N. PUK[I^ et al.: MOLECULAR DYNAMICS SIMULATIONS OF PLASTIC DEFORMATION OF METALLIC SURFACES
153–156
MOLECULAR DYNAMICS SIMULATIONS OF PLASTIC
DEFORMATION OF METALLIC SURFACES
SIMULACIJE PLASTI^NE DEFORMACIJE KOVINSKIH POVR[IN
Z METODO MOLEKULARNE DINAMIKE
Nu{a Puk{i~1,2, Monika Jenko1,2, Matja` Godec1
1Institute of Metals and Technology, Lepi pot 11, Ljubljana, Slovenia
2Jo`ef Stefan International Postgraduate School, Jamova cesta 39, Ljubljana, Slovenia
nusa.puksic@imt.si
Prejem rokopisa – received: 2016-12-12; sprejem za objavo – accepted for publication: 2016-12-23
doi:10.17222/mit.2016.334
An understanding of the physical properties of a wide array of geometries is important in the quest for ever smaller and more
fine-tuned devices and their parts. Surfaces play a key role in the deformation of nano-scale systems. Molecular dynamics
simulations of compressive and tensile deformation were performed on nickel and copper thin films with (111), (9 9 11) and (10
10 8) surface orientations at 10 K. The (9 9 11) and (10 10 8) surfaces are vicinal to (111) and consist of a series of equidistant
monoatomic steps. All the cases exhibit a yield stress asymmetry, with the yield stress being higher in compression than in
tension. The near-surface region is the first to plastically deform and dislocations nucleate at the surface. The influence of the
surface is most pronounced for the cases of the (10 10 8) surfaces deformed in compression, where parallel stacking faults
nucleate at the steps on the surfaces in both materials, overriding the primary slip systems.
Keywords: molecular dynamics (MD), metallic surfaces, thin films, deformation
Dobro razumevanje mehanskih lastnosti {iroke palete geometrij je pomembno pri izbolj{avah vedno manj{ih in zahtevnej{ih
naprav in njihovih delov. Povr{ine igrajo pomembno vlogo pri deformaciji sistemov na nano-skali. Z metodo molekularne
dinamike smo raziskali deformacijo (111), (9 9 11) in (10 10 8) orientiranih nikljevih in bakrovih tankih filmov ob raztezanju in
kr~enju pri temperaturi 10 K. Povr{ini (9 9 11) in (10 10 8) sta sosednji nominalni povr{ini (111) in sta sestavljeni iz
ekvidistantnih stopnic. Vse povr{ine imajo asimetri~no mejo plasti~nosti, ki je vi{ja pri stiskanju kot pri raztezanju. Obmo~ja tik
pod povr{ino se najprej deformirajo in dislokacije izvirajo na povr{inah. Vpliv povr{ine je najbolj izrazit za primera orientacije
(10 10 8) pri stiskanju, ko se oba materiala deformirata s serijo vzporednih napak zloga, ki izvirajo iz stopnic na povr{inah in, ki
nadomestijo primarne drsne sisteme.
Klju~ne besede: molekularna dinamika (MD), kovinske povr{ine, tanki filmi, deformacija
1 INTRODUCTION
Experiments at the nanoscale can be very time con-
suming and costly, in addition, they often turn out ambi-
guous due to lack of constraint on the thin foils
examined. Such experiments also require expensive
equipment and sensors, which further motivates us to use
atomistic simulations to better understand deformation
mechanisms at the nanoscale. Molecular dynamics (MD)
simulations can serve as an effective tool for analysing
dislocation nucleation mechanisms in metallic mate-
rials.1–4
Whereas the misorientation of adjacent grains deter-
mines the precise positioning of the atoms close to the
boundaries, leading to diverse defect nucleation sites, the
surface condition similarly influences the mechanical
response of a material to external loads or deformation
due to the relaxation of the topmost layers minimizing
the surface energy and the adjacent free space into which
the atoms can move.5–8
Vicinal surfaces, such as (10 10 8) and (9 9 11) inve-
stigated here, are produced by cutting a crystal close to a
dense plane, and consist of terraces divided by equidis-
tant monoatomic steps. When cutting or growing poly-
crystalline materials, such surfaces are unavoidable. As
is the case with grain boundaries, the steps on the surface
provide favourable nucleation sites for dislocations and
stacking faults, key elements of plastic deformation. We
show that deformation mechanisms in copper and nickel
are influenced by the presence of steps at the surface.
