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A bulk crystal can be cleaved with various terminations, and finding stable terminations, which may have high Miller indices, is a non-trivial task. We propose two independent and complementary descriptors, based on the atom positions of the crystal only, for surface energies of various terminations in a crystal. One is the ‘atom proximity function of a plane’,  p , where the Gaussian of the distance from a plane is summed up for atoms near the surface and then normalized. The other is the ‘surface roughness index’,  v , which is based on the density of surface atoms and the bonding environment, namely the solid angle of ‘open space’ around an atom. These descriptors contain parameters, but using predetermined suggested values make these descriptors effectively parameter-free. The validity of the descriptors is demonstrated on sc, fcc, and bcc crystals and oxides Li 2 O, Na 2 O, K 2 O, MgO, CaO, β-Ga 2 O 3 , θ-Al 2 O 3 , rutile structure TiO 2 , SnO 2 , and GeO 2 , anatase structure TiO 2 , β-Ga 2 O 3 , θ-Al 2 O 3 , and monoclinic ZrO 2 . Very stable terminations typically have both small  p  and large  v  compared to others.

Two descriptors avoiding explicit bond consideration on relative surface energies of various terminations in a crystal