# Statistical Molecular Dynamics Study of (111) and (100) Ni Nanocontacts: Evidences of Pentagonal Nanowires

Authors: P. García-Mochales; R. Paredes; S. Peláez; P. A. Serena
Journal: Journal of Nanomaterials
 (2008)

---

## Abstract

We present molecular dynamics calculations on the evolution of Ni nanowires stretched along
the (111) and (100) directions, and at two different temperatures. Using a methodology similar
to that required to build experimental conductance histograms, we construct minimum crosssection
histogramsH(Sm). These histograms are useful to understand the type of favorable atomic configurations appearing during the nanowire breakage. We have found that minimum crosssection
histograms obtained for (111) and (100) stretching directions are rather different. When
the nanowire is stretched along the (111) direction, monomer and dimer-like configurations appear,
giving rise to well-defined peaks in H(Sm). On the contrary, (100) nanowire stretching presents a
different breaking pattern. In particular, we have found, with high probability, the formation of
staggered pentagonal nanowires, as it has been reported for other metallic species.


---

## Body

## 1. Introduction

Nanotechnology involves the design, fabrication, and
application of structures by controlling their composition, shape, and size at
the nanometer scale [1]. In particular, the control of these properties will
allow to exploit a whole set of novel physical and chemical features in future
nanoelectronics development. Such development includes the study of the
electron transport through different candidates to be used as nanoelectronics
building blocks. Among these candidates, metallic nanowires or nanocontacts
will play a relevant role [2].The interest on metallic nanowires and nanocontacts
rises from their rich phenomenology. Electron transport through metallic
nanowires present ballistic features and, in addition, well-defined electron
transport modes or channels appear associated to the transversal confinement of
electrons for those nanowires with diameters of the order of few Fermi
wavelengthsλF. In the ballistic limit, the conductance G (inverse of the
nanowire resistance R, G=1/R) is described
in terms of the transmission probabilities  associated to these transport channels [3, 4].Several experimental techniques have been used to form
metallic nanocontacts and nanowires. Scanning tunneling microscopy
(STM) [5–7] and mechanically
controllable break junction (MCBJ) [8] methods are standard approaches to study the formation
and rupture of nanocontacts under different experimental conditions. Metallic
nanowires are also obtained using electron-beam irradiation inside ultrahigh
vacuum (UHV) transmission electron microscopes (TEM) [9] or using electrochemical
methods [10].The electric characterization of a metallic nanowire
is usually done during its rupture. This rupture is achieved using SPM or MCBJ
methods, leading to the acquisition of a nanowire conductance traceG(t). In order to obtain relevant information concerning
the electronic transport through nanowires of a given metallic species,
conductance histograms H(G) are constructed
by accumulating many different conductance traces. Usually, conductance
histograms present well-defined peaked structures, reflecting the existence of
preferred conductance values. Such conductance peaks are usually interpreted in
terms of conductance quantization [8] or favorable atomic arrangements [11, 12].The interpretation of a conductance histogram is a
very difficult task, since it merges mechanical and electrical information as
well as information coming from different conductance channels as it happens
for polyvalent metals [13]. In spite of these interpretation problems, conductance
histograms have become a standard tool to analyze the properties of metallic
nanowires [2].Electronic transport in atomic-sized magnetic
nanowires has been profusely studied [14–32] since magnetic nanowires
are a very interesting topic for future devices and
applications. However, to the presence of a new degree of freedom,
“spin” requires an additional effort to study and interpret experimental
conductance histograms.Among those studies dealing with magnetic nanowires,
several works have addressed the study of nickel conductance histograms. A
pioneering experiment (performed at RT and without applied magnetic field)
showed that Ni conductance histograms constructed with thousands of unselected
conductance traces presented a featureless structure [15]. However, very different
results, showing well-defined peaks, were reported for Ni conductance
histograms [16]
obtained in UHV. In particular, conductance histograms presented clear
evidences of fractional conductance quantization. Moreover, these experiments
showed that conductance histograms depend on the applied magnetic field as well
as on the temperature. A different set of experiments carried out at RT showed
that conductance histograms (constructed with less than 100 conductance traces)
suffered strong modifications when the applied magnetic increases [17, 29]. Finally, experiments
carried out at 4 K, in UHV conditions, and using thousand of conductance traces
showed Ni conductance histograms with two well-defined peaks around ∼1.6G0 and ∼3.1G0, respectively [21, 22, 24, 26, 31]. The position of both peaks was not modified under
application of strong magnetic fields. The position of the first peak is
consistent with previous experimental results [14] and may be explained in terms of monomer and dimer
configurations appearing during the last stages of the nanowire breaking
process [14, 33].Encouraged by the existence of contradictory
experimental results, we have focused the present study on the role played by
the mechanical behavior during the breaking process of Ni nanowires at low and
room temperatures. Both situations are well below the Ni melting temperature (Tm=1728 K) and, in principle, a similar mechanical behavior
is expected. However, we need to exclude this thermal effect as the origin of
those marked differences between low temperature
and room temperature H(G). The aim of the present work is to carry out a
statistical study of the structural evolution of Ni nanowires under stretching
at low and room temperatures following a well tested methodology [12, 34–37]. We will analyze the role
of the stretching direction  studying two different cases: (111) and (100). An
additional motivation for carrying out the present study is also related with
the different computational histograms that have been recently reported for (111)
and (100) orientations in Ni nanocontacts [31, 37, 38].The paper is organized as follows: in the following
section we describe the computational approach used to construct computational
histograms. In Section3, we present the results for two temperatures as well
as two nanowire stretching directions; and, finally, Section 4 summarizes our
main conclusions.


