This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48 UCRL 336674

Properties of Point Defects in Fe-Cr Alloys Harun Đogo

Faculty of Mechanical Engineering, Sarajevo, Bosnia and Herzegovina

French-Serbian European Summer UniversityVrnjačka Banja, October 23rd, 2006

Source: U.S. Department of Energy, Office of Nuclear Energy

Energy from Nuclear Fission

Source: U.S. Department of Energy, Office of Nuclear Energy

Generation IV Reactor Design – The SSTAR Project

•Global Nuclear Energy Partnership concept initiated at 2006 State of the Union Address

•Small, Sealed, Transportable Autonomous Reactor (SSTAR) currently under development at LLNL

Advanced Reactor Material Operating Environment

Source: SJ Zinkle, ORNL, Application of Computational Materials Science Multiscale Modeling to Fission Reactors, LLNL Workshop, December 14-16, 2005

Effects of Radiation Damage on Materials

Irradiation creep3

Radiation hardening and embrittlement4

High temperature He embrittlement2

Volumetric swelling from

void formation1

Vacancy – a vacant site in the crystal

lattice

Interstitial – an excess atom in the

crystal lattice5

Sources : 1. Computational Material Sciences Network, Basic Energy Sciences, U.S. DOE, 2. SJ Zinkle, ORNL, SJ Zinkle, ORNL, 4. JOM,53 (7) (2001), pp. 18-22., 5. S Domain & Becquart, PRB, 2001

Multi Scale Materials Modeling

Source: Wirth Research Group, Dept. of Nuclear Engineering, UC Berkeley

Research Methodology

Computational Materials Science

Source: Farrell and Byun, J. Nucl. Mater. 318 (2003) 274, A. Caro, D. A. Crowson, and M. Caro, Phys. Rev. Lett. 95, 075702 (2005).

Concentrated solution

• Positive heat of solution

• Magnetic frustration when Cr are nearest neighbors

neighbouring Cr's in Fe

??

Dilute solution

• Negative heat of solution

• Dilute Cr aligns anti-ferromagnetically in Fe

single Cr's in Fe

Research Objectives

1. Using the EAM potential, define the formation energy of a single crystal lattice vacancy in:

• Pure Fe

• Pure Cr

• As a function of Cr concentration

2. Define the formation energy for interstitials in all possible configurations and orientations in:

•Pure Fe

•Pure Cr

•As a function of Cr concentration

Possible Configurations:

•Fe-Fe – “self interstitial”

•Fe-Cr – “mixed interstitial”

•Cr-Cr – “self-interstital”

Possible Orientations:

•Interstitial pair displaced in X and Y axes, or the <110> interstitial

•Interstitial pair displaced in the X, Y and Z axes, or the <111> interstitial

Only 4 possible configurations examined as a function of Cr concentration. Cr-Cr self interstitials and interstitials oriented in <100> not examined as their formation energies are too high for them to have any measurable longevity.

Source: Domain & Becquart, Phys. Rev. B, 2001

Vacancy – a vacant site in the crystal lattice

Vacancy Formation Energy in Pure Elements

Vacancy in Iron Vacancy in Chromium

Linear Interpolation

1.721.84 1.85

2.041.89

1.63

1.95 2.02 2.071.86

0

0.5

1

1.5

2

2.5

This W

ork

Men

delev

#2, E

AM, F

ree V

, Rela

xed

Men

delev

#5, E

AM, F

ree V

, Rela

xed

Wall

enius

- EAM

, Free

V, R

elaxe

d

Acklan

d, DFT, F

ree V

, Unr

elaxe

d

Becqu

art E

AM, F

ree V

, Rela

xed

Becqu

art D

FT, Free

V, R

elaxe

d

Becqu

art -

DFT, Con

st. V

, Unr

elaxe

d

Dudare

v, DFT, C

onst.

V, U

nrela

xed

Experi

ment

[eV

]

2.56

2.14

2.64 2.56

2.1

0

0.5

1

1.5

2

2.5

3

This Work Wallenius - EAM,Free V, Relaxed

Dudarev, DFT,Const. V, Unrelaxed

Olsson, DFT, ConstV, Unrelaxed

Experiment

[eV

]

2.14

2.64

2.1

2.56

2.04

2.07

1.86

1.72

1.5

1.7

1.9

2.1

2.3

2.5

2.7

0 0.2 0.4 0.6 0.8 1

Cr Fraction

eV

Wallenius - EAM, Free V, Relaxed

Dudarev, DFT, Const. V,Unrelaxed

Experiment

This Work

Vacancy as a Function of Cr Concentration

HT-9 Steel

Vacancy – a vacant site in the crystal lattice

Interstitial Formation Energy in Pure Elements

3.443.61

3.52

3.95

3.56

3.96 3.94

4.66

3.88

4.28

4.03

4.72

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Formation Energy MixedInterstitial <110>

Formation Energy MixedInterstitial <111>

Formation Energy SelfInterstitial <110>

Formation Energy SelfInterstitial <111>

This WorkUSPP (Olsson)PAW (Olsson)

5.53

5.61

5.67 5.69

5.29

5.39

5.65

5.84

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

Cr self-interstitial <110> Cr self-interstitial <111>

[eV

]

This Work

Dudarev

USPP (Olsson)

PAW (Olsson)

Interstitials in Iron Interstitials in Chromium

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

0 0.05 0.1 0.15 0.2

xCr

eV

<110>

<111>

HT-9 Steel

Self Interstitial (Fe-Fe) Formation Energies

Conversion Function for Fe-Fe Self Interstitials

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Cr Concentration

eV

MIXED INTERSTITIAL <110>

MIXED INTERSTITIAL <111>

Mixed Interstitial (Fe-Cr) Formation Energies

HT-9 Steel

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

0 0.05 0.1 0.15 0.2

Cr Concentration

eV

SELF INTERSTITIAL <110>

MIXED INTERSTITIAL <110>

MIXED INTERSTITIAL <111>

SELF INTERSTITIAL <111>

Application of Results

MCCASK is a hybrid Monte Carlo-molecular dynamics code developed by A. Caro and B. Sadigh in 2005. MCCASK code performs sequences of Monte Carlo events and Molecular Dynamics time steps.  In this way, the equilibrium concentrations in the alloy are obtained, enabling precipitation and defect

studies on 106 atom scale. Shown is the performance of the EAM potential characterized in this work in simulating homogeneous Cr precipitation in a 20 % Cr sample, and the relationship of that precipitation

with a screw-type dislocation

Conclusions• The designed EAM potential approximates available

ab-initio data very well and performs well in simulations depicting defect interaction.

• It is possible to use the potential with the MCCASK code and kinetic Monte Carlo to project time evolution of defects and their mutual interaction

• The modeling continues…

Questions?