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					 Molecular Dynamics Calculations of
   Carbon/Hydrocarbon Reflection
Coefficients on Hydrogentated Graphite
                Surfaces
                   D. N. Ruzic, D. A. Alman
  Department of Nuclear, Plasma, and Radiological Engineering
                      University of Illinois
                        Urbana, IL USA


          10th International Workshop on Carbon Materials for
                           Fusion Application

                         September 17-19, 2003
                            Jülich, Germany
                  Outline of talk
• Motivation
   Why model hydrocarbons?
• Modeling procedure
   Molecular Dynamics
   Comparison of potentials for MolDyn code
• Results
   Simulations done at various molecules, energies,
      angles, and surface temperatures
     Soft (sooty, H:C) vs hard (0.4 H:C) hydrogenated
      graphite
• Conclusions
                    Motivation
• Carbon tiles (graphite or CFC) widely used
  as PFCs
• Advantages:
   Low Z
   Good thermomechanical properties
      Up to ~25 MW/m2 during normal operation
      Even higher during off-normal events, e.g. disruptions
• Disadvantages:
   Chemical sputtering - release of hydrocarbon
    molecules into plasma
      Dominated by methane (CH4)
      C2Hy and C3Hy can be ~50% at low incident H energy
      A whole spectrum is possible (up to C3H8)
     Erosion/Redeposition modeling
    • For example, WBC1
    • Used to investigate performance of various
        PFC materials
    •   Critical Plasma-Material Interaction (PMI)
        issues studied:
         Erosion of wall materials
         Contamination of core plasma
         Hydrogen recycling
1   J. N. Brooks, Phys. Fluids B 2 (1990) 1858-1863.
     Erosion/Redeposition modeling
              procedure
•   Models transport of sputtered material through edge
    plasma
      Impurities launched from wall
      Undergo numerous reactions with the background plasma
            The Alman-Ruzic model1 was recently added to WBC
      Tracked until lost to plasma or redeposited on a surface
•   High sticking/low reflection assumption
      Without better data, any molecule returning to surface is
        assumed to stick
•   Critical improvement – inclusion of realistic
    carbon/hydrocarbon reflection coefficients2

1 D. A. Alman, D. N. Ruzic, J. N. Brooks, Phys. Plasmas 7 (2000) 1421-1432.
2 J. N. Brooks, A. Kirschner, D. G. Whyte, D. N. Ruzic, D. A. Alman, J. Nucl. Mater. 313-316

(2003) 424-428.
              State of Hydrocarbon
             Reflection/Sticking Data
•   Reflection coefficient of hydrogen on graphite has been
    measured …
      Down to 30 eV 1,2
      H Atoms and H2 molecules at ~0.2 eV 3
      Energy range critical for fusion has not been measured
•   Experimental measurement of hydrocarbon radicals
    requires quantified source of molecules/radicals
      Very hard to create such a source
      Therefore, very little data exist on sticking coefficients of CxHy
       radicals
•   Recent cavity experiments at IPP Garching can
    measure “surface loss probability” of thermal
    hydrocarbons on self-similar surfaces
1 R. Aratari and W. Eckstein, J. Nucl. Mater. 162-164 (1989) 910.
2 M. Mayer, et. al., J. Appl. Phys. 77 (1995) 6609.
3 E. Vietzke et. al., J. Nucl. Mater. 266-269 (1999) 324.
Recent cavity experiments at Garching




                     In (a), the flux impinging at point 2 is given by
                                                    2 ~ (1   ) cos  em cos  in d1211
                                                                                      


                     where  em is the angle of emission (assumed to follow a cosine law), and  in is the
                     angle of incidence. The flux onto every surface inside the cavity after each reflection of
                     the impinging species can be calculated by integrating over all surfaces and all possible
                     angles.
Adapted from A. von Keudell, C. Hopf, T. Schwarz-Selinger, W. Jacob, Nucl. Fusion 39,
1451 (1999)
             Hydrocarbon Sticking Data

                  Surface Loss       Sticking
      Species      Probability      Coefficient                  Method                       Ref.
                                                                                               13
      CH2          0.025-0.028                           Decay in the afterglow
                       <10-3                             Decay in the afterglow                13

                    10-3-0.014                           Decay in the afterglow                14
                                                                                               15
      CH3             <0.014           0.006        Modeling of ITMS result measured
                                                     with diff. Pumped HIDEN MS
                                     10-4-10-2         Radical beam experiments                3
                                                                                               16
      C2H             0.92                                 Cavity experiment
                                                                                               17
      C2H3            0.35                                 Cavity experiment
      C2H5            10-3                                 Cavity experiment                   18




