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Molecular-dynamics simulation movies

The MPEG-movies are results of large-scale molecular-dynamics simulations performed with the SPaSM code using massive parallel computing systems, which enable us to follow in detail the dynamics of structural phase transformations and other modes of plasticity.
Most of the simulations were performed by using an embedded-atom method (EAM) potential (M.S. Daw and M.I. Baskes PRL 50, 1285 (1983.), M.S. Daw and M.I. Baskes PRB 29, 1285 (1983.)) which consist of a density depend and a two body potential term. The EAM potential is able to reproduce fundamental properties of metals in contrast to pure pair-potentials like the Lenard-Jones (LJ) potential.


Rayleigh-Taylor instability by particle methods:

The applications of the Rayleigh-Taylor instability---i.e. the mixing of a heavy fluid on top of a light in a gravitational field ---range from astrophysics (supernova explosions), to geophysics
 (formation of salt domes), all the way to inertial confinement fusion (collapse of ICF
 capsules), as well as the general turbulent mixing of fluids. Therefore, its fundamental understanding is of relevance not only to the foundations of hydrodynamics but also to a broad range of subjects, including physics, chemistry, biology, and geology.
We show that quantitative theoretical investigations on the atomistic level of the Rayleigh-Taylor instability --- as the classical example of complex turbulent hydrodynamic flows --- compare favorably to recent experiments. Using the latest generation of supercomputers (the LANL Q machine) we solve Newtonian equations of motion for up to 100 million particles for as many as 250,000 integration steps --- an enormous numerical venture. A quantitative comparison of these  ``nanohydrodynamic'' flows with continuum descriptions (Navier-Stokes equations) and macroscopic experiments demonstrates that large-scale atomistic simulations can provide insight into complex hydrodynamic  phenomena. 

The movie gives a nice impression of what happens during such instabilities; it shows a quasi 2 dimensional simulation including about 12 million atoms interacting via Lenard-Jones potentials (only the repulsive part for the AB interaction in order to maximize surface tension)

Computer power increased dramatically since 2003 and we were able to run the Rayleigh-Taylor problem with over 7 billion particles on BlueGene/L. Also, the Atwood number (A=(rho1-rho2)/(rho1+rho2), rho1/2=mass density of heavy/light fluid) dependence has been investigated in more detail.



2D-RT by MD, 12 million particles (0.9MB)

3D-RT by DSMC, 7 billion particles (3 MB)

2D-RT by DSMC A=0.29, 100 million particles (8 MB)

2D-RT by DSMC A=0.67, 100 million particles (8 MB)

2D-RT by DSMC A=0.98, 100 million particles (8 MB)


Proc. Natl. Acad. Sci. 104, 7741 (2007),  The Importance of Fluctuations in Fluid Mixing by K. Kadau, C. Rosenblatt, J.L. Barber, T.C. Germann, Z. Huang, P. Carles, and Berni J. Alder. (for supporting on-line material including movies click here)

Int. J. Mod. Phys. C 17, 1755 (2006), Molecular-Dynamics Comes of Age: 320 Billion Atom Simulation on BlueGene/L by K. Kadau, T.C. Germann, and P.S. Lomdahl.

Supercomputing `05 (2005)(SC05, ACM 1-59593-061-2/05/0011).[Gordon Bell Prize finalist paper] 25 Tflop/s Multibillion-Atom Molecular Dynamics Simulations and Visualization/Analysis on BlueGene/L, by T.C. Germann, K. Kadau, P.S. Lomdahl

Proc. Natl. Acad. Sci. 101, 5851 (2004),  Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability by K. Kadau, T.C. Germann, N.G. Hadjiconstantinou, P.S. Lomdahl, G. Dimonte,  B.L. Holian, and B.J. Alder. (for supporting on-line material including movies click here)

Int. J. Mod. Phys. C 15, 193 (2004), Large-Scale Molecular-Dynamics Simulation of 19 Billion particles by K. Kadau, T.C. Germann, and P.S. Lomdahl

DPG pro-physik.de, 08.04.2004, Supercomputer laesst 100 Millionen Atome tanzen by Rainer Scharf.