## 2. Computational Methods

The main goal of the present study is to understand
the role of temperature and nanowire orientation on the nanowire evolution from
a statistical perspective. We follow a similar strategy to the experimental
one, simulating hundreds of independent breaking events, in order to determine
whether the geometry presents some preferred configurations that give rise to
well-defined peaked structures in the conductance histogram.The simulation of metallic nanowire breaking events
has been carried out using standard molecular dynamics (MD) methods based on a
description of the atom-atom interaction based on the atomic electron
densities. MD has been extensively used to study the structure and rupture of
metallic nanowires. In the past years, metallic nanowire MD simulations focused
on the description of single formation or breaking events, using different
interatomic potentials but neglecting the study of statistical effects [6, 7, 39–49]. More recently, several MD
studies on breaking and formation processes of nanocontacts have statistically
analyzed the appearance of preferred atomic configurations in order to
establish correlations with these peaks found in experimental conductance
histograms at different temperatures [12, 31, 34–38, 50]. Some of these statistical
MD simulation studies [36, 38, 50] have been carried out using a hybrid scheme, where MD
configurations are used as starting point for the calculation of the electronic
transport using more sophisticated quantum methods. These studies reveal that
there is a complex relation between the atomic configuration and the
conductance histograms.We have simulated the nanowire dynamics using an MD
scheme where atomic interaction is represented by embedded atom method (EAM)
potentials [51, 52]. In
EAM, the potential energy function for the system reads(1)E=12∑ijϕ(rij)+∑iF(ρ¯i), where i and j run over the number of atoms. In the
first term, ϕ(r) corresponds to
a pair potential depending only on the distance rij between every
pair of “different” atoms i and j. The second term is the
so-called embedding energy, which
depends on the mean electronic density ρ¯i at atom i's location. This density is approximated
in EAM as the sum of the contributions due to the surrounding atoms, ρ¯i=∑j≠iρ(rij). Then, the embedding energy is calculated by
evaluating and summing the embedding
functionF(ρ) at each atom's
position. Depending on the material and the specific physical properties to be
studied, different pair potential ϕ(rij), embedding F(ρ), and density ρ(rij) functions can
be defined. In the present study, we have used the EAM parameterization
proposed by Mishin et al. [53]. This parameterization has
been constructed by fitting almost 30 different properties obtained from
experimental measurements or ab-initio calculations. These fitted properties
correspond to bulk as well as surface properties, therefore taking into account
low-dimensional configurations as those found during the last nanowire breaking
stages.Nanowire dynamics have been studied at constant
temperatureT using a standard
velocities scaling algorithm at every MD step. Two temperatures (4 K and 300 K)
have been considered in this work in order to describe the Ni nanowire dynamics
at low and room temperatures. The time interval of an MD step is δt=10−2 ps . Atomic trajectories and velocities were determined
using conventional Verlet velocity integration algorithms. We have checked that
the obtained minimum cross-section time evolution curves and histograms obtained
with this time step are very similar to that obtained with a shorter time
interval.The simulation of a single nanowire breaking event
consists of three stages. The first stage corresponds to the definition of the
initial unrelaxed structure. We consider a bulk super-cell with parallelepiped
shape, containing hundreds of atoms ordered according to an fcc structure with
