An Insight Into The Mechanism Of SFT formation Near Edge Dislocations In Al Under Irradiation

8/12/2019 An Insight Into The Mechanism Of SFT formation Near Edge Dislocations In Al Under Irradiation

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An insight into the mechanism of SFT formation near 1 / 2 110 edge dislocations in aluminum exposed to irradiation

R.E.Voskoboinikov 1

1 The Institute of Materials Engineering, Australian Nuclear Science and TechnologyOrganisation, New Illawarra Road, Lucas Heights 2234 NSW, Australia

Keywords: fast particle irradiation, aluminum, displacement cascades, vacancies,self-interstitial atoms, dislocations, strain, intrinsic stacking fault, stacking fault

tetrahedron, molecular dynamics simulations

Abstract

Recently molecular dynamics (MD) simulations have been carried out to study primarydamage formation in the vicinity of 1 / 2 110 screw and edge dislocations in aluminum[1, 2]. A few different interaction mechanisms of collision cascades with dislocations weredetected. In particular, dislocation climb accompanied by the formation of stacking faulttetrahedra (SFT) near the dislocation line was observed. In order to clarify the pecu-liarities of SFT formation, normal strain in the dislocation core was reconstructed ina defect-free aluminum crystal and MD simulations of displacement cascades were con-ducted there under different temperatures. It has been found that tension/compressionand the elevated temperature are the necessary but not sufficient conditions to formSFTs in aluminum. A vacancy supersaturation is required as well. In the vicinity of an

edge dislocation in aluminum it is created due to absorption of displaced atoms by thedislocation core.

Introduction

Being an endemic part of the microstructure of crystalline solids, dislocations can con-tribute to the kinetics of structural and phase transformations in materials subjected tofast particle irradiation. Most suggested models employ phenomenological approaches todescribe the interaction of dislocations with residual radiation defects, see for example,[3]-[19]. Preliminary results of our atomic-scale MD simulations of the athermal couplingof primary defects with isolated 1 / 2 110 edge and screw dislocations in aluminum at

the temporal scale of the order of the lifetime of a collision cascade were published in[1, 2]. A few mechanisms of the interaction of dislocations with displaced atoms andvacancies from the collision cascade region were revealed. In particular, it has been es-tablished that at room and especially at elevated temperature 1 / 2 110 edge dislocationclimb due to absorption of displaced atoms is accompanied by the formation of stackingfault tetrahedra (SFT) in the vicinity of the dislocation line, see Figure 1c and d. Nopoint defect clustering was observed in defect-free aluminum, see Figure 1a, and no SFTformation was detected in displacement cascades in aluminum in the vicinity of 1 / 2 110screw dislocations, see an example in Figure 1b.

In this study governing factors that could determine the formation of SFTs in dis-placement cascades in the vicinity of edge dislocations in aluminum were mimicked in

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a b

c d

Figure 1: 5 keV displacement cascades in aluminum at T=600 K. (a) No clustering isobserved in collision cascades in the pristine material. Only isolated vacancies and self-interstitial atoms are formed. (b) The interaction of 1 / 2 110 screw dislocation withcollision cascade led to the formation of a helical segment. (c) SFT above the glide planewas formed as a results of the interaction of 1 / 2 110 edge dislocation with a collisioncascade. (d) SFT is created below the glide plane due to coupling of 1/ 2 110 edgedislocation with a collision cascade. Red and blue spheres in gure (a) denote vacanciesand displaced atoms, respectively. Red, blue and white spheres in gures (b)-(d) denoteatoms with coordination numbers 10-11, 9, and less than 9, respectively.

the pristine material and MD simulations of collision cascades were conducted there.Since SFT formation in aluminum is not typical because of high stacking fault energy,the energy of the intrinsic stacking fault as a function of strain was examined as well.

The energy of the intrinsic stacking fault in strained aluminum

It has already been mentioned that the formation of SFTs in collision cascades in alu-minum has been observed near 1 / 2 110 edge dislocations only. No SFTs were formed

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in collision cascades in the vicinity of 1/ 2 110 screw dislocations under the same simu-lation conditions. According to [20], an isolated edge dislocation creates plane strain ina solid whereas a screw one generates anti-plane strain. The key difference between thetwo strain states is non-zero normal components of the strain tensor in the former case.Hence, normal strain could be the factor that reduces the actual stacking fault energyand therefore facilitates SFT formation near edge dislocations in aluminum.

In order to check this hypothesis the energy of the intrinsic stacking fault (ISF) in{111} plane in aluminum as a function of the uniform strain was evaluated.

Embedded atom method (EAM) [21] based interatomic potential [22] was employedfor calculating the interatomic forces between atoms in the simulated Al crystal. Follow-ing [23],we determined ISF in {111} by cutting the crystal along this plane and shiftingthe upper part of the crystal with respect to the lower part of the crystal by vector1 / 6 [11 2]. Periodic boundary conditions along [1 10] and [112] were applied. Crystal sizealong [111] crystallographic direction was chosen to be large enough to neglect boundaryeffects. The crystal was relaxed along [111], i.e. only atomic displacements normal to thefault plane were allowed while in-plane displacements were prohibited. The relaxationwas conducted using the conjugate gradients method, see, for example [24].

