ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS · ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS CEA, DEN, Service de Recherches de Métallurgie Physique Saclay, France M.-C. Marinica,

ENERGY LANDSCAPE OF POINT DEFECTS IN

BCC METALS

CEA, DEN, Service de Recherches de Métallurgie Physique

Saclay, France

M.-C. Marinica, R. Alexander, L. Ventelon, L. Proville,

F. Willaime

Materials under irradiation for the nuclear

industry (e. g. high fluxes of neutrons)

Defect or

Defect

clusters

T>>Ed => displacement cascade

• Isolated self-

interstitials

• Isolated vacancies.

• Interstitial clusters.

• Vacancies clusters.

+

• atomic mixing:

( ≈10Resplacements

/displacement ) Number of Frenkel pairs :

n T / (2.Ed)

interstitial

vacancy En

En-T

T

neutron

pka

pka = primary knocked atom

T = kinetic energy transferred to the

pka

| PAGE 2

Elementary defects induced by irradiation

, , ( )eq

v i v ic c TSupersaturation of defects

M.-C. Marinica | ICTP-IAEA Conference Trieste 2014 | 2-7 NOVEMBER

interstitial :

vacancy :

Annihilation (recombination) Clustering (agglomeration)

Vn + Vm → Vn+m

In + Im → In+m

annihilation: In + Vm → In-m (Vm-n)

+ →

V + V → V2

I2 + V → I

+

+

I + I → I2

→

→

system tend to recover the

ground state (bulk state)

+ →

I + V → bulk

(atom on a lattice

site)

Elimination on sinks

Dislocation lines (network

& loops),

Grain-boundaries

Free surfaces, voids,

bubbles.

Elementary defects induced by irradiation

| PAGE 3

( 0) ( 0)i vc t c t

( ) ( )eq eq

i vc T c Tf f

i vH H

Importance of the interstitials point defects under irradiation:

Unlike the thermal equilibrium because


MORPHOLOGY OF DEFECT CLUSTERS IN

METALS UNDER IRRADIATION

# defects in cluster

n=1 100-10 000 10

voids loops

2 nm

SFT

b

3D 3D 2D

2D | PAGE 4 M.-C. Marinica | ICTP-IAEA Conference Trieste 2014 | 2-7 NOVEMBER




n=1 100-10 000 10

voids loops

2 nm

SFT

b

3D 3D 2D

2D | PAGE 5 M.-C. Marinica | ICTP-IAEA Conference Trieste 2014 | 2-7 NOVEMBER

| PAGE 6

OUTLINE

1. Self-interstitial clusters in bcc metals

2. Vacancies in bcc metals


SELF-INTERSTITIAL CLUSTERS IN BCC

METALS

9 NOVEMBRE 2014

| PAGE 7

PERFORM 60 | 21 JUNE 2012

Structure and kinetics of interstitial type defects

# SIAs in cluster

n=2-100

Competition between

<110>, <111> and <100> ?

n=1 2 100-10 000 10

TEM:

Fe b=<100> or ½<111>

others: b = ½<111>

b

| PAGE 8

Mobility:

(e.g. resistivity

recovery experiments)

140 K – Fe

~2-10 K - others

D. Nguyen-Manh, A. P. Horsfield, et

S. L. Dudarev. PRB 73, 020101

(2006).

Morphology:

Fe: <110>

others: <111>

Stability:

Oxford group: X. Yi,M. L. Jenkins., M. Briceño, S. G. Roberts, Z. Zhou and M.A. Kirk: Philos. Mag. 93 1715 (2013)

W

In situ TEM: transformations <111> to <100> and from <100> to <111> Arakawa et al., PRL (2006) , Science (2007)

Fe

| PAGE 8 M.-C. Marinica | ICTP-IAEA Conference Trieste 2014 | 2-7 NOVEMBER

New type of clusters

# SIAs in cluster

n=1 2 100-10 000 3

I2 I8 Nano-cristals

D.A Terentyev et al.

Phys. Rev. Lett.

100, 145503 (2008)

MCM

F. Willaime

J-P Crocombette

Phys. Rev. Lett.

