Projects of Christian Anders

1. Interactive simulation of celestial mechanics and astronomical activities

2. Sputtering of cosmic ice surfaces

2.1 Energy-dependency of cluster-induced sputtering

2.2 Sputtering of water ice

2.3 Effect of binding Energy and mass

2.4 Molecular sputtering

3. Cluster surface interaction:

3.1 Penetration range dependence on cluster size

3.2 Cluster stopping

3.3 Penetration range dependence on cohesive energy

3.4 Ranges and stopping of Fullerenes

3.5 Deformation of Al clusters upon deposition

3.6 Desorption of Gold-Clusters from Graphite


1. Astronomical activities

Gravitational dynamics

1.1 Interactive simulation of Gravitational dynamics

The solar system and other planets. Pdf-presentation of the simulation-setup, Numerik der Himmelsmechanik auf deutsch
Planetenbewegungs-Präsentation am Tag der Physik 2003-5.

1.2 Solar telescope presentation

as member of the students' astronomy association SAGA at the day of physics 2007 and at the university for children 18.6.2008


Molecular dynamics

2. Model studies for sputtering of cosmic ice as in Saturn's rings

Saturn's ringsImpact

2.1. Linearity and additivity in cluster-induced sputtering: A molecular-dynamics study of van der Waals bonded systems
by Christian Anders, Herbert M. Urbassek and R.E. Johnson

Using molecular-dynamics simulation, we study sputtering of a condensed-gas solid (frozen argon as model system for ice) induced by the impact of atomic clusters with sizes 1 < n  <104. Above a nonlinear onset regime, we find a linear increase of the sputter yield Y with the total energy E of the bombarding cluster. We scale the kinetic energy of the projectile to the cohesive energy of the target ε = E/U with U = 0.0815 eV, so that the results can be transfered to other materials (as water ice). The sputter-limiting energy εs is introduced which separates erosion (ε  > εs) from growth ( ε <  εs)
-> Publication: Phys. Rev B 70 (2004) 155404
Sputterring Yield vs impact energy2.1.1Sputter Limiting Energy2.1.2
2.1.1 Sputter Yield Y vs bombarding energy ε for impact of an Ar100 projectile
2.1.2 Erosion limit  εs /n per particle. The limit is defined as the scaled energy εs necessary to sputter as much atoms as impacting. The green line is a fit to our data for different projectile sizes. The horizontal lines refer to the speed water ice projectiles need to have the same scaled energy E/U per molecule (U(H2O) = 0.5eV). Speeds from 10 km/s (at bottom) in 5 km/s steps to 30 km/s at top are possible in Staurn's rings.

Ar100Crater2.1.3Meteor Crater2.1.4

2.1.3. Movie: An Ar100 projectile impacting a target consiting of frozen amorphous argon at a total energy of 250 eV, E/U = 3070, the colors indicate temperatur in units of vaporisation temperature. Click here to see movie in cross section view, perspectivic view!

2.1.4. Meteor crater: Notice the similiarity between the microscopic craters in our model system and the macroscopic craters from cosmic impacts

2.2. Sputtering of water ice

Motivation Water ice is a common surface material in the outer solar system.
Movie: A frozen cluster of 100 water molecules inpacts a water ice target at a total energy of 3 keV, E/U = 5800, the colors indicate temperature in units of vaporisation temperature.  Simulating thousands of H and O atoms needs much cumputing efford. The target seems to be to small for this projectile energy (needed to compare to the argon system); so we wait for more computer power according the Moore's law...
Water ice target cross section Water Crater Water Dissociation Water Dissociation
1. cross section view
Color codes temperature:
0 (blue): 0 K, 1 (red): 373 K
2. perspectivic view
Color codes temperature:
0 (blue): 0 K, 1 (red): 373 K
3. Dissociation and recombination (+unchanged H2O, slab of 20 Å)
Color code see below
4. Dissociation and recombination (unchanged H2O not shown)
Color code see below

