Understanding Irradiation Growth through Atomistic ... · 17 May 2016 ASTM Conference, Hilton Head Island, SC –Understanding Irradiation Growth through Atomistic Simulations, 15

ASTM Conference, May 17 2016, Hilton Head Island, SC

Understanding Irradiation Growth through Atomistic

Simulations:

Defect Diffusion and Clustering in Alpha-Zirconium and

the Influence of Alloying Elements

M. Christensen, W. Wolf, C. Freeman, E. Wimmer,

Materials Design Inc., Santa Fe, NM, USA

R. B. Adamson, Zircology Plus, Freemont, CA, USA

L. Hallstadius, Westinghouse Electric Sweden, Västerås, Sweden

P. Cantonwine, Global Nuclear Fuels, Wilmington, NC, USA

E. V. Mader, Electric Power Research Institute (EPRI), Palo Alto, CA, USA

Overview

EPRI Channel Distortion Program

Simulation methods, Zr-Fe forcefield development

Point defect formation: vacancies, interstitials, H

Point defect diffusion: vacancy, SIA, H, O, alloying elements

Cluster formation in pure Zr

Defect cluster formation in Zr involving Fe atoms

Effect of Fe on Zr mobility and irradiation growth

Investigation on secondary phase particles (SPPs)

Summary on effects of Fe

17 May 2016 2ASTM Conference, Hilton Head Island, SC – Understanding Irradiation Growth through Atomistic Simulations,

Materials Design, Inc.

Overview on Computation Methods



MedeA® computational environment

Structural models with periodic boundary conditions (~100 atoms for

ab-initio, ~10000 atoms for forcefields)

Embedded atom potentials applied for large time- and length-scale

molecular dynamics simulations (LAMMPS): Defect cluster

formation, structure and energy of dislocation loops, diffusivities

MedeA’s Forcefield Optimizer for fitting forcefields to ab-initio data

Ab-initio calculations (VASP) for geometries, total energy and

formation energy for stable structures and transition states

Ab-initio calculations (VASP) for elastic moduli

Ab-initio phonon calculations for temperature effects within a

(quasi)harmonic approximation

Eyring’s transition state theory for diffusivities

Zr-Fe Forcefield: Development and

Application



Previously applied forcefields and references publishing the details:

• Zr-H system: ASTM STP 1543, 2015, pp. 55-92

• Zr - Fe, Cr, Ni, Nb, Sn: J. Nucl. Mater., Vol. 445, 2014, pp. 241-250.

Objective of current forcefield development for Zr-alloying element systems:

improve the accuracy of the Zr-Fe interactions in simulations with higher Fe

concentration, expected to be important for clustering

Ab-initio trainings set for interactions:

• Zr-Zr: MD-trajectories of interstitials and vacancies in Zr, hcp, fcc, and bcc Zr

for a set of different volumes

• Fe-Fe: bcc Fe at different volumes

• Zr-Fe: MD-trajectories of Fe interstitials in Zr, and Zr2Fe and Zr3Fe for a range

of different volumes

Validation: bulk densities (within 1%), elastic moduli (within a few percent)

Simulations: supercell of Zr with 11520 atoms and Fe (0.05%, 0.15%, or 0.5%).

Effect of irradiation is simulated by simultaneously inserting both vacancies and

Zr interstitials (0.05%, 0.1%, or 0.5%) in random positions followed by molecular

dynamics. Repeat this procedure 5 times and finally optimize the geometry.

Point Defects

Vacancy formation: +193 kJ/mol; 1% vacancies causes shrinkage by

0.25% in the a-direction and 0.43% in the c-direction

Self-interstitial formation: +286 at basal octahedral, +288 at octahedral, +304 at split and +321 kJ/mol at crowdion sites

H slightly prefers tetrahedral sites by a few kJ/mol, increasing with temperature, at operating temperatures about 94% of H atoms occupy the tetrahedral sites

H absorption isotherms and solubility were calculated from DFT, H solubility increasing under tensile strain (preferred hydride precipitation at crack tips)

Increased lattice dimensions and bulk moduli with H contents quantified

H is attracted by vacancies (up to 9 H atoms) and SIAs, increasing solubility, increased H solubility in irradiated Zr, recombination may cause supersaturation and provide nucleation sites for hydride formation

Alloying elements (Cr, Ni, Nb, Sn) prefer substitution (O interstitials) and (except Nb) tend to segregate to surfaces, grain boundaries, vacancies



Point Defect Diffusion

Self-interstitial diffusion: fast and anisotropic (a>c)

Hydrogen diffusion: medium, isotropic, DH = 1.13x10-7 e-42/(RT) (m2/s)