(2012)

4

F. Gao et all J. Nucl. Mater. 276, 213 (2000).

C. Domain, C. S. Becquart, Phys. Rev. B 65, 024103 (2001)

C.-C. Fu, F. Willaime, and P. Ordejon, Phys. Rev. Lett. 92, 175503 (2004).





n=1 100-10 000 10

voids loops

2 nm

SFT

b

3D 3D 2D

2D

3D

Prediction from

atomistic simulations


Building a new type of interstitial clusters

How to combine the triangle and ring defects ?

3i - 1v

I2 I3

6i - 3v

I3

9i - 6v

4 triangles

4 rings

I2

12i - 10v


C15

6IC15

8IC15

4IC15

2I

Building larger clusters


Z16 Frank-Kasper

polyhedra

9 NOVEMBRE 2014

Interstitial clusters in Cubic Phase of Laves C15 or MgCu2

M.C. Marinica, F. Willaime, J.-P. Crocombette, Phys. Rev. Lett.

(2012)

C15

BCC

-C15 coherent with

the BCC matrix

- C15 have 3D

structure in oposition

to the 2D structure of

dislocation loops


TECHNICALITIES

Empirical interatomic potential for Fe

- Embedded Atom Method type

- Parameters fitted to bulk and point defect

properties (DFT database)

Formation energies of self-

interstitial clusters (in all

bcc metals)

Cascade simulations

(Molecular Dynamics)

Energy landscape of

interstitial clusters

(Activation Relaxation Technique)

Representation

(Disconnectivity graph)

Density Functional Theory

- ab initio electronic structure calculations

- PWSCF (Quantum Espresso) code and

VASP recentely

- 250 to 432 atom supercells


| PAGE 15

Immobile

C15 Clusters

Very stable

110C15 C15

1 1I I In n

Growth

Large AF

moment

- 44 µB

C15

4I

1. Very stable

2. Immobile

3. Can growth

4. Large AF moment


STABILITY OF C15 INTERSTITIAL CLUSTERS IN FE

DFT calculations:

-PWSCF code,

- 250 - 686 atoms,

- tested against pseudopotential

(USPP and PAW), semicore

states, LDA/GGA, cell size

EAM potentials

Stability of C15 clusters against traditional loops

Ipara

IC15


9 NOVEMBRE 2014

Others BCC metals : I4 case

1. Not in other bcc metals para

C15 2. Ta has interesting property


LARGE INTERSTITIALS CLUSTERS

ENERGY LANDSCAPE: DEVELOPMENT

OF INTERATOMIC POTENTIALS FOR

MODELLING RADIATION DEFECTS FOR

IRON AND

TUNGSTEN USING AB INITIO DATA

9 NOVEMBRE 2014

| PAGE 18



DFT calculations, GGA-PBE, PAW

EAM potentials

M07: improved by including

in the fit a large data base

of DFT defect properties

(no C15 clusters)

Stability of C15 clusters against traditional loops

Ipara

IC15

*Malerba et al. JNM 406, 19 (2010)

with one typo corrected in:

MCM et al, PRL 108, 025501

(2012)


Data base:

Ab-initio / experiment

Fitting empirical potential

EAM formalism

Tests / Transferability

Validation of the potential

1. Bulk properties

• elastic constants, a0

• Cohesive energy BCC, FCC

2. Ab-initio database (Typical unit cell with 128 atoms)

mono-interstitial (5 configuration)

di-,tri-interstials

relaxed vacancy

40 Fe liquid configurations (around 100 atoms

for each configuration)

Our approach: EAM potential fitted on ab-initio data

F. Ercolessi and J. B. Adams, « Interatomic Potentials

from First-Principles Calculations: The Force-Matching

Method », Europhys. Lett., 26 (1994) 583

| PAGE 20

+


M. I. Mendelev, D. J. Srolovitz, G. J. Ackland, D. Y. Sun,

M. Asta, Phil. Mag., 83 (2003) 3977/

G. J. Ackland, M. I. Mendelev, D. J. Srolovitz, S. Han,

A. V. Barashev, J. Phys.: Condens. Matter, 16 (2004) 2629

Procedure proposed also in:

Experimental data/

ab-initio SIESTA

Fitting

Potential i+1

tests

POTENTIAL

Potential i

Relaxation

Fitting procedure is based on adjoint

method in order to estimates the

derivatives of the objective function

On-the-fly fitting:

a) Out off equilibrium configurations are

not relaxed

b) Equilibrium configurations are relaxed

with the previous version of the

potential. The ab initio positions are

used only in the first cycle. Then only

the energies are kept fixed.

