process, while it plays the role of enhancing the mobility of Ag shell atoms. .... CS nanostructures, radius of Cu core and length of CS NW respectively and aAg is ...
Contributed Papers from Materials Science and Technology 2016 (MS&T16) October 23 – 27, 2016, Salt Palace Convention Center, Salt Lake City, Utah USA Copyright © 2016 MS&T16®
ROOM TEMPERATURE MOLECULAR DYNAMICS SIMULATIONS ON THE SINTERING OF Cu-Ag CORE-SHELL STRUCTURES: NANOPARTICLES AND NANOWIRES Jiaqi Wang, and Seungha Shin* Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN, 37996-2210, USA. Keywords: Molecular Dynamics Simulation, Sintering, Core-Shell, Nanoparticles, Nanowires Abstract
Atomistic understanding of sintering mechanism is conducive to improve industrial applications such as printable nanoinks, electrodes, and catalysts. Nanojoining by sintering of nanoparticles and nanowires with different geometries are examined at room temperature (300K) with molecular dynamics simulations. The evolution of potential energy and local crystalline structure during sintering process are analyzed to identify sintering mechanisms. Depending on geometry, different sintering mechanisms including crystallization-amorphization, rotation, Shockley partial dislocation are detected. In all simulation cases, Cu core does not participate in sintering process, while it plays the role of enhancing the mobility of Ag shell atoms. In nanowire sintering, a three-stage scenario is also observed, similar to that of core-shell NP sintering. The Young’s modulus and yield strength of sintered nanowire obtained from tensile test are different from the reported values since they depend on many other parameters, such as NW size, strain rate, and temperature. Introduction
Ag nanomaterials have been broadly used in printed electronics [1] and electronics packaging [2] because of their high thermal and electrical conductivity as well as oxidation stability [3]. However, the high cost of Ag has hindered the commercial promotion of such nanotechnologies. As an alternative to Ag, Cu has been positively considered since the price of Cu nanopowder is much lower than that of Ag and it has comparable thermal and electrical conductivity. In order to prevent the oxidation of Cu nanostructures, a Cu-Ag core-shell (CS) nanoparticle (NP) is conceived and synthesized by researchers [1, 4]. In electronics packaging, Ag is used as a nanopaste to achieve joining with other devices through sintering [5]. The room-temperature sintering process does not involve heating at the interface. Therefore, the joint quality of the sintered structure is high due to its lack of local heating, which may cause damage to the sintered structures [6]. However, according to our best knowledge, nobody has conducted research on sintering process of Cu-Ag CS NP or nanowire (NW). Due to the existence of Cu core, mobility of shell atoms will be enhanced, distinct coalescence process and properties of final sintered structures are also expected.
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In the present work, we conduct theoretical analysis on sintering process with molecular dynamics simulation. After this introduction, the next section presents simulation and analysis methodology. In the Results and Discussion, sintering of NP with different geometries and sintering of two NWs are discussed. To test the reliability of the joint in the sintered NW, a uniaxial tensile test is performed to obtain Young’s modulus and yield strength. At last we present conclusions and perspectives. Methodology MD Simulation Implementation
The constructed embedded atom method (EAM) potential is selected as the force field to describe the interactions between Cu and Ag atoms. This EAM potential is constructed by Williams et. al [7], through combining the existed EAM potential for Cu and Ag, respectively. Pure Ag NP, Cu-Ag CS NP and Cu-Ag CS NW are modelled and used as our simulation subjects. Before sintering simulation, each nanostructure is relaxed at 300 K for 50 ps, so as to eliminate any effect induced by the instability of initial structures. Sintering simulations are conducted in NVT canonical ensemble (constant number of atoms, system volume and temperature) with Nosé-Hoover thermostat for keeping the sintering system at room temperature. Periodic boundary condition (PBC) is applied. The equations of motion are integrated with time step of 1 fs, using the Verlet algorithm. The duration of sintering simulation is 500 ps. For studying the mechanical properties of the NW sintered joint, a uniaxial tensile test is performed with a constant engineering strain rate of 0.03 ps-1. The stress tensor of each atom in x direction is calculated and summed every 0.2 ps. All aforementioned simulations of sintering and tensile test are conducted with LAMMPS code [8]. Analysis Method
In this research, potential energy (PE, E p ) evolution is analyzed to determine the sintering mechanisms. Shrinkage (ζ) characterizes the sintering process, and indicates the sinterability and bonding strength. It is defined as the ratio of change in distance of centers of mass (ΔL) to initial distance (L 0 ), equivalent to the sum of two sintered NPs’ radii or the length of the NW. Neck size is also measured where the curvature is the largest among the circumference.