13 H. Toyoda, H. Kojima, H. Sugai, Appl. Phys. Lett. 54, 1507 (1989)
14 M. Shirantani, J. Jolly, H. Videlot, J. Perrin, Jap. J. Appl. Phys. 36, 4752 (1997)
15 P. Kae-Nune, Plasma Sources Sci. Technol. 4, 250 (1995)
3 A. von Keudell, T. Schwarz-Selinger, M. Meier, W. Jacob, Appl. Phys. Letters 76, 676 (2000)
16 C. Hopf, K. Letoumeur, T. Schwarz-Selinger, W. Jacob, A. von Keudell, Appl. Phys. Lett. 74, 3800 (1999)
17 A. von Keudell, C. Hopf, T. Schwarz-Selinger, W. Jacob, Nucl. Fusion 39, 1451 (1999)
18 C. Hopf, T. Schwarz-Sellinger, W. Jacob, A. von Keudell, J. Appl. Phys. 87, 2719 (2000)
                 Goal of this work

• Model these plasma-surface interactions using
    Molecular Dynamics (MD)
•   Study reflection of
     Various carbon/hydrocarbon molecules
        C, C2, C3, CHx, C2Hx
     Incident at varying energies & angles
        0.0259-100 eV; 0, 45, 60, 75 degrees
     Hitting tokamak-like surfaces
        Hydrogen saturated graphite at room temperature (300 K)
        A “soft” redeposited carbon layer at 300 K and 673 K
    Molecular Dynamics Modeling
•   Calculates the evolution of a system of particles over
    time
•   Equations of motion are solved for each particle at a
    series of time steps
                          F  ma
•   Forces come from the potential energy function
                         F  U
•   Key physics input is the inter-atomic potential function
•   Wide range of techniques exist for:
      Solving/integrating equations of motion
      Describing the potential energy
                                 MolDyn code
•   Originally written by Keith Beardmore at Loughborough University
    (UK)
•   Modified to some extent by Karsten Albe while at the University of
    Illinois
•   Obtained from Robert Averback’s group (University of Illinois)
•   Uses the Brenner hydrocarbon potential (specifically parameter
    set II) 1
•   Temperature control by velocity scaling method of Berendsen 2
•   Integrator: Beeman method (third order, fixed timestep) 3
•   Used as a starting point. Modifications have been made to
    specifically study PMI problems

1 D. W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of
diamond films. Physical Review B, 1990. 42(15): p. 9458-9471.
2 H. J. C. Berendsen, J. P. M. Postman, W. F. v. Gunsteren, et al., Journal of Chemical Physics, 1984. 81: p. 3684.
3 D. Beeman, Some multistep methods for use in molecular dynamics calculations. J. Comp. Phys., 1976. 20: p.

130-139.
       Brenner hydrocarbon potential
•      Based on Tersoff’s covalent bonding formalism1

            Vij     f (r )V (r )  b V (r )
                    
                    j i
                           c   ij   R   ij    ij   A   ij
                                                            bij  1   
                                                                       n
                                                                             ij
                                                                              n n / 2




•      The bij term represents the “bond order” – essentially, the strength of the
       attractive potential is modified by the atom’s local environment
            For example, the C-H bond has a different energy in C-H, CH-H, CH2-H,
             CH3-H, etc.
            CH4-H is not attractive because carbon has already formed 4 covalent bonds
•      Brenner potential has additional terms in the bond order expression that
       correct for some shortcomings of the Tersoff Potential
            Overbinding of radicals
            Nonlocal effects to account for conjugated vs. nonconjugated binding
•      Fit to a database of small hydrocarbons, graphite and diamond lattices


1 J.   Tersoff, Physical Review B 37 (12), 6991 (1988).
              Trade-offs in the potential
• Competing goals: complexity vs. speed
• Brenner potential leaves out
        Dispersion
        Non-bonded repulsion
        Torsional potential
• Adaptive Intermolecular Reactive Bond Order
   (AIREBO) potential1
        Adds these components, while maintaining the
           reactivity of the Brenner (REBO) potential
          Found to be too slow for this work
1 S.   J. Stuart, A. B. Tutein, and J. A. Harrison, Journal of Chemical Physics 112 (2000) 6472.
        CPU time comparison
• Test runs on a small (145 atom) system:
   MolDyn code w/ AIREBO potential takes
    several days
       ~0.4 fs of simulation time/hour of CPU time
   Parallelized code w/AIREBO potential
    showed ~2-3x speedup
       Up to1.2 fs/hr
      (on 8 heterogeneous processors)
   MolDyn code with original Brenner
    potential takes only minutes (17,000 fs/hr)
Carbon reflection from a small graphite
 test surface using Brenner potential
Carbon reflection from a small graphite
 test surface using AIREBO potential
                               Comparison with VFTRIM-3D
                         1.0

                                                    MolDyn code
                                                    MolDyn: Brenner not reliable
                         0.8                        VFTRIM-3D
                                                    VFTRIM-3D: BCA not reliable
Reflection coefficient