Fitting procedure

| PAGE 21

DFT-GGA

M03/AM04

M07


1. Self-trapped configurations (I4)

2. Stabilized at high temperature

D.A Terentyev, T.P.C Klaver, P. Olsson,

M.-C. Marinica, F. Willaime,

C. Domain, L. Malerba,

Phys. Rev. Lett. 100, 145503 (2008)

| PAGE 22

+ 0.31 AM04

- 0.11 DFT

+ 0.02 M07

EAM potential fitted on ab-initio data


STABILITY AT LARGER SIZES IN FE

(M07 EAM POTENTIAL)

C15

<111> loops

1.5 nm

35 SIA cluster


ORIGIN OF THE LOW ENERGY OF C15 CLUSTERS

9 NOVEMBRE 2014

BCC

C15

« delocalized » defect :

2n BCC atoms replaced by 3n C15

atoms to make a n interstitial cluster

(Eshelby inclusion)

Volume (Å3/at.)

En

erg

y (

eV

)

FM bcc

FM C15 Low energy of

C15 structure

Low energy of the

interface (cubic structures)

Fe





n=1 100-10 000 10

voids loops

2 nm

SFT

b

3D 3D 2D

2D

3D

Prediction from

atomistic simulations


NUCLEATION OF C15 CLUSTERS IN CASCADES

Observed in cascades

- D.J. Bacon, F. Gao, Yu.N. Osetsky JNM 276 (2000) 1

- F. Gao et al. JNM 276 (2000) 213

13 SIA cluster

(F. Gao acknowledged for providing atomic positions)

Cascades using M07 potential:

- 20 keV ~ 5% of the SIAs are in C15 type clusters

- 80 keV ~ 10% of the SIAs are in C15 type clusters

(no temperature effect: 300 K , 500 K, 900 K)


9 NOVEMBRE 2014

| PAGE 27

W EAM Potentials

1. Bulk properties

• elastic constants, a0

• Cohesive energy BCC, FCC

2. Ab-initio database

mono-interstitial (5 configuration)

di-,tri-interstials

relaxed vacancy

40 W liquid configurations

M.-C. Marinica, L. Ventelon, M. R. Gilbert, L. Proville, S. L. Dudarev, J. Marian, G. Bencteux, and

F. Willaime, « Interatomic potentials for modelling radiation defects and dislocations in tungsten »,

J. Phys.: Cond. Matter, 25, (2013) 395502


9 NOVEMBRE 2014

| PAGE 28

W EAM Potential:surfaces and Gamma-surfaces

Unrelaxed surface energies:

• (110) the most stable

• Relative stabilities:

• (110) vs (100) – OK

• (100) vs (111) – Not OK.

(100) too low; (111) is not too high

• All others – mostly OK

111 110 111 211

GSF energies:

- Mostly OK for

EAM2 and EAM4


9 NOVEMBRE 2014

| PAGE 29

W EAM Potential: Bain path

• Good shape and agreement with the DFT

• BCC, BCT – minima ; FCC - saddle point

• It is not the case in Ackland or Dudarev

potential


[1]D. BRUNNER,

« COMPARISON OF

FLOW-STRESS

MEASUREMENTS ON

HIGH-PURITY

TUNGSTEN SINGLE

CRYSTALS WITH THE

KINK-PAIR THEORY »,

MATER. TRANS. JIM,

VOL. 41, P. 152-160, 2000. | PAGE 30

W EAM Potential: Dislocation

EAM2-4 the resulting Peierls barrier

exhibits a single-hump profile,

in agreement with the DFT.

The EAM4 predicts a barrier height that

agrees best with the DFT values

Only EAM3 has the good glide plane.