Vacancy diffusion: slow, anisotropic, Dbasal = 8.62x10-6 e-69/(RT) (m2/s)

Daxial = 9.87x10-6 e-73/(RT) (m2/s)

Oxygen diffusion: very slow, isotropic, Dplanar = 6.13x10-5 e-175.7/(RT) m2/s

Daxial = 4.64x10-5 e-173.7/(RT) m2/s

Substitutional Cr, Fe, and Ni exchange position with interstitial Zr

Initial rapid diffusion of Fe, Cr, and Ni mainly in the c-direction

Then, Fe, Cr, and Ni start to cluster, forming a precursor of an

intermetallic phase, which halts the diffusion

The diffusion of self interstitial atoms is impeded by Nb and at low

temperature, to a lesser extent, by Sn. At high temperature Sn has little

effect on SIA diffusion.



Defect Clusters Formation in pure Zr

Structures of SIA and vacancy clusters obtained by diffusion and aggregation of point defects using molecular dynamics (550 K).

Net expansion of the lattice in the a-directions driven by SIA clusters

Smaller contraction in the c-direction involving vacancy clusters



Christensen, M., Wolf, W., Freeman, C., Wimmer, E., Adamson, R. B., Hallstadius,

L., Cantonwine, P. E., and Mader, E. V., J. Nucl. Mater., Vol. 460, 2015, pp. 82-96.

Defect and Cluster Formation in Zr



Isolated Fe Atom in Zr



Site preference (from DFT):

• High-spin (2.8 mB) symmetric

substitutional site (not shown)

• Octahedral interstitial site (+10

kJ/mol)

• 3-fold coordinated interstitial in-

plane position

• Off-site low-spin substitutional

site (+61 kJ/mol)

Interstitial and some off-site

substitutional sites

(occupying vacancies) are

observed in FF dynamics

Interstitial Off-site substitutional

Fe Crowdion in Zr



Created by 2 Fe atoms

approaching a vacancy site

The Fe atoms and the

intermediate Zr atom are

located in the same Zr(0001)

layer

Formation energy (DFT):

-285 kJ/mol

Formation energy for Fe

filling a vacancy: -148 kJ/mol

Fe-Zr-Fe sequence

facilitated by vacancies

2 Fe Atoms and a Vacancy in Zr



Alternatively, the 2 Fe atoms are located in off-site interstitial

positions in two adjacent Zr(0001) planes with the

intermediate Zr atoms between the layers

Formation energy (DFT): -266 kJ/mol• 2 Zr48Fe (Fe in octa site) + Zr47 (vac.) → Zr47Fe2 (2 Fe in vac.) + Zr48 (Zr bulk)

3 Fe Cluster in Zr



2 Fe atom on opposite sides of a single Zr(0001) plane and

a 3rd Fe atom present, no vacancy involved

The propensity of Fe atoms to form configurations with 2 Fe

atoms on each side of an intermediate Zr atom indicates a

starting point for nucleation of Fe-Zr intermetallic phases

Fe

Fe

Fe

Zr

Fe Clustering Towards Zr2Fe phase

formation in Zr



Pattern (a): 4 Fe atoms clustering with 2 vacancies

Is similar to pattern (b): (110) layer of the Zr2Fe phase

De Carlan et al. observe nucleation of Fe-rich precipitates in

basal planes of irradiated Zircaloy, starting to form a Zr2Fe

layer

Fe

Fe Fe

FeFe

ZrZr

Zr

Fe Self Interstitial Pair in Zr



4-fold coordination of the Fe

atom

Spatial extension of the Fe-SIA

defect is quite large

Fe Atoms at Rim of Planar SIA Cluster

in Zr



The circular shape of planar SIA

clusters decorated by Fe atoms

at the rim could explain the ring-

shaped features of Fe found by

atom probe tomography (APT) in

irradiated Zircaloy-2 by Sundell et

al.

Smaller Fe atoms favor higher

density of atoms (dislocation

core)

Sundell, G., Thuvander M., Tejland, P., Dahlbäck, M., Hallstadius, L., and Andrén,

H.-O., J. Nucl. Mater. Vol 454, 2014, pp. 178-185.

