The problem of the carbonate substitution in bioapatites is studied via x-ray and neutron powder diffraction. A series of samples of low temperature carbonate hydroxyapatites with varying carbonate content was synthesized. The carbonate solubility in the hydroxyapatite system was studied with x-ray diffraction. The detailed crystal structure parameters of the synthetic carbonate hydroxyapatites were studied as a function of temperature and carbonate content from the analysis of Rietveld refinements of neutron powder diffraction data. The phosphate tetrahedron is distorted by the carbonate substitution. The tetrahedral bond lengths P-O1 and P-O2 decrease by 2--3%. The atomic displacement parameters (ADPs) of the tetrahedral P, O1, O2, and O3 sites reveal a static disorder in the carbonate hydroxyapatite specimens. The results of the present comparison are consistent with the mechanism of carbonate substitution on the mirror plane of the phosphate tetrahedron.