Excellent prediction for KP formation energy 1.63 eV

Recent value is 1.53 eV (DFT + FK line tension model)

9 NOVEMBRE 2014

| PAGE 31

EAM Potentials: Discussion & Summary

SIA VAC Surfaces Phonons Screw d

1,2 N>2 1,2 N>2 P Gp

Fe-Mendelev 2003 +/- +/- +/- +/- + +/- + - - +

Fe-Marinica 2007 + + + + + + + + - -

Fe-Ackland-Mendelev 2004 +/- +/- +/- +/- + +/- + + - -

Fe-Gordon Mendelev 2011 + + +/- +/- + +/- + + - +

Fe-Proville 2012 - - +/- +/- + +/- +/- +/- + +

Fe-Alexander 2014 +/- +/- +/- +/- + +/- + + +/- +

W-EAM4-Marinica 2013 + +/- +/- + +/- + + +/- + -

W-EAM3-Marinica 2013 +/- + +/- +/- +/- +/- + + +/- +

GSF 0p 0p

Probably we try to ask too much. A good approach is to:

- design potentials adapted for a well defined problem.

- Use the potentials as imaginary experiment s in order to understand

the physics


M.-C. Marinica, CEA Saclay | EFDA Kick-off Meeting, Paris, 01 April

Relative stability of SIA clusters

| PAGE 32

Large time-space scale simulations, cluster dynamics,

KMC, OKMC, require valuable inputs for the growth of

point-defect clusters

TEM: two families of dislocation loops are observed under electron or

neutron irradiation: <100> and 1/2<111> depending on conditions

DD05

M07

<100> with two habit planes:

{100} and {110}

1/2<111> {110}

Formation energies of

large dislocation

loops: potential-

dependent

For 1000 SIA you have a

spread over 120 eV in results

between various potentials: 20

% of the absolute values

Formation energy based on atomistic calculations

There is a possibility to have

potential – independent

values ?

Poster:

Ab initio based modelling of the

energetics of nanometric interstitial

clusters in W

Rebecca Alexander, SRMP, CEA

Saclay, France

DI-VACANCIES IN BCC METALS

9 NOVEMBRE 2014

| PAGE 33


METAL DEPENDENCE OF DI-VACANCY BINDING

ENERGIES IN BCC METALS

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Bin

din

g E

nerg

y (

eV

)

MendelevDFT

1 NN

2 NN

Fe

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Bin

din

g E

nerg

y (

eV

)

Cr Mo W

1 NN

2 NN

attractive

repulsive

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Bin

din

g E

nerg

y (

eV

)

V Nb Ta

1 NN

2 NN

| PAGE 34

L. Ventelon, F. Willaime, C.-C. Fu, M. Heran, et

I. Ginoux, JNM, 425, 16 (2012).

2 exp( / )v v b Bc A c F k TA: geometrical factor, Fb: binding free energy (Fb

>0 attraction)


9 NOVEMBRE 2014

| PAGE 35

Energy landscape of di-vacancy in tungsten

L. Ventelon, F. Willaime, C.-C. Fu, M. Heran, et

I. Ginoux, JNM, 425, 16 (2012).

- 1NN us slightly attractive or repulsive

depending on DFT: exchange –correlation

functional, PP approximation etc

- 2 NN is strongly repulsive

- 3 to 5 NN slightly repulsive or attractive

M.-C. Marinica et al. J. Phys.: Cond. Matter, 25, 395502, oct. 2013.

a M Muzyk et al, PRB, (2011) - VASP

b1 L. Ventelon et al, JNM (2012) - PWSCF

b2 Ventelon et al, JNM (2012) - SIESTA

c C. Becquart et al, JNM, (2010) - VASP


DI-VACANCY IN BCC METALS: BAND FILLING EFFECT

DFT predictions:

• strong band filling effect

• W: electronic entropy contribution should

be important

| PAGE 36

( )el F

S T E T


9 NOVEMBRE 2014

| PAGE 37

( , , ) ( , , ) ( , , )el vib

F V T N F V T N F V T N

( , , ) , , , ,el el el

F V T N E V T N TS V T N

( , , ) ( , , ) , ,vib vib vib

F V T N U V T N TS V T N

The free energy is the sum of the electronic and vibrational free energy

Free Energy: electronic + vibrational


9 NOVEMBRE 2014

| PAGE 38

2.2 kB 5.4 kB 7.0 kB Vacancy:

- negative interaction entropy

- 1NN gives the upper limit (-1.0 kB)

- 2NN gives the lower limit (-2.6 kB)

SIA

- 4.5 kB for mono-SIA in W

- 8.9 kB for di-SIA in W

Free energy: DFT vibrational contribution


9 NOVEMBRE 2014

| PAGE 39

( , , ) ,0, ( , , ) ,0, , , ( , , )el DFT el DFT el el

F V T N E V N F V T N E V N E V T N TS V T N

( )el F

S T E T

At 3400 K we have:

