The document discusses factors that govern the sink strength of semicoherent fcc-bcc metal interfaces. It notes that such interfaces contain arrays of misfit dislocations that separate coherent regions. Misfit dislocation intersections act as good traps for point defects, and the interaction of point defects with these intersections can drive interface reconstruction and evolution over time. The goal is to understand and predict how the interface structure and sink efficiency change as defects are absorbed using calculations of interface free energy and point defect mobilities along the interface.

1. On the Factors Governing the Sink Strength of
Semicoherent fcc-bcc Interfaces
Kedarnath Kolluri and Michael Demkowicz
Acknowledgments:
B. P. Uberuaga, A. Kashinath, A. Vattré, X.-Y. Liu, A. Misra, R. G. Hoagland, J. P. Hirth, M. A.
Nastasi, and A. Caro
Financial Support:
Center for Materials at Irradiation and Mechanical Extremes (CMIME) at LANL,
an Energy Frontier Research Center (EFRC) funded by
U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences

2. Predicting interface sink efficiency: Beyond v.1
Cartoon of defect
activity in radiation
environment
•
2
lb
b
Def f
Ac
ic
Def f
Point defects (lets assume the cascade occurs in bulk)
2
lb
b
Def f
•
arrive at the interface
•
reside and move at coherent regions of the interface until either
•
emit back into the bulk
•
embed into “non coherent” regions of the interface
•
dynamics of embedded defects
⌫e
E/kT
Ac
ic
Def f

3. Predicting interface sink efficiency: Beyond v.1
Cartoon of defect
activity in radiation
environment
•
2
lb
b
Def f
Ac
ic
Def f
Point defects (lets assume the cascade occurs in bulk)
2
lb
b
Def f
•
arrive at the interface
•
reside and move at coherent regions of the interface until either
•
emit back into the bulk
•
embed into “non coherent” regions of the interface
•
dynamics of embedded defects
⌫e
E/kT
Ac
ic
Def f
UNKNOWN

4. Interface sink efficiency: Formal definition
Cartoon of defect activity in radiation environment
µ2
Bulk
mobilities
µ1
M2
M1
m12
m13
JI
⌘= I
J0
J=
M rµ
Mi = Mib [ Mib,I
Interface mobi
where
δrµ
Interface thickness
lets assume 1 as
interface is rather sharp
=µ
bI
I
@F
@n
Interface free energy
µI

5. Interface sink efficiency
µ2
µ1
µ3
M2
Cartoon of defect activity in radiation
environment
M1
M3
m12
Hence,
⌘=
M
h
bI
@F I
µ
@n
M0 µbI
i
⌘=1
m13
@F I
@⇢
µbI
Interface free energy plays a crucial role in interface sink strength
Goal: Determine interface free energy

6. Interface structure evolves
uc
str
⌘=1
e
tur
@F I
@⇢
µbI
olv
ev
f (⇢, . . . )
es
Interface energy (f)
Schematic of free energy of an interface
void
Interfacial density (ρ)
FI ⌘
phase
transformation
(f (⇢, . . . ), Mi , m)
★ Interface structure evolves as defects interact with the interface

7. str
µ3
M2
M1
M3
m12
es
v
bulk
f (⇢, . . . )
i
µ bulk
Interfacial density (ρ)
I
F ⌘
m13
olv
µ
void
µ1
ev
@F I
@⇢
µbI
⌘=1
µ2
e
tur
uc
Interface energy (f)
Interface sink efficiency change as structure evolves
phase
transformation
(f (⇢, . . . ), Mi , m)
★ Different interface regions may have different densities
★ Different density region have different free energies

8. m12
f (⇢, . . . )
i
µ bulk
m13
Point defect activity under radiation
⌘(t) = 1
void
@F I
@⇢
µbI
v
bulk
es
M3
µ
olv
M1
ev
M2
e
tur
µ3
uc
µ1
str
µ2
Interface energy (f)
Holy grail: Predict sink efficiency as interface structure
evolves
Interfacial density (ρ)
phase
transformation
Schematic of interface free energy
FI ⌘
(f (⇢, . . . ), Mi , m)
Goal: To determine in the context of interface structure
•
Interface free energy (factors that determine the energy functional)
•
Point defect mobilities that will determine the interface evolution

9. Methods and model systems
•
Our focus is on
•
interfaces of immiscible fcc-bcc semicoherent metal systems
Cu-Nb, Cu-V, Cu-Mo, Cu-Fe, and Ag-V (in both KS and NW)
Kurdjumov-Sachs (KS):
(111)
fcc
|| (110)
and〈110〉 ||
〈111〉
bcc
fcc
bcc
〈100〉
Nishiyama-Wassermann (NW): (111) fcc || (110)bcc and〈110〉 ||
fcc
bcc
•
Atomistic simulations of few interfaces:
Molecular dynamics (at 800 K) and statics, EAM potential, LAMMPS
•
Develop insights that may be used to develop figures of merits for
classes of interfaces

