2. Crystallisation Experiments with Complex Plasmas M. Rubin-Zuzic 1, G. E. Morfill 1, A. V. Ivlev 1, R. Pompl 1, B. A. Klumov 1, W. Bunk 1, H. M. Thomas 1, H. Rothermel 1, O. Havnes 2, and A. Fouquét 3 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

3. 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

4. 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?

5. PKE-Nefedov (PK3) - Experimental Setup

6. Formation and Growth of Plasma Crystals Experimental parameters: Particle diameter: 1,28 µm ± 0,056 µm Particle number: ~ 10 7 Gas: Argon Gas pressure p = 0.23 mbar Laser sheet thickness: 80-250 µm Images: 1028 * 772 Pixel Intensity values: 8 bit Image rate: 15 images/sec 40*30 mm overview camera 6.4*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 resolution camera

7. Experimental observation – color coded movie

8. 6.4*4.8 mm, 15 Hz, superposition of 10 consecutive image Particles fall downThe 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

9. 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

10. 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

11. Comparison of structures – after recrystallisation Triangulation Lattice distance: 75  m

12. 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).

13. Sedimentation – after power variation Particles: 1.28 mm U eff (top)=22.7 V, U eff (bottom)=22.8 V U RF (forward)=0.39 V, U RF (backward)=0.018 V Pressure: 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

14. 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?.

15. Velocities in the yellow region Particle positions Mean velocity & Growth velocity Velocity distribution

16. Particle Velocity Variation – Numerical Result at 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.

17. Quantitative phase separation Overlap 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 stationary 0: particle has moved further than its image size

18. The „overlap“ technique Particle 1 (Frame 1) Particle 2 (Frame 1)

19. 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

20. Phase separation

21. Discovery of „nanocrystallites“ and „nanodroplets“ during crystal growth droplet crystallite Rubin-Zuzic et al. (Nature Physics,2006)

22. Fractal dimension of crystallisation front L n = 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:

23. Fractal dimension of (1D) crystallisation front 2.000 2.100 2.200 0.3 0.5 0.70.91.1  = - 0.2 -> D = 1.19 log (L) Log (n  ) 2  -> surface structure is scale-free

24. Fractal dimension of the crystallisation front Rough surface Smooth surface crystal growth follows a universal self-organization pattern at the particle level

25. MD simulations of the crystallization front Boris Klumov Particle positions and thermal energies Thermal velocities front has a complex structure with a transition layer and transient “temperature islands” Growth velocity crucial role of the dimensionality in strongly coupled systems – only the 3D simulations provide quantitative agreement with the experimental data (open circle)

26. 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