation short-circuit diffusion (continued)

Ring mechanism:

Vacancy mechanism:

Figure 8.18 Schematic rep-resentation of rotational ‘ring’mechanism for grain bound-ary diffusion. In the sequence(a ) → ( b ) , t he ma rked(shaded) atom replaces atom8, 8 replaces 7, and 7 replac-es the marked atom (Suttonand Balluffi 1995, p. 492).

Figure 8.19 Schematic rep-resen ta t i on o f vacancyexchange mechanism forgrain boundary diffusion. Inthe sequence (a) → (b), themarked ( shaded ) a t omexchanges places wi th aneighboring vacancy (Suttonand Balluffi 1995, p. 493).

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 5

• Mechanism of grain boundary diffusion (continued)

Vacancies and self-interstitials in grain boundary diffusion

Figure 9.9 Atom jumping events insymmetric tilt boundary in BCC-Fe calculated bymolecular dynamics using pair potential model. Theratios of the scales used in the drawing are

5 001 310∑ ( )

1 30[ ] : 310[ ]: 001[ ] = 1:1: 5

vacancy trajectory, con-fined to grain boundarysites

vacancy/interstitialpair creation

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 6

• Dislocation short-circuit diffusion

Dislocations, especially edge dislocations, can act asshort-circuit diffusion paths.

Dissociated dislocations have cores that are more spread out,connected by a ribbon of stacking fault:

r b

ˆ t

AB

AB

r b =

a

21 10[ ]

ˆ t = 1 1 2[ ] 6111( ) plane

ˆ t

A BA

CA B

ˆ t

r b 1 =

a

62 11[ ]

r b 2 =

a

61 21 [ ]

(b)(a) Perfect dislocation Dislocation dissociatedinto partials

(Allen and Thomas 1999, p. 324)

• Surface short-circuit diffusion

MIT 3.21 Spring 2001 © S.M. Allen Lecture 19 Monday, April 2 7

• Some practical phenomena where these short-circuit diffusion paths

are important

Sintering

“Coble” creep

Superplasticity