Nanometer-sized ionic crystals often undergo an ion exchange process when immersed in a suitable salt solution. some atoms of the crystals are replaced by atoms from the solution. Thermodynamics determines what will happen after the system reaches equilibrium. The concentration of the guest ions should reach a steady state, which is determined only by the chemical potential difference between the ionic species. In some crystals (e.g. cadmium sulfide immersed in a solution of silver ions) (1⇓–3) one observes modulated concentration patterns with length scales of many lattice spacings, which persist over the time of the experimental observation. According to thermodynamics, these patterns should not exist, especially in large crystals.
Frechette et al. (4) present a simple model that can describe this seemingly paradoxical phenomenon. The model is based on a simple lattice description where each site can be occupied by two types of ions (host or guest). Since the guest and host ions are of different sizes, the presence of guest ions induces an elastic strain that induces 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. In equilibrium, the probability of observing these waves is extremely small and vanishes when the crystal is very large. However, in agreement with experiments, simulations show that these transient waves are so long-lived that they are practically stable. Examples of these quasi-stable 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 nice explanation for this observation. When the original crystal is immersed in the solvent, a very rapid exchange takes place near the surface. The further diffusion of the gas ion species into the interior is consequently much slower. …
↵1E-mail: laio{at}sissa.it.
