We focus on primary polyps, the initial coral calcifying stage, of Stylophora pistillata, an ubiquitous Indo-Pacific stony coral species, grown under ambient and under acidic conditions (pH 8.2 and 7.6, respectively; NBS scale) predicted to occur by the end of the 21st century under the high greenhouse gas emission scenario RCP8.5. Here, we bring together results from scanning electron microscopy (SEM), synchrotron X-ray μCT, X-ray diffraction (XRD), and X-ray fluorescence (XRF) enhanced with Monte-Carlo simulations, to understand the behavior of backscattered electrons within coral skeleton material. This made it possible to determine the mineral phase composition, while revealing new sub-micrometer insights into the 3D mineral growth dynamics. Our results provide insights into newly formed coral skeletons including mineral characteristics, growth patterns and geometric relations of rapid accretion deposits (RADs) and thickening deposits (TDs) under normal and acidified oceans.This dataset is included in the OA-ICC data compilation maintained in the framework of the IAEA Ocean Acidification International Coordination Centre (see https://oa-icc.ipsl.fr). Original data were downloaded from Zenodo (see Source) by the OA-ICC data curator. In order to allow full comparability with other ocean acidification data sets, the R package seacarb (Gattuso et al, 2024) was used to compute a complete and consistent set of carbonate system variables, as described by Nisumaa et al. (2010). In this dataset the original values were archived in addition with the recalculated parameters (see related PI). The date of carbonate chemistry calculation by seacarb is 2025-10-28.