Lever Rule for the Uranium-Titanium Solid-Liquid Phase Diagram
A solid-liquid phase diagram for the uranium-titanium system shows the regions of phase stability as a function of the temperature and overall composition of the system. The phases are: (1) a liquid mixture of uranium and titanium of variable composition, (2) solid uranium (U), (3) solid titanium (Ti(s)), and (4) a solid phase compound with the formula TiU2(s). The phase boundaries are shown as solid black lines. The phase boundaries involving liquids are assumed to be a linear function of composition. When the temperature and composition are at a point above all the phase boundaries, only a liquid mixture is stable. At any point inside the phase boundaries, two phases are stable. The phases present and their relative amounts are shown in the bar graph on the right. When a liquid phase is present, its composition is found by drawing a horizontal line (dashed magenta line) to the appropriate phase boundary. For a solid phase, a horizontal line is drawn (dashed) to the vertical phase boundary corresponding to the pure solid. These horizontal lines are called “tie lines” or “levers”. The lever rule is used to calculate the relative amounts of the two phases, which are shown on the bar graph on the right. The liquid phase composition is indicated by the magenta dotted line and its numerically value is at the top of the liquid bar graph.
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Author: Lisa M. Goss, modified at the University of Colorado Boulder, Department of Chemical and Biological Engineering by Rachael L. Baumann. Open content licensed under CC BY-NC-SA
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