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We report measurements of the superfluid fraction rho(s)/rho of films of (3)He-(4)He mixtures confined between silicon wafers at 0.0483 microm separation. The data obtained using adiabatic fountain resonance (AFR) can be used to test for the first time expectations of correlation-length scaling in the case of planar mixtures. For the mixtures, the data for rho(s)/rho collapse well on a universal function. The dissipation associated with AFR can also be scaled, and indicates two-dimensional crossover. These results are in contrast to pure (4)He, where over a wider range of confinements, the data for rho(s)/rho are found not to scale.

We have measured the heat capacity of (3)He-(4)He mixtures confined in films of thickness 48.3 and 986.9 nm. The confinement is defined by direct bonding of two silicon wafers. The heat capacity is measured using an ac technique and then transformed to correct for exponent renormalization effects. The data address the expected universal critical behavior along the lambda line as function of (3)He concentration. We discuss the results of several analyses of the data, and we show that a universal collapse can be achieved for all the mixtures. However, this is on a locus which differs from that of the pure system. An alternative analysis is also presented which yields collapse of all the data under certain assumptions. We believe these data are the first to test universality of finite-size scaling for the specific heat along a locus of transitions.

We have measured the heat capacity of (3)He-(4)He mixtures confined in films of thickness 48.3 and 986.9 nm. The confinement is defined by direct bonding of two silicon wafers. The heat capacity is measured using an ac technique and then transformed to correct for exponent renormalization effects. The data address the expected universal critical behavior along the lambda line as function of (3)He concentration. We discuss the results of several analyses of the data, and we show that a universal collapse can be achieved for all the mixtures. However, this is on a locus which differs from that of the pure system. An alternative analysis is also presented which yields collapse of all the data under certain assumptions. We believe these data are the first to test universality of finite-size scaling for the specific heat along a locus of transitions.

The critical behavior at a second order phase transition is characterized by the divergence of the correlation length xi. We have studied the superfluid transition of 4He in a series of experimental cells in which this divergence of xi is modified due to finite-size confinement. In particular, the design of these cells is such that the smallest dimension is kept the same, 1 microm, but the geometry is such that one obtains crossover to dimensionality of 2, 1, and 0. This corresponds to films, channels, and boxes filled with helium. We measure the specific heat and compare these results with theoretical expectations. We identify surface and line specific heat contributions by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. The design of these cells is made possible by a combination of silicon lithography and direct wafer bonding.