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Crystallisation Crystallisation Experiments with Experiments with Complex PlasmasComplex Plasmas
M. Rubin-Zuzic1, G. E. Morfill1, A. V. Ivlev1, R. Pompl1, B. A. Klumov1,
W. Bunk1, H. M. Thomas1, H. Rothermel1, O. Havnes2, and A. Fouquét3
1. Max-Planck-Institut für extraterrestrische Physik, 85740 Garching, Germany
2. University of Tromsø, Department of Physics, 9037 Tromsø, Norway
3. Institut Polytechnique de l’Université d’Orléans 14, ESPEO, 45067 Orléans Cedex 2, France
Outline
• Objectives
• Experimental setup and procedure
• Observation of crystal growth fronts
• Identification of different states
• Identification of detailed growth process
• Comparison with numerical simulations
• Summary
Objectives for our experiments
Study of dynamics of single particles during crystallisation in real time without changing the plasma parameters
Questions:What are the self-organisation principles governing crystal growth?What is the resultant surface structure and its temporal evolution?What is the microscopic (kinetic) structure of interfaces?
PKE-Nefedov (PK3) - Experimental Setup
Formation and Growth of Plasma Crystals
Experimental parameters:
Particle diameter: 1,28 µm ± 0,056 µm
Particle number: ~ 107
Gas: Argon
Gas pressure p = 0.23 mbar
Laser sheet thickness: 80-250 µm
Images: 1028 * 772 Pixel Intensity values: 8 bitImage rate: 15 images/sec 40*30 mm overview camera6.4*4.8 mm high resolution camera
Experimental procedure:
A large vertically extended crystal (~80 µm lattice distance) is created (no horizontal layers!)
The system is disturbed by decreasing the ionization voltage from 0.88 V down to 0.39 V. The recrystallisation is investigated.
Overview
High resolution
High resolutioncamera
Experimental observation – color coded
movie
Experimental observation – color coded
movie
6.4*4.8 mm, 15 Hz, superposition of 10 consecutive imageParticles fall down The crystal dissolves from top to bottomThe crystallisation process starts at the bottomA crystallisation front is observedThe propagation velocity of the crystallisation front slightly decreasesDomains of different lattice orientation form below the frontAt the interface the thermal velocity of the particles is higher
Discovery of interfacial melting
Discovery of different crystal domains : a stable region of interfacial melting (a few lattice thicknesses) is located between two lattice domains. Similar phenomena have also been observed in colloidal systems.
16 sec later
Comparison of structures - before voltage decrease Triangulation
Lattice distance: 80 m
• No horizontal crystal layers (no influence of electrodes)• Plasma crystal is oriented in an arbitrary
angle towards the plane of the laser sheet• No information about 3d structure
Comparison of structures – after recrystallisation Triangulation
Lattice distance: 75 m
Numerical Results – Crystal Growth
Boris Klumov
2 D simulation box (molecular dynamics simulation, gravity, shielded Coulomb potential, neutral gas damping, Ar, Q=3000e, initial velocity is Gauss distributed with 3cm/sec, parabolic potential).
Fast dropping particles disturb the upper part of the crystal. They exchange their energy through Coulomb collisions .Energy dissipation: shock-and compressional waves).
Sedimentation – after power variation
Particles: 1.28 mmUeff (top)=22.7 V, Ueff (bottom)=22.8 VURF (forward)=0.39 V, URF (backward)=0.018 VPressure: 0.25 mbar
Experimental procedure: Voltage is increased (from 40 to 140 levels) and then quickly decreased back. Vertical extension and particle distance decrease with time.
40 sec later
40 sec later
Cooling - Numerical result
Boris Klumov
fcc, hcp and a small amount of bcc structure is present.The final ground state (fcc) is reached much slower than predicted by neutral gas damping (fcc/hcp volume ratio increases with time).
A reason might be that particles have a small size (charge) variation. This allows a large number of possible crystalline states. During the sedimentation the particles slowly rearrange to the state with lowest potential energy (very slow process – driven by thermal motion
In experiment: the cooling is slower - additional heating?.
Velocities in the yellow regionParticle positions
Mean velocity & Growth velocity Velocity distribution
Particle Velocity Variation – Numerical Resultat fixed time
Boris Klumov
3D simulation: Yukawa System crystallises from bottom upward (due to gravitational compression, box no periodic conditions).
The particle’s thermal velocity increases upward and reaches a local minimum at the position of the growing crystal front.
Quantitative phase separationOverlap technique:
- In the crystalline state particles overlap almost completely in consecutive images, in the disturbed (liquid) state they do not.
- Superposition of n images: Determination of ratio of overlapping particle area in all n images/particle area in the first image
1: particle is stationary0: particle has moved further than its image size
4( )11/ 0 ................... 0.5......................1
imageimage
particle particleimageA A
The „overlap“ technique
Particle 1 (Frame 1)
Particle 2 (Frame 1)
Particle 1 Frame 1+2
Ratio ~ 0.1
Particle 2 Frame 1+2
Ratio ~ 0.9
This yields a quantitative measure of particle kinetic energy
The „overlap“ technique
Phase separation
4( )11/ 0 ................... 0.5......................1
imageimage
particle particleimageA A
Discovery of „nanocrystallites“ and „nanodroplets“
during crystal growth
droplet
crystallite
Rubin-Zuzic et al. (Nature Physics,2006)
Fractal dimension of crystallisation front
Ln = n (length of „measuring rod“)
L = length of crystallisation front
1
2
Determination of the (linear) fractal dimension of the crystallisation front to obtain a quantitative measure for the variation of the interface front during the growth process:
Fractal dimension of (1D) crystallisation front
2.000
2.100
2.200
0.3 0.5 0.7 0.9 1.1
= - 0.2 -> D = 1.19
log (L)
Log (n)
2
-> surface structure is scale-free
Fractal dimension of the crystallisation front
Rough surface
Smooth surface
crystal growth follows a universal self-organization pattern at the particle level
MD simulations of the crystallization frontMD simulations of the crystallization front
Boris Klumov
Particle positions and thermal energies
Thermal velocitiesfront has a complex structure with a transition layer and transient “temperature islands”
Growth velocitycrucial role of the dimensionality in strongly coupled systems – only the 3D simulations provide quantitative agreement with the experimental data (open circle)
Summary (crystallisation experiment)Crystallisation starts mostly from bottom, because there the compression is higher (due to gravity) than on top
Crystal is build up with particles from the gaseous state located above. During crystallisation the particles in the “liquid” state lose energy through collisions with neighbours. Energy is dissipated by waves, which are propagating through the crystal medium (see numerical results).
Interfacial melting has been observed between domains, the layer is only 2-4 lattice planes wide.
The (transient) energy source could be the latent energy of converting an excited lattice state (hcp) into a lower (ground) state (fcc).
The transition region is characterised by numerous droplets (in the crystal regime) and crystallites (in the fluid regime) and oscillating variaton in roughness.
The crystallisation front obeys a universal fractal law down to the (minimum) lattice spacing.
Next steps: new camera (higher temporal and spatial resolution), fast 3D scans during crystallisation, identification of 3D crystal structure variation during crystal growth, …
Future: Investigation on the ISS