Interaction potential [Eq. (1)] with parameters , , and , in reduced units. The inset shows a zoom in the very small attractive part of the potential.
The dimensionless configurational energy per particle for the several crystal structures considered: face centered cubic (fcc), body centered cubic (bcc), simple cubic (sc), simple hexagonal (sh), hexagonal closest packing (hcp), and rhombohedral-60° (rh60). We see that the hcp has the lower configuration energy per particle for densities (see inset). Hence, the expected structure for our model at is the hcp for . For the bcc phase has the lower configurational energy between those studied (not shown).
The reduced pressure as a function of the reduced density. The seven isotherms show that the relation between and is monotonic.
The translational order parameter as a function of the density . From top to bottom, the 16 isotherms are , 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.70, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 5.0. The arrows (a), (b), and (c) correspond to the density range spanned by Figs. 5(a)–5(c), respectively. The bold line indicates the isotherm . For no anomalous behavior is observed for . The line connecting the points is just a guide for the eyes.
The radial distribution functions for and several densities: (a) , 0.06, 0.07, and 0.08; (b) , 0.11, 0.12, 0.14, and 0.16; and (c) , 0.20, 0.22, and 0.24. The arrows indicate the direction of increasing . The dashed line is the reduced interparticle potential shown in Fig. 1 multiplied by a factor of 0.5 just for clarity.
The orientational order parameter as a function of the density . From top to bottom, the 16 isotherms are , 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.70, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 5.0. For (not shown) the local maximum points occur at with a global minimum at . We do not study the cases where (see the text for more details). The line connecting the points is just a guide for the eyes.
The relationship between the several anomalies presented for our model. Curve B ends at and it is not entirely shown for clarity. See the text for more details. Between the maxima line (curve B) and minima line (curve A) both the translational and orientational order parameters and become anomalous, namely, decrease with density. We call this region the structural anomaly region. The diffusion extrema (DE) lines enclose the region inside which the diffusion decreases with density—the dynamic anomaly region. The temperature of maximum density (TMD) line englobes the region that density anomaly appears. Both the DE and TMD lines were obtained from previous work (Ref. 43). This cascade of anomalies presents the same hierarchy as that observed for the SPC/E water (Refs. 8 and 9).
The plane or order map. Each line corresponds to an isotherm and the arrows indicate the direction of density growth. From top to bottom, the isotherms showed here are , 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.7, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 5.0. Unlike the SPC/E water (Ref. 8), the paths formed by the and parameters developed a two dimensional region in the order map for temperatures and densities inside the structural anomalous region.
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