Supplementary material for: Nanoscale metal-metal contact physics
from molecular dynamics: the strongest contact size
Hojin Kim and Alejandro Strachan
School of Materials Engineering and Birck Nanotechnology Center
Purdue University, West Lafayette, Indiana 47907, USA
The following document contains supporting information regarding simulation cells used
and the analysis of the molecular dynamics trajectories as well as details of the analysis
of experimental data to compare with the MD predictions.
Supplementary Table 1. Details of MD simulation cells
Orientation
(001)
(111)
Incommensurate
Slab size (nm)
Total
Ncycle
9.8×9.8×20
atoms
233208
23
14.9×14.9×20
538960
13
24.7×24.7×20
1481640
8
39.2×39.2×20
3731496
7
49×49×20
5833496
2
98.1×98.1×20
23333984
1
10.1×9.99×20
252244
25
14.9×14.98×20
558584
16
24.99×24.97×20
1562360
9
49.84×49.95×20
6249112
5
99.97×99.89×20
24997808
1
10.6x10.6x20
27782
25
14.98x14.98x20
557620
18
Peak to peak distances of asperities for surface roughness are determined by half of the
x and y simulation cell size in each simulation cell. In order to simulate incommensurate
contact mode of (001) surface for the results of pullout force shown in Fig. 2 of our
paper, the top platinum slab was relatively rotated by 45° in the xy plane, creating a
[110] orientation.
MD simulation analysis: effective contact area calculation
After identifying the thinnest region of the contact along the z axis we extracted the x and
y positions of atoms in the region and marked their projected area in a square grid with
spacing 0.5 Å using an atomic radius of 1.97 Å. All unmarked grid points surrounded by
atoms were considered part of the contacts. The total effective contact in simulation cell
is then obtained from the number of occupied grid spaces (Ngrid) as Acontact = Ngrid×Agrid,
where Agrid is 0.5×0.5 Å2. The contact length (lc) used in article is the square root of
averaged contact area per asperity.
MD simulation analysis: classification of atoms
In order to study the sub-surface defects responsible the mechanical response of the
contacts atoms are classified in terms of: i) Their coordination number (the number of
nearest neighbors) using a cutoff distance of 3.3 Å; ii) The centrosymmetry parameter
(P)[S1, defined as P 
r r
i 1, 6
i
i 6
2
where ri and ri+6 are the vectors corresponding to the
six pairs of opposite nearest neighbors in the fcc lattice. Atoms with a centrosymmetry
parameter P<5 are labeled as fcc; atoms with centro-symmetry parameter P>14 or with
less 12 nearest neighbors are considered surfaces atoms with the remaining atoms
being labeled as hcp.
Calculation of contact area of AFM experiment
The AFM experiments [S2] measured a pull-out force of 19-21 nN was necessary to
open a nanoscale contact between approximately spherical Au asperities. In order to
compare the results with our simulations we need to estimate the effective contact area
in the experiment. To do so we use the applied closing force (estimated from Fig. 15 in
Ref. S2) to be ~18 nN) and an equation for the contact area between two elastic spheres
[S3],
AE  R
FE 
4 '
E R ( ) 3 / 2
3
where
1 1   12 1   22


E1
E2
E'
1
1
1


R R1 R2
and E1,ν1, R1 E2, ν2,R2 are the elastic properties and radii of sphere 1 and 2. The
parameters used to calculate the contact area are in Supplementary Table 2. (Table 3 in
Ref. S3)
Supplementary Table 2. Parameters used in calculations of contact area in AFM
experiment
E (GPa)
ν
R2 (nm)
R1 (nm)
Fad (nN)
112
0.44
60
40
19 ± 5
59
21 ± 3
Using the curvatures of the two spheres we obtain a contact area of ~10 nm2 that is
shown in Fig. 2 of our paper.
Supplementary Figures
Supplementary Figure 1. Snapshots of the first contact cycle for (111) contacts
with different sizes and at various times. The strongest contact size is shown in the
middle column. Red and blue spheres denote surface and hcp atoms respectively. Top
row corresponds to closed contacts and middle one to the beginning of opening. Bottom
row shows the increase of dislocation density during opening.
REFERENCES
[S1] C. Kelchner, S. J. Plimpton, J. C. Hamilton, Phys. Rev. B 58, 11085 (1998).
[S2] A. Zong et al., J. Appl. Phys. 100, 104313 (2006).
[S3]. V. Krithivansan, R. L. Jackson, Tribology Lett. 27, 31 (2007).