The evolution of local atom orders is identified through the common neighbor analysis (CNA) [9], Usually, two atoms are regarded as bonded, if their distance is less than a specified cutoff radius r cut ; e.g., for FCC structures, the cutoff radius is set to be halfway between the first and second neighbors. The obtained cutoff radii for Ag and Cu are 3.491 and 3.081 Å, respectively. Local orders of atoms are classified into three categories: (1) FCC (atoms in a local FCC order), (2) Hexagonal closed packed (HCP, atoms in a local HCP orders), and (3) amorphous (atoms in all other local orders). A single HCP layer in the FCC crystal are regarded as twin boundary (TB), while two HCP layers are considered to be stacking fault (SF) [10].
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Results and Discussion Sintering of Pure Ag and Cu-Ag CS NPs 2rcs=6aAg 2rc=3aAg
2rcs=6aAg 2rc=0
(a)
Pure Ag NP: Ag6Cu0
(b)
2rcs=5aAg
LNW=20aAg
2rc=2.5aAg
Cu-Ag CS NP: NPAg6Cu3
(c)
Cu-Ag CS NW: NWAg6Cu3
Figure 1. Initial configures of (a) pure Ag NP (NP-Ag6Cu0), (b) Cu-Ag CS NP (NP-Ag6Cu3), (c) Cu-Ag CS NW (NW-Ag5Cu2.5) for sintering simulations. Here r cs , r c and L NW are radius of CS nanostructures, radius of Cu core and length of CS NW respectively and a Ag is the lattice constant of Ag, equivalent to 4.0853 Å. Pure Ag NP is also denoted as a CS NP with a core radius of 0.
Sintering process of three pairs of NPs are investigated, they are Ag6Cu0-Ag6Cu0 (Pair1), Ag6Cu3-Ag6Cu0 (Pair2), and Ag6Cu3-Ag6Cu3 (Pair3) respectively. The detailed geometries of the nanostructures are show in Fig. 1. To eliminate the effect of facets, the two NPs are placed to each other, facing orientation with a separation distance of 4 Å, which is still within the cutoff range of the EAM potential. 0.15 Ag6Cu3-Ag6Cu3 0.12
ζ (∆L/L0)
Ag6Cu3-Ag6Cu0 0.09 0.06 Ag6Cu0-Ag6Cu0
0.03 0.00 0
100
200 300 Time (ps)
400
500
Figure 2. Shrinkage evolution of three pairs of NPs during sintering process. The sintered structures at 500 ps are also shown. The color scheme is the same as Fig. 1.
Figure 2 shows the shrinkage evolution of three NP pairs during sintering for 500 ps. The shrinkage is measured at the onset of sintering (two NPs start to have point contact). After 500 ps,
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the final shrinkages of Pair1, 2 and 3 are around 0.060, 0.075, and 0.120, respectively. The neck sizes of Pairs1, 2 and 3 are also measured as 19.33, 23.67 and 27.23 Å, which coincide well with the shrinkage. Obviously, the NP Pair3 yields highest shrinkage and neck size. As is known, the thermodynamic driving force for sintering is the reduction of surface energy, and it increases exponentially when a particle size decreases to nanoscale [11]. It can be assumed that with larger shrinkage and neck size, the reduction of surface area will also be larger; i.e., the reduction of surface energy will be larger. Thus, we checked the PE to see whether the calculated neck size and shrinkage coincide with the PE evolution and reduction.
