Tensile properties of monocrystalline gold film using molecular dynamics simulation

 ISSN 2354-0575
 TENSILE PROPERTIES OF MONOCRYSTALLINE GOLD FILM
 USING MOLECULAR DYNAMICS SIMULATION
 The-Van Tran, Anh-Son Tran
 Hung Yen University of Technology and Education
 Received: 21/01/2019
 Revised: 15/02/2019
 Accepted for publication: 05/03/2019
Abstract:
 In this paper, the tensile properties of the monocrystalline gold film are studied by using molecular 
dynamics simulation. The stress-strain relation, crack growth behavior and effects of different temperature 
are considered. The results show that the stress concentration is obviously distributed in the middle and 
corners of the specimen, leading to the cracks are formed and propagated in these positions. Under the 
tensile process, the transformation from the face-centered cubic (FCC) into hexagonal closest packed 
(HCP) structures occurred. From the stress-strain diagram, the tensile strength and Young’s modulus 
values decreased with increasing temperature. The RDF is decreased with a higher temperature.
Keywords: Molecular dynamics; tensile strength; monocrystalline gold.
1. Introduction 2. Methodology
 In recent years, crystalline metals have In this study, the effects of nanotension 
attracted intensive attention because of their on monocrystalline gold film are studied by
excellent mechanical properties. Many previous using MD simulations. Fig. 1 shows the physical 
studies investigated the mechanical properties sample of monocrystalline gold film used for the 
of crystalline metals by experimental methods. tensile simulation. The crystalline unit of the face-
However, as the size of the material decreases to centered cubic (FCC) Au substrate comprises x, 
the nanoscale, the use of experimental methods is y, and z-axes are directed along [100], [010], and 
not easy. With the rapid development of computer [001], respectively. The geometric dimensions are 
technology, molecular dynamics (MD) simulations approximately 2.04 nm (width) × 48 nm (length) 
have become more suitable than empirical methods × 35 nm (height). The two-dimensional (2-D) 
for studying the properties of nanomaterials. nanocrystalline nanomaterials are simulated in this 
Numerous processes have been investigated using study. In a real situation, 2-D nanomaterials can be 
MD simulations, including nanoindentation [1], patterned with different features at various scales. 
nanoscratch formation [2], nanotension [3], and These 2-D patterns have different geometries from 
nanowelding [4]. Among various test processes, three-dimensional (3-D) bulk nanomaterials. The 
nanotension is commonly used to analyze the 2-D model has been selected because it is simple 
deformation and mechanical properties of and nanofilms can be patterned. 2-D numerical 
nanocrystalline materials. models can be used with good accuracy instead of 
 Crystalline gold is widely applied in 3-D models if the in-plane stresses are primarily of 
electronic industries, for instance, the fabrication interest. It is expected to adequate for a qualitative 
of semiconductor, superconductor are used in investigation of the nanocrystalline films. The fixed 
electronic, optical, and magnetic applications. layers at the left and right sides of the sample along 
Therefore, the understanding of the mechanical the y-axis direction are set to a fixed thickness 
properties of crystalline gold is very important and of 6 Å. The lattice constant of gold is 4.08 Å, 
necessary for fabrication processes. the total numbers of atoms of the substrates are 
 In this paper, the author prepared approximate: 194,520. The periodic boundary 
monocrystalline gold film and focused to investigate condition is considered along the x-axis, while the 
the stress-strain relationship, deformation behaviors free-boundary condition is assigned to the z-axis. 
and crack nucleation of monocrystalline gold The tensile speed of the fixed layer in the y-axis 
film at room temperature. Besides, the effects of is fixed given unilaterally at 10 m/s until the set of 
different temperatures on the mechanical properties steps is completed. The movement is integrated by 
and the radial distribution function (RDF) of the velocity–Verlet algorithm with a time step of 2 
monocrystalline gold are also considered. fs.
Khoa học & Công nghệ - Số 21/Tháng 3 - 2019 Journal of Science and Technology 15
ISSN 2354-0575
 the material in the plastic zone. Finally, the strain 
 hardening stage is more likely to cause obvious 
 damage such as cracks and defects in the strain 
 hardening zone.
 It can be seen that the stress value rapidly 
 rises to the maximum value of 2.75 GPa at a strain 
 of 0.05. Then, the stress transmission is hindered 
 due to the displacement and the slippage, lead to 
 the decreasing of stress value. When the difference 
 or the slip condition rise up to a certain degree, the 
 stress value increases back to the relative value, 
 and gradually become zero as the strain increases. 
 The significant drop in stress value is due tothe
 formation of gaps, slips or void defects in the 
 specimen caused by the tensile process.
