Judith A' Harrison

1
Multifunctional Extreme Environment
Surfaces Nanotribology for Air Space
Cryogenic and Space Applications (Thrust area II)
Judith A. Harrison Chemistry Department United
States Naval Academy Annapolis, MD
21402 jah_at_usna.edu
G.T. Gao (MURI), J. D. Schall (AFOSR), K. Van
Workum (ONR) MURI Co-PIs (modeling) M. Zikry
D.W. Brenner
Supported by AFOSR MURI FA9550-04-1-0381
F1ATA04295G001
www.extremefriction.physics.ncsu.edu/
2
The Molecular-Scale Tribology of Solid Lubricants
Applications to the DoD
Solid Lubricants in space-based devices ?
Satellites in extreme environments
MEMs Micromachines ? Constructed from amorphous
carbon or silicon-based devices coated with SAMs
or amorphous carbon.
Si-C Chemical Process Pump Seals ? Coat with
UNCD or NCD to improve performance
UNCD MEMS (Freescale, Motorola, Intel)
Si MEMS
Artificial Joints ? coated with solid
hydrocarbon lubricants
John Carlie (Argonne Nat. Labs) John Crane
R. W. Carpick, U. Wisconsin at Madison
3
Multi-functional Extreme Environment Surfaces
Thrust area II Cryogenic and Space Applications

• Summary from Kickoff Meeting Nov 2005
• Short-Term Goals
• Large scale simulations of model nanocrystalline
  diamond (NCD).
• Examine mechanical, tribological, and transport
  properties in
• nanocrystalline diamond (temperature
  dependence) using
• molecular dynamics simulations.
• Long-Term Goals
• Develop flexible version of parallel REBO.
• Develop Global REBO (include tribologically
  relevant atoms H, C,
• N, Si, O, F).
• Use Global REBO to examine friction, stress,
  energy transfer
• mechanisms etc. at sliding interfaces.
• IV) Develop Multiscale codes (MD coupled to
  FE)

4
Method Molecular Dynamics Simulations
Initialize Simulation Positions, Velocities (temp)
Calculate Interatomic Forces F - dV/dr V
2nd-Generation REBO1, AIREBO2, XB3,
modified-XB4 (Tribochemistry Possible!)
Integrate Equations of Motion Predictor-Corrector,
Velocity Verlet Thermostat
Formal Analysis Forces, Contact Stress, Local
Temperatures, Heat Capacity, thermal
conductivity, Reaction mechanisms in contact
Animation Visualization and Intuition Reaction
Mechanisms, Flow
1Brenner et al., J. Phys. Condes. Matter, 14, 783
(2002). 2Stuart, Tutein, Harrison, J. Chem
Phys. 112, 6472 (2000). 3Dyson Smith, Surf.
Sci, 355, 140 (1996). 4Sbraccia, Surf. Sci., 516,
147 (2002).
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DLC versus DLC ? TRIBOCHEMISTRY!
Reactive potential (REBO) needed to model
Tribochemistry!
Gao et al., JACS 124, 7202 (2002) Gao et al. J.
Phys. Chem. B, 107, 11082 (2003).
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Survey of Bond-order (Reactive) Potentials
Bond-Order Potentials
Si-Si, C-C, Ge-Ge
Time
645 citations
RED Border Same form, good bond energies
lengths, poor mechanical properties
Tersoff, PRL 56, 632 (1986) PRB 39, 5566 (1989).
1st Generation REBO
914 citations
C-C, C-H, H-H (hydrocarbons)
Brenner, Phys. Rev. B. 42, 9458 (1990).
Extended Brenner (XB)
C-C, C-H, H-H Si-Si, Si-C, Si-H
Modified-XB
135 citations
2nd-Generation REBO
C-C, C-H, H-H Si-Si, Si-C, Si-H
Dyson Smith, Surf. Sci.. 355, 140 (1996).
C-C, C-H, H-H
26 citations
Brenner et al., J. Phys. Condes. Matter, 14, 783
(2002).
Sbraccia et al., Surf. Sci.. 516, 147 (2002).
8 citations
AFOSR Core Si-Si, Si-H, Si-C
AIREBO (Intermolecular REBO)
60 citations
Blue Border New Form, good bond energies
lengths, good mechanical properties!
Stuart, Tutein, Harrison, J. Chem Phys. 112,
6472 (2000).
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Form of the 2nd-generation REBO potential (CH)
Brenner et al., J. Phys. Condes. Matter, 14, 783
(2002).
Bond Order Potential - pair terms coupled to a
bond order