PE evolutions of Ag shell and Cu core during sintering at room temperature are shown in Fig. 3. Initial PE of three pairs is: PE Pair1 < PE Pair2 < PE Pair 3 . As a result, the Ag atoms in NP Pair3 has the strongest propensity of reducing the energy to reach the minimum-energy state. This also indicates that the Ag shell atoms in NP Pair3 have the highest mobility. The PE of Ag shell decreases dramatically once the sintering initiates, resulting from the annihilation of free surface. However, before the PE reaches equilibrium, it vibrates a lot due to the structural deformations. As Fig. 3(b) shows, the PE of Cu core does not show obvious decrease during the sintering, due to the fact that the Cu atoms do not participate in the sintering under MP. Therefore, the PE reduction (ΔE p ) of the whole system is mainly contributed by Ag shell. To compare the PE change of the sintering system, the changes in the PE normalized by the initial PE before sintering at 300 K is plotted in Fig. 3(c). It reveals that the PE drop of NP Pair3 is larger than NP Pair1 and Pair2. This validates our previous finding that the NP Pair3 has the largest shrinkage and neck size. -2.650
(c)
(b) -3.400 Ag6Cu3-Ag6Cu0 Ag6Cu3-Ag6Cu3
Ep of Cu (eV/atom)
Ep of Ag (eV/atom)
Fig. 5(V) -2.675 Fig. 5(III) Fig. 5(I)
-2.700
Ag6Cu0-Ag6Cu0 Ag6Cu3-Ag6Cu0 Ag6Cu3-Ag6Cu3
-3.425
-3.450
-3.475
-2.725 0
100
200 300 Time (ps)
400
500
∆Ep of the sintering system (%)
(a)
0.0
Ag6Cu0-Ag6Cu0 Ag6Cu3-Ag6Cu0 Ag6Cu3-Ag6Cu3
-0.1 -0.2 -0.3 -0.4 -0.5
0
100
200 300 Time (ps)
400
500
0
100
200 300 Time (ps)
400
500
Figure 3. Potential energy (PE, E p ) evolution of (a) Ag and (b) Cu in three NP pairs during sintering process. In NP Pair1, the PE of Cu is 0. (c) Normalized potential energy reduction (ΔE p ) of sintering system at 300 K verse sintering time.
To have a comprehensive understanding of sintering process, especially the initial neck formation and growth process, the structural deformation is characterized with respect to the PE evolution (Fig. 4). Before the onset of sintering for all pairs, the two NPs are attracted to each other by interatomic force. As they make contact with each other (i.e. neck formation), the PE energy drops quickly since the initial neck growth is very fast. It can be generalized that that duration from point a to b, g to h, and n to o is neck formation and fast growth (Stage I). In NP pair1 and 2, crystallization during Stage I [point b, Fig. 4(II); point h, Fig. 4(IV)] is observed. As a result, the PE reduction in Stage I of NP pair1 and 2 is partially contributed by the
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crystallization of the neck region. PE increases after Stage I (point b to c, h to i, and o to p), caused by amorphization of pre-crystallized atoms in the neck region. In NP Pair1, obvious clock-wise rotation of the left NP occurs [point c, Fig. 4(II)]. Afterwards, the left NP rotates anticlockwise, recrystallizes and reduces the PE [point c to d, Fig. 4(I)]. Also, SF forms with two adjacent planes of HCP atoms [point d, Fig. 5(II)], after nucleation and propagation of a Shockley partial dislocation through FCC crystal according to the theory of crystal dislocations. This SF is stable and does not disappear in the following sintering process. In NP Pair2, the rotation is not obvious; however, it does follow the similar pathways to recrystallize [point j, Fig. 4(IV)] and lower the PE [point i to j, Fig. 4(III)]. In NP Pair3, SF forms with two adjacent (111) planes of HCP atoms as well [point q, Fig. 4(VI)]. The SF has higher energy than FCC crystalline structure but less energy than amorphous structure, causing the PE reduction from point p to q. However, this SF is transient and gradually eliminated by the following adjustment of atom positions. After the recrystallization, shrinkage regression is observed in all NP pairs. This is because the NP approaches each other with high speed, resembling elastic collision behaviors. As a result, the NPs bounce back, increasing the surface area of the two NPs. Consequently, the PE increases a little bit [point d to e, j to k, and q to r respectively]. After -2.706
(I)
Ep of Ag6Cu0 (eV/atom)
a
Ag6Cu0-Ag6Cu0
-2.708
III
II
I
c
e
-2.710
-2.712
