gurpreet kaur, p. jegadeesan, d. murali, b.k. panigrahi, m ...bemod12/slides/kaur_bemod12.pdfcluster...

0.4 0.6 0.8 1.0 1.2 1.41E-27

1E-23

1E-19

1E-15

1E-11

KMC

Le Claire's model

Experiment

Y

Ti

FeD

iffu

sio

n C

oe

ffic

ien

t (m

2/s

)

1000/T (K-1

)

Gurpreet Kaur, P. Jegadeesan, D. Murali, B.K. Panigrahi, M.C. Valsakumar, C.S.SundarMaterials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, INDIA

gurpreet@igcar.gov.in

The strength of Nanostructured Ferritic Alloys depends on the distribution ofY-Ti-O nanoclusters in the matrix.

These nanoclusters are formed during the high temperature consolidation of the ballmilled (powdered) alloy.

Understanding the initial phase of formation of these nanoclusters is crucial to predicttheir overall behavior.

We have used first principles methods along with Lattice Kinetic Monte Carlo technique tostudy the kinetics of nanocluster formation in BCC Iron.

Introduction

Pairwise bondsFirst neighbour

(eV)Second neighbour

(eV)

Fe-Y 0.25 0.00

Fe-Ti -0.10 0.00

Fe-O 0.35 0.17

Fe- 0.25 0.00

Y-Y 0.19 0.01

Y-Ti 0.15 0.01

Y-O 0.45 -1.05

Y- -1.40 -0.25

Ti-Ti 0.23 0.13

Ti-O -0.25 -0.55

Ti- -0.25 0.16

- 0.15 -0.21

-O -1.55 -0.75

O-O 0.60 0.40

Pairwise bond energy parameters

Migration energy Em (eV)

Fe- 0.65

Y- 0.10

Ti- 0.40

O 0.55

Migration Energy Barriers

The bond energies are calculated

from Density Functional Theory

using VASP code with PAW (PBE)

psuedo potential with 128 atom

supercell.

The migration barriers for the solute

atoms in bcc iron were calculated

using the Nudged Elastic Band

(NEB) method

Diffusion coefficients of solute atoms

The diffusion coefficients of solute atoms in bcc Fe calculated using LKMC and compared

with the diffusion coefficients calculated from first principles using Le Claire’s nine

frequency model and also the available experimental values.

7.38906 20.08554 54.59815

2.71828

7.38906

Me

an

, S

igm

a

Time ( s)

Mean

Sigma

Size distribution of clusters

References:

G.R. Odette, M.J. Alinger and B.D. Wirth, Annu. Rev. Mater. Res. 38 (2008) 471.

D. Murali, B.K. Panigrahi, M.C. Valsakumar, Sharat Chandra, C.S. Sundar, Baldev Raj, J. Nucl. Mater. 403 (2010) 113-116

P. Jegadeesan, D. Murali, B.K. Panigrahi, M.C. Valsakumar, C.S. Sundar, International Journal of Nanoscience 10 (2010) 1-5 .

M. Ratti, D. Leuvrey, M.H. Mathon, Y.de, Carlan, J. Nucl. Mater. 386, 540-543 (2009).

V.A. Borodin and P.V. Vladimirov, J. Nucl. Mater. 386, 106 (2009).

1 10 1000

100

200

300

400

No

. o

f C

lus

ters

Time ( s)

3

10

100

Av

. C

lus

ter

Siz

e (

No

. o

f a

tom

s)

0 2 4 6 8 10 12 140

100

200

300

400

500

600

6.4 s

12.8 s

19.2 s

25.6 s

32.1 s

38.5 s

44.9 s

51.3 s

57.7 s

64.2 s

Nu

mb

er

of

clu

ters

R (in Angtrom)

3 4 5 6 7 8 9 10 11 12 13 140.0

0.2

0.4

0.6

0.8

1.0

Cu

mu

lati

ve

Dis

trib

uti

on

of

No

.of

clu

ste

rs

R (in Angtroms)

2.0x10-4

4.0x10-4

6.0x10-4

8.0x10-4

1.0x10-3

1.2x10-3

1.4x10-3

2.0x10-7

4.0x10-7

6.0x10-7

8.0x10-7

1.0x10-6

Do

Vacancy concentration

Ti

Fe

The LKMC Model

Two sublattices: 1st sublattice: regular bcc sites

with Fe, Y, Ti, vacancy ( )

2nd sublattice: octahedral interstitial sites

with Oxygen

One Monte Carlo sweep: all the Vacancy and O allowed to

jump once

A rigid bond model for total energy with interactions up to

second neighbor (fitted to first principle calculation)

Formation of Y-Ti-O clusters

Randomly distributed Y, Ti, O

and vacancy in Fe, evolved

by vacancy jumps and

interstitial O jumps, leading to

the formation of clusters

88 88 88 unit cells

(1.3 million sites) Y: 0.12%,

O: 0.2%, Vac: 1000 ppm

Temp. 1150 K

Evolution of clusters with time O to Y ratio in the clusters

Normal distribution is found to give the best fit for the

cluster size distribution (R >4 Å) out of Lognormal,

Normal and gamma distributions. [ignoring the initial

decaying portion(R < 4 Å) of size distribution].

51

tR

k ji

ijij knkE,

)()(

0 100 200 300 400 5000

25

50

75

100

125

150

175

200

Without titanium

Nu

mb

er

of

clu

ste

rs

Cluster size (No.of atoms)

0 100 200 300 400 5000

25

50

75

100

125

150

175

2004000

5000

With titanium (0.5at%)

Nu

mb

er

of

clu

ste

rs

Cluster size (No.of atoms)

Effect of Titanium

E-spE-init

E-final

Vacancy

Conclusions

Mechanism of growth is the coagulation of the clusters. The Cluster Size follow a normal distribution. Presence of titanium reduces the size of clusters .

Time exponent shows coagulation of clusters is the growth mechanism