Glass-Like Behavior in General Grain
Boundary During Migration
Hao Zhang1, David J. Srolovitz1,2
1
Princeton University
2
Yeshiva University
Jack F. Douglas, James A. Warren
National Institute of Standards and Technology
Are General Grain Boundaries Glassy?
• General Boundaries
• Exclude low angle, low S 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 Details
• Molecular dynamics in NVT ensemble
• EAM-type (Voter-Chen) potential for Ni
• [010] tilt general grain boundary with
q=40.23º
q
• 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
Z
energy difference due to crystal
anisotropy
• Driving force is constant during
simulation
X
Y
Grain 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?
 Q 
v / p  M 0* exp  

k
T
 B 
OR
v / p  M
*
VF


QVF
exp  

k
T

T


0 
 B
• 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
Catch Strings and Determine their Length
• The atom is treated as mobile if
0.35r0  ri  t   ri  0   1.2 r0
• Find string pair among mobile atoms using
min  ri  t   rj  0  , ri  0   rj  t    0.43r0
• The Weight-averaged mean string length:
n  t    n2P  n, t 
 nP  n, t 
“Typical” Strings
String-like Motion Within Grain Boundary
• 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. Temperature
•String length distribution
function P(n) follows
exp(-n/<n>)
• S 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 Behavior
Movie
Y
Z
Y
X
X
Z
Migration Mechanism at Low T
GB
Steps
GB

Stage I
GB
Stage II
• Grain boundary migration at low T is associated with
nucleation of steps/terrace
Further 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)
Grain Boundary Migration Model
• Overall Migration
 Q2 
v2 / p  M exp  

 kBT 
*
2
1
v / p 
 Q2 
1
t 1p / L  * exp 

M2
k
T
 B 
L
• Since the migration region
follows Arrhenius
GB Position
L / p
1
v / p 

t 1  t 2 t 1p / L  1/ M 2
t1
t2
t
Conclusion
• 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.