Applied Surface Science 293 (2014) 187 190

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Applied Surface Science

j ourna l ho me page: www.elsev ier .com

Atomic inberylliu

Xue YangCenter for Mate est La

a r t i c l

Article history:Received 15 OReceived in re21 December 2Accepted 22 DAvailable onlin

Keywords:Tungsten sputSurface bindinMolecular dynBinary collisioEmission anguEmission ener

lculae conMPS

. Theults. tely istinhe ITe mo

1. Introduction

Surface sputtering ymethod. Thcome in ormaterials, tmation eneas a good atungsten usthe heat of relates to asurface, nota surface atenergy, whering only quasichemaccount theing yield cainput and uestimated saccurate SB

CorresponE-mail add

In current and future fusion reactors, beryllium (Be) is beingused as the rst wall coating, because it is among the least plasma-

0169-4332/$ http://dx.doi.obinding energy (SBE) is a key parameter to accurateield calculation in binary collision approximation (BCA)is is the energy that the target surface atoms must over-der to leave the surface (sputtered). For most of thehe actual SBE values are unknown, and the heat of subli-rgy (or cohesive energy) is usually used in BCA methodpproximation. For example, the default SBE value ofed in BCA Monte Carlo (MC) codes is 8.68 eV. However,sublimation is assumed to be too low, because it only

half-space atom, which is atypical of an undisturbed to an in-surface atom [1]. The energy required to ejectom should be 3040% greater than heat of sublimationich is based on the pair potential calculation consid-the nearest neighbors [2]. This theory is based on theical variant of thermodynamics, which only takes into

nearest neighbor binding energy [1]. Because sputter-lculated by BCA method is very sensitive to the SBEsing heat of sublimation as the SBE will result in over-puttering yield, it is important to predict and supplyEs to the BCA codes.

ding author. Tel.: +1 7654049997.ress: yang99@purdue.edu (X. Yang).

polluting metals [3]. Due to the low SBE and low melting point of Be,it is subjected to strong physical sputtering [4]. The erosion rate ofBe can be an order-of-magnitude higher than tungsten, the divertormaterial, and the threshold for D Be sputtering is just severalelectron volts [5]. Therefore, Be is a common plasma impurity, andthe eroded Be atoms could migrate toward the divertor region. InITER, the Be fraction in plasma ranges from 0.01 to 0.10, leading toa Be incident ux of 1001000 monolayer (ML) s1 on ITER divertorsurfaces [6]. Be deposition on W may enhance W erosion, due to itslarger mass. In addition, the formed BeW alloy has lower meltingpoint, thus weakens W thermo-mechanical properties [7]. Exten-sive efforts have been devoted to the understanding of the complexwall surface evolution. Due to berylliums severe toxicity, numeri-cal simulations remain as the most available investigative methodsin this area. This paper presents the SBE calculation of tungstenusing molecular dynamic (MD) simulation. Using the corrected SBE,consistency between BCA and MD for beryllium induced tungstensputtering yield calculation is achieved.

2. Computation method

2.1. Molecular dynamic

Classical molecular dynamic methods are computer simula-tion techniques that compute the motions of individual atoms or

see front matter. Published by Elsevier B.V.rg/10.1016/j.apsusc.2013.12.129 scale calculations of tungsten surface bm-induced tungsten sputtering, Ahmed Hassanein

rial Under Extreme Environment, School of Nuclear Engineering, Purdue University, W

e i n f o

ctober 2013vised form013ecember 2013e 2 January 2014

tering yieldg energyamicn approximationlar distributiongy spectrum

a b s t r a c t

Tungsten surface binding energy is camany-body potentials. We present thment between molecular dynamic LAMnew surface binding energy (11.75 eV)to overestimated sputtering yield resshow that molecular dynamic accuradirections in bcc tungsten, while the dthe treatment of amorphous target. TThompson energy spectrum, while thspectrum./ locate /apsusc

ding energy and

fayette, IN 47907, USA

ted using classical molecular dynamic simulations with threesistency in tungsten sputtering yield by beryllium bombard-

code and binary collision approximation ITMC code using the commonly used heat of sublimation value (8.68 eV) could leadThe analysis of the sputtered tungsten angular distributionsreproduced the [1 1 1] most prominent preferential ejectionct shapes by typical MC codes such as ITMC code is caused byMC calculated emitted tungsten energy prole matches thelecular dynamic results generally follow the Falcone energy

Published by Elsevier B.V.

188 X. Yang, A. Hassanein / Applied Surface Science 293 (2014) 187 190

molecules. The trajectories of particles are numerically solved byNewtons equation of motion, where force and potential energyare determined by the interatomic potential. MD has been exten-sively used to model the interaction of energetic ions with material[814]. In thto perform foundation choice of ththree typesand suitablpotentials [are used in

For the tconsists of 2 layers of and velocitwalls are seditions are boundary wperature of size is set toatom at thetum towardenergy andis graduallyis very clostime. Thenbe the calcuthe momenonly set theto are set topotentials.