bulk Ni lattice parameter (a = 3.52 Å). The initial
parallelepiped height will correspond to the stretching direction and is larger
than the base edges. We define the z axis as the
stretching (pulling) direction. In the present study we have considered two
different stretching directions: (111) and (100). For the (111) case we have
used an initial nanowire formed by 18 layers containing 56 atoms each (i.e., a
total of 1008 atoms). For the (100) case we have used a nanowire of 21 layers
with 49 atoms per layer (i.e., 1029 atoms). Figure 1 shows the two initial
configurations corresponding to (111) and (100) nanowires. At the beginning of
the simulation, the velocity of each atom is assigned at random according to
the Maxwellian distribution that correspond to the simulation temperature.Initial configurations of (a) (111) and (b) (100) Ni nanowires.
(a)(b)The second stage corresponds to the relaxation of the
bulk-like initial structure. Firstly, we define two supporting bilayers at the
top and bottom of the supercell. Atomicx and y coordinates
within these bilayers will be kept frozen during
the simulation. The nanowire will remain attached to these two bulk-like
supporting bilayers during the relaxation stage. This stage lasts for 3000 MD
steps in order to optimize the geometry of the isolated parallelepiped-like
nanowire. Notice that the presence of both supporting frozen bilayers also
avoids the appearance of phase transformation upon loading as it has been
noticed for narrow Ni nanowires without such supporting bilayers [54].During the third stage (stretching process), thez coordinate of
those atoms forming the top (down) frozen bilayer
is forced to increase (decrease) a quantity ΔLz=10−4Å after every MD
step. This incremental process simulates the separation of the supporting
bilayers in opposite directions at constant velocity of 2 m/s, giving rise to the subsequent nanowire fracture. The
rest of the atoms move following the forces derived from their EAM-like
interaction with the surrounding atoms. Notice that the stretching velocity is
much larger than that used in experiments. However, our computational
description of the nanowire breaking is comparable to that of actual
experimental traces since the stretching velocity is smaller than the sound
speed in nickel.During the stretching stage, the accurate knowledge of
the atomic coordinates and velocities allows the determination of the minimum
cross-sectionSm. This quantity provides information on the favorable
configurations appearing during the nanowire evolution under stretching.
Furthermore, Sm provides a
first-order approximation of the conductance G [55, 56].The minimum cross-sectionSm is calculated
in units of atoms following standard procedures that have been successfully
used in previous studies [41, 42]. In our case, we define the radius r0 to be equal to
half the fcc (111)
interplanar distance (r0=d111/2). We assign a volume V0=4πr03/3 to each atom.
In order to calculate the cross-section Si at a given zi position, we
firstly compute the total atomic volume Vtot,i inside a
“detecting cursor” width Δz. We have used Δz=d111. The quantity Si=Vtot,i/V0 corresponds to
the nanowire section (in number of atoms) at the zi position. The
detecting cursor moves along the z-axis between
the two frozen bilayers, using a step equal to 0.1×d111. This allows to calculate the cross-section Si along the
nanowire. Finally, from the set of collected Si values, we
determine the minimum cross-section value Sm. Note that the cursor size Δz is kept fixed
independently on the nanowire crystalline direction along the z axis. This
allows a true comparison between histograms obtained for different
orientations, especially at the last breaking stages. In our study Sm is calculated
every 10 MD steps. We consider that the nanowire breaking process is completed
when Sm=0.


