Surface Energy

Python API · stjames models · API examples

How it works

Rank a crystal's symmetry-distinct faces by surface energy and estimate which faces appear in its equilibrium Wulff shape. Results include surface energies in J/m², each face family's share of the surface area, and a three-dimensional shape viewer.

Settings

  • Input: a fully periodic crystal. Miller indices refer to the standardized conventional cell used by the workflow.
  • Level of theory: choose a method that supports periodic structures and cell relaxation. The web form defaults to "UMA Small 1.2 (OMat)." For periodic DFT, leave "K-points" blank; a fixed grid is rejected.
  • Cell relaxation: "Optimize cell?" must be enabled. Rowan relaxes the bulk atoms and cell before cutting the slabs; slab cells stay fixed during relaxation.
  • Facet range: "Max Miller index" limits the largest absolute value of any scanned Miller index; the default is 1. Increasing it includes more orientations and increases calculation cost.

Notes

Surface energy is the energy cost per unit area of creating a crystal face. Rowan compares each slab's energy with a bulk reference containing the same proportion of each element, then divides the excess by the combined area of its two exposed faces.

For each orientation, Rowan considers cuts with the bulk composition and equivalent top and bottom surfaces. It compares their unrelaxed energies, relaxes only the lowest-energy candidate, and reports its surface energy. This screening does not guarantee the lowest energy among all relaxed terminations. Slabs are at least 10 Å thick, with 10 Å of vacuum. The bulk reference uses the same in-plane cell as its slab to reduce numerical mismatch; inconsistent references can cause surface energies to drift with slab thickness.

The Wulff shape

The Wulff construction estimates the shape that minimizes total surface energy at fixed volume. A reported area fraction sums all symmetry-equivalent faces; zero means that family is absent from the shape.

Skipped faces can distort the predicted shape. Any non-positive surface energy prevents shape construction and warrants checking the calculation. Slab thickness and vacuum are fixed, without a convergence check. Treat the result as a clean-surface equilibrium estimate: reconstructions, changes in surface composition, adsorbed solvent or capping agents, and growth kinetics can change the observed shape.

Further reading