TMS Annual Meeting, Orlando, 2007TMS Annual Meeting, Orlando, 2007 1

Hao ZhangHao Zhang11, David J. Srolovitz, David J. Srolovitz1,21,2

11 Princeton University Princeton University

22 Yeshiva University Yeshiva University

Jack F. Douglas, James A. WarrenJack F. Douglas, James A. Warren

National Institute of Standards and TechnologyNational Institute of Standards and Technology

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

Grain Boundary During MigrationGrain Boundary During Migration

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

Grain Boundary During MigrationGrain Boundary During Migration

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

• Exclude low angle, low Exclude low angle, low and coherent twin grain boundaries and coherent twin grain boundaries

•StructureStructure

• ““Amorphous-cement” model Amorphous-cement” model suggested that the metal grains in cast suggested that the metal grains in cast iron were “cemented” together by a thin layer of ‘amorphous’ iron were “cemented” together by a thin layer of ‘amorphous’

material (material (Rosenhain and Ewen, J I Met. Rosenhain and Ewen, J I Met. 1010 119,1913 119,1913) ) • The RDF suggests liquid like structure at high T (The RDF suggests liquid like structure at high T (Wolf, Wolf, Phys Rev Lett. Phys Rev Lett. 7777

2965, 1996; Curr Opin Solid St M. 2965, 1996; Curr Opin Solid St M. 55 435, 2001; Acta Mater. 435, 2001; Acta Mater. 5353 1, 2005 1, 2005 ))

• Others show partial crystalline structure (Others show partial crystalline structure (Gleiter, Gleiter, Phys Rev B. Phys Rev B. 3535 9085, 9085, 1987; Appl Phys Lett. 1987; Appl Phys Lett. 5050 472, 1987; Van Swygenhoven , Phys Rev B. 472, 1987; Van Swygenhoven , Phys Rev B. 6262 831, 831, 20002000 ))

•DynamicsDynamics• Grain boundary viscosity (Grain boundary viscosity (Ashby, Surf Sci. Ashby, Surf Sci. 3131 498, 1972 498, 1972 ))• Grain boundary migration and diffusion suggests structural transition Grain boundary migration and diffusion suggests structural transition

temperature (temperature (Wolf, Wolf, Acta Mater. Acta Mater. 5353 1, 2005 1, 2005 ))• Self-diffusion in the grain-boundary suggested that the diffusion Self-diffusion in the grain-boundary suggested that the diffusion

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

Sci. Sci. 4040 3155, 2005 3155, 2005 ))

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Simulation DetailsSimulation Details

• Molecular dynamics in NVT ensembleMolecular dynamics in NVT ensemble

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

• [010] tilt general grain boundary with [010] tilt general grain boundary with

=40.23º=40.23º

• Periodic boundary conditions in x and Periodic boundary conditions in x and

yy

• One grain boundary & two free One grain boundary & two free

surfaces surfaces

• Fixed strain, Fixed strain, xxxx and and yyyy

• Source of driving force is the elastic Source of driving force is the elastic

energy difference due to crystal energy difference due to crystal

anisotropyanisotropy

• Driving force is constant during Driving force is constant during

simulationsimulation

(001)

(001)

X

Z

Y

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Grain Boundary MigrationGrain Boundary Migration

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

• The waiting period becomes longer as temperature The waiting period becomes longer as temperature decreasingdecreasing

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

• TT00 denotes the temperature that mobility disappears denotes the temperature that mobility disappears

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• The atom is treated as mobile ifThe atom is treated as mobile if

• Find string pair among mobile atoms Find string pair among mobile atoms

using using

• The Weight-averaged mean string The Weight-averaged mean string

length: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

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““Typical” StringsTypical” Strings

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

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

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

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String Length vs. TemperatureString Length vs. Temperature

•String length String length

distribution function distribution function

PP(n) follows (n) follows

exp(-n/<n>)exp(-n/<n>)

• grain boundaries grain boundaries

have shorter strings, have shorter strings,

therefore they are less therefore they are less

frustrated than general frustrated than general

grain boundariesgrain boundaries

•String length increases String length increases

as temperature as temperature

decreasing, similar decreasing, similar

behavior is found in behavior is found in

supercooled liquidssupercooled liquids

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““Intermittent” Migration BehaviorIntermittent” Migration Behavior

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X

Z

Y

X

Y

Z

MovieMovie

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GBGB

StepsSteps Stage IStage I

Stage IIStage II

Migration Mechanism at Low TMigration Mechanism at Low T

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

GBGB

GBGB

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Further ObservationsFurther Observations

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

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

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t

GB

P

osit

ion

1 2

L

•Overall Overall MigrationMigration

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 Since the migration region follows Arrheniusfollows Arrhenius

21 *

2

1/

1/ exp

B

v pQ

p LM k T

Grain Boundary Migration ModelGrain Boundary Migration Model

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ConclusionConclusion

• Temperature dependence of Grain boundary migration in Temperature dependence of Grain boundary migration in

general tilt boundaries is found to be described by Vogel-general tilt boundaries is found to be described by Vogel-

Fulcher relation, which is characteristic in glass-forming Fulcher relation, which is characteristic in glass-forming

liquidliquid

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

those in liquid systemthose in liquid system

• It is reasonable to believe that string-like cooperative It is reasonable to believe that string-like cooperative

motion dominates the rate of grain boundary migration at motion dominates the rate of grain boundary migration at

low Tlow T

• The migration model suggests grain boundary migration is The migration model suggests grain boundary migration is

controlled by different atomistic mechanisms. The waiting controlled by different atomistic mechanisms. The waiting

period is associated with the nucleation of steps.period is associated with the nucleation of steps.