Md. Jahidur Rahman/ MATLS 702/ 20th January, 20121 Investigation of low angle grain boundary (LAGB) migration in pure Al: A Molecular Dynamics simulation.
Post on 17-Jan-2016
222 Views
Preview:
Transcript
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 1
Investigation of low angle grain boundary (LAGB) migration in pure Al: A Molecular Dynamics simulation
study in progress
Md. Jahidur RahmanDept. of Materials Science & Engineering
Supervisors: Dr. Jeff Hoyt
Dr. Hatem Zurob
Committee member: Dr. Gary Purdy
January 20, 2012: Departmental Seminar
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 2
Introduction
Grain boundary properties :
– microstructural property
– boundary motion: size and texture of grains – HAGB: θ > (11o ~15o) : – LAGB: θ < (~11o): - ∑ 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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 3
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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 4
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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 5
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±0.55o
– at T >500oC: mobility of low angle boundaries exceeds that of high angle
Fig. GB mobility vs misorientation angle in pure Al [Winning et al.]
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 6
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 loopBicrystal 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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 7
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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 8
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 → 7.785o
– x-axis is normal to the grain boundary
]11917[ ]211[ ]363339[__
]11719[ ]211[ ]363933[__
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]
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 9
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 2nd 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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 10
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 ns
t = 3.2 ns
t = 4 ns
t = 4.8 ns
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 11
LAGB motion velocity
Fig. LAGB velocity vs driving force at 300K LAGB mobility at different cut-offs:
y = 54.233x - 0.0054
y = 48.866x - 0.0135
y = 31.406x + 0.0024
y = 25.908x + 0.0044y = 20.255x + 0.0109
y = 11.167x + 0.0212
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.0005 0.001 0.0015 0.002 0.0025
Driving force (eV/atom)
GB
mig
rati
on
vel
oci
ty (
A/p
s)
0.25-0.75
0.20-0.80
0.30-0.70
0.35-0.65
0.40-0.60
0.45-0.55
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):
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 12
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
0
0.02
0.04
0.06
0.08
0.1
0 0.0005 0.001 0.0015 0.002 0.0025
Driving force (eV/atom)
GB
mig
ratio
n ve
loci
ty (A
/ps)
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:
175
180
185
190
195
200
0 2000 4000 6000 8000 10000 12000
Time (ps)
GB
po
siti
on
(oA
)
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 13
Random walk MD technique
600K
y = 0.1263x - 17.608
-20
0
20
40
60
80
100
120
140
160
180
0 200 400 600 800 1000 1200 1400t (ps)
<h2>
(A
2)
700K
y = 0.1834x - 10.578
-20
30
80
130
180
230
280
-20 380 780 1180 1580
t (ps)
<h2>
(A
2>
Fig. Variation of the mean square displacement (<h2>) at 500K, 600K, 700K with linear fit
500K
y = 0.0796x + 1.3156
0
20
40
60
80
100
120
140
0 450 900 1350 1800
t (ps)
<h2 >
(Ao)2
Mobility : < h2> = [2MKBT/A] t
[< h2> is mean square displacement of
boundary]
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 14
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
-18.5
-17.5
-16.5
-15.5
-14.5
-13.5
-12.5
-11.5
0.001 0.002 0.003 0.004 0.005
1/T (1/K)
ln (
M)
, Random Walk (RW)
, Artificial Driving Force (ADF)
?
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 15
Details of ADF technique
Artificial potential function:
– Original function:
– New odd function: Energy:
97532
393.22
718.82
756.112
432.6)(
iiiiru
Force:
lower cut off
higher cut off
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Order parameter
En
erg
y
New odd function
Original function
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1 1.2
Order parameter
Fo
rce
Original function
New odd function
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 16
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
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.0005 0.001 0.0015 0.002 0.0025
Driving force (eV/atom)
GB
mig
rati
on
vel
oci
ty (
A/p
s) New odd function
Original function
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 17
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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 18
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
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 19
THANK YOU
Questions and Answers
rahmanmj@mcmaster.ca
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 20
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.
3. M. Winning, A.D. Rollett, G. Gottstein, D.J. Srolovitz, A. Lim and L.S Shvindlerman, Philosophical Magazine, 90, 3107, 2010.
References
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 21
Supporting
Slides
Md. Jahidur Rahman/ MATLS 702/ 20th January, 2012 22
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 2nd crystal
– boundary migration: crystal2 shrinks
and crystal1 grows
Table : Rotation matrix of transformation and the nearest neighbour atoms at different axis
top related