1. Effects of twin boundaries on crystal growth
Jae-Wook Lee* and James R. Morris
Oak Ridge National Laboratory,
*Korea Institute of Materials Science
Oct. 1, 2010
NIST Workshop on Wires, Whiskers and Walls: Energy Applications at the Nanoscale

2. Twinned crystals (a) (b) parallel {111} twin planes
Fig. (a) TiO2-excess BaTiO3 specimen sintered at 1360 C for 15h (H. –Y. Lee, et al., J. Euro. Ceram. Soc. 20, 731 (2000)) (b) 0.5 mol%Nb2O5-BaTiO3 specimen sintered at 1250 C for 100h (B. –K. Park, et al., J. Am. Ceram. Soc., 84, 2707 (2001))

3. Twinned crystals (a) (b) perfect crystal twinned crystal
Fig. Twinned AgBr crystals grown in solution ((a) C. Goessens, et al., Microscopy Res. Tech., 42, 85 (1998) and (b) G. Bögels, et al., J. Cryst. Growth, 191, 446 (1998))

4. TPRE mechanism Twin-Plane-Reentrant-Edge (TPRE)
R. S. Wagner, Acta Metall., 8, 57 (1960).
D. R. Hamilton, & R. G. Seidensticker, J. Appl. Phys., 31, 1165 (1960).
141.1 trough
(111) twin planes
218.9  ridge
Enhanced layer nucleation on groove

5. Growth of tabular twinned fcc crystal

6. Question 1 ?
How does this face grow?

7. Question 2 Which nucleation is faster? (100) face (111) (111) (111)
B. W. van de Waal
(Phys. Rev. B 51, 8653 (1995))
S. Jagannathan, et al
(Phys. Rev. B 51, 8655 (1995))
(100) face
(111)
(111)
(111)
(100)
(111)
(111)
Which nucleation is faster?

8. Question 3 What does nucleus look like?
D. R. Hamilton, & R. G. Seidensticker,
J. Appl. Phys., 31, 1165 (1960).
W. A. Tiller in
The science of crystallization: microscopic interfacial phenomena (1991)

9. Confusions … g* ?  : step energy g : groove energy g  q
“No corresponding kinetic law for reentrant twins has been developed, but …”
J. W. Cahn, W. B. Hilling, and G. W. Sears,
Acta Metall., 12, 1421 (1964)

10. Confusions … g* ? If g* ≠ 0,  : step energy g : groove energy g q
 : step energy
g : groove energy
g* ?
If g* ≠ 0,
g* = -g both cancel out.
=90 (circle)
no energy barrier reduction

11. Confusions … g* ? If g* ≠ 0, If g* = 0,  : step energyq
 : step energy
g : groove energy
g* ?
If g* ≠ 0,
g* = -g both cancel out.
=90 (circle)
no energy barrier reduction
If g* = 0,
>90 (like a butterfly)
nucleus larger than a circle
energy barrier rather increases.

12. Nucleus should be asymmetric ?

13. Atomistic interpretation of line energy
: continuum
: atomistic
Line energy is the number of broken bonds (created - absorbed)
per atoms on unit length !
(Number of bonds inside nucleus doesn’t matter.)

14. Example - Step energy {110} step on <111> face
: Atome “A” creates 3 to top and 2 to side,
absorbs 3 from bottom
 Line energy : (3+2-3) ϕ = 2ϕ per atom

15. Groove energy {110} line at groove : Atome “ ” creates 2 to top,
absorbs 4 from bottom
 Line energy : (2-4) ϕ = -2ϕ per atom
 Negative line energy !

16. g* ? g* = 0, but g < 0. g  =60 nuclear area decreaseq
60
g* ?
g* = 0, but g < 0.
=60
nuclear area decrease
energy barrier decrease !

17. {110} line of semi-circle at groove
: Atome “ ” creates 4 to top,
absorbs 4 from bottom
 Line energy : (4-4) ϕ = 0 per atom
 Zero line energy !

18. b  b : boundary energy b = 0 =90
nucleus is an exact half-circle !

19. Answer. Nucleus at groove is symmetrical
More probable !

20. Which nucleation is faster?
(100) face
(111)
(111)
(111)
(100)
(111)
(111)
Which nucleation is faster?

21. On {100} face
More difficult !

22. Answer. {100} face grows faster than groove
(111)
(111)
(111)
(100)
(111)
(111)
Nucleation on {100} is faster
than nucleation on groove !

23. Layer advance across the ridge = nucleation of semi-circle at substep
: Atome “ ” creates 4 to top,
absorbs 4 from bottom
 Line energy : (4-4) ϕ = 0 per atom
 Zero line energy !

24. Answer. Layer cannot advance across ridge
More difficult !
This face cannot grow by layer advance.

25. New growth mechanism In contrast to TPRE mechanism,
layer advance across ridge is not allowed ! .
Layers are accumulated at ridge so that {100} face is formed
2D nucleation on narrow {100} face
J. -W. Lee, U. –J. Chung, N. M. Hwang and D. –Y. Kim,
Acta Cryst. A61, 405 (2005)