• Bond Order Potential - pair terms coupled to a
  bond order

8
Expand current tribochemical modeling
capabilities e.g.) Humid environments (O), Doped
Films (Si, F, O, N), Substrates (Si-C)
Issues to consider for Global REBO potential

• Add additional atom types to 2nd-Generation REBO
  potential (C-H). (covalent Interactions)

• Si-C-H Harrison AFOSR Core Program
  (current)
• C-O-H Sinnott Published work
• Ni, Lee, Sinnott, J. Phys. Condens. Matter,
  16 (2004) 7261.
• 3. C-F-H Sinnott MURI (current)

• Need to add charges (polarity) and long-range
  forces to 2nd-generation
• REBO in a way to preserve reactive nature of
  the potential and pre
• existing parameters.

1. AIREBO C-H long-range
interactions (no charges) Stuart,
Tutein, Harrison, J. Chem. Phys., 112 (2000)
6472-6486. 2. C-N-H Brenner
Extreme Friction MURI
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Expand current tribochemical modeling
capabilities e.g.) Humid environments (O), Doped
Films (Si, F, O, N), Substrates (Si-C)
V V(REBO)
V(coulomb) V(LJ)
Advantage of screening function add non-bonded
and Coulomb terms over pre-existing short-range
REBO terms. No refit of REBO covalent terms
needed!
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Nanocrystalline Diamond (NCD)
Films
Courtesy of Robert Nemanich, NC State University
Morphology of coatings varies depending upon
growth conditions.
H64
TEM images of NCD films Leigh Winfrey
nodular grains porous

• Thrusts I II
• Microwave Plasma Growth
• H2/ CH4 films have nanocrystalline
• domains and amorphous sp2 bonded
  boundaries.
• Ar/(H2)/CH4 films have
• nanocrystalline domains and sp2
• bonded grain boundaries.

H30
Smaller crystallites, continuous
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Model Nanocrystalline Diamond
Diamond crystals embedded in an amorphous carbon
matrix

• How mechanical properties (e.g., elastic
  constants) change with the size
• and shape of the crystalline domain? Want to
  elucidate the temperature
• dependence of these properties.
• Is there residual stress in the nanocomposite
  systems? If so, where is it
• distributed? What is the picture at the atomic
  level? How does the stress
• influence tribology?
• What is the temperature dependence of the
  transport and
• tribological properties (important for extreme
  environments)?

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Isotropic shape changes of the simulation
cell Pressure Control in MD Simulations
Andersen, J. Chem. Phys. 72, 2384 (1980).
Isotropic change of volume (no shape change)
ri Cartesian coordinate of an atom si Scaled
coordinate
Dynamic Equations
Pw the instantaneous pressure P the target
pressure
This method is unable to control the off-diagonal
terms of the pressure tensor, which are important
for solid state studies.
Coding changes done in FY05.
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Model Nanocrystalline Diamond
NPT Simulation at 300 K. P 0.
Four diamond crystals embedded in an amorphous
carbon matrix
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Lattice Constant of Diamond
Gao et al, J. Phys Conden. Matter, in press.

• N 1000
• NPT with P0

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Calculation of elastic constants at finite
temperatures Strain-fluctuation method
Variable Box-size MD
Parrinello and Rahman, Phys. Rev. Lett. 45, 1196
(1980).
h matrix h(c1, c2, c3)

• S stands for the fourth-rank elastic-compliance
  tensor. Related to C, elastic
• stiffness tensor.
• TtN ensemble (or HtN) (Allow the simulation box
  to change size and shape)

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Calculation of elastic constants
Strain-fluctuation method Gao et al, J. Phys
Condens. Matter in press.
Diamond 300 K
C12C13C23
N 1000
C44C55C66

• Issues
• Convergence
• difficult to get data lt 100 K

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Calculating Elastic Constants at Finite
Temperature Stress-Fluctuation Formula
Ray Rahman, J. Chem. Phys., 80, 4423 (1984).

• Issues
• Second derivative with respect to strain is
  challenging for the REBO formalism.
• Converges more quickly than the
  strain-fluctuation method.
• 
  (Van Workum et al., Phys. Rev. B
  in preparation.)

Coding changes done in FY05.
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Stress-Fluctuation Formula Diamond
Gao et al, J. Phys Condens. Matter in press.
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Calculated Bulk Modulus of Diamond (2nd-Generation
REBO)
direct strain stress exp
B (C112C12)/3
Gao et al, J. Phys Condens. Matter in press.
Expermental data Zouboulis et al., J. Chem.
Phys. 57, 2889 (1998)
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Calculated Elastic Constants of Diamond
Gao et al, J. Phys Condens. Matter in press.

