Equilibrium phase diagrams of isolated nano-phases

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Abstract
Materials processing and fabrication shows a strong trend toward manipulation of materials at ever decreasing sizes. This is especially true in microelectronics. Once the size of a material extends below the sub-micrometer level significant changes in the properties and behavior of materials emerges. It is sometimes difficult to determine if the changes observed at this nano-scale are a result of the process variables or are inherent to material because of its small size. In order to address this difficulty with regard to crystal structure and composition, phase diagrams as a function of size would be particularly useful. In the present paper experimental data on phase equilibria are presented as well as a thermodynamical analysis based on capillarity effects from surface curvature. The analysis and experimental data for binary phase diagrams agree with one another and show that isolated particles of less than 100 nm exhibit substantial decreases in liquidus temperature, factors of more than 10 increase in solubility, and narrowing of the two-phase fields. The details of the thermodynamic model and its predictive powers are presented along with a three-dimensional phase diagram which has temperature-composition-size as its axes.