- Almost 1.4 kB contribution for mono-vacancy

- 1NN 0.0 kB interaction entropy

- 2NN -1.0 kB interaction entropy

Free energy: electronic contribution


9 NOVEMBRE 2014

Free energy: Di-vacancy

| PAGE 40

- At 800 K 1NN di-vacancy becomes stable

- At 1800 K even 2NN di-vacancy becomes stable

- At 2500 K 1NN becomes more stable than 2NN

Formation free energy Binding free energy


| PAGE 41

SUMMARY

Unexpected results obtained from DFT/EAM calculations in

transition metals:

1. Di-vacancies in bcc metals: temperature stabilize the di-vacancy

2. Self-interstitials in bcc metals : 3D crystalline structure predicted for

self-interstitial clusters in bcc metals

- Very low energy structures in Fe, and to a lesser extend in Ta

- are formed in cascades

- can grow by capturing <110> dumbbells

- have large antiferromagnetic moments in Fe

- are immobile


Fe EAM potentials: screw dislocation

| PAGE 42


1,2 N>2 1,2 N>2 P Gp

Fe-Mendelev 2003 +/- +/- +/- +/- + +/- + - - +

Fe-Marinica 2007 + + + + + + + + - -


Refitting by changing the weights in

objective function in order to have more

equilibrated potential

L. Proville, D. Rodney, and M.-C. Marinica, Nature Materials,

11 (2012) 845


Fe EAM potentials: screw dislocation

| PAGE 43


1,2 N>2 1,2 N>2 P Gp

Fe-Mendelev 2003 +/- +/- +/- +/- + +/- + - - +

Fe-Marinica 2007 + + + + + + + + - -


Fe-Proville 2012 - - + + + +/- +/- +/- + +


H. Xu , R. E. Stoller , Y. N. Osetsky “Cascade defect evolution processes:

Comparison of atomistic methods

“ JNM, 443, (2013) 66

Ackland 04

A97

A04

M07

D09

| PAGE 44

Discussion: Escaping time


A04 M07

H. Xu , R. E. Stoller , Y. N. Osetsky “Cascade defect evolution processes:

Comparison of atomistic methods

“ JNM, 443, (2013) 66

23 years at 700 K

A04

Ackland 04

| PAGE 45

Discussion: Escaping time


9 NOVEMBRE 2014

| PAGE 46

Goal: Finite temperature corrections of an energy landscape

a.

Reaction coordinate

Energ

y

T= 0 K

T > 0 K

F=E-TS

a. Changes in the relative stability

of the energy landscape

b. b. Rearranging of the energy

landscape

M. Athènes et al J. Comp. Phys., 2010


# SIAs in cluster

n=1 2 100-10 000 3 4

n=2-100

Competition between

<110>, <111> and <100> ?

Exploring the

energy

landscape of

small SIA

clusters in Fe

| PAGE 47

5

# atoms

Fid

elit

y

Empirical

potential

Ab initio

DFT Entropy


Xi

Xi+1

Ci

A method to explore a potential energy surface: search

for saddle points and local minima

The Activation Relaxation Technique (ART)

XI is known the others minima {Xi} and the saddle points {Ci} must be

revealed by the method:

0 K method, local information; partial Hessian

Fast, adapted for defects

Tested for Fe, Cu, Zr, W, Si, SiC

M.C. Marinica, F. Willaime, N. Mousseau, Phys. Rev. B, (2011)

E. Cances, F. Legoll, M.C. Marinica, F. Willaime, J. Chem. Phys (2009)

A. Barkema, N. Mousseau PRL (1998) ; Phys. Rev. B (2000)


1106

I3 I4

1481


I2

I4

I3

Application to In: ART+HA


| PAGE 51

C15 Clusters

1. Very stable

2. Immobile

3. Can growth

4. Large AF moment

CEA | 26 NOV 2012

| PAGE 52

C15 Clusters Large AF

moment

- 44 µB

C15

4I

1. Very stable

2. Immobile

3. Can growth

4. Large AF moment

CEA | 26 NOV 2012

- 33 µB

Magnetic Moment

- 37 µB - 44 µB

DFT: 2.26 µB (bulk reference)

