World Journal Of Engineering
Mechanical behavior of metallic nanowires containing vacancy cluster defects
Pei-Hsing Huang, Lay Gaik Teoh, Yu-Ren Wu, Ming-Yue Huang, Hong-Yi Li
Department of Mechanical Engineering, National Pingtung University of Science and Technology, Taiwan.
phh@mail.npust.edu.tw
mechanical responses of a stretched NW. The detailed
simulation domains and mechanical deformations are
illustrated in Fig. 1.
Introduction
Since NWs are often used in complicated mechanical
surroundings [1,2,3], a thorough understanding of their
mechanical behavior is crucial for the design of functional
nanowire-based devices. However, when the dimensions of
the system become comparable to or smaller than the critical
size, the macroscopic continuum theory is inadequate for
predicting the mechanical behavior of NWs due to the
coupled effects of the large surface area to volume ratio
[4-6], anisotropic orientation dependence [5,7], and particle
confinement (including electrons and phonons) [3,8].
Exploring the microscopic mechanisms of the structural
evolution of NWs via experimental methods is challenging
because the critical stress generally occurs within a very short
period, which is within several picoseconds (ps) of the
natural vibration of an atom [9,10]. Therefore, molecular
dynamics (MD) study of the microscopic deformation and
mechanical behavior of NWs is required.
The effects of vacancy defects on the mechanical
behavior of nanowires are largely unknown. The present
study explores the coupled influences of VC defects,
operating temperature, and applied stress on the deformation
behavior of stretched Cu NWs using molecular dynamics
with the embedded-atom method (EAM) [11]. Elastic and
plastic behaviors related to the stretching of defective NWs,
including investigations of the microscopic mechanisms of
incipient yielding, the evolutions of plastic flow and transient
structure, stress-strain behavior, Young’s modulus, and
eventual fracture patterns, are analyzed.
Fig. 1 Schematic illustrations of atomic diagrams of Cu
nanowires containing various patterns of cluster defects,
including (a) single atomic-vacancy (VC1), (b) octahedral
vacancy cluster (VC6), and (c) octahedral vacancy cluster
(V19). Atoms are color-coded according to the value of their
potential energy in eV.
Numerical method
In the presented work, the generalized EAM potential
developed by Wadley et al. [11] is used because it can well
fit the basic material properties (such as the lattice constant,
the elastic constant, the bulk modulus, the sublimation
energy, and the heat of solution). More importantly, this
potential accurately expresses the vacancy formation energy,
which is crucial for analyzing the effect of VCs on the
mechanical behavior of a defective NW.
Cu NWs oriented along the [100] direction with an
initial length of 108.1 Å and a square cross-section were
studied, as shown in Fig. 2. Three cross-sectional
dimensions of the Cu NWs were adopted: (1) 18.1×18.1Å,
(2) 25.3×25.3Å, and (3) 36.1×36.1Å. The corresponding
FCC unit cells in the x, y, and z directions are (1)
30a0×5a0×5a0, (2) 30a0×7a0×7a0, and (3) 30a0×10a0×10a0,
respectively, where a0 (= 3.615 Å) denotes the lattice
constant of Cu. Three designated patterns of the vacancy
cluster were adopted: (1) single atomic-vacancy (VC1), (2)
octahedral vacancy cluster (VC6), and (3) octahedral
vacancy cluster (V19), where the subscripts denote the
number of atomic vacancies (see insets of Fig. 1). These
vacancy clusters were singly embedded inside of wires in
order to analyze the effect of vacancy clusters on the
The NW was thermally equilibrated at a given
operating temperature using Gauss's principle of least
constraint [12] for 50 ps. The equilibrium state of a NW was
determined by allowing the volumetric contraction to
saturate; this process is a function of the thermal relaxation
time. After the Cu NW reached the equilibrium state, a
uni-axial tensile loading at a constant true-strain rate of
8×108 s-1 along the x-direction was applied to the Cu NW as
follows: (1) one end of the Cu NW was fixed; (2) uni-axial
loading was applied to the other end of the Cu NW; (3) a
ramp stretch profile, which prevented shock waves from
being emitted at the fixed end of the Cu NW, was created by
assuming that the displacement of atoms linearly increases
along the loading direction from zero (at the fixed end) to a
maximum value (at the free end). Moreover, to investigate
the role of temperature in tensile deformation and
mechanical behavior, the system was assumed to experience
isothermal loading by idealized heat transfer to a
surrounding medium. Moreover, the atomic potential and
intermolecular forces of the system were derived in each
computational time step of ∆tMD = 5 fs. The neighbor list
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World Journal Of Engineering
trend is consistent with the reports by Liang and Upmanyu
[6]. Based on the simulation results, the formalization of
Young’s modulus (EY /Ebulk) as a function of
cross-sectional area and temperature of NWs can be
approximated in the analytic form as follows:
method with an appropriate list radius of 2.8 re (where re
denotes the equilibrium spacing between nearest neighbors)
was employed to decrease computational time. The velocity
and acceleration of atoms were accurately estimated and
updated using Gear’s fifth-order predictor-corrector
algorithm [13].


2
EY / Ebulk  0.8636e ( C A / S A )  0.3678  CT T  8.5434
(1)
where SA and T are the cross-sectional area and operating
temperature of the nanowires. CA denotes the size parameter
with a value of 3.267 nm2, and CT = 3.9527×10-4 K-1 is the
fitted coefficient of temperature.
Results and Discussion
Fig. 2(a) and (b) show the plots of stress (ordinate)
versus strain (abscissa) of stretched wires containing a VC6
vacancy cluster for various cross-sectional areas and
operation temperatures. As shown, for a given wire sectional
area, yield strength largely decreased with increasing
operation temperature. In elastic deformation ranges, the
slope of the linear segment distinctly increases with
decreasing operation temperature, indicating that the
Young’s modulus greatly depends on operation temperature.
Fig. 2(c) show that the stress-strain curves for a perfect wire
and wires with various vacancy cluster sizes. The
stress-strain curves are overlapped during elastic
deformation, indicating that the elastic modulus is
independent of the vacancy cluster defects.
Fig. 3 Young’s moduli as a function of operating temperature
for various wire cross-sectional areas.
Conclusion
A structural imperfection can increase atomic potential
energy and facilitate crystalline slip under critical stress.
Extensive atomistic simulations of the mechanical
deformation of defective NWs were performed using the
embedded-atom molecular dynamics modeling approach.
The stress-strain behaviors show that the elastic modulus is
independent of the vacancy cluster defects. Quasi-linear
decreasing Young’s moduli were observed with increasing
operation temperature. For a given operation temperature,
NW Young’s modulus increased with increasing NW size.
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Fig. 2 Stress-strain behavior of tensile stretching of defective
NWs for various vacancy defect sizes
Fig. 3, shows the Young’s moduli as a function of
operation temperature for a given NW sectional area. NW
Young’s moduli decreased with increasing operation
temperature. Simulation results show that NW Young’s
moduli are smaller than that of bulk copper (110 GPa) [14],
which is mainly due to the de-cohesion effect of the surface
atoms; at this size scale, the nanowires consist of about
22-38 % surface atoms. The modulus of elasticity values for
[100] Cu nanowires increase with increasing wire area. As
the cross-sectional size of the nanowires increases, the
Young’s modulus gradually approaches the bulk value. This
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