Shock-induced structural phase transformation in bcc iron:

Shock waves were initiated by a 'momentum mirror' (B.L. Holian and P.S. Lomdahl, Science 280, 965 (1998)), which specularly reflects any atoms atoms reaching reaching the face of of the perfectly flat infinitely massive piston (left) moving at a piston velocity. The resulting shock waves in the iron single crystal moves (from left to right) along the (001)  direction in the initial bcc structure (gray). Above the threshold for the structural transformation (about 15GPa, about 10 percent uniaxial compression, or about a piston velocity of 5 percent of the longitudinal sound velocity) into the close-packed structure (red) many grains of the close-packed material nucleate in a displacive manner (martensitic-like) within the uniaxially compressed bcc structure (blue). Crystallographic different oriented grains are separated by grain boundaries (yellow). Depending on the shock strength the transformed region can be a mixed phase region and the resulting shock wave structure is a split two-wave structure consisting of an elastic precursor and a slower transformation wave. The initial nucleation takes place along the (bcc011) close-packed planes transforming into the close-packed planes of the close-packed material. The comparison of the nucleation process for three different shock strength (increasing from left to right in the movie) is shown in the last movie where only atoms with a lateral displacement larger than about 1/6 of the nearest neighbor distance are shown. The samples consist of aprox 8 million atoms (i.e. 40.2nm x 40.2nm x 57.4nm) and was simulated for 8.76ps.


Shock along Fe-bcc(001), piston velocity=417m/s
Shock along Fe-bcc(001), piston velocity=471m/s
Shock along Fe-bcc(001), piston velocity=689m/s

Nucleation of close-packed material for 3 different shock-strength


Phys. Rev. Lett. 98, 135701 (2007), Shock Waves in Polycrystalline Iron by K. Kadau, T. C. Germann, P. S. Lomdahl, R.C. Albers, J.S. Wark, A. Higginbotham, and Brad Lee Holian. (for supporting on-line material including movies click here)

Phys. Rev. B 72, 064120 (2005), Atomistic Simulations of Shock-Induced Structural Transformations in bcc Iron Single Crystals for Different Crystallographic Orientations by K. Kadau, T.C. Germann, P.S. Lomdahl, Brad Lee Holian.

Phys. Rev. Lett. 95, 075502 (2005), Direct Observation of the alpha-epsilon Transition in Shock-Compressed Iron via Nanosecond X-ray Diffraction by D.H. Kalantar, J.F. Belak, G. W. Collins, J. D. Colvin, H.M. Davies, J.H. Eggert, T.C. Germann, J. Hawreliak, B.L. Holian, K. Kadau, P.S. Lomdahl, H.E. Lorenzana, M.A. Meyers, K. Rosolankova, M.S. Schneider, J. Sheppard, J.S. Stoelken, J.S. Wark.

Science 296, 1681 (2002), Microscopic View of Structural Phase Transitions Induced by Shock Waves by K. Kadau, T.C. Germann, P.S. Lomdahl, and  B.L. Holian.

Frankfurter Allgemeine Zeitung, 12.06.2002, Nr. 133 / Seite N2, Schock im Eisenkristall by Rainer Scharf.

Science 280, 965 (1998), Plasticity Induced by Shock Waves in Nonequilibrium Molecular-Dynamics Simulations by B.L. Holian and P.S. Lomdahl.

Temperature induced displacive structural transformations (austenite/martensite)


Cubic iron-nickel alloy nano-particles (only half of the sample is shown in order to see the interior) undergo a martensitic transformation (first movie) from the high temperature fcc austenitic phase (red) into the low temperature bcc martensitic phase (green) (due to technical reasons the surface is green or blue depending on the orientation of the surface). The heterogeneous nucleation starts at defects like corners and grows into the interior of the nano-particle with a fraction of the sound velocity (that is, the growth velocity depends on the crystallographic direction.) with a transient mixed phase region having a needle-like pattern. The final structure is twinned and  can undergo a transformation back to the original austenite structure (second movie). The sample contains one million atoms (edge length=24nm) and was simulated for 67.5ps.


martensitic transformation at low temperatures
austenitic (back) transformation at high temperatures


Phase Transitions 75, 59 (2002), Atomistic investigations of the thermodynamical stability and martensitic nucleation of Fe80 Ni20 nanoparticles by K. Kadau and P. Entel.

