1. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20121 Investigation of low angle grain boundary (LAGB) migration in pure Al: A Molecular Dynamics simulation study in progress Md. Jahidur Rahman Dept. of Materials Science & Engineering Supervisors: Dr. Jeff Hoyt Dr. Hatem Zurob Committee member: Dr. Gary Purdy January 20, 2012: Departmental Seminar

2. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20122 Introduction Grain boundary properties : – microstructural property – boundary motion: size and texture of grains – HAGB: θ > (11 o ~15 o ) : – LAGB: θ < (~11 o ): - ∑ 1 boundary - discrete dislocations - nucleation of recrystallizattion Low angle grain boundary migration in pure Al Fig. Discrete dislocations at low angle grain boundary [2] Fig. Al-alloys uses in automotive parts of Audi-A8 [1] Aluminium in automotives: – weight reduction: less fuel consumption – corrosion resistance, ductility and castability – for inner body parts of automotive

3. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20123 Why is LAGB important Nucleation of recrystallization: – recovery kinetics (LAGB mobility) – critical nucleus size Fig: Subgrain growth process: (a) formation of nucleus, (b) growth of subgrain, (c) critical size of nucleus is reached for the nucleation of recrystallization [Zurob et al.] (a) (c) (b) Subgrain growth rate, v(t) = M G(t) M = LAGB mobility, G(t) = Stored energy Low angle grain boundary High angle grain boundary

4. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20124 Motivation for LAGB migration Previous investigations: – Experimental: - less studied: complicated to identify and observe LAGB motion - average mobility from some growth processes – Computational: - LAGB motion: rarely studied for pure and alloy system - recovery kinetics and nucleation of recrystallization: poorly understood Objective of the project: – compute mobility of low angle boundary migration at different temperature and misorientation angle – observation of LAGB migration mechanism – investigate solute interaction with LAGB motion – provide plausible explanation of experimental results Preliminary work: pure aluminum

5. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20125 Previous work on experimental investigations Winning et al. and Molodov et al.: – stress induced migration in pure Al – discontinuous jump at transition misorientation angle: 13.6±0.55 o – at T >500 o C: mobility of low angle boundaries exceeds that of high angle Fig. GB mobility vs misorientation angle in pure Al [Winning et al.]

6. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20126 Computational methods for GB mobility Curvature controlled migration in MD: – motion of U-shaped half-loop bicrystal – M *, reduced mobility, not the bare mobility, M Elastically driven migration of flat GB: – biaxial strain to planar interface – driving force: difference in stored elastic energy – applicable: crystal geometry with elastic anisotropy Fig. : Half loop Bicrystal geometry[Zhang et al.]. Fig. : Asymmetric planar grain boundary in a bicrystal geometry [Zhang et al.] GB mobility from boundary fluctuation in MD: – stiffness and mobility: kinetics of equilibrium fluctuation spectrum of boundary – suitable approach for continuum model such as HAGB case

7. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20127 MD methods for GB mobility (contd…) Artificial driving force approach in MD: – any random planar GB: symmetric and assymetric – orientation dependent PE added to one crystal: ↑ in free energy causes boundary motion Fig. Symmetric 55◦ boundary in f.c.c. Al [Janssens et al.] Random walk technique: – no driving force is required – by tracking 1-D random walk of mean boundary position Fig. 1-D random walk fluctuation of boundary [Trautt et. al] In this study: Both ADF and RW technique will be investigated in pure Al

8. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20128 Artificial driving force approach Bi-crystal system for pure Al: – crystal-1: x =, y =, z = – crystal-2: x =, y =, z = – symmetric tilt boundary: - misorientation angle → 7.785 o – x-axis is normal to the grain boundary z x a b Fig.: The initial set up of (a) crystal-1 and (b) crystal-2 at 300K Fig. schematic view of dislocation arrangement in LAGB [3]

