Syntheses, crystal structures, and comparisons of rare-earth oxyapatites Ca2 RE 8(SiO4)6O2 (RE = La, Nd, Sm, Eu, or Yb) and NaLa9(SiO4)6O2

X-ray powder diffraction was used to determine the structures of six different rare-earth oxyapatites that were shown to be isostructural.


Chemical context
For immobilization of the radionuclides in the high-level waste (HLW) raffinate stream following aqueous reprocessing of used nuclear fuel, glass-ceramic waste forms are being developed as an alternative to borosilicate glass (Crum et al., 2012(Crum et al., , 2014(Crum et al., , 2016. As a result of the chemical diversity in the HLW raffinate stream, several crystalline phases including powellite [(AE)MoO 4 ], rare-earth borosilicate [(RE) 3 BSi 2 O 10 ], cerianite (Zr x Ce 1-x O 2 ), and oxyapatite [(AE) 2 (RE) 8 (SiO 4 ) 6 O 2 ], where AE and RE are alkaline earth and rare-earth metals, respectively, crystallize from the glass matrix upon slow cooling inside the waste canister during the waste form fabrication process (Crum et al., 2012(Crum et al., , 2014(Crum et al., , 2016. Understanding the crystal chemistry and formation of these phases is important in the development of the glass-ceramic waste forms. In the actual waste form, each crystalline phase containing RE elements contains a distribution matching that within the waste stream. However, for characterization purposes, simplified versions of these phases were synthesized so that the individual contributions towards the chemical durability of the overall waste form could be evaluated (Neeway et al., 2019). In this work, we report the synthesis method and crystal structures of oxyapatites, Ca 2 RE 8 -(SiO 4 ) 6 O 2 (RE = La, Nd, Sm, Eu, Yb) and NaLa 9 4) 6 O 2 . Additional information on the synthesis can be found in our previous paper (Peterson et al., 2018). The crystal structures of Ca 2 RE 8 (SiO 4 ) 6 O 2 (RE = La, Ce, Nd; Schroeder & Mathew, 1978;Fahey et al., 1985;Massoni et al., 2018) were studied in detail previously as in Inorganic Crystal Structure Database (ICSD) entries 5268, 92041, and 62174 for La, Ce, and Nd, ISSN 2056-9890 respectively, but the crystal structures of Ca 2 RE 8 -(SiO 4 ) 6 O 2 (RE = Sm, Eu, Yb) and NaLa 9 (SiO 4 ) 6 O 2 have never been reported in detail before. The oxyapatites with La and Nd in this study are re-refined structures and are reported to compare with previously reported structures. We compare the general structural parameters of these isostructural oxyapatites with different RE cations.
In a study by Lambert et al. (2006), the structural models of La 9.33 (SiO 4 ) 6 O 2 , La 9 Ba(SiO 4 )6O 2+ , La 9 Sr(SiO 4 ) 6 O 2+ , and La 9 Ca(SiO 4 ) 6 O 2+ were refined against neutron powder diffraction data within the P6 3 /m, P6 3 , and P3 space groups, and the best results were obtained using the P6 3 symmetry. They found that a symmetry difference by m [001] between P6 3 / m and P6 3 allows two independent sites for lanthanum for P6 3 symmetry, and their occupancies are uncorrelated. However, they mention that the framework shows a pseudo-symmetry to P6 3 /m as the symmetry breaking by m [001] is very small. In the study by Sansom et al. (2004), the neutron powder diffraction data of Ga-doped La 9.67 Si 5 GaO 26 and La 10 Si 4 Ga 2 O 26 were fit within the P6 3 /m, P6 3 , and P3 space groups, and both P3 and P6 3 symmetries resulted in better fits than P6 3 /m for the   Crystal structure of Ca 2 RE 8 (SiO 4 ) 6 O 2 . Table 1 Summary of data on Ca 2 RE 8 (SiO 4 ) 6 O 2 (RE = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Er, Yb, Lu) from the current study and literature.  (Ito, 1968) Ca 2 Gd 8 (SiO 4 ) 6 O 2 9.421 6.888 529 6.030 PDF 00-028-0212 Ca 2 Dy 8 (SiO 4 ) 6 O 2 9.37 6.81 518 6.298 (Ito, 1968) Ca 2 Er 8 (SiO 4 ) 6 O 2 9.33 6.75 509 6.534 (Ito, 1968) Ca 2 Yb 8 (SiO 4 ) 6 O 2 9.2974 6.6975 501 6.785 Current study Ca 2 Lu 8 (SiO 4 ) 6 O 2 9.28 6.68 498 6.884 (Ito, 1968) cation-deficient La 9.67 Si 5 GaO 26 compound, whereas all three space groups gave similar fitting results for the stoichiometric La 10 Si 4 Ga 2 O 26 compound. They chose the P6 3 /m space group for the La 10 Si 4 Ga 2 O 26 compound as it is the highest symmetry space group and concluded that lowering of the space group from P6 3 /m to P6 3 allows for variation in occupancy for the lanthanum site(s) as the La1 site becomes two with P6 3 symmetry, whereas there is only one site for La1 in P6 3 /m; this resulted in a better fit for cation-deficient La 9.67 Si 5 GaO 26 in P6 3 symmetry. However, an a posteriori symmetry analysis using SUPERFLIP (Palatinus & van der Lee, 2008), shows that oxyapatites in this study crystallize in the P6 3 /m space group.
The cations in the P6 3 /m space group occupy Wyckoff positions of 4f and 6h. The 4f site is occupied by RE and A atoms coordinated by nine oxygen atoms whereas the 6h site is mostly occupied by RE coordinated by seven oxygen atoms (Fig. 1), and the isolated [SiO 4 ] 4À tetrahedra are linked by the cations (Fig. 2). Detailed atomic coordinates, bond lengths, and angles are given in the supporting information.
The unit-cell parameters, unit-cell volumes, and densities of the synthesized Ca 2 RE 8 (SiO 4 ) 6 O 2 (RE = La, Nd, Sm, Eu, Yb) compounds were well fit to the trendlines calculated from the previously reported values of RE oxyapatites (Fig. 3), and details of unit-cell parameters, cell volumes, and densities of Ca 2 RE 8 (SiO 4 ) 6 O 2 from the literature and this work are provided in Table 1. The unit-cell parameters and unit-cell volumes increase linearly with increases in the ionic crystal radii (Shannon, 1976) of nine-coordinated RE 3+ cations whereas the density decreases non-linearly with the ionic crystal radii of larger nine-coordinated RE 3+ cations. The parameters of Ca-Yb oxyapatite are reported for the first time, and they match closely to predicted values shown by trendlines based on the literature data.

