LAUSR

Nanometer-scale ionic crystals, when immersed in an appropriate salt solution, often undergo a process of ion exchange; some atoms of the crystals are replaced by atoms from the solution. Thermodynamics dictates what will happen after the system reaches equilibrium. The concentration of the guest ions should reach a steady state dictated just by the difference in chemical potential between the ionic species. However, in some crystals (for example, cadmium sulfide immersed in a solution of silver ions) (1–3), one observes modulated concentration patterns with length scales of many lattice spacings persisting over the time of experimental observation. These patterns, according to thermodynamics, should not exist, especially in large crystals. Frechette et al. (4) introduce a simple model capable of describing this apparently paradoxical phenomenon. The model is based on a simple lattice description, in which each site can be occupied by two kinds of ions (host or guest). Since the guest and host ions have a different size, the presence of guest ions induces an elastic strain, inducing a pair potential interaction between the sites. According to this model, the concentration waves are determined by a subtle interplay between diffusion and elastic forces. At equilibrium, the probability of observing these waves is extremely small and vanishes if the crystal is very large. However, consistent with experiments, simulations show that these transient waves are so long lived that they are practically stable. Examples of these quasistable concentration waves are shown in figure 10 in ref. 4 for model nanocrystals with a geometry that resembles the experimental geometry. Frechette et al. (4) provide a neat explanation of this observation. When the original crystal is immersed in the solvent, a very fast exchange happens close to the surface. Further diffusion of the guest ionic species toward the interior is subsequently much slower. If no further ions are exchanged with the solvent (for example, because the solvent is removed), the concentration wave close to the surface looks like an ordered stripe. At this point, longrange elastic deformation plays a key role; the lattice mismatch between the host and guest ionic species determines a coherent strain on the scale of several lattice spacings, which, in turn, favors the diffusion and the subsequent stabilization of host ions only at a specific distance from the previous concentration stripe. This effect can then propagate toward the interior of the crystal and persist for a very long time.