Phase Diagram Calculation of Gas Mixtures for Refrigeration; Reflection & Transmission Coefficients and the Effective Mass: Superconducting Proximity IV Measurements.
Abstract
The efficiency of JouleThomson refrigerators greatly improves with the addition of hydrocarbons to nitrogen as coolant, and is highly dependent on the mixture composition. To optimize it, we calculated the mixture phase diagram using the PengRobinson equation of state. A program was developed to solve numerically a set of coupled nonlinear equations for the equilibrium of the vapor and liquid phases of each mixture component. The program is highly efficient, quite stable, and reliable. Gases can be easily added to the program's database. We found that the cooling efficiency of the mixtures has a sharp ridge in composition space, and explain this. To better understand tunneling spectra of the high T_{rm c} cuprate superconductors, we analyzed the onedimensional behavior of the wavefunction of a free particle striking a crystal interface. We describe the free particle using a wavepacket of plane waves, and the crystal using the KronigPenney model. We find that when the wavepacket is spread over many unit cells, it behaves like a free particle wavepacket striking a small potential step. The reflection and transmission coefficients are derived and one finds that they do not contain the particle's effective mass. We determine that the boundary conditions used in a standard effective mass approach must be modified to make it work. We conclude that one should not use the effective mass approximation in treating high T_{rm c} superconductor interfaces. We measured the dynamic resistance of a superconducting normal metalnormal metal (SNN') geometry and observed that N', a superconductor at low enough temperatures, displays superconducting properties above its critical temperature. They disappear well below the critical temperature of S. We present a simple model of the proximity effect, which is selfconsistent at any temperature and good for arbitrary thicknesses of N. The model shows how the superconducting gap decays with the distance from S. We observe that the proximity effect is longranged when the temperature is not much above the critical temperature of N'. We also present a calculation of the Andreev reflection coefficient in an SNS geometry, that may help to explain sharp resistive peaks previously observed by Holcomb.
 Publication:

Ph.D. Thesis
 Pub Date:
 1996
 Bibcode:
 1996PhDT.........7F
 Keywords:

 Physics: Condensed Matter