Tension and Stiffness of the Hard Sphere Crystal-Fluid Interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of $0.66k_{\mathrm{B}}T/{\sigma }^2$ with a small anisotropy of about $0.025k_{\mathrm{B}}T$ and stiffnesses with, e.g., $0.53k_{\mathrm{B}}T/{\sigma }^2$ for the (001) orientation and $1.03k_{\mathrm{B}}T/{\sigma }^2$ for the (111) orientation. Here $k_{\mathrm{B}}T$ is denoting the thermal energy and $\sigma$ the hard-sphere diameter. We compare our results with existing experimental findings.

Figure 1

In the left panel, the surface orientations, as listed in Table , are indicated on an octant of the unit sphere. The right panel shows a Wulff plot of the corresponding interfacial tension $\gamma (\widehat{n})$; here, the colors display the value of the tension for a given orientation.

Figure 2

DFT results: (a) Laterally integrated density profiles $\overline{\rho }(z)$ for the five surface orientations, as indicated, (b) contour plots at $x=0$. The periodic length of the total profiles in $z$ direction is $50.15\sigma$ (001), $53.19\sigma$ (011), $65.15\sigma$ (111), $56.07\sigma$ (012), and $61.42\sigma$ (112).

Figure 3

$q$-dependent interfacial stiffness $\overline{\gamma }(q)$ for the (001) and (111) orientation (a) as well as the (011) and (112) orientation for the indicated directions (b). Note that for (112) only the $[\overline{1}10]$ direction is shown because $\overline{\gamma }(q)$ for the $[11\overline{1}]$ direction is very similar to that of the latter direction.