f
b d -2.714 0
10
20
30
40
50
60
Time (ps)
-2.665
g
Ag6Cu3-Ag6Cu0
(III)
Ep of Ag (eV/atom)
I
II
III
i
-2.670
k -2.675
h
j
m
-2.680 0
10
20 30 Time (ps)
40
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-2.656
n
Ag6Cu3-Ag6Cu3 II
(V)
Ep of Ag (eV/atom)
I -2.660
p
III
r
-2.664
o
q
-2.668
s -2.672 0
20
40
60
80
100
Time (ps)
Figure 4. (I) Potential energy (E p ) evolution of sintering processes of three NP pairs. (II) Characteristic structural deformation at each instant. The color scheme is the same as Fig. 1. that, the NP Pairs1 and 2 reach equilibrium [point f, Fig. 4(II); point m, Fig. 4(IV)] within a short time (around 10 ps), while the NP Pair3 takes much longer time (around 44 ps) to reach stable. We characterize the process from point b to f, h to m and o to s as transient neck formation stage (Stage II), while the sintering process after point f, m and s are equilibrium stage (Stage III). During Stage II of NP Pair3, the two NPs are continually approaching to each other after the shrinkage regression induced by the higher diffusivity of neck-region shell atoms, causing the gradual reduction in PE. Therefore, it yields larger shrinkage and neck size. During the equilibrium stage (Stage III), all NP pairs are repeating the bouncing behavior along the shrinkage direction, resulting in the oscillation in shrinkage. Sintering of Cu-Ag CS NWs
Normal welding through sintering involves high temperature and molten liquids. However, in this research we investigate the cold-welding of NWs at room temperature without heating and compressing. Two CS NWs are placed next to each other in an end-to-end configuration with a separation distance of 4 Å, similar to the initial configuration of two NPs. Fig. 5 shows the structural evolution of NW during welding process. A three-stage sintering scenario is proposed by the shrinkage and PE curves as shown in figure 6, which is divided by sintering rate indicated
Figure 5. Snapshot of end-to-end welding of two CS NWs. Image (t) shows onset sintering, in image (u), a neck with size of NW diameter can be see. Image (v) shows the formation of
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stacking faults. In the final sintered structure (w), stable SF is observed, which are defects detrimental to electrical and thermal properties. The color scheme is the same as Fig. 1. by slopes of both curves. Amorphous atoms located in two ends quickly crystallize in Stage I, reducing the surface energy from point t to u. Process from (t) to (u) occurs faster than any other process since it does not require thermal activation, instead it is driven by large intrinsic atomic force. A joint with size of NW diameter is formed at (u), and interestingly, the neck size is not enlarged in the following welding process although the NWs are still approaching to each other. After the joint formation, several SF are observed in Cu core, circled in Fig. 5(v), which increases the PE. Contrarily, SF formation is not distinguishable in Ag shell, thus the PE increment of Ag shell is not obvious either. After Stage I, NWs slow the sintering rate. In the final sintered structure, defects like stacking faults can be observed, which can deteriorate electrical and thermal transport properties. Research on the calculation and improvement of properties of the final sintered structures are also underway. Figure 6(c) is the stress-strain curve of the sintered NW. As the simulation box deforms in x dimension, the NW also elongates in x direction, and before 1.2 ps, it is elastic deformation. The Young’s modulus (YM) is determined as 8.29 GPa by fitting the curve within the elastic deformation, while the yield strength (σ y ) of the NW is determined as 0.43 GPa. Since the stresscurve is strain-rate, temperature and size-dependent, the obtained YM is much lower than the bulk counterparts, which means the NW is very easy to deform under present conditions. Once the strain goes over the elastic deformation regime, the NW shows very obvious elongation and necking forms at 35 ps. At last, the NW breaks at 51.2 ps. Surprisingly, the NW is fractured at different point from the joint, suggesting that the resistance to rupture at the joint can be higher than the CS NW itself.
