Simulation of grain growth in nanocrystalline nickelinduced by ion irradiation

Wolfgang Voegeli, Karsten Albe *, Horst Hahn

Technische Universit€aat Darmstadt, Institut f€uur Materialwissenschaft, Petersenstrasse 23, D-64287 Darmstadt, Germany

Abstract

Molecular dynamics simulations of 5 keV cascades in nanocrystalline nickel with grain sizes of 5 and 10 nm are

presented. If the spike volume is exceeding the grain size or overlapping the grain boundary (GB) area we observe ion-

beam induced grain growth for both grain sizes. In contrast cascades located in the grain volume lead to the formation

of vacancies and interstitials, where the latter are mostly accommodated by the GBs upon annealing. Finally, we show

that ion-beam induced grain growth is a direct result of recrystallisation of the thermal spike and therefore inherently

different to grain growth observed in long time thermal annealing simulations.

� 2002 Elsevier Science B.V. All rights reserved.

PACS: 61.80.Jh; 61.82.Rx; 81.40.)zKeywords: Radiation damage; Nanocrystalline materials; Molecular dynamics

1. Introduction

Nanocrystalline (nc) metals exhibit a number

of peculiar materials properties compared to

conventional polycrystalline samples [1]. Due to

the small grain size of a few nanometers, grain

boundaries (GB) play a dominant role for the

elastic and plastic behavior of these materials. GBs

are effective sinks for irradiation-induced defects.

This was proven by computer simulations of cas-cades in the vicinity of an infinite R5 GB in silver

[2]. Because of their large volume fraction of GBs,

nc-materials are therefore considered to be radia-

tion resistant. Experimental studies showed that

irradiation induced damage is significantly smallerin nc than in polycrystalline samples. Rose et al. [3]

studied the defect evolution in palladium and re-

ported a decreasing defect density with decreasing

grain size. Chimi et al. [4] measured the electrical

resistivity of irradiated nc-gold and found enlarged

defect accumulation with decreasing temperatures.

Recently, Samaras et al. [5] investigated primary

damage states in nc-Ni using molecular dynamicssimulations. They observed the formation of va-

cancy clusters in 5–12 nm grains for energies <20

keV and dislocation networks for 30 keV cascades.

They did not report, however, on the observation

of grain growth. On the other hand, there is ex-

perimental evidence for grain growth by ion irra-

diation. Rose found a significant increase of the

average grain size from 20 to 45 nm in nc-Pd [6],with a clear dependence on dose and temperature.

*Corresponding author. Tel.: +49-6151-166323; fax: +49-

6151-166335.

E-mail addresses: albe@hrzpub.tu-darmstadt.de, albe@tu-

darmstadt.de (K. Albe).

0168-583X/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0168-583X(02)01862-1

Nuclear Instruments and Methods in Physics Research B 202 (2003) 230–235

www.elsevier.com/locate/nimb

It still remains unclear, however, under which

conditions grain growth occurs, and whether it is

mainly caused by thermal activation or induced by

irradiation.In the present study we performed computer

simulations in order to answer the question whe-

ther grain growth can occur as a direct conse-

quence of the primary state of damage. We used

molecular dynamics simulations, which are a

powerful and appropriate tool for studying such

processes, since collision cascades are confined to

relatively small volumes and appear on short timescales [7].

2. Method

Classical molecular dynamics simulations using

the parallel code PARCAS [8] were performed to

simulate collision cascades in nc-Ni. 3D-periodicboundary conditions were applied to the fixed-size

simulation cell. The temperature of the cell was

initialized to 0 K and scaled softly down to 0 K

at the outermost atomic layers during the cas-

cade. Ni recoil atoms were started at the center of

the simulation cell in approximately the direction

of the z-axis. The simulations were run for 20 ps

and afterwards cooled down to 0 K during ap-proximately 10 ps. Although using an ambient

temperature of 0 K appears to be unrealistic, it

simplifies the analysis of the damage production.

Moreover, it is well known that damage produc-

tion does not significantly depend on temperature

below 100 K [8]. For calculating energies and

forces we used the embedded-atom-method po-

tential by Foiles et al. [10,11] modified to repro-duce the correct melting point and high-energy

behavior [8].