10. General features of semicoherent fcc-bcc interfaces
〈112〉 〈112〉
Cu
Nb
Cu-V
〈110〉 〈111〉
Cu
Nb
An example of a semicoherent interface

11. View of the Interface

12. View of the Interface

13. View of the Interface

14. View of the Interface

15. View of the Interface

16. View of the Interface

17. General features of semicoherent fcc-bcc interfaces
〈112〉 〈112〉
Cu
Nb
Cu-V
〈110〉 〈111〉
Cu
Nb
An example of a fcc-bcc semicoherent interface
Patterns corresponding to periodic “good” and “bad” regions

18. General features of semicoherent fcc-bcc interfaces
〈112〉 〈112〉
Cu
Nb
Cu-V
〈110〉 〈111〉
Cu
Nb
Interface contains arrays of misfit dislocations separating coherent
regions

19. 〈112〉 〈112〉
Cu
Nb
General features of semicoherent fcc-bcc interfaces
Cu-Nb
〈110〉 〈111〉
Cu
Nb
Cu-V
Interface contains arrays of misfit dislocations separating coherent
regions

20. MDI
1 nm
〈112〉
Cu
General features of semicoherent fcc-bcc interfaces
Cu-Nb KS 〈110〉
Cu
Cu-V KS
•
Two sets of misfit dislocations with Burgers vectors
•
Misfit dislocation intersections (MDI) where different sets of
dislocations meet

21. 0 0
00
Defects on misfit dislocations are good traps to point
defects
150
150
0.2
0.2
0.4
0.4
100
100
0.6
0.6
50
50
0.8
0.8
0
0
1
10
0
0.2
0.2
0.4
0.4
0.6
0.6
Cu-Nb KS
Cu-Nb KS
0.8
0.8
1
1
0.28
0.28
0.26
150 0.45
1500.26
0.24
150
0.2 0.2
0.2
150
0.2 0.45
0.24
0.2 0.2
0.2
0.2
0.22
0.4
0.22
0.4
0.2
100
1000.2
0.4 0.4
0.4 0.35 0.4
100
100
0.4 0.4
0.18
0.4 0.35 0.4
0.18
0.16
0.3 0.6
0.6 0.6
0.6 0.3
50
50 0.16
0.14
0.6 0.6
0.6
0.6
50
50
0.14
0.25
0.12
0.8 0.8
0.8
0.8 0.25
0.1 0.12
0 0.8
0 0.1
0.8 0.8
0.8
0.2
0.08
0
0
0.2
1
0.060.08
1 0.15 1
1
0
0.2 0.2
0.4 0.4
0.6 0.6
0.8 0.8
1
0
0.2
0.8
1
1
0.06
1 0.15 0.2
0
1
0
0.4 0.4 0.6 0.8
0.6
11
1
0
0.2 0.2
0.4 0.4
0.6 0.6
0.8 0.8
1
0
0.2
0.4
0.6 0.8
0.8
0
1
0
0.2
0.4
0.6
11
0
0
0
0 0.5
0
0 0.5
0
0
Angle with -ve x axis
Angle with -ve x axis
0
0
0
Cu-Fe NW
Cu-Fe NW
0.2
0.4
0.6
0.8
Cu-V KS
Cu-V KS
0
0
0
0.2
1.2
0.4
0.6
1
0.6
0.8
1.2
0.6
0.8
0
0.2
0.4
0
0.2
1 nm 0.4
1 nm
0.6
0.6
0.8
0.8
0.6
1
1
1.4
0.2
1.2
1.2
0.4
1.2
0.4
1
1
1
1
0.6
0.6
0.8
0.6
0.8
0.6
0.8
0.8
0.8 0.8
0.8
1
0.2
0.4
1
1.4
1.4
0.2
1.2 0.4
0.4
0
1.4
1.4 0.2
0.2
1
0
0
1.4
0.8
1
0.6
0
1
1
0
1
0.8
0.6
0.6
0.8
0.2
0
0.4
10.2 0.4
nm
1 nm
0.6
0.6
0.8
0.8
1
1
Formation energy (eV)
Formation energy (eV)
Different fcc-bcc semicoherent interfaces with misfit dislocations
0.2
0
0.4
0.2
1.4 nm 0.4
1.4 nm
0.6
0.8
0.6
0.6
1
0.8
1
Vacancy formation energies (similar trend for interstitials as well)
1
0
0.2
0.4
0.6
0.8
01
0
0

