Helium confined to a restricted geometry: A study of lower dimensionality crossover and universality
Kimball, Mark O
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This thesis tests the ideas of finite-size scaling theory using homogeneous confinements in well characterized geometries. We use structures which are homogeneously small in one dimension, thus leading to two-dimensional (2D) crossover; and, structures which are small in all three dimensions leading to 0D crossover. These confinements are created using photolithography of silicon oxide thermally grown on two inch silicon wafers. Two wafers are bonded together to complete the structure and create a cell. High precision heat capacity measurements are made using a modified AC technique which involves oscillating the sample temperature while simultaneously regulating the average cell temperature. The superfluid fraction of helium is also measured in order to test scaling theory. We make use of a superfluid oscillation between a helium reservoir outside the cell and the cell itself. The frequency at resonance is proportional to the amount of fluid in the superfluid phase of the confined helium. We call this Adiabatic Fountain Resonance (AFR) since the mass flow is driven with minimal heat transport. This work also includes the use of 3 He- 4 He mixtures and compares this to previous work with pure 4 He. Mixtures are not expected to change the physics except to increase an intrinsic length which characterizes the critical behavior. We find that the heat capacity of mixtures in a planar geometry do not scale with the data of pure 4 He in the same geometry unless a metric factor is introduced to the scaling variable of the mixtures. The mixture superfluid density data also do not scale well unless an additional confinement length is included in the analysis. We cannot scale the 0D heat capacity data since we only have one cell with 0D confinement. However, we attempt to scale mixtures and pure 4 He data. We find that these data do not scale and that the mixture data for 0D confinement have an unusual behavior below the superfluid transition.