Althougof the topmSBE value satom is ejevacancy canimation. Hothe relaxatiformation evalue than SBE and use

Tungstecalculated btions for thby above thare denedfunction. Ththe Tersoffthe Tersoff there is oninteraction by 55 latticbottom are the side watoms are mostat. For(2a) above 200500 eVand a randotracked till boundary osubstrate). phase with the step sizbombardm

ungstault a

nary

tunsed is (ITMte thotenintere thpotees an

inctiles

ult a

ngst

MDtenting .01 eetwe pourn b

other, and the average value of 11.75 eV is considered as SBE, which will be used in the subsequent BCA simula-It is 35.4% greater than the tungsten heat of sublimation

(8.68 eV), i.e., falling in the range of 3040% mentioned.

1 displays the Be-induced tungsten sputtering yield calcu-y ITMC with default and new SBE and LAMMPS with threebody potentials. In this region of incident energies, the sput-yield can be treated as linear with incident energy. The ttedcurves are drawn in Fig. 1 as well, and they are extendedaxis. All three MD potentials yield similar results. Sputter-ld by ITMC with default SBE is overestimated, about twogreater than the MD results. Using the MD predicted tung-E, the ITMC code produces identical sputtering yield as MDd. This consistency indicates correct SBE calculation pro-

and value. The extensions of the sputtering yield curveshat the threshold for Be W physical sputtering is aroundis research, the classical MD code LAMMPS [15] is usedthe MD simulations of ion-target interactions. The basicof the MD method is the interatomic potential and thee potential can signicantly affect the results. There are

of tungsten many-body potential available in literaturese for LAMMPS code: two EAM (embedded atom model)16,17] and a Tersoff-type potential [18], and all of themthis study for comparison.ungsten SBE calculation, the used bcc tungsten sample21 by 21 by 21 lattice constants (3.165 A). The bottomatoms are xed in the space at all time and the forcey are zeroed out. The boundary conditions on the sidet to periodic, while the top and bottom boundary con-set to non-periodic and xed (atoms move across suchill be removed from system). At the beginning, the tem-the entire tungsten sample is set to 0 K, and the time step

1 fs. In order to calculate the SBE, a rst layer surface center of tungsten (0 0 1) surface is given a momen-

the surface normal [19]. By monitoring the remaining the location of the ejected atom, the initial momentum

adjusted until the ejected atoms remaining energye to zero and it could leave the surface at the same, the initial energy assigned to the surface atom willlated SBE. It should be noted that SBE only considerstum vector perpendicular to the surface. Therefore, we

initial velocity along z-axis (vz,0), while the vx,0 and vy,0 0. This calculation procedure is repeated for all three

h it is possible to calculate the cohesive energy per atomost layer (denoted by Ecoh,surf) using MD simulations, thehall not be simply considered as 2Ecoh,surf. If the surfacected sufciently rapid, and the relaxation around the

be neglected, the 2Ecoh,surf is then a good SBE approx-wever, the atom removal process is usually slow, andon effect could not be ignored. Taking surface vacancynergy into consideration leads to somehow smaller2Ecoh,surf [1]. Therefore, we followed the denition ofd this procedure to accurately calculate it.

n sputtering yield by beryllium bombardment is alsoy the MD method in order to provide reference solu-

e BCA simulation. The WW interactions are describedree many-body potentials, while the BeW interactions

by ZieglerBiersackLittmark (ZBL) universal screeninge ZBL formula has a few variations. This work adopts

/ZBL formula in LAMMPS manual [20] by eliminatingpart. Because the bombardment is non-cumulative andly one single Be atom in the system at a time, BeBeis not dened. The tungsten substrate size is 10 by 10e constants. The atoms of 3 lattice constants from thexed in space. The atoms of one lattice constant aroundall and two lattice constants above the bottom xedmaintained at room temperature by Berendsen ther-

each bombardment, the Be is randomly placed 6.33 Athe tungsten (0 0 1) surface, then an initial velocity of

is assigned to the Be atom, with a 45 polar anglem azimuthal angle. The Be projectile is continuously

the Be atom escapes from the upper or lower simulationr its kinetic energy is lower than 0.5 eV (trapped in theThen, the substrate is restored to its initial undamageda new incident Be projectile. During the bombardment,e is set to 0.5 fs, and each simulation contains 2000

ent.