22. Interface structure evolution depends on
MDI interactions with point defects
3.5
Formation energy (eV)
3
Cu-Mo KS
2.5
2
1.5
1
Cu-Nb KS
0.5
0
-0.5
-1
-10
B
-8
-6
-4
Ag-V NW
C
A
-2
0
2
4
6
8
10
Size of point defect cluster at an MDI
Interface reconstruction dominated by MDI-point defect interactions

23. Interface structure evolution depends on
MDI interactions with point defects
A’
B’
3.5
Cu-Nb
Formation energy (eV)
3
Cu-Mo KS
2.5
2
1.5
1
Cu-Nb KS
0.5
0
-0.5
-1
-10
B
-8
-6
-4
Ag-V NW
C
A
-2
0
2
4
6
Size of point defect cluster at an MDI
Interface reconstruction dominated by MDI-point defect interactions
8
10

24. Interface structure evolution depends on
MDI interactions with point defects
A’
B’
3.5
Cu-Mo
Formation energy (eV)
3
Cu-Mo KS
2.5
2
1.5
1
Cu-Nb KS
0.5
0
-0.5
-1
-10
B
-8
-6
-4
Ag-V NW
C
A
-2
0
2
4
6
Size of point defect cluster at an MDI
Interface reconstruction dominated by MDI-point defect interactions
8
10

25. Interface structure evolution depends on
MDI interactions with point defects
A’
C’
3.5
Ag-V
Formation energy (eV)
3
Cu-Mo KS
2.5
2
1.5
1
Cu-Nb KS
0.5
0
-0.5
-1
-10
B
-8
-6
-4
Ag-V NW
C
A
-2
0
2
4
6
Size of point defect cluster at an MDI
Interface reconstruction dominated by MDI-point defect interactions
8
10

26. m12
void
f (⇢, . . . )
i
µ bulk
m13
Point defect activity under radiation
P
@F I
Mi @⇢
P
Mi µ I
i
⌘=1
v
bulk
es
M3
µ
olv
M1
ev
M2
e
tur
µ3
uc
µ1
str
µ2
Interface energy (f)
Holy grail: Predict sink strength as interface
structure evolves
Interfacial density (ρ)
phase
transformation
Schematic interface free energy
FI ⌘
(f (⇢, . . . ), Mi , m)
Goal: To determine
•
Interface free energy (or factors)
•
point defect mobilities that will determine the interface evolution

27. 0
0
0.55
Point defect migration along the interface depends on
0
0.5
150
0.2
0.45
0.2
the distance between defects0.2on misfit dislocations
0.4
150
0.45
0.2
0.2
0.4
100
0.4
0.4
0.4
0.35
1 nm
(a)
0.6
0.6 0.3 0.6
50
0
0.8
0.6
1
0.8
0.8
(b)
0.25
0.8
0.8
0.2
1 0.15 1 1
0.2
0.4 0.6
0.8 111
0 0 0.2 0.4 0.4 0.6 0.6 0.8
0.8
0
0.2
1
W
0.28 0
0.26
150
0.24
0.2
0.22
0.2
100
100 0.4
0.18
0.16
0.6
5050
0.14
0.12
0.1 0.8
0 0
0.08
0.06 1
0
Angle with -ve x axis
0.5 0 0
150
0.45
0.2
0.6
100
0.4
0.4
0.6
(c)
0.6
50
0.35
0.3
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0.2
0.
0.4 0.4
0.6 0.6 0.8
0.4
0.6
0.25
0.8
Cu-V KS
Cu-Nb KS
0.2
0.4
0.4
0
0
0.5
1
0.8
0.2
0
1
0
0.4
0.2
0
0.6
0.4
0.2
0.8
0.8 0.8 0.6 1
0.6
0.4 1
0.8
0.2
1 0.15
0.8
0
Cu-Fe NW
0
1
0
1
0.2
Cu-V KS
0
Cu-Nb KS
1.4
0.2
0.2
1.2
1.2
0.4
0.4
0.2
0.2
1.2
0.4
0.4
0.4
1 1
1
0.6
0.6
0.6
0.6
0.6
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.6
0.6
0.6
1
1
0
1.4
1.4
0.2
0.8
0
0
0
1
0 0.2 0.2 0.4 0.4
1.4 1 nm
nm
0.6
0.6
0.8
11
1
0
1
1
0
Formation energy (eV)
0
0
0
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1.4
150
150
0.2
1.2
100
0.4
100
1
0.6
5050
0.8
0.8
0 0
0.6
1
00
0.2
0.4
0.2 0.2 0.4 0.4
1 nm
0.6
0.6
0.6
0.8
0.8
0.8
1
11
0
1
0.2
0
1
0.2
00.4
1.4 nm
Point defects migrate from MDI to MDI by collective atomic motion
0.40.6 0.6 0.8
0.2
0.4 0.

