Despite its importance in many industrial, geological and biological processes, the mechanism of crystallization from supersaturated solutions remains a matter of debate. Recent discoveries show that in many solution systems nanometre-sized structural units are already present before nucleation. Still little is known about the structure and role of these so-called pre-nucleation clusters. Here we present a combination of in situ investigations, which show that for the crystallization of calcium phosphate these nanometre-sized units are in fact calcium triphosphate complexes. Under conditions in which apatite forms from an amorphous calcium phosphate precursor, these complexes aggregate and take up an extra calcium ion to form amorphous calcium phosphate, which is a fractal of Ca 2 (HPO 4 ) 3 2 À clusters. The calcium triphosphate complex also forms the basis of the crystal structure of octacalcium phosphate and apatite. Finally, we demonstrate how the existence of these complexes lowers the energy barrier to nucleation and unites classical and non-classical nucleation theories.

Many living organisms contain biominerals and composites with finely tuned properties, reflecting a remarkable level of control over the nucleation, growth and shape of the constituent crystals. Peptides and proteins play an important role in achieving this control. But the general view that organic molecules affect mineralization through stereochemical recognition, where geometrical and chemical constraints dictate their binding to a mineral, seems difficult to reconcile with a mechanistic understanding, where crystallization is controlled by thermodynamic and kinetic factors. Indeed, traditional crystal growth models emphasize the inhibiting effect of so-called 'modifiers' on surface-step growth, rather than stereochemical matching to newly expressed crystal facets. Here we report in situ atomic force microscope observations and molecular modelling studies of calcite growth in the presence of chiral amino acids that reconcile these two seemingly divergent views. We find that enantiomer-specific binding of the amino acids to those surface-step edges that offer the best geometric and chemical fit changes the step-edge free energies, which in turn results in macroscopic crystal shape modifications. Our results emphasize that the mechanism underlying crystal modification through organic molecules is best understood by considering both stereochemical recognition and the effects of binding on the interfacial energies of the growing crystal.

Assembly of two-dimensional (2D) molecular arrays on surfaces produces a wide range of architectural motifs exhibiting unique properties, but little attention has been given to the mechanism by which they nucleate. Using peptides selected for their binding affinity to molybdenum disulfide, we investigated nucleation of 2D arrays by molecularly resolved in situ atomic force microscopy and compared our results to molecular dynamics simulations. The arrays assembled one row at a time, and the nuclei were ordered from the earliest stages and formed without a free energy barrier or a critical size. The results verify long-standing but unproven predictions of classical nucleation theory in one dimension while revealing key interactions underlying 2D assembly.

Environmental scanning electron microscopy was used to image meniscus formation between an AFM tip and a surface. At high relative humidity, 70%-99%, the meniscus formed is 100 to 1200 nm in height, orders of magnitude larger than predicted by the Kelvin equation using spherical geometry. The height of the meniscus also demonstrates hysteresis associated with increasing or decreasing relative humidity.