                         0.6
                                                                                         Reflection of carbon on
                                                                                         H saturated graphite at
                                                                                         45 degrees
                         0.4




                         0.2




                         0.0
                               0.01   0.1            1             10              100
                                            Incident energy (eV)
Comparison: MolDyn to experimental
              data
                         • While these
                             results are
                             reasonable,
                             we’ll see,
                             the
                             particular
                             surface
                             you’re
                             hitting
                             makes a big
                             difference !
                                        Surface 1 – Hydrogen Saturated Graphite
                              0.5




                              0.4
Ratio of hydrogen to carbon




                              0.3




                              0.2




                              0.1




                              0.0
                                    0        1000       2000         3000      4000
                                                # of hydrogen atoms incident




                                        •   Started with pure graphite <0,-1,0> lattice
                                        •   Bombarded with over 4000 H atoms at 20 eV
                                        •   Cumulative result - graphite with a H:C ratio near 0.4
Movie showing carbon reflection
Movie showing carbon sticking
Reflection of Carbon Atoms on
Hydrogen Saturated Graphite
                                          Energy distribution of reflected atoms
                                                                                     Er/Ein=1
Average energy of reflected atoms (eV)




                                          10
                                                                                                Carbon atoms
                                                                                                incident at 45°
                                           1




                                          0.1
                                                                              Er/Ein ~ 0.32

                                                                                                Energy, angular
                                         0.01                                                   distributions of
                                                                                                reflected particles are
                                                                                                important input to
                                                                                                erosion/redeposition
                                                0.01      0.1           1              10       modeling
                                                       Incident energy (eV)
Elevation angle distribution of reflected
                atoms
                           10



                            8
    Percent of particles




                            6



                            4



                            2                             o
                                                 C at 45 and 0.0259 eV
                                                        o
                                                 C at 60 and 0.0259 eV

                            0
                                0    15     30       45       60         75   90
                                    Reflected elevation angle (degrees)
          Azimuthal angle distribution of
                reflected atoms
                                   o
                o
                              90
C at 45
                                                                                  •
                          o             o
        o           120                60
C at 60                                                                               0.0259 eV carbon
            o                                         o
                                                                                      incident at 45° and
      150                                        30
                                                                                      60°
                                                                                  •   Reflected atoms
180
      o
                                                          0
                                                              o
                                                                                      tend to continue in
                                                                  Direction of        the forward direction
                                                                  incident atom
                                                                                  •   This effect is more
      210
            o
                                                 330
                                                          o                           pronounced for the
                                                                                      60° (more glancing
                    240
                          o
                                       300
                                             o                                        angle) case
                                   o
                              270
          Reflection of carbon dimer (C2)
            and trimer (C3) molecules
•   Carbon dimers tend                                                         1.0

    to stick more readily




                              Total Carbon Reflection coefficient (Cout/Cin)
                                                                                                                             o
    than trimers                                                                                                  C2 at 45

•
                                                                                                                             o
                                                                               0.8                                C3 at 45
    The fully bonded
    central atom in the C3
    molecule may play an
                                                                               0.6
    important role
        Repulsive forces
         between this atom
                                                                               0.4
         and the surface
         push the entire
         molecule away from
                                                                               0.2
         the surface
        Hence, C3 reflects
         more
                                                                               0.0
                                                                                  0.01   0.1                  1                  10
                                                                                           Incident Energy (eV)
Carbon Dimer Sticks
Carbon Trimer Reflects
Reflected Species for CH4
Reflected Species for CH3
Reflected Species for CH2
Reflected Species for CH
Movie of CH4 showing breakup
           Reflection on Hydrogen
          Saturated Graphite - CHx
                                                         1.1
                                                                                                        o
                                                         1.0                                          45 incidence
                Carbon reflection coefficient Cout/Cin                                                Tsurf=300 K
                                                         0.9
Sum the
amount of                                                0.8
carbon
                                                         0.7
reflected in
each fragment                                            0.6

                                                         0.5

                                                         0.4
                                                                   C
                                                         0.3       CH
                                                                   CH2
                                                         0.2
                                                                   CH3
                                                         0.1       CH4

                                                         0.0
                                                            0.01    0.1          1               10           100

                                                                          Incident energy (eV)
       Reflection on Hydrogen
      Saturated Graphite – C2Hx
                                         1.1

                                         1.0                                               C2
                                                                                           C2H1
Carbon reflection coefficient Cout/Cin


                                         0.9
                                                                                           C2H2
                                         0.8                                               C2H3
                                                                                           C2H5
                                         0.7

                                         0.6

                                         0.5

                                         0.4

                                         0.3
                                                     o
                                         0.2       45 incidence
                                                   Tsurf=300 K
                                         0.1

                                         0.0
                                            0.01         0.1          1               10    100