C15

4IC15

2IC15

3I


| PAGE 54

C15 Clusters

Very stable

Large AF

moment

- 44 µB

C15

4I

1. Very stable

2. Immobile

3. Can growth

4. Large AF moment


| PAGE 55

Immobile

C15 Clusters

Very stable

Large AF

moment

- 44 µB

C15

4I

1. Very stable

2. Immobile

3. Can growth

4. Large AF moment


1. Two basins: C15 and parallel dumbells ; confirms that C15 is the lowest energy structure

2. shows that it is immobile (confirmed by MD simulation over ms)

3. . Older clusters identify a particular branch of the C15 basin

En

erg

y (

eV

) - M07 EAM potential for Fe

- Activation Relaxation Technique (ART)

- disconnectivity graph representation O. M. Becker and M. Karplus, J. Chem. Phys. 106, 1495 (1997)

D. J. Wales, M. A. Miller, and T. Walsh, Nature 394, 758 (1998)


- ARTn

110C15 C15

1 1I I In n

C15

4IC15

2IC15

3I

Growth of C15 Clusters


Bulk dumbbell

migration

110C15 C15

2 1 3I I I

Doesn’t exceed the barrier for <110> dumbbell migration


C15 110

3I I

Bulk dumbbell

migration

C15

4I

110C15 C15

3 1 4I I I

Doesn’t exceed the barrier for <110> dumbbell migration


Example: di-interstitial

• Result depends on the potential ; M07 more reliable (according to DFT)

• Lower energy barriers are not excluded

• In the absence of low energy barrier (from right to left), nucleation from isolated

SIAs (electron irradiation) is unlikely

A97

A04

M07

D09

| PAGE 60

NUCLEATION OF C15 CLUSTERS IN CASCADES


« tetra-interstitial »

18 interstitials+14 vacancies

Proposed in Mo

R.C. Pasianot, V.P. Ramunni Comp. Mat. Sc. 48, 783 (2010)

Discussion Discussion


9 NOVEMBRE 2014

| PAGE 62

SIA clusters in W

<100> and ½<111>


9 NOVEMBRE 2014

| PAGE 63

SIA clusters in W


9 NOVEMBRE 2014

| PAGE 64

SIA clusters in W


DISCUSSION: OTHER OBSERVED CLUSTERS

D.J. Bacon, F. Gao, Yu.N. Osetsky JNM 276 (2000) 1

« This symmetric, three-dimensional cluster was created in about half the

cascades simulated. Higher-order SIA clusters in -iron exhibit more complicated

variants of defects such as these [F. Gao et al. JNM 276 (2000) 213] ».


DISCUSSION:PROPERTIES OF « SESSILE »

CLUSTERS F. Gao et al. JNM 276 (2000) 213

- In Fe, sessile clusters include 3D symmetrical clusters, that can grow by retaining their 3D

symmetrical structure

- According to the Finnis-Sinclair potential, these clusters are metastable wrt dislocation loops

Present work:

- these structures were rediscovered while searching for low energy configurations

- they have a well identified crystalline structure (C15 Laves phase)

- they are much more stable than loops according to DFT calculations (from 4 to at least 8 SIAs)

8 and 19 SIA clusters


Di-interstitial

1. Low formation energy (ab initio): + 0.71 eV (compared to 110 cluster, 0.12

eV binding energy)

Z16 Frank-Kasper polyhedra

4. Large formation entropy (some empirical potential): + 24 kB (4 kB in the

case of 110)

3. Small formation volume (ab initio)

2. Very large antiferromagnetic moment: -33 µB compared to the bulk !

(-8 µB in the case of <110> dumbbell)


2MgCuCubic Phase of Laves

C15 or MgCu2

Identification of the crystal structure: C15 Laves phase


9 NOVEMBRE 2014

| PAGE 69

Summary

Based on EAM formalism we have fitted potentials for Fe and W.

Using EAM-DFT interaction we were able to:

Fe

- predict a new class of SIA clusters in iron (using adapted potentials for

SIAs)

W

- demonstrate the existence of <100> loops in W

- show the effect of the temperature on the relative stability of <100> and

<111> loops


EAM potential fitted on experimental and ab-initio data

They add to standard bulk properties:

- FCC, BCC, lattice parameters

- elastic constants,

- Unrelaxed vacancy

- Some mono self interstitials configurations

- Surface energies

.

