md. jahidur rahman/ matls 702/ 20th january, 20121 investigation of low angle grain boundary (lagb)...

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


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


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


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


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.]


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 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


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]


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


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


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):


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


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

)


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]


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)

?


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


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


GB

mig

rati

on

vel

oci

ty (

A/p

s) New odd function

Original function


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


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


THANK YOU

Questions and Answers

[email protected]


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


Supporting

Slides


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

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