Synthesis and crystallization
The following chemicals were used as-received: Ca(NO 3 ) 2 Á4H 2 O (Sigma-Aldrich, !99%), NaNO 3 (Sigma-Aldrich, 99 O, 80 mL of ethanol, and 80 mL of glacial acetic acid were stirred in a Pyrex beaker until the solution became clear, and then 40 mL of TEOS was added and mixed for 24 h. After 24 h of mixing, the solution was dried at 353 K for 6 d, and the dried product was heat treated at 473 K for 1 h and milled, calcined at 873 K for 4 h, then at 1273 K for 1 h and milled, and pressed into 2-cm diameter pellets using a cold isostatic press at 110 MPa. Finally, the pellets were fired at 1823 K for 8 h, and pure Ca-Nd oxyapatite was crystallized. More details of synthesis are provided elsewhere (Peterson et al., 2018). For all other oxyapatites, the same procedures were used with 0.2Â quantities, and for Na-La oxyapatite, the molar ratio of Na:La in the precursors was 1:9.
The P-XRD analysis was performed on the synthesized oxyapatites using a Bruker D8 Advance diffractometer (see Table 2 for collection parameters). The P-XRD results showed the samples to be pure oxyapatites except for the Ca-Yb compound, which also contained some Yb 2 O 3 and Yb 2 (SiO 4 )O phases. The elemental compositions of each oxyapatite sample were measured with a JEOL 8530 Hyperprobe EPMA. Each sample was analyzed at five to eight different locations and the averages and standard deviations of these measurements are given in Table 3, on an elemental mass% basis. Because of the inaccuracy of measuring oxygen directly, it was calculated indirectly, based on target stoichiometry with the cations, using direct measurements of the cations (i.e., AE, A, RE, and Si). Table 3 also gives the molar elemental ratios of each element normalized to total atoms in the oxyapatite structure per unit cell = 42 atoms. Fig. 4 shows that the EPMA measurements confirm that samples were all on target to the batched compositions.

Figure 4
Comparison of the number of atoms per unit cell between stoichiometric and measured A-RE oxyapatites. Note that error bars are shown for measured values but are too small to see and, in most cases, are smaller than the size of the datapoints.