****NON-TECHNICAL ABSTRACT**** This collaborative award supports a program primarily directed towards issues that stem from recent experimental observations of a supersolid state. A supersolid is a new state of matter in which part of the atoms in the solid show frictionless motion with respect to the rest of the solid, or the container that holds it. This resembles such phenomena as superconductivity and superfluidity. The precise nature of the supersolid state is currently a matter of lively debate. A combination of mechanical and x-ray experiments aims at correlating phenomena observed at the macroscopic level with the microscopic structure of the solid. This will provide critical information for a more general understanding of supersolidity. The project is a vehicle for intensive and sustained collaboration between research groups at the University of Delaware, Western Michigan University, Northern Illinois University, and Pennsylvania State University focused on experiments at the Advanced Photon Source at Argonne National Laboratory. This setting gives both the undergraduate and graduate students involved a much wider view of the physics enterprise, and their potential role in it, than is usually the case. It also provides a mechanism for the students to build up a network of contacts among peers early on and forms an excellent preparation for a scientific career.
The central goal of this collaborative project is to provide critical information necessary to interpret recent observations of a possible supersolid state in 4He. A series of combined x-ray diffraction, torsional oscillator (TO) and dielectric constant experiments will be used to investigate several questions: 1. Are there features in the x-ray diffraction directly indicative of a supersolid transition? E.g., a careful study of the Debye-Waller factor may provide limits on the Bose condensate fraction. 2. What aspects of crystal quality are important for the formation of a supersolid state? X-ray measurements will be used to determine the crystal quality, and will be combined with TO measurements in a simultaneous experiment. In addition, disorder will be introduced in a controlled way by growing the solid in porous media such as aerogels. 3. Does 4He form a commensurate solid at T = 0, or is the zero-point vacancy concentration > 0? High precision measurements of the temperature dependence of the lattice constants at constant volume, can distinguish between thermal and non-thermal vacancy populations. The training of graduate as well as undergraduate students forms an important part of this project. Its collaborative nature, as well as the fact that part of the work is done at the APS/ANL, gives students a much broader exposure to modes of research than is normally the case, and will form an excellent preparation for a scientific career.
The main objective of the research under this grant was to perform synchrotron x-ray diffraction experiments on solid helium at cryogenic temperatures at the Advanced Photon Source at Argonne National Laboratory. The central question was: Can we observe any signature either in the static structure or in the dynamics that can be associated with a transition from a normal solid to a supersolid state. In the end, the answer to this question turned out to be: NO. Neither the lattice constant, nor the intensity of the diffraction peaks showed any temperature dependence in the range of temperatures where the putative supersolid transition was believed to take place. We performed experiments on solid helium in several porous media, including Vycor and aerogels of various porosities. While we did not observe a supersolid transition, we did find transitions between solid phases of different crystalline symmetry. It appears that confinement stabilizes the bcc phase (which in the bulk occupies only a tiny sliver in the phase diagram). The smaller the pore size, the larger the pressure that is required to form the hcp phase. We found, both in the x-ray scattering experiments as well as in measurements of the shear modulus, that it can occasionally take surprisingly long for the solid to reach a (quasi) equilibrium configuration. Diffraction measurements showed parts of the crystal rotating their crystalline orientation without ever coming within alignment, and in some experiment the shear modulus was observed to change substantially randomly for days on end, even at temperatures as low as 50 mK. What prevents the system to reach an equilibrium state in some cases, but not in others is at this point obscure.
