Surface energy (γ) is the energy cost per unit area of cleaving a bulk crystal to expose a face. It is facet-dependent, since cutting along different planes severs different numbers of bonds per unit area, and that dependence sets which faces a crystal exposes.
Rowan takes one fully periodic crystal, ranks its symmetry-distinct low-index faces by γ, and builds the equilibrium shape they imply.
max_miller_index (1 by default) sets the largest absolute value of any single Miller index in the scan.
The crystal is relaxed once, cell included, and its space group is redetected on the relaxed geometry. Every face is cut from that one geometry, since relaxing per orientation would make the surface energies incomparable. A failed bulk relaxation aborts the scan.
Symmetry-distinct Miller indices are then enumerated, and for each face Rowan scans the available terminations, building a slab at least 10 Å thick with 10 Å of vacuum. Only symmetric, stoichiometric cuts are kept, since γ is taken as the slab's energy above bulk split evenly between its two faces. A face with no valid cut is skipped with a reason. Each surviving slab is relaxed at fixed cell, and the termination giving the lowest γ is reported.
The bulk reference is recomputed on the oriented bulk cell each face is cut from, rather than taken from the original cell. The two then share an in-plane lattice, so their Brillouin-zone sampling error cancels, the Fiorentini–Methfessel matched reference. An unmatched reference makes γ drift with slab thickness. For the same reason a fixed k-point grid is rejected rather than overridden: a slab needs a single k-point along its vacuum, and its reference has to match its in-plane mesh.
Results stream as the scan runs, published after the bulk relaxation and after each Miller-index level. Unphysical results are flagged rather than raised: Rowan warns on a slab whose relaxation left its two faces inequivalent, on a negative surface energy, on faces missing from the scan, and on energies that enclose no bounded shape.
A crystal free to choose its own shape minimizes total surface energy at fixed volume. Because γ is anisotropic, that shape is the Wulff construction: place a plane perpendicular to each face normal at a distance proportional to its γ, and take the inner envelope.
Rowan builds this as a halfspace intersection, with every symmetry equivalent contributing its own plane, and reports each face's share of the resulting surface area. Low-energy faces sit close to the center and dominate the exposed area. A face cut away entirely by its neighbors gets an area fraction of zero. A negative surface energy, which usually means a layered crystal is missing a dispersion correction, suppresses the shape entirely.
Slab thickness and vacuum are fixed rather than converged per system, and chemical-potential-dependent γ, magnetic ordering, and growth kinetics are out of scope. The computed shape is a clean-surface baseline. A synthesis with a solvent or capping agent binding preferentially to one face will depart from it.