Fig. 1. Twith def

2.2. Bi

Theboth upoundsimulaKrC pBeW describversal energibut theprojec

3. Res

3.1. Tu

Thesoff poremainthan 0tance bthan thnot retto eachthe Wtions. energyearlier

Fig.lated bmany-tering linear to the ing yietimes sten SBmethocedureshow t60 eV.en sputtering yield by beryllium bombardment calculated by ITMCnd new SBE and LAMMPS with three many-body potentials.

collision approximation

gsten heat of sublimation and MD calculated SBE aren the BCA code, Ion Transport in Materials and Com-C) [21], part of the HEIGHTS code package [2226], to

e Be W sputtering process. The ITMC calculations usetial [27,28] with Firsov screening length to describe theaction. The Kr-C potential was originally developed toe Kr and C interactions, but it turns out to be a good uni-ntial for atomic collision modeling [29]. The Be incidentd polar angle are kept the same as the MD parameters,ident azimuthal angle is xed at 0. There are 100,000per ITMC simulation.

nd discussion

en SBE and sputtering yield

calculated tungsten SBE using EAM, EAM-FS, and Ter-ials are 11.56, 12.00, and 11.69 eV, respectively. Theenergies of the ejected W atoms of all cases are lowerV. The ejected W atoms are tracked till the vertical dis-een the ejected atom and the surface is much greatertential cut-off distance, to ensure that those atoms willack. The calculated SBE from three potentials are close

X. Yang, A. Hassanein / Applied Surface Science 293 (2014) 187 190 189

Fig. 2. Sputtered tungsten polar angle prole (incident beryllium energy: 500 eV). Inthis gure, 0 means the sputtered tungsten atom travels along the surface normal.

3.2. Sputtered atom angular distribution

During tsputtered tThe ejectioof 10, and Be projectiFigs. 2 and affects the calculation

Fig. 3. Sputte500 eV).

Fig. 4. Sputter

Angularexhibit precrystal axestions (oftenclosed-packstructures. azimuthal apreferentiaresults are tions are ac

rphofromesulto the

utter

physe u] givehe simulation, the polar and azimuthal angles of theungsten traveling directions are documented as well.n angles are collected into multiple bins with a sizethe counts are normalized by dividing the number ofles. For 500 eV Be bombardment, they are shown in3, respectively. In BCA calculation, changing SBE onlyradius, not the shape. Therefore, for ITMC results, onlyusing new SBE is displayed for a concise view.

as amoferent Fig. 3 rleads t

3.3. Sp

Forparticl[33,34red tungsten azimuthal angle prole (incident beryllium energy:

(E, )dEd

where, : emission enIntegratingenergy spec

(E) (E +

Howeveof the Thom[33]. The Fparticles co

(E) (E +

Ec = (

= 4M(M1

where, M1ed tungsten energy prole (incident beryllium energy: 500 eV).

distributions of particles sputtered from single crystalsferential ejections in the direction of certain preferred, and the most prominent preferential ejection direc-

called Wehner spots [3032]) usually correspond toed lattice rows: e.g., [1 1 1] in bcc and [1 1 0] in fcc [2]For bcc tungsten (0 0 1) surface, polar angle of 54.7 andngles of 45, 135, 225, and 315 are the theoretical

l ejection directions. As shown in Figs. 2 and 3, all MDclose to each other, and the preferential ejection direc-curately reproduced. In ITMC, the substrate is treatedus material, so its angular distribution proles are dif-

the MD simulation. The unsymmetrical oval shape ins from the xed incident azimuthal angle of 0, which

preferential ejection at the opposite side.

ed atom energy spectrum

ical sputtering, the energy distribution of the sputteredx can be described by the Thompson energy spectrumn by:

E(E + Eb)3

cosdEd (1)

sputtered particle ux; : emission polar angle; E;ergy; Eb: surface binding energy; and : solid angle.

Eq. (1) over and yields Eq. (2), which decribes thetrum of the sputtered atoms.E

Eb)3

(2)

r, for small bombarding energies and light ions, the tailspson energy spectrum dieviates from the reference

alcone energy spectrum for bombardment with lightnsiders the single knock on regime of sputtering [33]:

E

Eb)2.5

ln(

EcE + Eb

)(E + Eb < Ec) (3)

1)E01M2

+ M2)2(4)

and M2 are the mass of projectile and target atoms.

190 X. Yang, A. Hassanein / Applied Surface Science 293 (2014) 187 190

The energies of the sputtered tungsten atoms calculated by MDand BCA codes are collected into mutiple bins with a width of 4 eV.The results of 500 eV bombardment are plotted in Fig. 4 along withthe two empirical formulas. All curves are normalized as the peakis set to 1. The ITMC peak location (at Eb/2) and the falloff towardhigh energies match the Thompson energy spectrum well. The MDresults have large uctuation due to low number of projectiles ineach run, but in general, the MD results are close to the Falconeenergy spectrum, which best describes this sputtering scenario oflight particle with low incident energy bombardment.

4. Conclusion

The surfmolecular dbody poten11.75 eV, wlimation 8.6based Monberyllium nand ITMC Bcalculated bITMC resultThis consistare more apangular distthrough theMD simulatITMC exhibtarget usedculated by MD solution

Acknowled

This worOfce of Fu

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Atomic scale calculations of tungsten surface binding energy and beryllium-induced tungsten sputtering1 Introduction2 Computation method2.1 Molecular dynamic2.2 Binary collision approximation

3 Result and discussion3.1 Tungsten SBE and sputtering yield3.2 Sputtered atom angular distribution3.3 Sputtered atom energy spectrum

4 ConclusionAcknowledgementReferences