Shock-Wave Simulations Using Molecular Dynamics

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Shock-Wave Simulations Using Molecular Dynamics
Matthew R. Farrow Department of Physics,
University of York, United Kingdom

• CCP5 and Marie Curie Actions Methods in
  Molecular Simulation Summer School 2006

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Outline

• Introduction
• What is it I am doing?
• Why am I doing it?
• How will I do it?
• What is a Shock-wave?
• Recent work
• Shock-wave in Argon
• Discussion and conclusions

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What am I doing?!
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Shock-wave research

• My research is to use shock-waves in solids to
  investigate material properties, using molecular
  dynamics (MD) simulations
• Aim to probe the Equations of State to enhance
  understanding of material properties
• Perhaps find new applications?

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Why shock-wave research?

• Allows us to go places inaccessible to the
  current level of experiment
• Astrophysics
• Planetary core modelling
• High temperature physics
• Explosives modelling!

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How am I supposed to do THAT?!
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Classical or Ab-initio MD?

• Classical MD uses empirical potentials and so
  is computationally cheap
• Classical MD simulations should scale linearly
  with number of processors for both speed of
  computation and number of atoms
• Shock waves in systems with 109 atoms have been
  simulated1 using Classical MD.
• Ab-initio MD calculations are limited in the
  number of atoms that can be simulated due to the
  extreme computational cost of calculating the
  many-body interactions
• Ab-initio is more accurate!

1 K.Kadau,T.C.Germann,P.S.Lomdahl,B.L.Holian,Sci
ence,296,1681 (2002)
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What is a shock-wave?
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Shock-waves

• Possible to have the propagation of the
  pertubation move faster than the acoustic
  velocity of discontinuous pressure waves2
• Shock-waves through solids, liquids and gases
• Navier-Stokes Equations
• Rankine-Hugoniot equations

2 G.G.Stokes, M. Poisson (1800s)
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Shock-waves and Equations of State (EOS)

• The Equations of State (EOS) gives the all the
  properties of the material in terms of Pressure,
  P, Volume, V and Energy, E (or Temperature, T)
  
• For example, the ideal gas EOS PV RT
• However, the full EOS for most materials are very
  difficult to determine.
• Hugoniot is a line on the EOS
• All possible states after a material has been
  shocked

Hugoniot Curve Exemplar3
3 Equations of State Article in Discovery,
the AWE Science and Technology Journal (1989)
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Recent Work with Argon
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Shock-waves in Argon

• For Argon we can use the well known Lennard-Jones
  potential5

5 M.P. Allen and D.J Tildesley, Computer
Simulation of Liquids, Oxford University Press
(1987)
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Shock-wave movies
No shockwave
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Shock-wave movies
5X Velocity of Sound
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Shock-wave movies
10X Velocity of Sound
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Discussion and Conclusions

• Shock-waves are characterised by their Hugoniot
• Line on the Equations of State surface
• Have plenty of materials to choose from
• Different shock-wave velocities seen to produce
  different responses

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Future Work

• To model a shock-wave through
• Metals (e.g. Aluminium)
• Insulators
• Much bigger system of atoms (10,000)
• NB one cubic cm 1023 atoms.
• Create the EOS and predictions!

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Thanks for listening!Any questions?
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