Supplementary Materials
Semi-empirical potentials
Here we provide details for the Na and W potentials used in the present study.
The W potential was developed by G.J. Ackland and was taken from [1]. Its
explicit analytical form is as follows:
(r)=90.3*(2.7411-r)^3*exp(-1.2*r)*H(2.7411-r)
+(3.25-r)^2*(47.1346499-33.7665655*r+6.2541999*r^2)
(r)=(1.896373*(4.400224-r))^2
-^0.5
where H(r) is the Heaviside function.
The Na potential (Na1) was developed in the present work following essentially
the same procedure as was used for the potential #5 in [2]. The potential satisfactorily
reproduces the melting point data and the liquid structure. Potentials Na2 and Na3 were
developed to explore the effect of the liquid structure and the latent heat on the SLI free
energy. They are not designed to simulate the properties of real Na. All “Na” potential
can be found in the LAMMPS format [3] here and in [1].
Capillary fluctuation method
Figures S1 and S2 visualize the anisotropy of the SLI free energy and stiffness,
respectively. It is important to note that in Fig. S1 the observed anisotropy has been
magnified by a factor of 5, whereas no magnification has been applied in Fig. S2.
References:
[1]
C. A. Becker, F. Tavazza, Z. T. Trautt, and R. A. B. de Macedo, Current Opinion
in Solid State & Materials Science 17, 277 (2013). http://www.ctcms.nist.gov/potentials
[2]
M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, D. Y. Sun, and M. Asta,
Philos. Mag. 83, 3977 (2003).
[3]
S. Plimpton, J. Comput. Phys. 117, 1 (1995).
Figure S1. The anisotropy in the solid-liquid interface free energy, magnified and plotted
along selected cross-sectional slices of direction space. Each curve represents the quantity
𝛾̂(𝑛𝑥, 𝑛𝑦 , 𝑛𝑦 ) = 1 + 5[𝛾(𝑛𝑥 , 𝑛𝑦 , 𝑛𝑧 )/𝛾0 − 1], where 𝛾(𝑛𝑥 , 𝑛𝑦 , 𝑛𝑧 ) is given by Eq. 12 in
the main text, using coefficients listed in Table III. A thin dotted circle has been included
to indicate the perfectly isotropic case, i.e. 𝛾̂(𝑛𝑥, 𝑛𝑦 , 𝑛𝑦 ) = 1.
Figure S2. Solid-liquid interface stiffness     , normalized by the average SLI free
energy 0 and plotted along selected cross-sectional slices of direction space. The curves
were computed directly from Eq. (12) using coefficients listed in Table III in the main
text. The thin dotted circle corresponds to the case in which the free energy is perfectly
isotropic.