When and Why Like-Sized, Oppositely Charged Particles Assemble into Diamond-like Crystals

Like-sized, oppositely charged nanoparticles are known to assemble into large crystals with diamond-like (ZnS) ordering, in sharp contrast to analogous molecular ions and micrometer-scale colloids, which invariably favor more closely packed structures (NaCl or CsCl). Here, we show that these experimental observations can be understood as a consequence of ionic screening and the slight asymmetry in surface charge present on the assembling particles. With this asymmetry taken into account, free-energy calculations predict that the diamond-like ZnS lattice is more favorable than other 1:1 ionic structures, namely, NaCl or CsCl, when the Debye screening length is considerably larger than the particle size. A thermodynamic model describes how the presence of neutralizing counterions within the interstitial regions of the crystal acts to bias the formation of low-volume-fraction structures. The results provide general insights into the self-assembly of non-close-packed structures via electrostatic interactions.