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The exp-6 potential for (solid line, left vertical axis) and the corresponding force (dashed line, right vertical axis). The force has a maximum strength in the region of the soft-repulsive core. Hence, a new “soft” length scale emerges in the system in addition to the hard-core diameter . With increasing , decreases while gets larger. For instance, when grows from 11 to 13, varies from about to whereas varies from about to .
High -high phase diagram of the exp-6 model for . Pressure and temperature are in units of and , respectively. Coexistence curves are represented as solid lines. Open circles mark coexistence points as estimated through exact free-energy calculations (errors are smaller than the symbols size). The full circle is the outcome of a total-energy calculation. The boundary between the fluid phase and the fcc crystal at extremely high pressures corresponds to the lower stability threshold of the solid. In the intermediate-pressure region (from about to ), additional phases at low temperature are likely present (a BC8 solid, various instances of SH solids, and a SC solid, see text), whose precise boundaries, however, were not computed. The locus of density maxima, , in the fluid phase is represented as a dotted line. All lines in the figure are guides to the eyes. Inset: reduced number density as a function of temperature for .
Spatial correlations in the exp-6 system for . Top panel: radial distribution function for ; (solid line), (dashed line), (dotted line), and (dashed-dotted line). Inset: height of the first peak of the structure factor as a function of pressure at . Bottom panel: for ; (dotted line), (dashed-dotted line), (dashed line), and (solid line).
chemical potential , plotted as a function of pressure , for a number of crystal arrangements, choosing the fcc lattice (blue solid line) as a reference (both and are in reduced units; the chemical potentials of structures that are never stable are not shown): bcc (triangles and red solid line), SC (boxes and black solid line), SH (dots and light blue solid line), BC8 (magenta dotted line), and cI16 (green dashed line). The optimized cI16 crystal is actually a bcc crystal up to the pressure where the BC8 solid prevails over bcc. From there onward, the cI16 line runs over the BC8 line, departing from it only for .
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