Force matching method on “liquid” iron configuration

.

dSIA=2.1 A

a1NN=2.44 A

a2NN=2.87 A

d > 2.0 A

M. I. Mendelev, D. J. Srolovitz, G. J. Ackland, D. Y. Sun,

M. Asta, Phil. Mag., 83 (2003) 3977/

G. J. Ackland, M. I. Mendelev, D. J. Srolovitz, S. Han,

A. V. Barashev, J. Phys.: Condens. Matter, 16 (2004) 2629

F. Ercolessi and J. B. Adams Europhys. Lett., 26 (1994)

583

| PAGE 70

+

DFT-GGA

M03/AM04


The empirical potentials which are fitted only on the

bulk properties are not very reliable when

used for point defects such as interstitials and

vacancies.

EAM potentials fitted on experimental data

An example: One of the best potential for iron

developed by G. Ackland in 97 and which fit very

well the perfect bulk properties as:

- FCC, BCC, lattice parameters

- elastic constants,

- phonons spectrum

. G. J. Ackland et al. Phil. Mag. A, 75, (1997) 713

Fails for description of mono interstitial in iron:

D. Nguyen-Manh, A. P. Horsfield, et S. L. Dudarev. PRB 73,

020101 (2006).

C. Domain, C. S. Becquart, Phys. Rev. B 65, 024103 (2001)

C.-C. Fu, F. Willaime, and P. Ordejon, Phys. Rev. Lett. 92,

175503 (2004).

<110> dumbbell Huang scattering

Migration:

- Em=0.3 eV

- Em(I2)=0.4 eV

(resistivity recovery) WHY?

| PAGE 71

• Johnson (1965)

• Johnson and Oh (1989)

• Harrison et al. (1989)

• Haftel et al. (1990)

• Calder and Bacon (1993)

• Simonelli et al. (1993)

• Ackland et al. (1997)

• Ludwig et al. (1998)

+

fitted only on the

bulk properties


With this new Fe potentials we are able to

be in good agreement over many ab-intio

data which are not included in the fit:

Rotation/migration of 1 SIA

Exp DFT-GGA Mendel

ev

M07

2.35±0.20

eV

2.1-2.2 eV 1.84 eV 2.12

eV

migration of mono vacancy *Malerba et al. JNM 406, 19 (2010) with one typo

corrected in:

Mihai-Cosmin Marinica et al, PRL 108, 025501 (2012)

| PAGE 72

EAM potential fitted on ab-initio data

DFT-GGA

M03/AM04

M07



DFT calculations: PWSCF code, 250 atoms, tested against

pseudopotential (USPP and PAW), semicore states, LDA/GGA, cell size

EAM potentials

M07: improved by including

in the fit a large data base

of DFT defect properties

(no C15 clusters)

Stability of C15 clusters against loops

Ipara

IC15


Relative stability of large clusters

Calculations based

on the anisotropic

elasticity

approximation there

is a change in

relative stability at

500 K.

S. L. Dudarev, R. Bullough, et P. M. Derlet, « Effect of the alpha-

gamma Phase Transition on the Stability of Dislocation Loops in bcc

Iron », Phys. Rev. Lett., vol. 100, 135503, (2008).

[H. Xu, R. E. Stoller, Y. N. Osetsky, et D. Terentyev, « Solving the Puzzle of

⟨100⟩ Interstitial Loop Formation in bcc Iron », Physical Review Letters, vol.

110, (2013).

J. Marian, B. D. Wirth, et J. M. Perlado, « Mechanism of Formation and

Growth of $?100?$ Interstitial Loops in Ferritic Materials », Phys. Rev. Lett.,

88, 255507, 2002.


Ackland 97

M07

Dudarev 2005 <100> with two habit

planes: {100} and {110}

1/2<111> {110}

AM 2004

Relative stability of large clusters

For 1000 SIA you have

a spread over 120 eV in

results between various

potentials: 20 % of the

absolute values

Formation energies of large

dislocation loops: potential-

dependent


Documents

ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS · ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS CEA, DEN, Service de Recherches de Métallurgie Physique Saclay, France M.-C. Marinica,