Hao Zhang1, David J. Srolovitz1,2

1 Princeton University

2 Yeshiva University

Jack F. Douglas, James A. Warren

National Institute of Standards and Technology

Glass-Like Behavior in General Glass-Like Behavior in General

Grain Boundary During MigrationGrain Boundary During Migration

Are General Grain Boundaries Are General Grain Boundaries Glassy?Glassy?•General Boundaries

• Exclude low angle, low and coherent twin grain boundaries

•Structure

• “Amorphous-cement” model suggested that the metal grains in cast iron were “cemented” together by a thin layer of ‘amorphous’ material (Rosenhain and Ewen, J I Met. 10 119,1913)

• The RDF suggests liquid like structure at high T (Wolf, Phys Rev Lett. 77 2965, 1996; Curr Opin Solid St M. 5 435, 2001; Acta Mater. 53 1, 2005 )

• Others show partial crystalline structure (Gleiter, Phys Rev B. 35 9085, 1987; Appl Phys Lett. 50 472, 1987; Van Swygenhoven , Phys Rev B. 62 831, 2000 )

•Dynamics• Grain boundary viscosity (Ashby, Surf Sci. 31 498, 1972 )• Grain boundary migration and diffusion suggests structural transition

temperature (Wolf, Acta Mater. 53 1, 2005 )• self-diffusion in the grain-boundary suggested that the diffusion

mechanism is similar to that in bulk metallic glasses (Mishin, J Mater

Sci. 40 3155, 2005 )

Simulation DetailsSimulation Details

• Molecular dynamics in NVT ensemble

• EAM-type (Voter-Chen) potential for Ni

• [010] tilt general grain boundary with

=40.23º

• Periodic boundary conditions in x and

y

• One grain boundary & two free

surfaces

• Fixed strain, xx and yy

• Source of driving force is the elastic

energy difference due to crystal

anisotropy

• Driving force is constant during

simulation

(001)

(001)

X

Z

Y

Grain Boundary MigrationGrain Boundary Migration

• Grain boundary migration tends to be continuous at high temperature, while shows “intermittent” at lower temperature

• The waiting period becomes longer as temperature decreasing

Mobility vs. T – Arrhenius?Mobility vs. T – Arrhenius?

*0/ exp

B

Qv p M

k T

OR

*

0

/ exp VFVF

B

Qv p M

k T T

• Temperature dependence of grain boundary mobility can be nicely fitted into Vogel-Fulcher Form, which is commonly used in super-cooled liquid system

• T0 denotes the temperature that mobility disappears

• The atom is treated as mobile if

• Find string pair among mobile atoms

using

• The Weight-averaged mean string

length:

2 , ,n t n P n t nP n t

0 00.35 0 1.2i ir t rr r

0min 0 , 0 0.43i j i jt t r r r r r

Catch Strings and Determine their Catch Strings and Determine their LengthLength

““Typical” StringsTypical” Strings

String-like Motion Within Grain String-like Motion Within Grain BoundaryBoundary

• String-like cooperative motion within grain boundary is significant at low temperature

• The fraction of non-trivial strings in the mobile atoms can be over 40% at 780K

String Length vs. TemperatureString Length vs. Temperature

•String length

distribution function

P(n) follows

exp(-n/<n>)

• grain boundaries

have shorter strings,

therefore they are less

frustrated than general

grain boundaries

•String length increases

as temperature

decreasing, similar

behavior is found in

supercooled liquids

““Intermittent” Migration BehaviorIntermittent” Migration Behavior

X

Z

Y

X

Y

Z

MovieMovie

GB

StepsGB

GB

Stage I

Stage II

Migration Mechanism at Low TMigration Mechanism at Low T

• Grain boundary migration at low T is associated with nucleation of steps/terrace

Further ObservationsFurther Observations

• “Selected” migration region can be best described by Arrhenius law

• The activation energy is about 0.37 eV (smaller than the apparent activation energy)

t

GB

P

osit

ion

1 2

L

•Overall Migration

1 2 1 2

/ 1/

/ 1/

L pv p

p L M

* 22 2/ exp

B

Qv p M

k T

• Since the migration region follows Arrhenius

21 *

2

1/

1/ exp

B

v pQ

p LM k T

Grain Boundary Migration ModelGrain Boundary Migration Model

ConclusionConclusion

• Temperature dependence of Grain boundary migration in

general tilt boundaries is found to be described by Vogel-

Fulcher relation, which is characteristic in glass-forming

liquid

• String-like atomic motion in grain boundaries is similar to

those in liquid system

• It is reasonable to believe that string-like cooperative

motion dominates the rate of grain boundary migration at

low T

• The migration model suggests grain boundary migration is

controlled by different atomistic mechanisms. The waiting

period is associated with the nucleation of steps.