Many species e.g. sea urchin form amorphous calcium carbonate (ACC) precursor phases that subsequently transform into crystalline CaCO₃. It is certainly possible that the biogenic ACC might have more than 10 wt% Mg and ∼3 wt% of water. The structure of ACC and the mechanisms by which it transforms to crystalline phase are still poorly understood. In this dissertation our goal is to determine an atomic structure model that is consistent with diffraction and IR measurements of ACC. For this purpose a calcite supercell with 24 formula units, containing 120 atoms, was constructed. Various configurations with substitution of Ca by 6 Mg ions (6 wt.%) and insertion of 3-5 H ₂O molecules (2.25-3.75 wt.%) in the interstitial positions of the supercell, were relaxed using a robust density function code VASP. The most noticeable effects were the tilts of CO₃ groups and the distortion of Ca sub-lattice, especially in the hydrated case. The distributions of Ca-Ca nearest neighbor distance and CO₃ tilts were extracted from various configurations. The same methods were also applied to aragonite. Sampling from the calculated distortion distributions, we built models for amorphous calcite/aragonite of size ∼ 1700 nm³ based on a multi-scale modeling scheme. We used these models to generate diffraction patterns and profiles with our diffraction code. We found that the induced distortions were not enough to generate a diffraction profile typical of an amorphous material. We then studied the diffraction profiles from several nano-crystallites as recent studies suggest that ACC might be a random array of nano-cryatallites. It was found that the generated diffraction profile from a nano-crystallite of size ∼ 2 nm³ is similar to that from the ACC.