Towards an improved, empirically derived model describing real nucleation and particle growth reactions at the atomic level

Nanostructured materials have revolutionised all types of industrial sectors in the past, and their potential for addressing worldwide challenges in the future is immense. Yet, the straightforward design and synthesis of new nanomaterials is frustrated by the scantiness of knowledge on the fundamental mechanisms governing crystal formation. While the classical nucleation theory, the LaMer model and alternative multi-step models offer theoretical descriptions and important concepts, still none of them can explain the complexity of real nucleation and growth reactions on the atomic scale, nor can they reliably predict crystal formation processes. Experimentally accessing information of particle formation in liquids has also not been feasible in the past due to technical difficulties to directly observe dynamic processes <em>in situ</em> at the atomic scale. However, recent developments in liquid-phase microscopy have opened new opportunities for overcoming this hurdle. In this article, we describe the current state-of-the-art electron microscopy methods that allow particle growth reactions to be observed in situ, and in liquid phase, at the atomic scale. Applying these methods for studying nucleation and growth reactions of different metal nanoparticles allows us for disentangling and classifying the different reactions present during early particle formation. Based on our summarised results, we propose a conclusive and generally valid phenomenological growth model that deepens the comprehension of initial material formation at the atomic scale. Moreover, the growth behaviour of other (metallic) particles in liquid phase can be predicted based on our model, which offers a crucial step towards controlling atomic-scale nanomaterial synthesis in the future.