| Summary: | Thirty-three samples from natural apatite (Ap) solid solutions, ideal structural formula <sup>[9]</sup>Ca1<sub>2</sub><sup>[7]</sup>Ca2<sub>3</sub>(<sup>[4]</sup>PO<sub>4</sub>)<sub>3</sub><sup>[3]</sup>(F,OH,Cl), (Z = 2) were examined with electron-probe microanalysis, synchrotron high-resolution powder X-ray diffraction (HRPXRD), and Rietveld refinements. Apatite has space group <i>P</i>6<sub>3</sub>/<i>m</i> for the general chemical formula above. In Ap, the two different Ca sites are generally occupied by Ca, Mn, Sr, Na, or REE<sup>3+</sup> cations; the P site is occupied by P, Si, or S, and the X is occupied by F, OH, Cl, O<sup>2−</sup>, or (CO<sub>3</sub>)<sup>2−</sup> anions. However, it may be possible for CO<sub>3</sub><sup>2−</sup> + F<sup>−</sup> anions to partially replace PO<sub>4</sub><sup>3−</sup> groups. In this study, the unit-cell parameters <i>a</i>, <i>c</i>, and <i>c</i>/<i>a</i> ratio, vary smoothly and non-linearly with the unit-cell volume, <i>V</i>. The data falls on two distinct trend lines. The average <P-O>[4] distance is nearly constant across the Ap series, whereas the average <O-P-O>[6] angle decreases linearly. The coordination numbers for the atoms are given in square brackets in the general chemical formula above. The average <Ca1-O>[9], <Ca2-O>[6], <Ca2-O,X>[7], and Ca2-X distances change non-linearly with increasing <i>V</i>. Although Cl<sup>−</sup> anion is larger than OH<sup>−</sup> and F<sup>−</sup> anions, the <i>c</i> unit-cell parameter in F-Ap is larger than that in Cl-Ap. In Cl-Ap, the Ca2 polyhedra are larger than in F-Ap, so the O and Cl anions are under-bonded, which cause the Ca1 polyhedra to contract and charge balance the anions. Alternatively, the Ca1 polyhedra are smaller in Cl-Ap than in F-Ap, so the Ca1 polyhedra in Cl-Ap cause the <b>c</b> axis to contract compared to that in F-Ap.
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