Visualisation of dissociation and recombination
(Simulation with different cutoff-procedure than in 1+2, see diploma thesis of Christian Anders, if someone wonders, why the crater in 3 is smaller)
Color code:
dark blue: unchanged H2O
light cyan blue: partner lost (H+,OH-)
red: recombined H2O with new partners
purple: partner gain (H3O+)
3. Dissociation and recombination (embedded in unchanged H2O, slab of 20 Å), slab of 10 Å
4. Dissociation and recombination (unchanged H2O not shown)
5. Temperature coded movie for this simulation (slab of 10 Å)
6. Temperature coded perspectivic view, higher perspectivic view

2.3. Effect of binding Energy and mass in cluster induced sputtering of van-der-Waals bonded system
by Christian Anders, Herbert M. Urbassek

We perform a model study of cluster-induced sputtering. By using van-der-Waals bonded systems with Lennard-Jones interaction, we obtain an overview of the influence of the effects of binding energy and mass on the sputtering behavior. We work in the so-called linear regime where the sputter yield is proportional to the total energy of the incident cluster. By varying the cohesive energies Up and Ut of the cluster projectile and the target, we find that the sputter yield is inversely proportional to Ut and rather independent of Up. Varying the mass of the projectile atoms, Mp, with respect to that of the target atoms, Mt, gives maximum sputter yields when the projectile atom mass is in the range 0.25Mt  < MpMt. Furthermore, we study preferential sputter effects in heterogeneous systems. These consist of a random stoichiometric mixture containing equal concentrations of two species. We find that the more weakly bound species is preferentially sputtered. The preferentiality is roughly inversely proportional to the cohesive energy of the pertinent species. We also identify a mass effect on sputtering such that the lighter species is preferentially ejected.
Yield with varying cohesive energy crater decreasing with cohesive energy Yield depending on mass ratio
Fig 2a: Sputter yield vs total energy of the projectile for varying cohesive energies of the target. The reference target with the nominal cohesive energy of argon produces the middle fit line. Nine series of simulations have been performed which differ in the binding energies of projetile Up and target Ut. All energies are scaled to the cohesive energy of the unmodified argon ice Uo, first column: ratio of target cohesive energy Ut/Uo, second column: ratio of projetile cohesive enrgy Up/Uo. Soft bounded material yields to more sputter yield, hard bounded to less sputtering relative to the reference.

Fig 3: Cratersizes correnspondig to sputter yield also show inverse proportionality to the cohesive energy: Uppermost picture: low cohesive energy, middle picture: reference case, lowest picture: high cohesive energy. All pictures taken at 20 ps after impact of Ar100 with 250 eV (E/Uo = 3070).

Fig 4: Sputter yield vs total energy of the projectile for varying mass ratio of projectile to target. The reference case with projectle and target having the same atomic mass creates the uppermost fit line for highest sputter effieciency. Nine series of simulations have been performed which differ in the masses of projetile Mp and target Mt. All masses are scaled to the mass of unmodified argon Mo: first column: ratio of target mass Mt/Mo, second column: ratio of projetile mass Mp/Mo. The sputter efficiency depends only on the mass ratio of projectile vs target: equal atomic masses result in high sputter efficiency, while mass-missmatch reduces it.
-> Publication: NIM B 228 (2005) 84-91, presented at Cosires Conference 2004

2.4 Sputtering of molecular solids

by Christian Anders and Herbert M. Urbassek

For cluster-induced sputtering two model systems of diatomic molecular solids are employed, which have identical cohesive energy but differ in their dissociation energy and the possible reaction pathways. Sputtering occurs by the flow of gasified material out of the spike volume into the vacuum above it. Due to the entrainment of radicals and radical products with the flow, only a minority of this debris is left behind in the target. The excitation of internal molecular degrees of freedom (rotation and vibration) slightly reduces the sputter yield in comparison to the sputtering of atomic system, while the chemical energy release due to exothermic reactions of radicals formed enhances the yield in proportion.
-> Publication: Physical Review Letters, 99:027602, 2007.