## 3. Results and Discussion

The evolution ofSm versus time
shows a typical staircase trace. In Figure 2 we show four examples of Sm(t) that illustrate
this behaviour. Sm(t) traces show a
stepped profile with well-marked jumps associated to atomic rearrangements occurring
at the nanowire. We have verified that these jumps are correlated with jumps in
the force acting on the supporting slabs. In general, Sm monotonically
decreases between two subsequent jumps reflecting the existence of elastic
stages. These elastic stages have been associated to the experimentally
observed conductance plateaus. As it is expected, Sm presents at RT
larger fluctuations than at 4 K. This has been observed for both stretching
orientations.Minimum
cross-sectionSm evolution of simulated breakage processes of Ni nanowires along the (111) (black curves) and
(100) (grey curves) stretching directions at 4 K (a) and 300 K (b).
(a)(b)In order to visualize the possible differences between
low and room temperatures and between (111) and (100) stretching directions, we
have depicted in Figure3 five atomic configurations for each trace shown in
Figure 2. Although it is very difficult to make comparisons among those
structural evolutions, we can see that, in general, the nanowires break-forming
three types of configurations at the last stage of the breaking process:
monomers, dimers, and others. The monomer structure is characterized by a
central atom standing between two pyramid-like structures. This configuration
usually shows a plateau around Sm∼1. In the dimer structure, the apex atoms of two
opposite pyramidal configurations form a diatomic chain. The third type of
final configurations presents more complex structures. In these cases we
generally observe an abrupt jump from Sm≥2 (i.e.,
structures formed by two or more atoms) to Sm=0. As expected [45], we have not found the presence of long atomic chains
(formed by three or more atoms).Figure 3
Snapshots at different evolution times of those nanowires whoseSm(t) traces were shown in Figure 2. Each column corresponds to a given combination of the
nanowire stretching direction ((111) or (100)) and temperature (T=4 K or
T=300 K). Each snapshot includes information on the simulation time and the
minimum cross-section Sm at that time.In our study we have found that monomer and dimer
structures usually appear for nanowires stretched along (111) direction. On the
contrary, more complex structures (i.e., not classifiable as monomers or
dimers) appear with higher probability at the latest stages of nanowires
strained along the (100) stretching directions.The minimum cross-section histogramsH(Sm) have been built
by accumulating Sm(t) traces acquired
during the simulation of hundreds of nanowire stretching processes. In Figure 4
we show the histograms H(Sm) for 4 K and 300
K, constructed with 300 independent breakages for the (111) and (100)
stretching directions. The different histograms are depicted in the range 0<Sm<12. A first inspection of these figures reveals the
existence of well-defined peaks associated to preferred nanowire configurations
as it has been shown in previous works [12, 34–37].Minimum cross-sectionSm histograms built with 300 independent Ni nanowire ruptures under stretching along the
(111) (a,c) and (100) (b,d) directions at T=4 K (a,b) and 300 K (c,d).
(a)(b)(c)(d)TheH(Sm) histograms
associated to the (111) stretching direction present a well-defined peaked
structure at low and room temperature. The main difference we have found
corresponds to the small increase of the peak located at Sm∼5 at RT. For the
(100) case, the low-temperature histogram presents a noisy structure whereas at
T=300 K the histogram peaks show rounded shapes and the general structure has
less noise. Small peaks at T=4 K correspond to metastable configurations with
slightly higher cohesive energies with respect to other metastable
configurations. The increase of temperature allows the exploration of more
configurations during the stretching process, and, in this way, those
metastable configurations with local minimum energy are easily accessible,
leading to a better definition of their associated H(Sm) peaks. In
addition, the (100) H(Sm) histogram
presents a well-marked Sm=5 peak at T=300 K.
We will discuss later the origin of this protruding peak which is not developed
at low temperatures.Our main finding is thatH(Sm) histograms are
very dependent on the stretching (i.e., the nanowire axis) direction. Whereas
the (111) direction provides histograms with well-defined decreasing peaked
structure in the low Sm region, the
situation dramatically changes when we consider the (100) direction. The later
case presents H(Sm) histograms with
