Open Access
Liu, Guoxing
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
September 06, 2011
Committee Members:
  • Julian Decatur Maynard Jr., Dissertation Advisor
  • Julian Decatur Maynard Jr., Committee Chair
  • Moses Hung Wai Chan, Committee Member
  • Jorge Osvaldo Sofo, Committee Member
  • Victor Ward Sparrow, Committee Member
  • resonant ultrasound spectroscopy
  • Helium
Recent experiments have indicated some interesting phenomena in solid helium. We have been adapting resonant ultrasound spectroscopy (RUS), which can be used to measure all of a solid's elastic moduli, for use with solid helium. In the RUS technique, a cell with known geometry is attached with ultrasound drive and receive transducers so that a number (10-30) of the cell's natural frequencies may be measured; by analyzing the natural frequencies, valuable information about elastic moduli of the cell’s content (solid helium) can be gained. For RUS to work, it is essential that the normal modes of the cell be well understood. We developed a cell which will maintain robust normal modes when the cell is cycled in temperature and pressure. Normal modes of the vibration of the can fall into two distinct classes: In one class, nearly all energy is in the steel can, and the modes and natural frequencies of this group are almost the same as the empty can. However, helium inside does move with the can and slightly shifts the natural frequency. The second class only show up when there is helium inside the cell and they depend mostly on the helium properties. It was anticipated that the transducers, being outside of the can, would not be sensitive to the second class of normal modes. The plan was to determine elastic properties of helium by analyzing the small frequency shifts of the first class of normal modes. It turns out that transducers are able to determine the natural frequencies of some of the second class modes, which are much more sensitive to helium properties. A finite element method is used to track how resonance frequencies change as 4He (elastic) properties change. This is achieved by comparing the similarity of the resonance modes. We find that resonance frequencies that are sensitive to solid 4He increase by ~2% from 1 K to 2 K in our experiment. According to our calculation, this corresponds to a ~4% increase in solid 4He shear modulus. This shear modulus change could be explained using dislocation theory with appropriate parameters.