Developments in the field of nanostructures open new ways for designing and manufacturing innovative materials. Here, we focused on new original ways of calculating energy changes during the substitution of foreign ions into the structure of apatites and bioapatites. Using these tools, the energetic costs of ion exchanges were calculated for the exemplary cases known from the literature. It was established that the most costly were ion exchanges of some cations inside apatites and of anions, and the least costly exchanges in tetrad channel positions. Real energy expenses for bioapatites are much smaller in comparison to mineral apatites due to the limited involvement of magnesium and carbonates in the structure of hard tissues. They are of the order of several electron volts per ion. The rigorous dependences of the energy changes and crystallographic cell volumes on the ionic radii of introduced cations were proved. The differentiation of the positioning of foreign ions in locations of Ca(I) and Ca(II) could be calculated in the case of a Ca-Pb reaction in hydroxyapatite. The energetic effects of tooth aging were indicated. The ability of energy change calculation during the ion exchange for isomorphic substances widens the advantages resulting from X-ray diffraction measurements.
Keywords: X-ray diffraction; apatites; bioapatite; energy changes; ion exchanges.