small peaks in the region Sm<2. These differences between (111) and (100) stretching
directions are consistent with previously published results [37, 38].We have pointed out that the peak located atSm∼5 of the
histograms H(Sm) increases when
the temperature goes from T=4 K to RT. This increase is small for the (111)
case. The situation is rather different for the (100) case, noticing that this
peak increases a factor of 2 approximately (see Figure 4). The MD simulation
approach allows to monitor the evolution of the full set of atomic coordinates
during the breaking process. In order to know with more detail the origin of
the Sm=5 peak appearing
in the (100) case, we have depicted in Figure 5 a typical nanowire stretched
along the (100) direction. We have chosen a snapshot corresponding to the 4.5<Sm<5.5 region. It is
clear that the origin of the huge peak is related to the tendency of the system
to form long wires with Sm∼5. In general, this type of nanowires beaks without a
progressive diminishing of its atomic section, that is, the system does not form
monomers or dimers just before the rupture. At this point we should mention
that these long structures are very common for the (100) stretching direction.
However, these long rod-like structures appear seldom in the (111). This
smaller probability agrees with the slight increase detected for the H(Sm=5) peak when T
increases.Figure 5
Longitudinal (left) and cross-section (right) views of a nanowire stretched along the (100)
direction. The snapshot was acquired for an atomic configuration with minimum
cross-section close toSm∼4.6. The cross-section image shows a perspective view of
the nanowire as seen from the position indicated on the longitudinal view. This
image illustrates the appearance of staggered pentagonal structures –5–1–5–1–.A closer inspection to Figure5 allows to determine
the atomic structure of these long wires. We have found that these wires
present a well-defined sequence ⋯–5–1–5–1–⋯. This sequence does not correspond to any
crystallographic fcc or bcc structure. This type of arrangement is not seen at
4 K because a larger temperature is required to explore and overcome those
energy barriers leading to configurations able to develop these pentagonal
chains. In addition, we can easily see that these pentagonal nanowires are
formed by subsequent-staggered parallel pentagonal rings (with a relative
rotation of π/5) connected
with single atoms. A similar, but shorter, structure was found for Cu (111)
breaking nanowires using MD simulations [57]. The stability of such pentagonal Cu nanowires was
later confirmed by ab-initio calculations [58], demonstrating that staggered pentagonal nanowires
are favorable configurations. More recently, MD tight-binding calculations have
determined the presence of such pentagonal –5–1–5–1– nanowires during the
breaking process [59]
of (110) Cu nanowires although these pentagonal patterns were not frequently
observed for nanowires along (100) and (111) directions. Pentagonal motives
also appear in infinite Al nanowires [60]. Therefore, it seems that the formation in MD
simulation of staggered pentagonal Ni nanowires follows the trend observed for
other metallic species.We have checked that formation of staggered pentagonal
nanowires is favorable within the EAM scheme using the Mishin et al. potential.
In fact, we have found from a set of conjugate gradients geometry minimization
procedures that staggered nanowires present a cohesive energy of 3.66 eV per
atom whereas the cohesive energy of the nonstaggered configuration (without the
relative rotation ofπ/5) is 3.40 eV.
The optimized geometry of the staggered pentagonal Ni nanowire presents two
subsequent parallel pentagonal rings separated each other by a distance d5−5=2.22Å. The optimized pentagonal ring side takes the value l5=2.55Å. The geometry parameters we have found for those
pentagonal nanowires obtained from the stretching procedure present values of d5−5 and l5 very similar to
those obtained for the free pentagonal nanowire. We have also found, using MD
simulations, that the pentagonal nanowire structure is rather stable in the
temperature range 3–300 K.Therefore, it seems that the nanowire stretching along
the (100) direction provides some mechanisms that allow to reach this favorable
structures. In some sense, the stretching-induced formation of pentagonal
nanowires is very similar to the formation of linear atomic chains (LACs) where
single atoms are consecutively incorporated into the LAC from the stretched
nanowire before its final breakage [2]. However, the formation of pentagonal chains involves
units of 6 atoms (1 + 5 structures) and a full description of the underlying
mechanical process is a very complicated task that will be afforded in a deeper
study.


