1. Texture transition due to stacking fault energy
POSTECH
Department of Materials Science and Engineering
Jaimyun Jung

2. Texture transition in fcc metals
Result of deformation (slip) related grain rotation
Difference in texture may occur for materials with same crystal structure
Different textures lead to different formability, strength, and fracture toughness
(a),(c) {1 1 1}, (b),(d) {2 0 0} after 96% reduction Hu et al., 1952
Transition
Rolling: Copper to brass-type transition
Copper-type (Copper, S, and Bs-orientation; beta-fiber) vs brass-type (Goss and Bs-orientation; alpha-fiber)
Extrusion/drawing: <111>-fiber to <100>-fiber transition

3. Result of the transition
Texture transition
Cause of transition
The cause of this transition is now generally accepted as due to cross-slip events (Leffers et al., 2009)
The lack of cross-slip in certain fcc alloy types nurtures the formation of twins and shear bands
Result of the transition
Non-cube recrystallization texture after rolling
Reduced formability after rolling
Reduced strength after extrusion/drawing

4. Stacking fault energy calculation (0K)
Method
Calculate stacking fault energies
Compare against observed texture transition
Stacking fault energy calculation (0K)
Construct perfect lattice with y-direction parallel to <111>
1500 atoms for single elements 3000 atoms for alloys
Relaxation at 0K
Either remove a center layer or displace it
Relaxation at 0K (free surface along <111> direction)
For first method, {𝐸 𝑓 −( 𝐸 0 − 𝐸 𝑟𝑒𝑚𝑜𝑣𝑒𝑑 )}/(𝑆𝑡𝑎𝑐𝑘𝑖𝑛𝑔 𝑓𝑎𝑢𝑙𝑡 𝑎𝑟𝑒𝑎)
For second, { 𝐸 𝑓 − 𝐸 0 }/(𝑆𝑡𝑎𝑐𝑘𝑖𝑛𝑔 𝑓𝑎𝑢𝑙𝑡 𝑎𝑟𝑒𝑎)
Single element: Ni Ag Cu Al Pd Pt Au
Binary:
Ni-W
Ni-Cu
Ni-Al
Ni-V
For binary alloys, 2~3 specimens with random solute mixture are used to alleviate the effect of solute concentration on the stacking fault
For each alloy, the solute concentration is ensured to fall within the range of single phase or mostly single phase fcc

5. Calculated stacking fault energies
Solute frac.
SFE (𝐦𝐉/ 𝐦 𝟐 )
Ref.[2]
Ni-W
125
250
0.05 71 65
0.07 54 55
0.1 45 50
Ref.[3]
Ni-Cu
225
0.25
101
100
0.5 84
Cu-Ni 44
0.2 56 70
0.3 69
Ref.[4]
Ni-Al
132
0.03 --
109
119
118
Ni-V
116 68
127
145
Calculated
Ref.[1] Ni
125 Ag 21 Cu 44 42 Al
141 Pd
100 Pt
110 Au 40
[1] B.J. Lee, J.H. Shim, M.I. Baskes, Phys. Rev. B (2003) 68
[2] T.J. Rupert, J.C. Trenkle, C.A. Schuh, Acta. Mater. (2011) 59
[3] B. Somerday, P. Sofronis, R.H. Jones, Effects of hydrogen on materials: proceedings of 2008 interational hydrogen conference (2008)
[4] S. Shang, H. Fang, Y. Wang, Y. Du, J Phys.: Condens. Matter(2012) 24

6. Published results on texture
Single element experimental results:
Ni, no transition up to 80% (Park, 1996)
Ag, always Brass-type (Smallman, 1964)
Cu, no transition up to 80%, prominent Brass at 97% (Hu, 1974)
Al, no transition up to 95% (Lee, 2014)
Au, no transition up to 95% (Smallman, 1964)
Ni-Al experimental results:
Ni-18at%Al no transition up to 95%, two phase (Li, 2008)
Ni-V experimental results:
Ni-10wt%V no transition up to 95% (Watanabe, 2000)
Ni-11at%V no transition (Petrisor , 2002)
Cu-Ni experimental results:
Cu-10at%Ni no transition up to 95%(Sarma, 2007)
Cu-35at%Ni no transition up to 95% (Sarma, 2007)
Cu-45at%Ni no transition up to 99% (Tian, 2015)
Ni-W experimental results:
Ni-5at%W no transition at 97% (Bhattacharjee, 2009)
Ni-9at%W transition at 95% (Sarma, 2004)
Single element:
Ni, Ag, Cu, Al, Pd, Pt, Au
Binary alloy:
Ni-Al
Ni-V
Ni-Cu
Ni-W

7. Results Red: No transition observed Blue: Transition observed
Black: No experimental data

8. Conclusion Transition criteria
From experimental evidence, only Ag and Ni-10at%W exhibit brass-type texture after <50% and 95% reduction ratios, respectively.
The above mentioned results, coupled with MD results, indicates 45 mJ/ m 2 as threshold SFE for transition at 95% and 21 mJ/ m 2 for transition at <50%.
Cu and Au fall within the threshold SFE for transition at 95%, which is not true
More low SFE fcc elements/alloys should be investigated to provide a better criteria (Cu-Al, Ni-Co, Cu-Zn)

9. References
[1] B.J. Lee, J.H. Shim, M.I. Baskes. Phys. Rev. B (2003) 68.
[2] T.J. Rupert, J.C. Trenkle. C.A. Schuh, Acta. Mater. (2011) 59.
[3] B. Somerday, P. Sofronis, R.H. Jones, Effects of hydrogen on materials: proceedings of 2008 interational hydrogen conference (2008).
[4] S. Shang, H. Fang, Y. Wang, Y. Du. J Phys.: Condens. Matter (2012) 24.
[5] Y.B. Park, D. Raabe, T.H. Yim. Metals and Mater. (1996) 2.
[6] R. Smallman, I. Dillamore, P. Dobson. J. de Phys. (1966) 27.
[7] R. Smallman, D. Green. Acta. Metall. (1964) 12.
[8] H. Hu. Texture of metals (1974).
[9] V.S. Sarma, J. Eickemeyer, C. Mickel, L. Schultz, B. Holzapfel. Mater. Sci. Eng. A (2004) 380.
[10] H. Tian, H. Suo, Y. Liang, Y. Zhao, J.-C. Grivel. Mater. Lett. (2015) 141.
[11] V.S. Sarma, J. Eickemeyer, L. Schultz, B. Holzapfel. J. Mater. Sci. (2007) 42.
[12] D. Li, K. Kishida, M. Demuar, T. Hirano. Intermetallics (2008) 16.
[13] T. Watanabe, T. Maeda, K. Matsumoto, N. Uno, M. Ikeda, I. Hirabayashi. Advances in Superconductivity XII (2000).
[14] T. Petrisor, V. Boffa, G. Celentano, L. Ciontea, F. Fabbri, V. Galluzzi, U. Gambardella, A. Mancini, A. Rufolonoi, E. Varesi. Physica C (2002) 377.
[15] T. Leffers, R.K. Ray. Prog. Mater. Sci. (2009) 54.
[16] P.P. Bhattacharjee, R.K. Ray, N. Tsuji. Acta Mater. (2009) 57.