ISF energy, E IS F , is then given by

E IS F = E (1 / 6 [11 2]) E (0 ) , (1)

where the total energy E (1 / 6 [11 2]) of the crystal with ISF is evaluated using [21]

E = 1/ 2 i,j

ij (r ij ) + i

F i (i ) , i = j = i

j (r ij ) , (2)

and E (0) corresponds to the total energy of the regular crystal. In Eq.(2) ij (r ij ) is theenergy of pair interaction of atoms i and j , rij is the distance between atoms, F i (i ) isthe embedding energy of atom i and i is the electron density induced by all surroundingatoms j at the location of atom i [21].

ISF energy as a function of the uniform strain is shown in Figure 2. At zero strain,it is equal to 0.116 J/m 2 that well matches 0.115 J/m 2 predicted by the interatomicpotential used in the calculations [22]. Applying tensile strain gradually reduces E IS F down to zero at 4.2%.

The dependence of ISF energy on compression is not uniform. The increase of ISFenergy up to 0.190 J/m 2 at 4% compression is followed by decrease down to zero at

8.6% strain. Such a high strain can hardly be achieved at a macroscopic linear scaleunder normal fabrication or operation conditions but it occurs locally in the vicinityof edge dislocation core above the glide plane at distances of the order of a few latticeparameters from the dislocation line. It coincides with one of the two locations whereSFTs were formed after relaxation of 5 keV displacement cascades, see a typical examplein Figure 1c. The other position resides under the glide plane of the dislocation atdistances 10 lattice parameters from the dislocation line, see Figure 1d. The tensilestrain produced by the dislocation in this area is 1-3%, i.e. it matches the range thatcorresponds to low ISF energy in Figure 2.

The qualitative comparison of strain dependence of ISF energy with the results of theinteraction of dislocations with collision cascades indicates that both compression and

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Figure 2: ISF energy in aluminum as a function of the uniform strain.

tension produced by the edge dislocation could cause SFT formation in its vicinity. Inthe following section it is checked by conducting MD simulations of collision cascades ina strained aluminum crystal.

MD simulations of collision cascades

The same interatomic potential [22] was employed for MD simulations of displacementcascades in strained Al crystals. At short distances the pair part of the potential was

tted with ZBL universal repulsion potential [25, 26] following the procedure described in[27]. The corresponding threshold displacement energy, 14 eV E d 15 eV , predictedby the modied potential matches the experimentally measured value of 16 3 eV [28, 29].

Three ambient crystal temperatures were considered, namely 100, 300, and 600 K.The model crystals were equilibrated for approx. 10 ps at the selected simulation tem-perature prior to initiation of the PKA. The MD simulation box had cubic shape with{100} faces. It was maintained at constant volume, with the lattice parameter set to geta uniform strain ranging from 8% compression to 3% tension. Periodic boundary con-ditions along all three 100 crystallographic directions were employed. The number of atoms in the box was approximately equal to 5 105 . No energy/temperature dampingwas used. The energy introduced by PKA was not extracted. The temperature increase

after relaxation of a collision cascade did not exceed 40 K in any of the simulations.At least 8 cascades for each set of investigated conditions (strain, temperature, etc. )were simulated in order to ensure reliability of the results. To avoid recoil-atom chan-nelling events, PKAs were introduced along one of 123 crystallographic directions.

Three different methods were applied to identify point defects and their clustersformed in collision cascades. One is based on the analysis of Wigner-Seitz cells and isused to identify vacant sites (=cells with no atoms) and self-interstitial atoms (=cellswith more than one atom). The second is equivalent spheres (ES) analysis sometimescalled displaced-atom analysis based on the position of atoms with respect to lattice sites.The third method, cluster conguration analysis [30], uses the output of ES analysis toidentify point defect clusters and gets the overall number, N F P , of surviving Frenkel

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4 and 5. No/few small SFTs were formed in strained aluminum at low and room temper-ature, see examples in Figure 4a and b. The outcome of MD simulations is drasticallydifferent at T=600 K . Large SFTs were formed in strained Al in all simulated cascades,see typical examples in Figures 4c and d, whereas MD simulations of collision cascadesin aluminum with excessive vacancies but without strain do not reveal tendency to formSFTs, see Figures 5a and b.

a b

c d

Figure 4: Typical residual radiation defects created in collision cascades in aluminum

with excessive vacancies under 7% uniform compression at T=100 K (a), T=300 K (b)and T=600 K (c), and 1% uniform tension at T=600 K (d). Colour coding used issimilar to that employed in Figure 1a.

Conclusion

An insight into the governing factors of the formation of SFTs in collision cascades inthe vicinity of 1/ 2 110 edge dislocations in aluminum has been gained by conductingatomic-scale simulations. Various strain and temperature conditions as well as the redis-

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e f

Figure 5: Typical residual radiation defects created in collision cascades in strain-freealuminum with excessive vacancies at T=100 K (a) and T=600 K (b). Colour codingused is similar to that employed in Figure 1a.

tribution of radiation damage from the collision cascades in the dislocation core regionwere mimicked in a defect-free aluminum crystal. It has been found that (i) a loweredISF energy due to tension/compression near the dislocation line, (ii) facilitated diffusionof radiation defects at elevated temperature and (iii) the excessive residual vacancies thatremained because of the absorption of SIAs by dislocation core are the three necessaryfactors that determine the formation of SFTs in collision cascades near 1 / 2 110 edgedislocations in aluminum.

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An Insight Into The Mechanism Of SFT formation Near Edge Dislocations In Al Under Irradiation