## 4. Conclusions

We have carried out hundreds of MD simulations of Ni
nanowire breaking processes using the EAM approach to describe the interatomic
many body interaction. From these simulations we are able to follow the
evolution of the nanowire minimum cross-sectionSm(t). By adding hundreds of Sm(t) traces, we have
constructed computational minimum cross-section histograms H(Sm) that statistically
unveil the presence of preferred configuration during the elongation and
breaking history. The last stages of the nanowire breaking process are of
special interest since electron transport is determined by a cross section
formed by few atoms. We have found that monomers, dimers, and other more
complex structures are present at the latest stages of the breaking events. We
did not find linear atomic chains of three or more atoms for all the systems
and stretching directions we analyzed.We have found thatH(Sm) histograms do
not depend dramatically on the temperature within the analyzed temperature
range (below 300 K). In general, we have only noticed rounding of the peaked
structure of H(Sm), the suppression of small Sm fluctuations,
and the increase of the peak located at Sm=5. This increase is larger for the (100) case. The
absence of large temperature effects is consistent with the fact that bulk Ni
melting temperature is rather large (≈1728 K), and then RT is not enough to activate additional
mechanisms as surface diffusion effects that could modify the nanowire breaking
dynamics.During stretching along the (111) direction, the
system tends to form a bipyramid structure that forms monomers and dimers at
the narrowest nanocontact region. These monomers and dimers give rise to theSm∼1 peak appearing in H(Sm).For the (100) stretching direction,H(Sm) does not
present large peaks in the low Sm region (Sm<2), thus indicating that monomers and dimers appear
with less probability than for the (111) situation. The nanowire is deformed
under stretching forming elongated (rod-like) structures. The formation of
these long structures increases when temperature increases from 4 K to RT. At RT
we found a dramatic increase of those peaks located at Sm∼5. We have confirmed that this peak is caused by the
presence of long staggered pentagonal chains with ⋯–5–1–5–1⋯ structures.
These pentagonal nanowires were also occasionally found for the (111) case
(giving rise to the increase of the peak H(Sm∼5)). In relation
with the formation of long chains in MD simulations, a recent work [61] points towards the higher
ductibility predicted by EAM potentials in comparison with other interatomic
potentials, leading to the formation of long structures. However, more detailed
statistical analysis is required in order to know the actual effects of the
chosen potential on the formation of elongated structures (including the
pentagonal ones we have described).In spite of our model limitations to perform the
comparison with experiments, we can extract few key ideas from the present MD
simulations. (i) The presence of well-markedH(Sm) peaks is
consistent with the appearance of preferred conductance values in the
conductance histogram. (ii) The behavior of H(Sm) at 4 K is rather
similar to that noticed at  T=300 K, and this implies that mechanical aspects do
not explain differences between low and room temperature experimental
conductance histograms. (iii) The first broad conductance peak appearing in
experiments is consistent with the presence of monomers and dimers appearing
during the last stages of the breaking process associated to (111) stretching
direction. (iv) We have detected the formation of long pentagonal nanowires at
RT for the (100) stretching direction. These structures contribute to the
formation of a large Sm=5 peak. However,
this large peak has not been observed in RT
experimental conductance histograms. At this point we must be cautious when
interpreting experimental conductance histograms, specially at RT, since the
complex behavior of Ni conductance histograms may be attributed to
chemiadsorbed atoms on the nanowire [26] or to ballistic magnetoresistence (BMR)
effects [19, 20].



---

*Source: 361464-2008-04-08.xml*