Figure. 1. Physical model of monocrystalline gold 
 film for the tensile simulation at room temperature
 The second–momentum approach of the 
many–body tight–binding (TB) potential [5] is 
used to express the Au–Au atomic interaction in the 
substrate. The TB potential is indicated as:
 i i
 EETB =+/ ()R EB (1)
 i
 -1
 ip- [rij /r0 ]
 EAR = / e (2)
 j
 -1 1
 iq22- [rij/r0 ] 2
 EeB =-{}/ p (3)
 j
 i i
where ER is the repulsive energy, EB is the attractive Figure 2. Stress-strain diagram of monocrystalline 
potential of atom i, rij is the distance between atoms gold film for the tensile simulation at 300K
i and j, and r0 is the first-neighbor distance. The 
four parameters ξ, A, p, and q are determined from Fig. 3 shows the stress distributions of the 
the cohesive energy experimental values, lattice monocrystalline gold film under different strains 
parameter, bulk modulus, and elastic constants, at 300 K. By comparison with Fig. 2, it can be 
respectively. The parameters for Au-Au interaction found that the deformation behavior of specimen 
are A = 0.189 eV, ξ = 1.743 eV, p = 10.400, q = in Fig. 3(a) at ε = 0.059 is within the elastic stage 
 range. The slight necking has occurred in the 
3.867, and r0 = 0.288 nm [6]. The used temperature 
is Kelvin temperature. four corners of the material, where the stress is 
 obviously observed. Transfer behavior is shown in 
3. Results and discussion Fig. 3(b). The strain value in the plastic stage, the 
3.1. Uniaxial stress-strain response and twin crystal phenomenon appears on the left side 
deformation behaviors of monocrystalline gold of the specimen. Similar to Fig. 3(a), the stress is 
film at room temperature concentrated in the four corners. In addition, the 
 Fig. 2 presents the stress-strain curve of the stress is segmented at the boundary of the 45° dotted 
monocrystalline gold film under tensile test at 300 line in the middle of the specimen. In Fig. 3(c), 
K. The phenomena can be roughly divided into the strain value is in the stage of strain hardening, 
three stages, namely the elastic stage, the plastic and the stress concentration position is formed by 
stage, and the strain hardening stage. In the elastic the extension of the boundary line appearing in 
stages, the deformation of substrate can still be Fig. 3(b). The cracking occurs due to stretching, 
restored to the original shape. The second stage is and the stress is continuously concentrated in the 
the plastic stage, which cannot be restored to the four corners of the specimen. The strain value is 
original shape of the material at the beginning, and also on the strain hardening stage, however, the 
16 Khoa học & Công nghệ - Số 21/Tháng 3 - 2019 Journal of Science and Technology
 ISSN 2354-0575
cracking damages from the corner and middle 
of the specimen are formed due to the very high 
value of intermediate stress concentration at these 
positions, as shown in Fig. 3(d). Due to the high 
local stress concentration in the corners and middle 
of specimens, the link between atoms is weakened. 
Therefore, the link breakdown occurs, leading to 
the cracks are formed. Slippage also occurs in the 
middle and it is a cause of cracking specimen. In 
addition, near the fixed layer end on the left side of 
the material, the twinning phenomenon is continued 
until the end during the tensile process.
 Figure 4. CNA diagrams of the monocrystalline gold 
 film under the tensile process at room temperature
 Fig. 4(d) presents the interesting phenomena. 
 When the strain is 0.360, the FCC structures are 
 extremely changed into HCP structures (position C) 
 due to the slip and steering caused by the intense 
 tensile strain. The stresses are very high and 
 concentrated in this area. In addition, the material is 
 fractured from the intersection of the 45° boundary 
 line in the middle and the right fixed layer from the 
 corner. The vertical dislocations still exist on the 
 left side of the specimen (position A).
 Finally, the transformation from the FCC 
 into HCP structures is mainly exhibited, the cracks 
Figure 3. The stress distributions of the monocrystalline occurred in the middle and corner areas of the 
 gold film under tensile process at 300 K specimen with the increasing of strain under tensile 
 process.
