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