  Amorphous calcium carbonate (ACC) is an important precursor for
biomineralisation in marine organisms. Among the key outstanding problems
regarding ACC are how best to understand its structure and how to rationalise
its metastability as an amorphous phase. Here, we report high-quality atomistic
models of ACC generated by using state-of-the-art interatomic potentials to
help guide fits to X-ray total scattering data. Exploiting a recently-developed
inversion approach, we extract from these models the effective
Ca$\boldsymbol\cdots$Ca interaction potential governing ACC formation. This
potential contains minima at two competing distances, corresponding to the two
different ways in which carbonate ions bridge Ca$^{2+}$-ion pairs. We reveal an
unexpected mapping to the Lennard-Jones--Gauss (LJG) model normally studied in
the context of computational soft-matter, with the empirical LJG parameters for
ACC taking values known to promote structural complexity. In this way we show
that both the complex structure of ACC and its resilience to crystallisation
are actually encoded in the geometrically-frustrated effective interactions
between Ca$^{\boldsymbol 2+}$ ions.

Materials Science