text: Nanogeoscience deals with structures, properties and behaviors of nanoparticles in soils, aquatic systems and atmospheres. One of the key features of nanoparticles is the size-dependence of the nanoparticle stability and reactivity. This arises from the large specific surface area and differences in surface atomic structure of nanoparticles at small particle sizes. In general, the free energy of nanoparticles is inversely proportional to their particle size. For materials that can adopt two or more structures, size-dependent free energy may result in phase stability crossover at certain sizes. Free energy reduction drives crystal growth (atom-by-atom or by oriented attachment ), which may again drive the phase transformation due to the change of the relative phase stability at increasing sizes. These processes impact the surface reactivity and mobility of nanoparticles in natural systems.
  Well-identified size-dependent phenomena of nanoparticles include:
  * Phase stability reversal of bulk (macroscopic) particles at small sizes. Usually, a less stable bulk-phase at low temperature (and/or low pressure) becomes more stable than the bulk-stable phase as the particle size decreases below a certain critical size. For instance, bulk anatase (TiO) is metastable with respect to bulk rutile (TiO). However, in air, anatase becomes more stable than rutile at particle sizes below 14 nm. Similarly, below 1293 K, wurtzite (ZnS) is less stable than sphalerite (ZnS). In vacuum, wurtzite becomes more stable than sphalerite when the particle size is less than 7 nm at 300 K. At very small particle sizes, the addition of water to the surface of ZnS nanoparticles can induce a change in nanoparticle structure  and surface-surface interactions can drive a reversible structural transformation upon aggregation/disaggregation.  Other examples of size-dependent phase stability include systems of AlO, ZrO, C, CdS, BaTiO, FeO, CrO, MnO, NbO, YO, and Au-Sb.
  * Phase transformation kinetics is size-dependent and transformations usually occur at low temperatures (less than several hundred degrees). Under such conditions, rates of surface nucleation and bulk nucleation are low due to their high activation energies. Thus, phase transformation occurs predominantly via interface nucleation  that depends on contact between nanoparticles. As a consequence, the transformation rate is particle number (size)-dependent and it proceeds faster in densely packed (or highly aggregated) than in loosely packed nanoparticles. Complex concurrent phase transformation and particle coarsening often occur in nanoparticles.
  * Size-dependent adsorption on nanoparticles  and oxidation of nanominerals.
  These size-dependent properties highlight the importance of the particle size in nanoparticle stability and reactivity.