J. Phys. IV France 11, Pr8-17 (2001), Large-scale molecular-dynamics study of the nucleation process of martensite in Fe-Ni alloys by K. Kadau, P. Entel, T.C. Germann, P.S. Lomdahl, and B.L. Holian.

Phys. Rev. B 57, 5140 (1998), Martensite-austenite transition and phonon dispersion curves of Fe1-xNix studied by molecular dynamics simulations by R. Meyer and P. Entel.

J. Magn. Magn. Mater. 177-181, 1409 (1998), Numerical simulation of martensitic transformations in magnetic transition-metal alloys by P. Entel, R. Meyer, K. Kadau, H.C. Herper, M. Acet, E.F. Wassermann.

Mechanical properties of nano-phase metals (tensile test)

We model tensile testing of  nano-phase Al (Al modelled by an EAM potential described in: Phase Transitions 75, 265 (2002), Atomistic modeling of diffusion in Aluminum by S. Grabowski, K. Kadau, and P. Entel.) by either sintering from spherical nano-particles or setting up by a Voronoi construction.
Different crystallographic oriented grains (red) are separated by grain boundaries or pores (yellow). Under tensile testing different modes of plasticity such as grain rotation and grain-boundary movements are observed. In addition to that and in contrast to  other materials like Cu, No, and Pd (see Literature) crack propagation along the grain-boundaries at high strains (around 10 percent depending on grain size) is observed. As in the case of Cu,Pd, and Ni an inverse Hall-Petch effect (i.e. softening at smallest grain size) is observed.  the case of the sintered nano phase material the remaining pores significantly reduce the strength of the material (growth of pores). For some quantitative results check here.


tensile test nanophase Aluminum (sintered)
tensile test nanophase Aluminum (Voronoi-constructed)


NANOTECH 2002 Proceedings of the second International Conference on Computational Nanoscience and Nanotechnology, 338 (2002), Molecular-dynamics study of physical properties in sintered nano-particles by K. Kadau, P.S. Lomdahl, P. Entel, D. Kadau,  M. Kreth, T.C. Germann, B.L. Holian, F. Westerhoff, and D.E. Wolf.

Nature 391, 561-563 (1998), Softening of nanocrystalline metals at very small grain sizes by J. Schiøtz, F. D. Di Tolla and K. W. Jacobsen.

Science 296, 66 (2002), Grain Boundaries and Dislocations by H. van Swygenhoven.

Impact of a Nano-Meteor with 11 miles/sec

Motivated by a visit at the Meteor Crater or Barringer Crater near Flagstaff in Arizona we model  an impact of a nano-meteor consisting of  418 iron atoms smashing into a slab of one million bcc ordered iron atoms. The impact velocity was chosen to 11 miles/sec which was the impact velocity of the Meteor Crater, the incident angle in the simulation is  45 degree. It's amazing how fast the kinetic energy is transformed into  potential energy (i.e. deformation). As early as  4 pico seconds after the impact a crater has formed which consumed about half of the kinetic energy of the meteor (see graph) . Another interesting aspect is the formed aspect ratio (the ratio between the crater depth and width) which is for the meteor crater about 1/5 for the time being (that might has been different directly after the impact). The nano-meteor has an aspect ratio of 1/3 four pico seconds after the impact.  As you can see in the movies the crater seems to get larger in diameter, so things are going into the right direction. We also find that a perpendicular impact doesn't change that much the crater formation and the energy transformation. For this simulations we worked with an integration time step of 0.125 femto second s -and increase to 0.25 femto seconds didn't change the picture but rather led to numerical instabilities at later times ...
By the way the Barringer Crater has a diameter of about a mile and was impacted some 50,000 years ago by a meteor consisting of an iron nickel compound with a diameter of 150 feet and  weighed  no less than 300,000 tons. Between miles and nanometers there is a factor of 10 to the power of 12, but still there are similarities, at least for certain situations ...


3 dimensional view of impact
side view
airplane view


Theoretical Low-Temperature Physics (University Duisburg, Germany)
Theoretical Division (T-11) (LANL, USA)
Kai Kadau's home page