Stacking Fault Energy (SFE) and Hardness Calculation in Au and Its - - PowerPoint PPT Presentation

Stacking Fault Energy (SFE) and Hardness Calculation in Au and Its Alloys

Anuj Goyal, Yangzhong Li, Aleksandr Chernatynskiy, Simon Phillpot Department of Material Science and Engineering University of Florida

Outline and Previous Task

• Surface orientation simulation (pg 3, 4)
• Compare H and E for (111), (100) and (110)

surface

• GB orientation simulation (pg 5)
• Compare H in two different GB orientation
• Characterize twinning during indentation
• SFE from multiple potentials (pg 6,7)
• H vs SFE plot (pg 8-11)

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Surface Orientation Simulation

• EAM: (111) ~ (100) > (110)
• Exp: (111) ~ (110) > (100)

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Surface Plastic H Yield H Exp Yield H E Exp E (111) 5.40 ± 0.25 7.24 7.3 ± 0.5 88.7 78 ± 1 85 ± 7 5.18 ± 0.39 7.21 89.3 (100) 6.91 ± 0.28 7.34 5.5 ± 0.4 77.7 57± 3 7.06 ± 0.17 7.48 80.8 (110) 5.02 ± 0.25 5.96 7.8 ± 0.7 81.9 82 ± 6 5.21 ± 0.23 5.74 80.8

Exp ref: J Kiely and J Houston, PRB 57, 12588 (1998)

Mechanism of Au Hardening

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• (111): generates many SF inter-blocking

each other to provide hardening

(111) Side (111) Bottom (100) Side (100) Bottom (110) Side (110) bottom

• (100): generates

and emits the 4- side loop to provide continuous hardening

• (110): generates

defect in a smaller scale; weaker hardening

GB Orientation Simulation

• 60º GB forms dense twinning

layers to provide hardening

• 30º GB forms sparse, non-blocking

SFs; no twinning, no hardening

• GB makes defect nucleation

easier thus decrease yield H

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GB orientation Plastic H Yield H 60º 5.30 ± 0.54 6.21 5.76 ± 0.21 6.19 30º 4.96 ± 0.44 5.70 4.85 ± 0.32 5.46 0º (no GB) 5.40 ± 0.25 7.24 5.18 ± 0.39 7.21 60 side 60 top 30 side 30 top

Twinning planes (parallel double SFs)

SFE Calculation: Slab Method

• Use vacuum (100 Å ) along

Z axis

6 6 vacuum vacuum ε

vacuum vacuum

shear Z

• J. A. Zimmerman, H. Gao et al., Modelling Simul. Mater. Sci. Eng. 8 (2000) 103–115

SFE of Pure Au

• Only two EAM potentials are able to

perform alloying simulation

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EAM-potential Stable SFE (mJ/m2) Alloying elements Ward (2012) 3.55 FCC(Ag, Al, Cu, Ni) HCP(Ti, Zr) Zhou (2004) 4.18 FCC(Ag, Al, Cu, Ni, Pb, Pd, Pt) BCC(Fe, Mo, Ta, W) HCP(Co, Mg, Ti, Zr) Sheng (2011) 49.9 No Foiles (1986) 4.72 No Exp (1972) 32 ± 5 DFT 28

L Ward, arXiv:1209.0619 X Zhou, PRB 69, 035402 (2004) H Sheng, PRB 83, 134118 (2011) S Foiles, PRB 33 7983 (1986) M Jenkins, Phil Mag 26, 747 (1972)

Stable SFE vs. Concentration

• SFE calculation shows great variations

and sometimes results in negative values

• Methods are being refined to improve the

result

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• 40
• 30
• 20
• 10

10 20 30 40 50 60 0% 1% 2% 3% 4% 5% 6% SFE (mJ/m2) Concentration Ag Al Cu Ni Ti Zr

Correlation between H and SFE

• Two independent variable
• Element (ele), concentration (con)
• Two dependent variable
• H(ele, con), SFE(ele, con)
• Two analysis performed
• Fix con, plot H(ele) vs. SFE (ele)
• Fix ele, plot H(con) vs. SFE (con)

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H vs SFE under Fixed Concentration

• 1% shows a strong negative correlation; but

quantitative relation cannot be drawn due to large variation

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4.5 5 5.5 6 6.5 7 7.5

• 35
• 25
• 15
• 5

5 15 25 35 45 Plastic H GPa) SFE (mJ/m2) 1% 2% 3% 5%

H vs SFE under Fixed Elements

• Ag, Ni and Ti shows a negative correlation

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5.5 6 6.5 7 7.5 8 8.5 9

• 40
• 20

20 40 60 Plastic H (GPa) SFE (mJ/m2) Ag Al Cu Ni Ti Zr

Conclusion

• EAM is able to consistently correlate H variation and

defect generation, despite the actual H different from experiment

• GB decrease yield H, and provide hardening by

generating twinning SF

• Only 2 EAM potentials are suitable for alloying

simulation; EAM-zhou is currently running

• Due to high variation of SFE by EAM-ward potential,
• nly qualitative trend can be drawn
• Currently running indentation and SFE calculation by

EAM-zhou potential; preliminary SFE results show variation with much smaller magnitude

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