Fundamental global model for the structures and energetics of nanocrystalline ionic solids

This paper presents a general theory elucidating the relationships between the structures and cohesive energetics of alkali halide nanocrystals consisting of small sections of bulk rocksalt structures with m(1) and m(2) rows but infinite along the z axis. The theory introduces the electrostatic interactions between the ions treated as point charges and the short-range repulsions between the closest ion neighbors with the latter terms written in the Born form Ar-n. Minimum energy structures are defined by the distances a(e) and b(e) separating the closest ions perpendicular and parallel to the z direction. The ratio a(e)/b(e) defining the crystal shape, is independent of the strength A of the short-range repulsion, greater than the bulk value of unity, and increases with decrease of the crystal cross section or n. This ratio tends toward unity in the hard sphere limit of infinite n. Both b(e)/R-e(6:6) and a(e)/R-e(6:6) with the bulk separation R-e(6:6), are less than one, increase with increase of the crystal cross section or n, and are independent of A if this is independent of structure. The structural dependence of A increases its value with a decreasing crystal cross section rendering closer to unity the ratios a(e)/b(e), b(e)/R-e(6:6), and a(e)/R-e(6:6). Energy gains on relaxing the crystal toward equilibrium from its bulk separations decrease with increase of the crystal cross section or n, being about 60 kJ/mol for a one-dimensional chain with n = 6 but 0.5 kJ/mol for m(1) = m(2) = 4 with n = 12. The energy gained on relaxing to a structure with a(e)/b(e) constrained at unity is about 10 times greater than the further energy gains consequent on removing this constraint. The present theory neglecting the interaction between ions and the encapsulating nanotube explains the experimentally measured b(e)/R-e(6:6) ratios. The observation that the a(e)/R-e(6:6) values are greater than one shows that ion-wall interactions are important in determining the values of a(e).