The model nc structures consisted of about

6� 105 atoms for the 5 keV cascades corre-

sponding to 16 and 128 grains for the 10 and 5 nm

grain size samples, respectively.

The grains were generated using the Voronoi

tessellation method and constructed from an initialset of points corresponding to a bcc structure. The

cells were then filled with atoms in different, ran-

domly chosen lattice orientations for each cell. At

the GBs a gap of a few �AAngstrom was left to avoid

too small atomic separations. These structures

were relaxed in a variable cell MD-simulation at 0

bar and 600 K for 15 ps and subsequently cooled

down to 0 K. This procedure allows to locallyrelax the GBs.

Since nc structures are thermodynamically

metastable configurations, structural changes can

occur over longer annealing periods depending on

the temperature and activation energy needed for

structural changes. Therefore we compared the

microstructure of the irradiated samples with those

obtained by long time thermal annealing at a hightemperature. Details will be given in Section 3.

The resulting structures consist of grains of

similar size with the shape of truncated octahe-

drons (the shape of the bcc Wigner–Seitz cell)

which is the typical shape of nano grains observed

in nc-metals. An alternative would be a structure

with random arrangements of grains, possibly fit-

ted to experimental grain size distributions. Ran-dom structures, however, very often include grains

of artificial shape, while the regular arrangement

chosen here has the advantage of being a well-

defined structure with monodisperse size-distri-

bution, which simplifies the structural analysis.

Furthermore, the cascades extend only over very

few grains for the recoil energies studied here,

minimizing the advantage of a more realistic grainsize distribution.

For analyzing the local structure we have used a

pair counting scheme as proposed by Honeycutt

and Andersen [9], which allows to distinguish GB

atoms from those located on ideal lattice positions.

Compared to the potential energy criterion this

method is more precise as it only takes into ac-

count the local geometry, although it remains tosome extent an arbitrary method.

3. Results

The influence of collision cascades on the mi-

crostructure was studied for nc samples with 5 and

10 nm average grain size, random orientation ofthe grains and monodisperse size distribution.

The evolution of a collision cascade induced by

a 5 keV primary knock-on atom (PKA) in nc-Ni

with 5 nm grain size is shown in Fig. 1(a)–(c),

W. Voegeli et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 230–235 231

where the individual grains have been labeled with

numbers to clarify this discussion. A slice of atoms

parallel to the initial direction of the PKA is de-

picted, where grey atoms correspond to ideal lat-tice positions. The PKA is started in grain ‘‘1’’ and

directed towards grain ‘‘2’’. Fig. 1(a) shows the

initial structure as obtained after 10 ps relaxation

before the collision cascade is started. The thermal

spike gets to its maximum extension after ap-

proximately 1 ps, where the volume compares to

that of an individual grain as shown in Fig. 1(b).

During cooling and shrinking of the cascade, at-oms at the border of the spike volume are recrys-

tallizing. During this phase, grain ‘‘1’’ in the lower

part of the spike can expand over the former GBs

into the central grain ‘‘2’’ (see Fig. 1(c)).

Afterwards, a number of additional PKAs were

started at similar positions in the same sample, in

order to study the effect of overlapping cascade

volumes. Each event was run for 20 ps before thesample was cooled down for 10 ps and a new PKA

was started. The change of the GB positions of

grain ‘‘2’’ after 1, 2 and 3 PKAs is schematically

shown in Fig. 2 and depicted by the grey atoms in

Fig. 3(a). The GBs moved up to about 4–5 �AA.

In the xy-plane significant shrinking can only be

observed after the third PKA, while in the xz-planethe projected grain area constantly decreases afterevery event. Obviously, the central grain is shrink-

ing even more during a short annealing procedure

over 100 ps at 600 K. The vacancy clusters inside

of the shrunken grain are stable during the

annealing procedure, while atoms in the area of

GBs and GB junctions relaxed to more favour-

able positions.

The result after five cascades is represented bythe light grey atoms in Fig. 3(a). Since the thermal

spike occurred in approximately the same region in

all five cascades, the lower grain ‘‘1’’ was able to

expand further into the central grain ‘‘2’’, which

lost about half of its volume.

