Simulation methodology

Simulation methodologySimulation methodology

• Embedded-atom method potential for the Cu-Ag system (Mishin at al.)

• Simulation block is constructed by joining together Cu and Ag single crystals with the same orientation. The conic tip was obtained by removing all atoms of the upper crystal (Ag) outside of the cone given geometry (radius of the contact area is ~15A). Size of the block: 77 x 85 x 71 A (total atoms: 27,198; dynamic atoms: 4,254 Ag-tip, 10,560 Cu-substrate) with periodic boundary conditions in the substrate plane (XZ-plane).

• Relaxation at 10K during 0.1 ns

• Slip studies: V=1 m/s, sim. time 2 ns; V=5 m/s, sim. time 1 ns. All runs are at 10K.

• Stress tensor calculated using the virial expression for the dynamics atoms of the substrate.

• Interface structure examined by the common-neighbor analysis

• No loading force applied

X (1 0 -1)

Z (1 -2 1)

Y (1 1 1)

Cu (dynamic)

Ag (dynamic)

Ag (fixed)

Cu (fixed)

V

Actual tip displacements vs. imposed tip displacement

Actual tip displacements are calculated as the displacement of the “center of mass” of atoms of the bottom layer of the tip

Slip?

Stresses in the tip

Stresses are calculated using the standard virial expression over all dynamic atoms of the tip

Shear components Normal components

Displacements of the tip and shear stresses

“0”“1”

“0”“1”

A

B

C

Top layer ofthe substrate

Geometric registry at the tip (Ag) – substrate (Cu) interface

X (1 0 -1)

Z (1 -2 1)

Y (1 1 1)

FCC stackingsequence in Ag

Cu

Ag

XY-projection

HCP registry

Red triangles shoe groups of atoms of the substrate,which are in HCP registry (BC) with the atoms of the tip.Only the atoms of the top layer of the substrate (golden)

and B-layer of the tip (blue) are shown.

Atomic registry at the tip (Ag) – substrate (Cu) interface

FCC registry

Black triangles shoe groups of atoms of the substrate,which are in FCC registry (ABC) with the atoms of the tip.Only the atoms of the top layer of the substrate (golden)

and A-layer of the tip (blue) are shown.

Contact area

X (1 0 -1)

Z (1 -2 1)

Atomic registry at the tip (Ag) – substrate (Cu) interface. Contd.

FCC

FCC FCC

HCP

HCP HCP

Only the top layer of the substrate (golden atoms) is shown.

X (1 0 -1)

Z (1 -2 1)

Atomic rows of the substratewhich are not in

registry with the tip

Lattices mismatchdislocations

We do not need to create them.They pre-exist due to lattice

mismatch between Ag and Cu.

Atomic registry at the tip (Ag) – substrate (Cu) interface.Common-neighbors analysis

http://www.physics.gmu.edu/~vivanov/afm/cuag/movies/agcu_1ms_2ns_10K_noforce.mpeg

HCP

“0”

“1”