We present a new approach to solid solution thermodynamics using the concept of cell theory. We looked particularly at the influence of packing effects on freezing. To isolate this contribution we studied substitutionally ordered and substitutionally disordered binary hard sphere solid solutions. The absence of long range interactions makes the influence of inhomegeneities in composition and molecular sizes readily measurable. Such mixtures not only exhibit a freezing transition but the shape of the pressure-composition phase diagram depends drastically on the size difference between particles. Our predictions agree well with available Monte Carlo simulation results. In the case of substitutionally disordered binary hard sphere mixtures our predictions also agree with the Hume-Rothery rule which states that a substitutionally disordered binary alloy cannot exist for size differences greater than 15%. This approach is also capable of predicting the formation of some compounds such as AB (NaCl structure) $AB\sb2$ $(AlB\sb2$ structure) and $AB\sb{13}$ $(NaZn\sb{13}$ structure) as well as their domain of stability in terms of molecular size differences. The similarity between the solid-fluid phase diagrams we obtained in the case of binary hard sphere mixtures and that of binary organic systems is a sign that packing effects may actually play a much more important role in the freezing of real mixtures than what was previously believed. To investigate this question and broaden the applicability of our approach we added attractive forces in the form of a 12-6 Lennard-Jones potential to our model. Predictions for the pure component were in good agreement with published simulation results, especially when correlations between the motions of the particles were considered. In the binary case such correlations were not included for simplicity. Preliminary results obtained at constant pressure indicate that the size ratio of the particles dictates the overall shape of the solid-fluid phase diagram while the effect of attractive interactions is to position the diagram in terms of temperature. In addition, the equilibrium lines are relatively insensitive to pressure. A comparison with experimental data for methane and rare gas mixtures was done and yielded good qualitative agreement.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-7626 |
| Date | 01 January 1996 |
| Creators | Cottin, Xavier |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
Page generated in 0.0019 seconds