2 EXPERIMENTAL PART
The simulations were performed on an array of sub-
strates, with surface orientations (111), (9 9 11) and (10
10 8). The (9 9 11) and (10 10 8) surfaces are vicinal to
(111) and consist of a series of equidistant monoatomic
steps that have (001) and (-1-11) oriented microfacets,
respectively.
Copper and nickel single crystal thin films of 10 nm
thickness were simulated. The simulations of the tensile
and compressive uniaxial deformations were performed
at 10 K, applying engineering strain at a strain rate of
±2.5% /ps. The strain direction was perpendicular to the
steps.
The boundaries of the simulation boxes were periodic
in the x and y directions and fixed in the z direction.
Materiali in tehnologije / Materials and technology 51 (2017) 1, 153–156 153
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967-2017) – 50 LET/50 YEARS
UDK 67.017:669.058:620.172.2 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(1)153(2017)
In the z direction the simulated films were bound by
a free surface at the top and by a layer of fixed atoms at
the bottom to prevent the loss of atoms at the border of
the simulation box and to simulate defect-free bulk. The
thickness of this frozen layer was 1.2 nm. These atoms
were fixed at the positions they had when equilibrated to
10 K and were remapped at every deformation of the
simulation box. All the forces acting on these atoms
were otherwise reset to zero.
In the y direction the size of the simulation box was
subject to requirements for periodicity of the terraces and
steps for vicinal surfaces. The number of steps and
terraces included was 8.
To simulate engineering compressive and tensile
strains, the simulation box was deformed in the y direc-
tion in increments of 0.5 % with 200 fs periods of equili-
bration in-between, resulting in the overall strain rate of
2.5% /ps. The stress in the x direction was kept to zero.
The molecular dynamics simulations were carried out
using the LAMMPS Molecular Dynamics Simulator9 and
EAM potentials by Y. Mishin et al.10 OVITO11 was used
for visualization and analysis of the simulation data.
Dislocation detection algorithm by A. Stukowski11 im-
plemented in OVITO was used in post-processing.
3 RESULTS
Deformation mechanisms of copper and nickel (111),
(9 9 11) and (10 10 8) surfaces were investigated.
Stress-strain curves are shown in Figures 1 and 2. As is
expected from the direction of the strain, the Young
modulus (expressed as the steepness of the stress-strain
curve) is highest for the (9 9 11) surfaces and lowest for
the (10 10 8) surfaces.
Yield stress is lower in copper than in nickel. Both
materials exhibit the yield stress asymmetry, with yield
stress being higher in compression than in tension. This
is connected to the fact that the deformation mechanisms
in compression and tension are not the same for any of
the surfaces we investigated, although strict geometric
analysis suggests otherwise: primary slip systems,
namely {-111}(0-11) and {1-11}(-101), are the same for
all the surfaces we investigated, with Schmidt factors of
0.408 for the (111) surface, 0.377 for (9 9 11) and 0.433
for (10 10 8).
In the case of Cu(111) surface deformed in tension,
mostly stair-rod dislocations form throughout the bulk
and are not limited to the near-surface region, while in
compression, dislocations first nucleate at the surface as
Schockley partials and no trailing partials detach from
the surface.
In the case of Ni(111) surface deformed in tension,
Schockeley partial dislocations nucleate in the bulk,
while in compression, Schockley partials nucleate at the
surface and trailing partials detach from the surface.
For all the (9 9 11) surfaces, Schockley partial dislo-
cation nucleate at the surface and trailing partials detach
from the surface. Stair-rod dislocations form in Cu(9 9
11) and Ni(9 9 11) deformed in tension, Figures 3b and
3f.
In the case of Cu(10 10 8) surface deformed in ten-
sion, Figure 3a, stair-rod dislocations nucleate at the
surface, while in compression, Figure 3c, parallel stack-
ing faults nucleate at the steps and grow into the bulk.
In the case of Ni(10 10 8) surface deformed in ten-
sion, Figure 3e, Schockley partial dislocation nucleate at
the surface and in the near-surface region, while in
compression, Figure 3g, parallel stacking faults nucleate
at the steps and grow into the bulk.
4 DISCUSSION
We found two cases of easy glide where only one slip
system is active: Cu(10 10 8) and Ni(10 10 8) surfaces
deformed in compression, Figures 3c and 3g. Schockley
partial dislocations nucleate at all the steps on the
surface and grow evenly into the bulk. The stress-strain
curves have a small plateau in the region just before the
peak of the curve is expected, more pronounced in the
case of nickel, and the peak is moved to higher strains,
Figures 1a and 2a.