For comparison we carried out an alternative

simulation where thermally activated grain growth

could be observed by keeping the structure at 1000K for 1 ns simulation time. In Fig. 3(b) the GB

structure after 100 ps (grey) and 1 ns (light grey) is

depicted. Obviously, the thermally induced grain

growth after 100 ps is much less than that caused

Fig. 1. (a) Initial structure with 5 nm grain size. Atoms on fcc

positions are colored grey, all other dark. (b) Cascade volume

of a 5 keV recoil after 1 ps. (c) Final structure after cooling

down of the cascade.

232 W. Voegeli et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 230–235

by five cascades during the same simulation time.

While grain ‘‘1’’ has somewhat shrunk after 100 ps

annealing time, the size of grain ‘‘2’’ is almost the

same. In contrast, grain ‘‘2’’ is significantly re-

duced in size after a number of collision cascades,

while much less shrinkage can be observed after

the annealing procedure. The opposite holds true

for grain ‘‘1’’, which was shrinking during theannealing procedure but was growing with the

number of collision cascades. This observation

gives strong evidence that the ion-induced grain

growth is not just an artifact of unstable GB

structures.

In order to understand the role of the cascade

position and volume we have additionally calcu-

lated 5 keV cascades in samples of 10 nm grainsize. First, simulations were run in which the cas-

cade volume did not exceed the grain size. Fig. 4(a)

shows an example of such an event after the col-

lision cascade has cooled down. In contrast to the

previous 5 nm case, the spike is confined to the

grain volume and no grain growth is observed.

Inside the central grain point defect clusters have

been formed, while the GB positions remainedunaffected. After thermal annealing at 1000 K for

100 ps a vacancy and divacancy are left in grain

‘‘1’’, while the interstitials were annealed and ag-

gregated at the GB, which is in line with results

reported by Samaras et al. [5] for energies below 20

keV. At the same time the triple junction between

grain ‘‘1’’, ‘‘2’’ and ‘‘3’’ has been moving along the

GB between grain ‘‘1’’ and ‘‘3’’.

In contrast we find that grain growth can occur

even for 10 nm grains if the cascade volume islocated in the area of GBs or triple junction. One

example is shown in Fig. 5. Here the cascade vol-

ume was located close to the triple junction ‘‘1–2–

3’’. Comparing the initial and final structures, it

Fig. 2. Schematic GB positions change after 1, 2, 3 collision

cascades and subsequent annealing for 100 ps at 600 K.

Fig. 3. (a) Grain structure after five collision cascades. Dark

atoms depict the initial GB structure, grey atoms the micro-

structure after three collision cascades and the light grey atoms

the final configuration after five cascades. (b) The same struc-

ture annealed at 600 K for 100 ps (grey atoms) and 1 ns (light

grey atoms).

W. Voegeli et al. / Nucl. Instr. and Meth. in Phys. Res. B 202 (2003) 230–235 233

gets obvious that the triple junction has moved

towards the center of grain ‘‘1’’ leading to a small

shrinkage of the central grain. Obviously, this

motion of the triple point is different to that ob-

served in the thermal annealing procedure before.In conclusion, we note that the kinetic activa-

tion of grain growth induced by thermal annealing

is different from that of collision cascades. There-

fore the structural changes are not identical and

occur on different time scales. Ion irradiation leads

to modifications of the microstructure that can not

be obtained by annealing procedures.

4. Conclusions

We have studied 5 keV cascades in monodis-

perse nc-Ni samples of 5 and 10 nm grain size.Using molecular dynamics simulations we show

that ion-induced grain growth is observed if the

thermal spike volume is larger than the grain vol-

ume or overlaps the GB area. Shrinkage or growth

of grains is accumulated over several events. If the

spike volume does not reach the GB area we do

not observe ion-induced grain growth. In all cases

vacancies and vacancies clusters are formed, whileinterstitials are accommodated by the GBs.

Acknowledgements

This work has been partly support by a grant

from Deutsche Forschungsgemeinschaft (DFG)

under project number AL578. Drs. Balogh andGafhari as well as W. Berky are gratefully ac-

knowledged for helpful discussions.

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