28. 150
0.45
0
0.2
0.4
100
0.4
(a)
0.6
50
0.35
0.3
0.4
1 nm
(b)
0.6
0.25
0
0.8
0.6
0.8
0.8
0.2
1 0.15
1
0
1
0.8
1
0
0.2
0.2
0.4
NW
0.6
0.28
0.26
0.24
0.22
0.2
0.18
0.16
50
0.14
0.12
0.1
0
0.08
0.06
0.4
0.6 0.6
0.8
0.8
0.4
0.8
1
11
(c)
0.6
0
0
0.2
0.4
0.6
0.8
1
0.35
0.3
0.25
0.2
0.15
0.1
0.05
Cu-V KS
Cu-V KS
0
0
1.4
1.4
0.2
0.2
1.2
1.2
0.4
0.4
1
1
0.6
0.6
0.8
0.8
0.8
0.8
0.6
0.6
1
0.8
1
1
0
0.2
0.4
1.4 nm
0.6
0.8
1
0
Formation energy (eV)
0.6
.4
0.5
Angle with -ve x axis
0
0
0.55
Point defect migration along the interface depends on
0.5
150
0.2
0.2
0.45
the distance between defects on misfit dislocations
0.4
100
0
150
0.2
100
0.4
50
0.6
0
0.2
0.4
0.6
0.8
1
Point defects migrate from one dislocation defect to another by
collective atomic motion
0.8
1
0
0.2

29. 100
0.4
0.4
0.35
100 0.4
0.3 0.6
0.6
50
0.25
0.8
0.8
0.8
0
0.2
0
0.6
50
1 0.15
0
150
0.24
150 0.45
0.2
0.22
0.2 0.4
100
100
0.18
0.4 0.35
0.16
50
0.6 0.3
500.14
0.12
0.25
0.1
0.8
0 0 0.2
0.08
0.2
0.4
1 nm
0.6
0.8
1
1
0
0.2
0.4
0.6 0.8
0.8 1
0.2 1 0.2 0.2 0.60.6 0.8 0.8 1
1
0
0 0.4 0.4 0.4
0.6
0.2
0.4
0.6
0.2
0.4
0.6
0.8
0.8
1
1
0.06
1 0.15
1
0
0
0.2
0
0.2
0.4
Cu-V KS
Cu-Fe NW
KS
0.6
0.8
0.2
0
1.4
0
0.2
1.2
1.2
0.4
0.4
1 1
0.6
0.6
0.6
0.6
1
1
0
1.2
100
100
1
5050
0.8
0.80.8 0.8
0.8
0.8
1
0.8
0.8
0.8
0.8
150
150
0.60.6 0.6
0.6
0.6
1.4
0.40.4 0.4
1
1
0
0.20.2 0.2
1.2
1.2
0.8
1
1.4
1.4
0
0.2
0.2 0.4 0.4 0.6
0.6
1 nm
1.4 nm
0.8
0.8
11
0
1 1 1
0.2
0.4
0.6
0.6
0 0 00.2 0.2 0.40.4 0.6
1.4 nm
0.8
0.8
0.8
0.2
0.4
0
0 0 0
1.4
0.2
0.6
11
0.45
0.2
0.4
0.35
0.4
0.3
0.25
0.6
0.2
0.15
0.8
0.1
0
0.05
1
0.8
1
0
Cu-V KS
Cu-Fe NW
0
0.2 0.60.4 0.8
0.4
0.6
0.8
0.28
0.26
150
0.24
0.22
0.2
100
0.18
0.16
50
0.14
0.12
0.1
0
0.08
0.06
11 1
0 0.6
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
Formation energy (eV)
0.4
1
1
0
0.45
0.2 150 0.2
1
0.8
0.8
0.28
0.260.5
Angle with -ve x axis
150
0
0
Formation energy (eV)
0.8
.6
0.6
0.5
Angle with -ve x axis
0
0.55
Point0 defects migrate along misfit dislocation lines
0
0
0.5
1
0
1
0.2
0
0.4
0.2
0.6
0.4 0.8

30. Summary
• Interface sink strength is a dynamic, evolving property of the interface
• In semicoherent fcc-bcc interfaces, interface sink strength depends on
– Density of misfit dislocation intersections and other dislocation defects
– The ability of the misfit dislocation intersections to trap point defects
– Point defect transport along the interfaces
• Distance between misfit dislocation defects
• character of the misfit dislocations