Fe Atoms in Interior of SIA and

Vacancy Clusters in Zr



Fe atoms in the interior of a vacancy cluster (a) or a SIA

cluster (b)

Only for vacancy and SIA clusters grown to extend over a

few Zr(0001) layers are Fe atoms found inside the

clusters rather than at the rim

FeFe

Fe Fe

Fe

Fe Fe

Fe

Fe Fe

Effects of Fe on Diffusion and Zr mobility



Fe promotes defect cluster formation

Fe may increase the mobility of Zr atoms (consistent with

observed increase of vacancy diffusivity by Fe)

APT measurements (Sundell et al.) have shown that Fe

exists as small clusters (0.5-10nm) of low Fe concentration

(5%) aligned along basal planes, which seem related to

small Fe-Zr defect formation in simulations

APT measurements and DFT simulations confirm that Fe

(and Cr) tend to segregate to grain boundaries

Indications for Fe Effects on

Irradiation Growth



Fe atoms are attracted by vacancies and fill the generated

vacancy clusters forming structures with similar Fe-Zr

bonding than in intermetallic phases

Fe containing vacancy clusters might act as nucleation

sites for Fe-Zr intermetallic phase precipitation

Hypothesis: Less vacancy clusters are available for

vacancy c-loop formation associated with breakaway

growth -> decreased growth rate due to alloying with Fe

On the other hand: Fe or Zr2Fe precipitates are speculated

to act as nucleation sites for c-loop formation -> this would

increase the growth rate

Fe was shown to decrease growth and increase strengths

in Fe-Nb containing alloys, when released from SPPs

Intermetallic Phases of SPPs



Fe, Cr and Ni have low solubility in a-Zr and tend to

precipitate as Secondary Phase Particles (SPPs)

Phases investigated by DFT: Zr3Fe, Zr2Fe (Fd-3m and

I4/mcm), ZrCr2-xFex (0 ≤ x ≤ 2) Laves phase (C15, three

random samples at each stoichiometry)

It is favorable for Cr to cluster together in ZrCr2-xFex with

low Cr concentration (x ≥ 1.5), no clustering appears at

high Cr contents

Energy and Volume of SPP Phases



Equilibrium Zr-Fe phase

diagram: Zr2Fe metastable

relative to Zr3Fe, but

reported as precipitate in Zr

Zr2Fe is tetragonal rather

than cubic

Volume increase upon Fe

dissolution in Zr (per Fe):

3.65 Å3 for Zr3Fe

4.13 Å3 for Zr2Fe

3.47 Å3 for ZrFe2

Vacancy formation cause

contraction-> Zr2Fe forms

preferably at vacanciesZr Zr2Fe ZrFe1.5Cr0.5 ZrFe0.5Cr1.5

Zr3Fe ZrFe2 ZrCrFe ZrCr2

Zr Zr2Fe ZrFe1.5Cr0.5 ZrFe0.5Cr1.5


EOF = EDFT(ZrnFekCrl) –

n × EDFT(Zr) – k × EDFT(Fe) –

l × EDFT(Cr)

I4/mcm

Fd-3m

Cmcm

Fd-3m

Fd-3m

CmcmI4/mcmFd-3m

Fd-3m

Fd-3m

Elastic Moduli of SPP Phases



Zr2Fe and Zr3Fe

phases have similar

or slightly higher

elastic moduli than

a-Zr

Zr(Cr,Fe)2 Laves

phases have

significantly higher

elastic moduliZr Zr2Fe ZrFe1.5Cr0.5 ZrFe0.5Cr1.5


Bulk Moduli

Young’s Moduli

Shear Moduli

Fd-3m

I4/mcm

Fd-3mI4/mcm

Summary on Effects of Fe

Alloying element atoms including Fe are trapped by vacancies and SIAs

Defect clusters involving several interstitial Fe atoms at vacancies or SIAs

are exothermically formed, resulting in Fe-Zr-Fe sequences and patterns

similar to the local atomic configuration in Zr2Fe intermetallic phase

High mobility of Fe interstitials being attracted by vacancies and SIAs and

the propensity of Fe to form such defect clusters is seen as a starting point

for nucleation of Zr-Fe intermetallic phases occurring in SPPs

Fe increases Zr mobility, possibly enhancing vacancy diffusivity, promotes

small cluster formation and may thereby bind vacancies, which are not

anymore available for vacancy c-loop formation -> reduced growth

SPP phases: formation energy, dimensional changes, elastic moduli

Dissolving Zr-Fe SPPs is accompanied by an increase in volume, more

pronounced for Zr2Fe than for Zr3Fe, confirming MD simulation results

Interstitial Fe released from SPPs exerts anisotropic pressure in [0001],

can be relieved by formation of vacancy c-loops17 May 2016

22ASTM Conference, Hilton Head Island, SC – Understanding Irradiation Growth through Atomistic Simulations,


Documents

Understanding Irradiation Growth through Atomistic ... · 17 May 2016 ASTM Conference, Hilton Head Island, SC –Understanding Irradiation Growth through Atomistic Simulations, 15