Structures and Surface Energies of (100) and Octopolar (111) Faces of Halite (NaCl): an Ab initio Quantum-Mechanical and Thermodynamical Study

Abstract

The structures of the (100), octopolar (111) Na-terminated [(111)Na], and (111) Cl-terminated [(111)Cl] surfaces of halite (NaCl) were determined by means of ab initio quantum mechanical calculations (density functional theory, DFT). The (111) surfaces show higher surface relaxation with respect to the (100) surface. The surface energies (γ) at T = 0 K for relaxed and unrelaxed (100) and (111) faces were determined at DFT level. The values of the surface energy for the relaxed faces are γ(100) = 160, γ(111)Cl = 390 and γ(111)Na = 405 erg/cm2; therefore, the stability order of relaxed surfaces reads: (100) < (111)Cl < (111)Na. For the unrelaxed faces, the surface energies are higher: γ(100) = 161, γ(111)Cl = 552 and γ(111)Na = 551 erg/cm2.To check if the octopolar (111) faces can belong to the equilibrium morphology of the crystal/vapor system, the relaxed surface energies at T > 0 K were calculated by considering both the vibrational motion of atoms and the surface configurational entropy. From these calculations it resulted that the octopolar (111)Na and (111)Cl faces cannot belong to the equilibrium morphology. Octopolar reconstruction and both surface vibrational and configurational entropy then allow us to explain why the {111} NaCl form cannot enter the equilibrium shape of the crystal.