 Fig. 4 shows the common neighbor analysis 
(CNA) diagrams of the monocrystalline gold film 3.2. Temperature effects
under the tensile process at 300 K. Fig. 4(a) shows Temperature is a factor that greatly influences 
that the position of the slip is the same as the the deformation mechanism of the material. 
position of the stress distribution, which is formed Therefore, to obviously analyze the different 
from the four corners of the specimen. At a strain transitions in deformation mechanisms with 
of 0.156 in Fig. 4(b), a boundary is produced along increasing temperature, the substrate temperatures 
the 45° line in the middle of the material (position are respectively determined of 300, 500, 700, 900 
B), which could not be easily judged in the stress and 1000 K in this study.
map, the stress transmission is less obvious. The 
twin dislocation is evidently observed on the left 
side of the specimen (position A), which causes 
the different direction of the slippage, leading 
to the obvious change can be seen in the stress 
transmission. While the 45° boundary in the middle 
of the specimen only cuts off the original difference, 
there is no change the directionality, no obvious 
change in stress transmission. The twin dislocations 
are transferred into the vertical dislocations at a 
strain of 0.250 in Fig. 4(c). However, the stress 
transmission is still in the original direction and 
did not change following the shift of the row slip. 
In addition, the 45° boundary line can be clearly 
seen in the middle of the specimen. The stress is Figure 5. Stress-strain diagram of monocrystalline 
significantly concentrated on this line. gold films at different temperatures
Khoa học & Công nghệ - Số 21/Tháng 3 - 2019 Journal of Science and Technology 17
ISSN 2354-0575
 Fig. 5 illustrates the tensile stress-strain The RDF is calculated to give valuable 
diagram of monocrystalline gold films at different information about the structural disorder of the 
temperatures. When the strain is at about 0.04 - material to organize the structural analysis. The 
0.06 range, the corresponding stress is maximized. RDF diagram of monocrystalline gold films at 
Then, the stress is vibrated by the tensile alteration, different temperatures is shown in Fig. 6. Each 
resulting in the dislocation is distributed in the individual RDF curve shows a complete loss of the 
sample. On the other hand, Fig. 5 shows that the structural order of the material. The peak value of 
temperature is increased, the slope is decreased. That RDF decreased with the increasing temperature, 
means Young’s modulus is greater with the lower which means that the structural stability of the 
temperature. This phenomenon can be interpreted material increases with the decreasing temperature. 
by a larger amplitude of atoms fluctuating around It can also be presented that the material at lower 
its balance position at a higher temperature, which temperatures is relatively more stable due to the 
leads to that atomic bond is easier to be broken under motions of the atoms are weaker. This result is a 
applied load than lower temperature. In addition, the good agreement with a previous study by Hussain 
mobilization of preexisting dislocation generated et al. [9]
in diffusion bonding at high temperature also 
contributes to the lower yielding stress. The similar 4. Conclusion
results are found in a previous simulation study [7]. The tensile properties and deformation 
Atomic activity is more intensely enhanced and the behaviors of monocrystalline gold films are 
material is softer as increasing temperature, lead to investigated by using MD simulations. The 
the tensile strength decreases. The tensile strengths conclusions of this study are listed as follows:
are 2.75, 2.48, 2.20, 1.8 and 1.46 GPa at 300, 500, (1) The stress concentration is obviously 
700, 900 and 1000 K, respectively. distributed in the middle and the corners of the 
 specimen, leading to the cracks are formed and 
 propagated in these positions.
 (2) The transformation from the FCC into 
 HCP structures occurred under the tensile process.
 (3) The tensile strength and Young’s modulus 
 values decreased with increasing temperature.
 (4) The RDF decreased with the higher 
 temperature.
Figure. 6. The radial distribution function of 
 monocrystalline gold at different temperatures
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 TÍNH CHẤT CHỊU KÉO CỦA MÀNG NANO VÀNG ĐƠN TINH THỂ
 SỬ DỤNG MÔ PHỎNG ĐỘNG LỰC HỌC PHÂN TỬ
Tóm tắt:
 Trong bài báo này tính chất chịu kéo của màng nano vàng đơn tinh thể được nghiên cứu sử dụng 
mô phỏng động lực học phân tử. Mối quan hệ giữa sức căng và ứng suất, trạng thái mở rộng của vết nứt và 
những ảnh hưởng của nhiệt độ khác nhau được điều tra. Kết quả cho thấy ứng suất tập trung được phân bố 
chủ yếu ở giữa và tại các góc của mẫu, dẫn đến các vết nứt được hình thành và mở rộng tại các vị trí này. 
Dưới ảnh hưởng của quá trình kéo, sự chuyển đổi từ cấu trúc nguyên tử FCC thành cấu trúc HCP đã xảy 
ra. Từ biểu đồ sức căng và ứng suất, giá trị của độ bền kéo và mô đun đàn hồi giảm xuống khi nhiệt độ tăng 
lên. Chức năng phân phối xuyên tâm (RDF) của vật liệu cũng giảm dần với nhiệt độ cao hơn.
Từ khóa: Động lực học phân tử; độ bền kéo; vàng đơn tinh thể.
Khoa học & Công nghệ - Số 21/Tháng 3 - 2019 Journal of Science and Technology 19