Movies

Please click on the pictures for full view!
Cluster-Cluster collision partially shown at COSIRES 2006: a cluster with 100 molecules of the reactive model species AB impacts another cluster of the same size with a total kinetic energy of 1750 eV triggering the exothermic reaction
2 AB -> A2 + B2 (inspired by) 2 NO -> N2 + O2,
since AB is modelled with only 2 eV binding energy, while A2 and B2 both have 5 eV.

Cluster-Cluster Species Demo
Species
yellow: A ("N")
blue: B ("O")

Reaction
Reaction: coded by color
blue: AB no change
purple: more than 1 partner
red: partner changed
yellow: partner lost

Temperature
Temperature
1 (red): 10000 K
0 (blue): 0 K

Reaction Products
Produced molecular species depending on collision energy E/Ec, Ec = 0.107 eV

Cluster-Target impact with 2 keV into the model-system as in the PRL publication. An AB100 impacts a target of amorphous frozen AB. Slab of 10 Å for all.

Cluster-Target Species
Species
yellow: A ("N")
blue: B ("O")

Reaction
Reaction: coded by color
blue: AB no change
purple: more than 1 partner
red/orange: partner changed (to A2/B2)
yellow: partner lost

Temperature
Temperature
1 (red): 1000 K
0 (blue): 0 K

Pressure
Pressure
1 (red): +1 GPa
0 (green): 0 GPa
-1 (blue): -1 GPa
purple: overflow,
dark purple: underflow

For Comparison for 0.55 keV impact energy
Species Reaction Temperature

3.1 Projectilesize dependence of penetration ranges


We determine the ranges of Aun clusters (n = 1, 13, 43, 87, 201, 402) at fixed energy per atom, 100 eV/atom. We study three targets with different bonding properties and mass: a condensed amorphous argon sample, a gold crystal with a (100) surface, and a graphite crystal with a (0001) surface. We find that the ranges follow a power law R ~ nα, where α  = 0.3 in a gold target, and  α = 0.4 in the graphite and argon targets. Bigger projectiles penetrate deeper with the first impacting atoms clearing the way for the sucessors.

Movies

Small projectile in GraphiteGraphite Big Porjectile in GraphiteAu402 in fcc ArArgon (frozen)

The both left boxes: Simulating the impact of different sized gold projectiles (yellow) into a graphite target (blue) left: small (n=13) middle: big (n=402)

right: The Au402 cluster impacts a condensed fcc argon target restoring an implanted gold cluster (the same happens in amophous argon)
Please click on the pictures to see the movies!

-> Publication: NIM B 228 (2005) 57-63, presented at Cosires Conference 2004

3.2 Nonlinear stopping of heavy clusters in matter

by Christian Anders and Herbert M. Urbassek

When impacting on a solid, heavy cluster atoms are stopped less then equi-velocity atoms. Using molecular-dynamics simulation, we study this effect systematically for the exemplary case of Aun clusters (n = 1 - 402) with energies in the range of Eat = 10-1000 eV/atom. We find that cluster stopping is reduced by a factor n-0.36 with respect to that of equi-velocity atoms. This result agrees with recent discussions of the clearing-the-way effect of heavy clusters, in which the total cluster stopping increases in proportion to the cross-sectional area of the cluster, rather than its volume.
-> Publication: Nuclear Instruments and Methods in Physics Research B, 258:497-500, 2007.

