Temperature Dependence of Grain Boundary Migration in 3-D

Hao ZhangDavid J. SrolovitzPrinceton University

Princeton Materials Institute (PMI)

Acknowledgements

Moneesh Upmanyu ORNLLasar Shvindlerman Russian Academy of Sciences/RWTHGunther Gottstein RWTH AachenS. Srinivasan LANL

Outline

• Atomic Simulation Model

• Modeling Approach

• Driving Force Dependence of Migration

• Recent 3-D Results (Temperature Dependence)• Reduced Mobility• Grain Boundary Energy• Mobility• Activation Energy

• Conclusions

Grain boundary migration

• Absolute reaction rate theory (Turnbull, 1951)

• Grain growth (capillarity-induced migration)

)Tk

Q(MM

B

gbO expFMv gb

gbF )( gbgbMv

Grain Boundary Migration

• Local velocity

• Steady-state velocity

v(y)

• Boundary energy

t

A

tE

)2

w( g

gb

• U-shaped half loop geometry

][MMFv

Modeling Approach• FCC Aluminium <111> Tilt Grain Boundary

• EAM – Al

• Periodic along X, Y and Z

*Mww

Mv

w

Av

g

gA*MM

Driving Force Dependence of Migration

Driving Force /w (nm-1)M

igra

tion

rat

e v

(r

o/)

Red

uce

d M

obil

ity

Mgb

gb

(ao/

)

Gra

i n B

oun

dar

y E

ner

gy (

J/m

2 )For sufficiently low driving forces :

• Reduced mobility is independent of driving force (2-D)

• Migration rate is proportional to driving force (2-D)

• Grain Boundary Energy is large (3-D)

gbA

E

gA*MM

t

A

tE

)2

w( g

gb

7 Grain Boundary at T=427K

Grain Boundary Migration

M* vs. Misorientation

13 7(m

4/Js)

(deg)

13 7

Mobility and γ vs. Misorientation

t

A

tE

)2

w( gb

gb

gbA*MM

713

(J/m

2)

(m4/Js)

(deg) (deg)

Mobility vs. Misorientation

13 7(m

4/J

s)

(deg)

Simulation

Experiments

Temperature Dependence of Mobility

Activation Energy vs. Misorientation

experiment

Misorientation (deg)

Q (

e V)

Simulation 7

(eV

)

(deg)

• Reduced mobility shows local maxima at low 7

• Mobility shows maxima at low misorientations

• Boundary energy exhibits minima at low misorientations

• Magnitude of activation energy in simulation << than in

experiment

• Possible reasons: simulations do not represent the true physics

impurities

Conclusions