In the case of Cu(10 10 8) deformed in tension, Fig-
ure 3a, Schockley partial dislocations wrapped around
stair-rod dislocations form, also nucleating at the steps
on the surface. As the stair-rod dislocations only move
with diffusion, which is limited at this temperature, the
N. PUK[I^ et al.: MOLECULAR DYNAMICS SIMULATIONS OF PLASTIC DEFORMATION OF METALLIC SURFACES
154 Materiali in tehnologije / Materials and technology 51 (2017) 1, 153–156
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967-2017) – 50 LET/50 YEARS
(a) Copper, compressive deformation (b) Copper, tensile deformation
Figure 2: a) Stress-strain curves for copper deformed in a) compres-
sion and b) in tension.
Slika 2: Diagrama napetost-raztezek za baker: a) pri kompresiji, b) pri
napetosti
(a) Nickel, compressive deformation (b) Nickel, tensile deformation
Figure 1: a) Stress-strain curves for nickel deformed in compression
and b) in tension.
Slika 1: Diagrama napetost-raztezek za nikelj; a) pri kompresiji, b) pri
napetosti.
effect on stress is the same as if only one slip system
were active and the stress-strain curve exhibits a change
in slope, Figure 2b.
A. Zimmerman et al.12 studied Au(111) surfaces with
single monoatomic steps at 0K and found that when the
indenter came into physical contact with the step, the
deformation mechanism beneath the indenter switched
from dislocation emission from the surface to slip
aligned with the step.
D. Shan et al.13 performed a similar study of
nanoindentation on thin copper films and found that
when the indenter came into contact with the step, there
was a significant difference in the strength of the first
dislocation emission.
H. Lu and Y. Ni14 and H. Lu et al.15 investigated the
effects of surface steps on nanoindentation in Al and
found that the shear stress resulting from the step
influences the choice of the active slip systems and
lowers the threshold for plastic deformation.
Our analysis shows that it is not only the presence of
steps that influences deformation mechanisms. While a
switch to slip aligned with the steps occurs for the (10 10
N. PUK[I^ et al.: MOLECULAR DYNAMICS SIMULATIONS OF PLASTIC DEFORMATION OF METALLIC SURFACES
Materiali in tehnologije / Materials and technology 51 (2017) 1, 153–156 155
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967-2017) – 50 LET/50 YEARS
Figure 3: Dislocation nucleation in copper and nickel thin films deformed in tension and in compression. Two views are shown for each case:
dislocations as lines (left) and atoms with centrosymmetry parameter CS > 2 (right). Black lines denote Schockley partial dislocations and pink
lines denote stair-rod dislocations.
Slika 3: Za~etki plasti~ne deformacije v bakrovih in nikljevih stiskanih in raztezanih tankih filmih. Vsak primer prikazujeta dva pogleda:
dislokacije ozna~ene s ~rtami (levo) in atomi s parametrom sredi{~ne simetrije CS > 2 (desno). ^rne ~rte ozna~ujejo Schocklyeve delne
dislokacije, roza ~rte pa Lomer-Cottrell stike.
8) surfaces deformed in compression for both materials
we investigated, we found no such switch for the (9 9 11)
surfaces.
The near-surface region is the first to plastically
deform and dislocations nucleate at the surface, therefore
the surfaces are softer than the bulk. We conclude that
the stress inherent in the steps also lowered the threshold
for plastic deformation in our systems.
5 CONCLUSIONS
Deformation mechanisms of copper and nickel thin
films we investigated are more complex than geometric
analysis would suggest. The surfaces are softer than the
bulk, as the near-surface region is the first to plastically
deform and dislocations nucleate at the surface. We con-
clude that the stress inherent in the steps lowered the
threshold for plastic deformation in the thin films we
investigated.
In tensile deformation in both materials, stair-rod
dislocations nucleate at the surfaces and are not created
by dislocation interactions.
The influence of the surface is most pronounced for
the cases of the (10 10 8) surfaces deformed in com-
pression, where parallel stacking faults nucleate at the
steps on the surfaces in both materials, overriding the
primary slip systems. The presence of the steps does not
in itself influence the choice of slip systems. While a
switch to slip aligned with the steps occurs for the (10 10
8) surfaces deformed in compression for both materials
we investigated, we found no such switch for the (9 9 11)
surfaces.
Acknowledgement
The authors acknowledge the financial support of the
Slovenian Research Agency (ARRS).
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N. PUK[I^ et al.: MOLECULAR DYNAMICS SIMULATIONS OF PLASTIC DEFORMATION OF METALLIC SURFACES
156 Materiali in tehnologije / Materials and technology 51 (2017) 1, 153–156
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967-2017) – 50 LET/50 YEARS