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Surface Energy

Computes the surface (cleavage) energy of one or more slab terminations for a given Miller index.

Overview

SurfaceAnalyzer relaxes the bulk structure (cell and atoms) to obtain a reference energy per atom, then uses SurfaceTransformation to build one or more inequivalent, vacuum-padded slab terminations for the configured miller_index (via pymatgen.core.surface.SlabGenerator). Each slab is relaxed with the cell fixed (only atomic positions move, so the vacuum spacing and slab thickness are preserved exactly as generated), and its surface energy is extracted from the difference between the relaxed slab energy and the energy an equivalent slab of bulk material would have.

Theory

For a slab of \(N\) atoms and total energy \(E_{\text{slab}}\), with bulk reference energy per atom \(E_{\text{bulk}}\) and surface area \(A\) exposed on each of the slab's two faces, the surface energy is

\[ \gamma = \frac{E_{\text{slab}} - N E_{\text{bulk}}}{2A} \]

the standard supercell-method surface energy. Division by \(2A\) rather than \(A\) accounts for the two free surfaces a slab necessarily creates. This estimate is only meaningful once min_slab_size is large enough that the slab's interior recovers bulk-like coordination (so the two surfaces don't interact through the slab) and min_vacuum_size is large enough that a slab doesn't interact with its own periodic image across the vacuum gap. Both are hkl-plane-count or Angstrom thicknesses depending on in_unit_planes. symmetrize=True (the default) restricts slab generation to terminations with the same surface on both faces, which is what makes the simple "divide by \(2A\)" form above valid without needing to separately resolve two different surface energies for an asymmetric slab. gamma_J_m2 reports the same quantity converted from eV/Ų to J/m².

References