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.

High-energy nickel (Ni)–rich cathode will play a key role in advanced lithium (Li)–ion batteries, but it suffers from moisture sensitivity, side reactions, and gas generation. Single-crystalline Ni-rich cathode has a great potential to address the challenges present in its polycrystalline counterpart by reducing phase boundaries and materials surfaces. However, synthesis of high-performance single-crystalline Ni-rich cathode is very challenging, notwithstanding a fundamental linkage between overpotential, microstructure, and electrochemical behaviors in single-crystalline Ni-rich cathodes. We observe reversible planar gliding and microcracking along the (003) plane in a single-crystalline Ni-rich cathode. The reversible formation of microstructure defects is correlated with the localized stresses induced by a concentration gradient of Li atoms in the lattice, providing clues to mitigate particle fracture from synthesis modifications.

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* These authors contributed equally # Correspondence and request for materials should be directed to JJDY (jjdeyoreo@lbl.gov).Nucleation in the natural world often occurs in the presence of organic interfaces. In mineralized tissues, a range of macromolecular matrices are found in contact with inorganic phases and are believed to direct mineral formation. In geochemical settings, mineral surfaces, which are often covered with organic or biological films, surround the volume within which nucleation occurs.In the classical picture of nucleation, the presence of such interfaces is expected to have a profound effect on nucleation rates, simply because they can reduce the interfacial free energy, which controls the height of the thermodynamic barrier to nucleation of the solid phase.However, the recent discovery of a nearly monodisperse population of calcium carbonate clusters Ñ so called pre-nucleation clusters Ñ and the many observations of amorphous precursor phases have called into question the applicability of classical descriptions. Here we use in situ observations of nucleation on organothiol self-assembled monolayers (SAMs) to explore the energetics and pathways of calcite nucleation at organic interfaces. We find that carboxyl SAM-directed nucleation is described well in purely classical terms through a reduction in the thermodynamic barrier due to decreased interfacial free energy. Moreover, the differences 2 in nucleation kinetics on odd and even chain-length carboxyl SAMs are attributable to relative differences in these energies. These differences arise from varying degrees of SAM order related to oxygen-oxygen interactions between SAM headgroups. In addition, amorphous particles formed prior to or during crystal nucleation do not grow and are not observed to act as precursors to the crystalline phase. Instead, calcite nucleates independently. These results imply that the recently proposed model of calcite formation as a non-classical process, one which proceeds via aggregation of stable pre-nucleation clusters that form an amorphous precursor from which the crystalline phase emerges, is not applicable to template-directed nucleation and does not provide a universal description of calcite formation.

The physical basis for how macromolecules regulate the onset of mineral formation in calcifying tissues is not well established. A popular conceptual model assumes the organic matrix provides a stereochemical match during cooperative organization of solute ions. In contrast, another uses simple binding assays to identify good promoters of nucleation. Here, we reconcile these two views and provide a mechanistic explanation for template-directed nucleation by correlating heterogeneous nucleation barriers with crystal-substrate-binding free energies. We first measure the kinetics of calcite nucleation onto model substrates that present different functional group chemistries (carboxyl, thiol, phosphate, and hydroxyl) and conformations (C11 and C16 chain lengths). We find rates are substrate-specific and obey predictions of classical nucleation theory at supersaturations that extend above the solubility of amorphous calcium carbonate. Analysis of the kinetic data shows the thermodynamic barrier to nucleation is reduced by minimizing the interfacial free energy of the system, γ. We then use dynamic force spectroscopy to independently measure calcitesubstrate-binding free energies, ΔG b . Moreover, we show that within the classical theory of nucleation, γ and ΔG b should be linearly related. The results bear out this prediction and demonstrate that low-energy barriers to nucleation correlate with strong crystal-substrate binding. This relationship is general to all functional group chemistries and conformations. These findings provide a physical model that reconciles the long-standing concept of templated nucleation through stereochemical matching with the conventional wisdom that good binders are good nucleators. The alternative perspectives become internally consistent when viewed through the lens of crystal-substrate binding.B iological systems are unique in their ability to organize minerals into functional materials with complex patterns and architectures. A substantial body of evidence suggests specialized macromolecules, particularly proteins (1, 2) and carbohydrates (3, 4), provide preferential sites for nucleation to direct the placement, timing, and orientation of crystals (5), both intra-and extracellular. Within the biomineralization community, the conventional view of biologically directed nucleation is that macromolecular matrices present an interfacial match to the crystal lattice that assists in forming the crystal nucleus. This cooperative view of directed nucleation is rooted in the collective action of multiple residues that guide the organization of ions into a configuration defining the energetic minimum for the system. A series of in vitro observations have reinforced this picture by showing that highly ordered organic monolayers can control the location and orientation of calcite crystals precipitated from solution (6). In this approach, good templates are revealed through a direct functional assay, i.e., nucleation. Over the years, this view of mineralization, both in the context of natural stru...