Theoretical study of anisotropic effects in crystal growth on the example of concrete and calcium oxalate monohydrate

Abstract: While many crystals, both natural and artificial, grow isotropically, there are examples of crystals growing anisotropically. The aim of this theoretical study was to confirm the growth modes displayed by three different crystals, representing 3D, 2D and 1D structures. This was done by using energetic calculations with both molecular mechanics, with ReaxFF$_{ \textrm {SiO}}$ as the force field, and semi-empirical methods, with PM6 as the method. To start with, the 3D structure was represented by CaO, and both the ReaxFF$_{\textrm{SiO}}$ and PM6 results confirmed the isotropic growth mode of this rock salt structure. As for the 2D structure, nanoplatelets of calcium silicate hydrate (C-S-H), which make up the bulk phase in concrete, were investigated. These were modelled as C-S-H clusters with approximate cylinder shapes and adjustable chemical bonds and compositions. The ReaxFF$_{\textrm{SiO}}$ calculations showed that the energetic gain was higher when the radius was increased than when the height was increased. This was in agreement with the platelet shape of real C-S-H nanoparticles. However, the high computational costs of semi-empirical methods meant that the PM6 results did not represent a large enough cylinder size span to confirm the ReaxFF$_{ \textrm {SiO}}$ results. Lastly, the 1D structure was represented in the form of calcium oxalate monohydrate (COM), which may form elongated shapes such as raphides and styloids. Due to the ReaxFF$_{\textrm{SiO}}$ force field not being optimized for COM crystals, only PM6 calculations were performed. However, the computational demands of semi-empirical methods again limited the number of PM6 data points considerably. Therefore, it could not be concluded if the 1D growth mode was the most energetically favourable.