Computer simulation can be a valuable complement to experiment, especially for probing the atomic scale detail during crystal growth. However, this is contingent on being able to address several key challenges, namely length-scale, time-scale and the accuracy of the underlying potential energy landscape.  The aim of this presentation will be to describe some of the approaches available for tackling these challenges for crystal growth of minerals from aqueous solution. In particular, the case of calcium carbonate formation will be examined. Here the process of nucleation and growth is made more intriguing by the presence of prenucleation species, both liquid and solid amorphous phases, in addition to the question of polymorphism.

In this work the derivation and application of an accurate force field for describing aqueous calcium carbonate systems will be discussed.  In contrast to previous models, considerable emphasis has been placed on the accurate reproduction of the thermodynamics of the system, rather than just structural or mechanical properties [1]. By fitting the properties of both the hydrated ions and two of the bulk mineral phases, calcite and aragonite, the simulation model is able to reproduce the solubility and key relative polymorph energetics.  Based on this, several questions regarding the growth of calcium carbonate from aqueous solution have been addressed:

1) What is the nature of prenucleation species in calcium carbonate solution?

Gebauer et al [2] have concluded that stable species exist in solutions of calcium and carbonate ions prior to nucleation. Subsequently, Pouget et al [3] identified nm-sized clusters using cryo-TEM. Given the difficulty of directly characterising the structure and dynamics of these species in situ by experiment, this represents an ideal opportunity for simulation. Here molecular dynamics indicates that the initial association of ions is in the form of an ionic supramolecular polymer that is dynamically changing [4]. As the concentration increases, enhanced sampling techniques show that this transforms to more compact structures that remain significantly hydrated [5]. Significantly, no minimum is observed in the free energy landscape that would give rise to a preferred cluster size. 

2) How do organics influence the nucleation of calcium carbonate?

During biomineralisation organic molecules clearly have a strong influence on the growth and assembly of calcium carbonate. This raises the question of how much of this influence occurs prior or subsequent to nucleation? Here the interaction of three simple carboxylate-containing molecules with various calcium carbonate species will be discussed along with the implications for the broader impact of organics on nucleation/growth [6].

3) Why does amorphous calcium carbonate appear as a precursor to crystalline phases?

Under certain conditions amorphous calcium carbonate (ACC) is observed to occur as a precursor to formation of crystalline polymorphs. One explanation for this might be that nucleation of the amorphous phase is faster and so this is just a matter of kinetic control.  Simulations of the thermodynamics of nanoparticles of ACC and calcite indicate that below a size of approximately 4 nm the former material is actually the thermodynamically stable species [7]. Therefore under homogeneous conditions it appears likely that both thermodynamics and kinetics will favour initial formation of ACC. Furthermore, the ACC nanoparticles are able to lower their free energy by incorporating more water as the size of the particle increases. Under kinetically controlled growth conditions this would therefore lead to a heterogeneous distribution of water through out the nanoparticle, consistent with the proposed structure of ACC from Goodwin et al [8].

4) How do ions attach to calcite during growth?

Growth of calcite from solution is well known to occur via attachment of ions to steps/kinks on the dominant (104) surface. A subtle question is whether ions attach directly from solution or whether they first coordinate to the flat surface and then diffuse to the more reactive growth sites?  Due to the presence of two strongly ordered water layers above this surface, which is observed by X-ray reflectivity and well described by the present simulation model (at least in terms of the water structure) [9], it appears that neither Ca²⁺ or CO₃^2- ions are able to coordinate directly to the (104) facet. Using an approach previously demonstrated for barite [10], that is able to yield quantitative rate constants for multistep growth processes, we are beginning to explore both the thermodynamics and kinetics of ion attachment to calcite.

[1] P. Raiteri et al, J. Phys. Chem. C, 114, 5997-6010 (2010)

[2] D. Gebauer et al, Science, 322, 1819-1822 (2008)

[3] E. Pouget et al, Science, 323, 1455-1458 (2009)

[4] R. Demichelis et al, Nature Comm., 2, 590 (2011)

[5] A.F. Wallace et al (submitted)

[6] P. Raiteri et al, Faraday Discussions, 159, 61-85 (2012)

[7] P. Raiteri and J.D. Gale, J. Am. Chem. Soc., 132, 17623-17634 (2010)

[8] A.L. Goodwin et al, Chem. Mater., 22, 3197-3205 (2010)

[9] P. Fenter et al, J. Phys. Chem. C., 117, 5028-5042 (2013)

[10] A.G. Stack et al, J. Am. Chem. Soc., 134, 11-14 (2012)

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1. In situ TEM investigations of particle-mediated crystal growth
2. Revealing structural and thermodynamic details of calcium carbonate crystallization intermediates through ab initio methods