• 2nd-Gen REBO gives the correct
• qualitative trends with temp!

direct strain stress exp
C11 (GPa)
Mod-XB Potential
C12 (GPa)
C44 (GPa)
Experimental data Zouboulis et al., J. Chem.
Phys. 57, 2889 (1998)
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Thermal Expansion Coefficient (a) Diamond
Quantum effects important when a is below 1.4 x
10-5 K-1 !
Barron et al, Adv. Phys. 29, 609 (1980).
Gao et al, J. Phys Condens. Matter in press.
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Model Nanocrystalline Diamond Systems
System Sizes N8000, LxLyLz3.6nm
d 1.0 nm
d 2.0 nm
Periodic Boundary Conditions
d 3.0 nm
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Model Nanocrystalline Diamond
D 1.0 nm at 300 K
Strain-fluctuation
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Ultrananocrystalline Diamond (UNCD)
Courtesy of John Carlisle, Argonne National Labs
UNCD Grain Boundaries
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Local Stress Calculation with MD
Simulation box is subdivided into small cells
Local stress of cell m is
x, y, or z direction
Volume of cell m
Force in i direction between atom a and b
Distance between a and b
Line segment of rab located in cell m
Coding changes done in FY05.
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Local Stresses
Boxes 20 x 20 x 20
d 2 nm
Depends on cell partitioning!
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Atomic Level Stresses
Van Workum et al., Phys. Rev. B in prep.
Stress on the atom a
?a atomic volume of atom a
Distribution of atomic level s11 for system with
d 2.0 nm.
(GPa)
Coding changes done in FY05.
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Atomic Level Stresses
Future Examine local and atomic stresses while
sliding! Examine crystal size,
shape, and amorphous domain size.
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Nanocrystalline Diamond Systems Effects
of Crystal Shape
Current model systems
Crystal 455 atoms 1.4 nm diameter
Crystal 165 atoms 1 nm diameter
Crystal 969 atoms 1.8 nm diameter
All three systems contains 8000 carbon atoms.
Each nanocrystalline diamond inside the amorphous
carbon network forms a octahedron with the (111)
facets on the surface. (Future (220) facets
exposed.)
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X-Ray Diffraction of NCD Films
Courtesy of Robert Nemanich, NC State University
Data Leigh Winfrey
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Tribological Performance of NCD
Nemanich (NC State University), Wahl (Naval
Research Lab)
Reciprocating with Sapphire Counterface
After 300 cycles of sliding Minimal wear
Rich Chromik Kathy Wahl

• Contact stresses of 0.72 GPa
• Sliding speed 1 mm/s
• 35-45 RH

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Simulated Tribology of Model NCD Preliminary
Studies
Ntot 9183, Ntip1200, Nsub2560, Ncrystal615,
Namorph 4808
ltloadgt 69.79 nN
ltFrictiongt 2.77 nN
100 K
hexagon (100)
dodecahedron
Top view
57.1 A X 25.7 A
Side view
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Simulated Tribology of Model NCD Potential
Energy Contours
H2 NCD
Gao et al. J. Phys. Chem. B, 107, 11082 (2003).
H2 Film I (a-C)
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Parallelization of the 2nd-generation REBO
Algorithm Choice

• Atomic Decomposition
• Force Decomposition
• Spatial Decomposition

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Atomic Decomposition
Parallelization of the 2nd-generation REBO

• Atomic data (r,F) replicated across all
  processors.
• Each processor calculates a forces for n/p
  atoms.
• Because of the bond-order terms (many body), the
  forces must be summed over all nodes.
• Coordinates must be redistributed at each
  timestep.

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Testing Parallel REBO
Scaling efficiency
Speed-up tp/t0
Results for diamond 95,000 atoms.
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Summary Model Nanocrystalline Diamond Films
Gao et al, J. Phys Condens. Matter in press.
Van Workum et al., Phys. Rev. B in preparation.

• Empirical potentials are fit to 0 K data. Force
  constants change with temperature.
  Temperature-dependent parameters would be needed
  to quantitatively reproduce experimental numbers.
  ( But one functional form gives flexibility!)
• Form of the 2nd-generation REBO allows for
  qualitative description of mechanical properties
  as a function of temperature. (Other
  reactive-potential formalisms do not reproduce
  qualitative behavior.) Quantum effects are
  important!
• Elastic constants increase with increasing size
  of diamond crystals. Other parameters such as
  temperature, crystal shape etc. need to be
  examined. Tribological properties as a function
  of composition and shape need to be examined.