# Role of Internal Stress in the Early-Stage Nucleation of Amorphous Calcium Carbonate Gels
## 1 Introduction  
Calcium carbonate (CaCO\({}_{3}\)) is ubiquitous in nature and plays an important role in biomineralization [1]. For instance, CaCO\({}_{3}\) binding phases are commonly formed by organisms that produce an exoskeleton, e.g., snails, clams, and mollusks, and in cemented granular soils formed by bacteria [2, 3]. On the technological side, calcium carbonate is key for CO\({}_{2}\) utilization approaches relying on mineralization [4], which offer a promising route to turn CO\({}_{2}\) (usually considered as a waste) into a resource, e.g., concrete binders [5, 6].  
The development of novel carbonation routes enabling low-cost and low-energy CO\({}_{2}\) capture has thus far been largely limited by a lack of understanding of the physical and chemical featuresthat govern the carbonation process [4]. Indeed, despite its ubiquitous nature, the mechanism of the precipitation of calcium carbonate remains poorly understood [7]. The carbonation process usually occurs via a dissolution-precipitation reaction, wherein a solid phase (e.g., Ca(OH)\({}_{2}\)) dissolves in an aqueous environment, reacts with dissolved carbonate species, and precipitates as an amorphous, hydrated precursor calcium carbonate gel phase [8]. Crystalline CaCO\({}_{3}\) then forms upon the drying and crystallization of the amorphous precursor [9]. Notably, the nucleation of amorphous calcium carbonate is barrierless in highly supersaturated calcium carbonate solutions and does not follow conventional nucleation pathways [10]. Although the existence of some stable prenucleation clusters has been suggested, the atomic scale mechanism of calcium carbonate nucleation in an aqueous condition remains largely unknown [11; 12]. Since amorphous calcium carbonate often acts as a precursor before the formation of subsequent crystalline carbonate phases, it is important to understand the formation mechanism of the amorphous calcium carbonate gel [13; 14].  
As an alternative route to experiments, molecular dynamics (MD) simulations can offer some valuable insights into the atomic mechanism governing the precipitation of gels [15; 16]. Indeed, although MD simulations are limited to small systems and timescales, they can offer a direct access to the time-dependent structure of calcium carbonate during its early-stage nucleation [17]. In particular, [PERSON] et al. recently developed a thermodynamically-consistent forcefield, allowing the full modeling of the nucleation of carbonates, ranging from aqueous complexes to solid carbonates [18; 19]. This forcefield was found to accurately reproduce the dynamics and thermodynamics of alkaline-earth carbonate solutions and to yield an excellent agreement with experimental data. These recent developments now make it possible to investigate the atomic mechanism behind the carbonation reaction.  
Here, based on MD simulations, we investigate the early-stage nucleation of an amorphous calcium carbonate gel in supersaturated conditions. We show that the gelation reaction manifests itself by the formation of some calcium carbonate clusters that grow over time. As a key novelty resulting from this study, we demonstrate the existence of some local, competing atomic stress acting in calcium carbonate gels, which arises from the significantly different coordination environments exhibited by Ca and C atoms. Such internal stress is found to be progressively released upon gelation and acts as a driving force for early-stage nucleation.