3.3 Dependence of cluster ranges on target cohesive energy

by Christian Anders and Herbert M. Urbassek

We show that for small impact energies, E0 ≤ 100 eV/atom, the range D depends on the target cohesive energy U as D ~ U. The exponent -β increases with decreasing projectile energy and assumes values up to -β = 0.25 for E0 = 10 eV/atom. For higher impact energies, the cluster range becomes independent of the target cohesive energy. These results have their origin in the clearing-the way effect of the heavy Au-cluster; this effect is strongly reduced for E0 ≥ 100 eV/atom when projectile fragmentation sets in, and the fragments are stopped independently of each other. These results are relevant for studies of cluster stopping and ranges in soft matter.
-> Publication: Nuclear Instruments and Methods in Physics Research B, 266:44-48, 2008

3.4 Ranges and stopping of Fullerenes

by C. Anders, H. Kirihata, A. Yamaguchi and H. M. Urbassek

Using molecular-dynamics simulation, we study the impact of C60 fullerene molecules with energies up to several tens of keV on various target materials: graphite, fullerite, Au, and a condensed Ar solid. For all target materials, fragmentation of the fullerene projectile sets in at around 1 keV impact energy; it starts the earliest in the heavy Au target. Full atomization of the projectile is observed at around 10 keV impact energy. The projectile ranges, on the other hand, depend strongly on the target material. The highest ranges are achieved in the weakly bonded Ar target. Also ranges in the fcc-C60 solid are systematically larger than in the graphite target. Interestingly, at energies above 5 keV, the fullerene penetrates deeper into the Au target than into graphite, even though the Au has a considerably higher mass and efficiently reflects the fullerenes at lower bombarding energies; this indicates the dominant role of the target cohesive energy. The energy dependence of the range of fullerene molecules is surprisingly flat and varies between E1/3 and E2/3 at smaller impact energies, E ≤ 10 keV. At higher impact energies, where the projectile has been fully atomized, the energy dependence becomes more pronounced, proportional to E.
-> Publication: Nuclear Instruments and Methods in Physics Research B, 255:247-252, 2007

Movies

Reflection of a Fulleren-molecule impacting with 100 eV onto a small patch of Graphite. For higher impact energy (using a more extended target) pentration and fragmentation occurs as shown in the publication. This movie using this small target is just for demonstration. Please click on the pictures for full view!

Front temperature
Front view: Color codes temperature
blue-red: 0 K up to 0.2 ·Ts (sublimation-temperature of graphite Ts = 3820 K)
purple T > 0.2 ·Ts

Perspective temperature
Perspective view: Color codes temperature, scale as on the left

Pressure
Front view: Color codes pressure
5 (red): +1 GPa
0 (green): 0 GPa
-5 (blue): -1 GPa
purple: overflow,
dark purple: underflow

3.5 Deformation of Al clusters upon deposition

by Christian Anders, Sebastian Meßlinger und Herbert M. Urbassek

Using molecular-dynamics simulation, we investigate the self-deposition of Aln clusters (n ≤ 4000) on an Al substrate at velocities below the velocity of sound. Both cold crystalline and hot liquid clusters are studied. We examine the cluster deformation after impact on the surface, which we quantify by its height and base radius. At a given cluster velocity, the shape of deposited crystalline clusters is rather independent of the cluster size; only at small cluster sizes, n ≤ 40, the clusters are less strongly deformed. With increasing cluster size, liquid clusters are more strongly deformed than crystalline clusters. Faster projectiles become more strongly flattened by the deposition process. Even clusters depositing with vanishing velocity show a finite deformation, which is considerable for smaller clusters. At large cluster speed, clusters penetrate deeper into the (100) surface than into the (111) surface and also deform more strongly.
-> Publication: Surf. Sci., 600:2587-2593, 2006.

Movies

Please click on the pictures for full view!
A liquid Al864-cluster (red) landing on a (100) Al-surface (blue) at different speeds.
707 m/s 1414 m/s 2828 m/s 5657 m/s

v=707m/s

v=1414m/s

v=2828m/s

v=5657m/s

Temp v=707m/s
Color codes temperature:

Temp v=1414m/s
blue-red

Temp v=2828m/s
0 - 2000 K

Temp v=5657m/s

3.6 Desorption of Gold-Clusters from Graphite

(link to seperate presentation)

Back to AG Urbassek homepage

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last update 12.5.2008 by D.C.A.