Dendritic melting of spin polarized Helium three
The phenomenon of dendritic growth is well known to many: when a crystal grows into an undercooled liquid, the interface of the crystal does not stay flat or smooth, but develops protrusions. Often, the structures that grow out after a long time are dendrites, tree-like structures with sidebranches. Through the combined effort of many researchers in the second half of the eighties and the early nineties, the mechanism that determines the dendritic tip shape and speed is now well understood. While the mathematical formulation of this dendritic selection mechanism is quite complicated, the physical origin of the instability that leads to dendritic growth is actually rather simple. In this context it is often refered to as the Mullins-Sekerka (1964) instability. Basically, the mechanism is that of diffusion-limited or laplacian growth: ahead of the interface, in the undercooled melt, a temperature boundary layer builds up as a result of the heat release at the interface. Hence, when a part of the interface bulges outward into the undercooled melt, the temperature gradients increase. This in turn leads to a larger heat transport away from the interface, and hence a further enhancement of the growth velocity.
The Mullins Sekerka mechanism underlies many interfacial instabilities associated with diffusion limited or Laplacian growth. You can find some discussion of this, and entries into the literature in my summerschool article Three basic issues concerning interface dynamics in nonequilibrium pattern formation.
In fact, whether an interface is stable or unstable upon growth depends both on the size and on the sign of the gradients before and behind the front. A remarkable illustration of this is the prediction by Puech et al. a number of years ago, that when a polarized 3He crystal melts, the interface could also show the dendritic instability. In the 3He community, melting of polarized 3He crystal is studied as one of the ways in which can produce highly polarized liquid 3He (liquid 3He is not easy to polarize by brute force with a magnetic field as it is a Fermi liquid). According to the calculations of Puech et al., the instability should occur in this case due to the buildup of a polarization boundary layer in the solid 3He upon melting.
Melting of polarized 3He has been studied already for a number of years in the low temperature group of my experimental colleagues Giorgio Frossati and Reijer Jochemsen of the Kamerlingh Onnes Laboratory. Recently, Alexei Marchenkov (then a graduate student), Hikota Akimoto (then a postdoc) and Richard van Rooijen (a graduate student at the Kamerlingh Onnes Laboratory) have for the first time observed this dendritic melting. However, there are some surprises which were not anticipated by the theory of Puech et al.: while the analytical theory appeared to predict that the instability would set in very quickly, in the experiments it often occurs only tens of seconds after the melting started (how long the waiting time lasts, depends on the speed of melting).
We have collaborated on the interpretation of these melting experiments with the experimental low temperature group, and we think we understand them in detail now. Basically, the linear instability remains suppressed in the transient regime as long as there is a stabilizing gradient on the liquid side, because the liquid spin diffusion coefficient is very much larger than the solid spin diffusion coefficient. Recent measurements of the time dependent polarization profiles (done by applying a field gradient in the NMR experiment) confirm this picture.
References
L. Puech, G. Bonfait and B. Castaing, Polarized 3He: dendritic melting, J. Physique 47 723 (1986).
A. Marchenkov, Optical studies of growth and melting dynamics of solid 3He at ultra low temperatures and in high magnetic fields (thesis, Leiden, 1997).
H. Akimoto, R. van Rooijen, R. Jochemsen, G. Frossati and W. van Saarloos, Melting Process and Interface Instability of Highly Magnetized Solid 3He: Role of Magnetization Gradient, Phys. Rev. Lett. 85, 1894 (2000). (pdf file)
E. R. Plomp, R. van Rooijen, H. Akimoto, G. Frossati, R. Jochemsen, and W. van Saarloos, Analysis of the Melting Process of Magnetized Solid 3He, J. Low. Temp. Phys. 124 169-188 (2001) (link to journal).
last update March 22, 2001
[Pattern formation] [Wim van Saarloos] [Instituut-Lorentz]