9. Md. Jahidur Rahman/ MATLS 702/ 20th January, 20129 Grain boundary migration Application of MD technique: – NVT ensemble: free surface at the end – introduce orientation: transformation of axis: [New] = [R] × [Old] – orientation dependent PE to 2 nd crystal Tracking boundary migration : Fig.: Centro-symmetry parameter vs. x-position Fig.: PE profile at 0.0008 eV/atom driving force at 300K Fig.: Energy distribution in the bicrystal

10. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201210 Snapshots of LAGB migration t = 0 ns Fig.: Snapshots of simulation: grain boundary migration with the driving force of 0.0008 eV/atom at 300K t = 1 ns t = 2 nst = 3.2 ns t = 4 ns t = 4.8 ns

11. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201211 LAGB motion velocity Fig. LAGB velocity vs driving force at 300K LAGB mobility at different cut-offs: LAGB velocity: – higher driving force: moves faster – linear in lower driving force region – lower driving force regime – mobility: slope of velocity vs. driving force Order Parameter (OP):

12. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201212 LAGB mobility LAGB mobility in pure Al: – at 300K, M = 3.48×10 -7 m/s/Pa 200K, M = 2.11×10 -8 m/s/Pa – experiment at 473K, M = 2.5×10 -10 m/s/Pa Fig. Average LAGB velocity vs driving force at 300K LAGB mobility at different T: – T = 200K to 800 K – slope of PE plot at T > 300 K:  scattered over whole span of OP cut-off – LAGB at T > 300 K:  prediction: ADF might not be effective  large thermal fluctuations overcomes the orientational difference between nearest neighbour vectors – at 200K:

13. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201213 Random walk MD technique Fig. Variation of the mean square displacement ( ) at 500K, 600K, 700K with linear fit Mobility : = [2MKBT/A] t [ is mean square displacement of boundary]

14. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201214 Mobility comparison and activation energy Activation energy of LAGB in Al: – RW: 7 KJ/mol – ADF: 14 KJ/mol – experiment: 134 KJ/mol – discrepancy: absence of impurity and dislocations – MD technique: intrinsic mobility ADF vs. RW technique: – LAGB mobility from RW > mobility from ADF approach – reasons might be : – order parameter cut-off value – governing function in ADF technique ?

15. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201215 Details of ADF technique Artificial potential function: – Original function: – New odd function: Energy: Force: lower cut off higher cut off

16. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201216 Mobility comparison LAGB mobility in pure Al: – Original function: 3.48×10 -7 m/s/Pa at 300K – New odd function: 5.59×10 -7 m/s/Pa at 300K

17. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201217 Conclusion  Low angle boundary migration at different driving force and different temperature regime  Temperature dependent mobility of 112 tilt low angle boundary in pure Al utilizing two MD techniques (ADF and RW).  Computational results compared with experimental  Detail mechanism of Artificial driving force method

18. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201218 Future work  Computation of boundary mobility as function of misorientational angle  Computation of gb mobility of Al-alloy system by including some solutes (Mg)  Observation of LAGB mobility in presence of dislocations and vacancy

19. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201219 THANK YOU Questions and Answers rahmanmj@mcmaster.ca

20. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201220 1. Courtesy to master’s thesis of Sanjay Kumar Vajpai [http://www.keytometals.com]. 2. http://www.tf.uni- kiel.de/matwis/amat/def_en/kap_7/backbone/r7_2_1.html.http://www.tf.uni- kiel.de/matwis/amat/def_en/kap_7/backbone/r7_2_1.html 3. M. Winning, A.D. Rollett, G. Gottstein, D.J. Srolovitz, A. Lim and L.S Shvindlerman, Philosophical Magazine, 90, 3107, 2010. References

21. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201221 Supporting Slides

22. Md. Jahidur Rahman/ MATLS 702/ 20th January, 201222 Simulation details (contd …) Application of MD technique: – NVT ensemble: free surface in normal to grain boundary – for orientation: transformation of axis using rotation matrix [New] = [R] × [Old] – orientation dependent potential energy is added to 2 nd crystal – boundary migration: crystal2 shrinks and crystal1 grows Table : Rotation matrix of transformation and the nearest neighbour atoms at different axis