                                                               Incident energy (eV)
    Surface 2 – “Soft” Redeposited Carbon Layer
•   Similar procedure
    to surface 1
        Starts as pure
         graphite
        Bombarded with
         low energy H,
         CH, CH2
        Stopped after
         surface grew ~20
                                                                                                                         0.7                                                     400
         Angstroms                         1400
                                                                                                                                                                Carbon


•   Notable
                                           1200

                                           1000
                                                                                                                         0.6


                                                                                                                         0.5
                                                                                                                                                                Hydrogen
                                                                                                                                                                H:C ratio
                                                                                                                                                                                 300

    Characteristics:                        800




                                                                                                                                                                                       Number of atoms
                             Gain of C/H




        H:C ratio can
                                                                                                                         0.4




                                                                                                             H:C ratio
                                            600                                                                                                                                  200

         exceed 0.4 in                      400
                                                                                                                         0.3



         redeposited layer                  200                                                                          0.2
                                                                                                                                                                                 100


        Lower density                        0
                                                                Gain of carbon atoms ("soft" surface)
                                                                Gain of hydrogen atoms ("soft" surface)
                                                                Gain of hydrogen atoms (0.42 H:C graphite)
                                                                                                                         0.1



        Carbon is less
                                           -200
                                                  0   1000   2000      3000         4000         5000                    0.0
                                                                                                                               -20           -10            0               10
                                                                                                                                                                                 0


         strongly bound                                        Incident flights                                                Distance into original surface (Angstroms)
Reflection of carbon incident at 5 eV
and 45 degrees on the “soft” surface
 Sticking of carbon incident at 5 eV
and 45 degrees on the “soft” surface
Carbon reflection on “soft” layer
Energy distributions of reflected
             atoms


                          Reflected energy
                          is much lower,
                          due to “softer”
                          surface
                          (compare to
                          ~32% on 0.4
                          H:C graphite)
Elevation angle distribution of
       reflected atoms


                      •   Compared to 0.4
                          H:C graphite
                            Not as much data
                            Still, there is
                             evidence of a shift
                             towards larger
                             angles
Azimuthal angle distribution of reflected
                atoms
Breakup of methane molecule incident at
5 eV and 45 degrees on the “soft” surface
Reflection on “Soft” Layer CHx




                            Reflection
                            coefficients
                            decrease
                            compared to the
                            0.4 H:C graphite
Reflection on “Soft” Layer C2Hx




                             Again,
                             reflection
                             probability is
                             uniformly
                             lower
Preparation of a higher temperature surface
     The saturated graphite surface was heated to 400 °C (673 K)
          A temperature relevant to fusion
          Significantly different from room temp. to show temperature effects
     The saturation level of hydrogen in graphite decreases with
        temperature
       However, simply heating the cell does not instantaneously evolve
        hydrogen
          The timescale for detrapping, diffusion, and desorption of hydrogen
           is much longer than can be modeled in MD
     Therefore the surface was first heated, then hydrogen was
        removed (one at a time, equilibrating in between)
       Two surfaces result:
          673 K graphite with almost 0.4 H:C
          673 K graphite with the equilibrium saturation (0.13 H:C1)
1 J. N. Brooks, H. F. Dylla, A. E. Pontau et al., presented at the 9th topical meeting on
the technology of fusion energy, Oak Brook, Illinois, 1990
Carbon incident on graphite with varying
             temperature
CH incident on graphite with varying
            temperature
CH2 incident on graphite with varying
            temperature
CH3 incident on graphite with varying
            temperature
CH4 incident on graphite with varying
            temperature
Angular Dependence of Reflection Coefficients
Comparison with Experiment for CH2 and 3
Comparison with Experimental Data for C2Hx
                         Conclusions
•   A Molecular Dynamics code has been optimized for
    looking at plasma-surface interactions
•   MD calculations have been done for various carbon and
    hydrocarbon molecules incident on fusion-relevant
    surfaces under a variety of different conditions
•   Comparison to the BCA code VFTRIM-3D showed results
    in the same ballpark
•   Comparison to experimental sticking coefficients showed:
      Proper trends in the data when comparing sticking of different
       molecules
      Some deviation in terms of the magnitudes of sticking coefficients
•   One reason for the deviation could be that the surface
    used to deduce experimental data from cavity experiments
    does not match either of the two surfaces studied here.
•   The results show that reflection/sticking probability is
    sensitive to the composition of the surface. The surfaces
    studied here should be reasonable approximations of
    those found in fusion devices.
       Acknowledgements
• The authors would like to thank the
 following individuals for their assistance:
   Jeffrey Brooks – for providing the
    motivation for this work
   Keith Beardmore – Initial author of MolDyn
   Robert Averback – for providing the
    MolDyn code used as a starting point
• This work is funded by DOE-ALPS
• Workshop organizers for the invitation

				
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