Structure and Dynamics of Solid Helium

Individually, a helium-4 atom is one of the simplest objects in the universe: two protons, two neutrons and two electrons. At high temperatures, a collection of such atoms behaves as the classical ideal gas. At low temperatures, in liquid form, quantum mechanics comes into play, and the collective behavior of many helium atoms together is radically different from that observed in other liquids. The He-4 atoms are bosons, and so in the right conditions, Bose-Einstein condensation occurs, creating the superfluid state. Under pressure, the liquid solidifies, but the crystal formed is, as might be expecte, a little unusual. It is a quantum crystal, so named because quantum effects (zero point motion) dominate thermal effects. In fact, the atomic zero point motion is so large that classically, the solid should melt. Nonetheless, the solid exists!

In the 1960s and 1970s, several people wondered whether or not a state analogous to the superfluid might form in the solid state: the supersolid state [ref]. However, no experimental evidence for such a thing was found at that time. In 2002, John Goodkind at UCSD saw some anomalies in the transmission of ultrasound through solid helium crystals, and speculated that they were due to interactions with excitations of delocalized defects [ref].

In 2004, Eunseong Kim and Moses Chan at Pennsylvania State University observed the predicted signature of the supersolid, a change in the rotational inertia of solid helium away from the values expected for a classical solid [ref]. These measurements have since been reproduced by several other groups. However, the interpretation of these results remains controversial.

We are collaborating with the Goodkind group at UCSD and Collin Broholm at Johns Hopkins University to investigate the structural and dynamical properties of solid He-4 crystals in the relevant temperature and pressure ranges using neutron scattering.

 FIG: A 2D layout of the detector banks on MAPS.  The black dots and streaks are Bragg reflections from the solid helium

The samples were grown in situ in a large stainless steel chamber in a dilution refrigerator. Helium gas was pumped into the cell through a thin capillary and then liquefied and finally solidified. The crystals were grown using the blocked capillary technique: helium is pushed in at a high pressure and relatively high temperature. Eventually, a plug of solid forms in the capillary and the helium trapped in the sample cell is cooled. This technique usually results in poor quality crystals, and in fact, in our experiment, several crystallites were formed.

 FIG: Stainless steel sample cell.

Nonetheless, specific Bragg peaks were easily identified from their characteristic momentum transfer (position in reciprocal space) and the temperature dependence of these peaks was monitored from 0.14 K to 0.80 K. By looking at the change in intensity of peaks from the same crystallite, we can extract information on atomic displacements about their average positions. For helium, the mean square displacement is very large (approximately one third of the atomic separation) and should be sensitive to certain types of changes in the local environment brought about by the appearance of a supersolid conensate. Over the temperature range studied here, this quantity is temperature independent.

We can also monitor the evolution of the lattice parameters as a function of temperature. Making certain assumptions, the temperature dependence of the lattice parameters can be mapped to the temperature dependence of the vacancy concentration in the crystal. Together with data over a higher temperature range obtained from x-ray diffraction experiments by Fraass, Granfors and Simmons [ref] our data show that this temperature dependence is clearly exponential in nature, with an apparent vacancy activation energy of 8.6 K.

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