Supplementary material for Nanoscale metal-metal contact physics from molecular dynamics the strongest contact size

Supplementary material for: Nanoscale metal-metal contact physicsfrom molecular dynamics: the strongest contact size Hojin Kim and Alejandro Strachan School of Materials Engineering and

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 Slab size (nm) Total

atoms

Ncycle

(001)

9.8×9.8×20 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 2333398

4

1

(111)

10.1×9.99×20 252244 25 14.9×14.98×20 558584 16 24.99×24.97×2

0

1562360 9 49.84×49.95×2

0

6249112 5 99.97×99.89×2

0

24997808 1

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 (l c) 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 2

6 , 1

6











i

i

i r r

P where r i and r i+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 SError: Reference source not found) to be ~18 nN)and an equation for the contact area between two elastic spheres [S3],

2 / 3 ' ( )

3

4







R

E

F

R

A

E

E





where

2

1

2

2 2 1

2

1

'

1

1

1

1 1

1

R

R

R

E E

E











and E 1,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 SError: Reference source not found)

Supplementary Table 2 Parameters used in calculations of contact area in AFM

experiment

E (GPa) ν R2 (nm) R1 (nm) Fad (nN)

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

1[S] C Kelchner, S J Plimpton, J C Hamilton, Phys Rev B 58, 11085 (1998)

2[S] A Zong et al., J Appl Phys 100, 104313 (2006)

3[S] V Krithivansan, R L Jackson, Tribology Lett 27, 31 (2007)