I
Ep of Cu (eV/atom)
0.15
Cu Ag
0.10
v -2.64
-3.425
w
20
20
200
73
-2.65
u
-3.430
0.05
0
100
200
300
Time (ps)
400
500
0
σy 0.4
necking
0.3 fracture
Slope = 8.28879 0.2 0.1
73
200
-3.435
0.00
0.6 0.5
-2.63
-3.420
(c)
-2.62
III
-3.415
0.20
ζ (∆L/L0)
II
I t
III
II
Stress (GPa)
(b) -3.410
0.25
Epof Ag (eV/atom)
(a)
100
200
300
Time (ps)
400
-2.66 500
0.0 0.0
0.4
0.8
1.2
1.6
Strain
Figure 6. Evolution of (a) Shrinkage (ζ) (b) Potential energy (PE, E p ) of both Ag shell and Cu core during cold welding process. A three-stage sintering scenario can be observed (indicated by I, II, and III). (c) stress-strain curve. The yield strength (σ y ) is determined as 0.43 GPa and the Young’s modulus is 8.29 GPa. Conclusions
Sintering processes of Cu-Ag core-shell nanoparticles and nanowires are evaluated from the energetic perspective. A three-stage sintering scenario is determined for all nanostructures,
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depending on the sintering rate indicated by the slope of shrinkage curve. Compared with pure Ag nanoparticle, Cu-Ag core-shell nanoparticle can enhance the mobility of the Ag shell atoms; thus resulting in higher sinterability and joint strength. The obtained Young’s modulus of the NW indicates that the Cu-Ag core-shell NW is easy to deform. For additional enhancement in the Cu-Ag CS NP or NW sintering and more comprehensive evaluation of the structure, the morphology and crystallographic orientation effects on the sintering mechanisms, mechanical, thermal and electrical properties of the sintered structures, as well as quantum size effects in small clusters can be further studied. References [1] C.K. Kim, G. J. Lee, M.K. Lee, and C.K. Rhee, “A Novel Method to Prepare Cu@Ag Core– Shell Nanoparticles for Printed Flexible Electronics”, Powder Technology, 263 (2014), 1-6. [2] A. Hu, J.Y. Guo, H. Alarifi, G. Patane, Y. Zhou, G. Compagnini, and C.X. Xu, “Low Temperature Sintering of Ag Nanoparticles for Flexible Electronics Packaging”, Applied Physics Letters, 97 (2010), 153117. [3] D. Kim, and J. Moon, “Highly Conductive Ink Jet Printed Films of Nanosilver Particles for Printable Electronics”, Electrochemical and Solid-State Letters, 8 (2005), J30. [4] H.T. Hai, J.G. Ahn, D.J. Kim, J.R. Lee, H.S. Chung, and C.O. Kim, “Developing Process for Coating Copper Particles with Silver by Electroless Plating Method”, Surface and Coatings Technology, 201 (2006), 3788-3792. [5] H.A. Alarifi, M. Atis, C. Özdoğan, A. Hu, M. Yavuz, and Y. Zhou, “Molecular Dynamics Simulation of Sintering and Surface Premelting of Silver Nanoparticles”, Materials Transactions, 54 (2013), 884-889. [6] C.D. Wu, T.H. Fang, and C.C. Wu, “Effect of Temperature on Welding of Metallic Nanowires Investigated Using Molecular Dynamics Simulations”, Molecular Simulation, 42 (2015), 131-137. [7] P.L. Williams, Y. Mishin, and J.C. Hamilton, “An Embedded-Atom Potential for the Cu–Ag System”, Modelling and Simulation in Materials Science and Engineering, 14 (2006), 817-833. [8] S. Plimpton, “Fast Parallel Algorithms for Short-Range Molecular Dynamics”, Journal of Computational Physics, 117 (1995), 1-19. [9] Y. Tamura, and N. Arai, “Molecular Dynamics Simulation of the Melting Processes of Core– Shell and Pure Nanoparticles”, Molecular Simulation, 41 (2014), 905-912. [10] S. Jiang, Y. Zhang, Y. Gan, Z. Chen, and H. Peng, “Molecular Dynamics Study of Neck Growth in Laser Sintering of Hollow Silver Nanoparticles with Different Heating Rates”, Journal of Physics D: Applied Physics, 46 (2013), 335302. [11] Z.Z. Fang, and H. Wang, “Densification and Grain Growth during Sintering of Nanosized Particles”, International Materials Reviews, 53 (2013), 326-352.
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