Modeling Nucleation and Growth

Crystallization from a supersaturated solution frequently proceeds through a series of transient, metastable phases prior to the formation of the lowest-energy, stable polymorph. This phenomenon, popularly referred to as “Ostwald’s Rule of Stages”, has been observed across nearly all classes of solid-state materials: from inorganic minerals and functional technological materials to organic crystals and biological protein crystals. Despite there being a lower thermodynamic driving force for the formation of a metastable polymorph, a metastable phase can still dominate the kinetics of crystallization if it has a lower nucleation barrier than the equilibrium phase. Following the complete crystallization of a metastable phase, the next more-stable polymorph nucleates and grows – consuming the previous metastable phase in a recursive, energetically-cascading series of polymorphic stages down to the lowest-energy, equilibrium phase.

Calculated nanoparticle shapes of various manganese (hydr)oxides. Nanoscale aqueous stability diagrams calculated by combining these surface energies with E-pH (Pourbaix) diagrams

By computing the energy of a critical nucleus in equilibrium with an aqueous environment, we can model how pH, redox potential, and alkali ions can influence the relative nucleation rates between competing polymorphs. We developed new high-throughput tools to compute the surface energies of various crystal structures using DFT. By combining these surface energies with bulk free energy calculations solid-aqueous equilibria, we built a theoretical framework that can explain why the high-pressure Aragonite polymorph of CaCO3 nucleates under ambient conditions in seawater, and can rationalize the multistage crystallization of manganese oxide polymorphs in solution. Our computed ‘synthesis maps’ successfully capture which metastable polymorphs nucleate first, the order of their appearance, and their relative lifetimes.

During solid-state synthesis, metastable materials often appear as non-equilibrium reaction byproducts—which form ubiquitously during materials formation, but are difficult to anticipate within existing theoretical frameworks. We are building new kinetic theories to unify classical thermodynamics, nucleation, diffusion, and crystal growth theories, to enable the prediction of Temperature-Time-Transformation (TTT) diagrams for solid-state ceramic synthesis. These TTT diagrams aim to capture crucial features in the kinetic evolution of ceramic powder precursors; including reaction sequence, reaction onset temperature, phase decomposition, liquid formation, and metastable intermediates. Guided by these TTT diagrams, a solid-state chemist can more rationally navigate through the thermodynamic and kinetic energy landscape towards the phase-pure synthesis of target materials.

Relevant Publications

Bianchini, Matteo, et al. "The interplay between thermodynamics and kinetics in the solid-state synthesis of layered oxides." Nature Materials 19.10 (2020): 1088-1095.

Powell-Palm, Matthew J., Boris Rubinsky, and Wenhao Sun. "Freezing water at constant volume and under confinement." Communications Physics 3.1 (2020): 1-8.

Wenhao Sun, D. Kitchaev, D. Kramer, G. Ceder, “Non-equilibrium crystallization pathways of manganese oxides in aqueous solution” Nature Communications 10, 1 (2019)

B.R. Chen, Wenhao Sun, G. Ceder, M. F. Toney, L. T. Schelhas, et al., “Understanding crystallization pathways leading to manganese oxide polymorph formation” Nature Communications, 9, 1, (2018)

Wenhao Sun, G. Ceder, “Induction time of a polymorphic transformation”, CrystEngComm (2017)

Wenhao Sun, S. Jayaraman, W. Chen, K. Persson, G. Ceder, “Nucleation of metastable aragonite CaCO3 in seawater” PNAS 112, 11 (2015)

Wenhao Sun, Gerbrand Ceder, “Efficient creation and convergence of surface slabs” Surface Science 617, 53, (2013)