Crystal Structure Refinements of Four Monazite Samples from Different Localities

This study investigates the crystal chemistry of monazite (APO4, where A = Lanthanides = Ln, as well as Y, Th, U, Ca, and Pb) based on four samples from different localities using single-crystal X-ray diffraction and electron-probe microanalysis. The crystal structure of all four samples are well refined, as indicated by their refinement statistics. Relatively large unit-cell parameters (a = 6.7640(5), b = 6.9850(4), c = 6.4500(3) Å, β= 103.584(2)◦, and V = 296.22(3) Å3) are obtained for a detrital monazite-Ce from Cox’s Bazar, Bangladesh. Sm-rich monazite from Gunnison County, Colorado, USA, has smaller unit-cell parameters (a = 6.7010(4), b = 6.9080(4), c = 6.4300(4) Å, β= 103.817(3)◦, and V = 289.04(3) Å3). The a, b, and c unit-cell parameters vary linearly with the unit-cell volume, V. The change in the a parameter is large (0.2 Å) and is related to the type of cations occupying the A site. The average <A-O> distances vary linearly with V, whereas the average <P-O> distances are nearly constant because the PO4 group is a rigid tetrahedron.

. Polyhedral representation of the monazite structure: (a) isolated PO4 tetrahedra and CeO9 polyhedra that share edges or corners to form chains parallel to the c axis, and (b) CeO9 polyhedra share common edges along the (a) axis, whereas PO4 tetrahedra and CeO9 polyhedra share corners along the (b) axis.

Sample Description
Two detrital (1 and 3) and two pegmatitic (2 and 4) monazite samples were used in this study (Table 1). The detrital monazite-rich heavy mineral fractions were separated from two raw beach placer sand samples collected from Cox's Bazar, Bangladesh. Zircon samples from this locality were previously characterized [16,17]. Fragments of monazite crystals were separated from the pegmatitic samples using a knife. All the samples were examined with a stereomicroscope and a polarizing microscope to assess their physical and optical characteristics. High-quality, inclusion-free, and highpurity crystals were selected for examination using single-crystal X-ray diffraction (SCXRD) and electron-probe microanalysis (EPMA), as described below. This study investigates the crystal chemistry of four monazite samples from different localities using SCXRD and electron-probe microanalysis (EPMA). Variations among unit-cell parameters, bond distances, and chemical compositions of monazite are explained using crystal-chemical principles.

Sample Description
Two detrital (1 and 3) and two pegmatitic (2 and 4) monazite samples were used in this study ( Table 1). The detrital monazite-rich heavy mineral fractions were separated from two raw beach placer sand samples collected from Cox's Bazar, Bangladesh. Zircon samples from this locality were previously characterized [16,17]. Fragments of monazite crystals were separated from the pegmatitic samples using a knife. All the samples were examined with a stereomicroscope and a polarizing microscope to assess their physical and optical characteristics. High-quality, inclusion-free, and high-purity crystals were selected for examination using single-crystal X-ray diffraction (SCXRD) and electron-probe microanalysis (EPMA), as described below.

Electron-Probe Microanalysis (EPMA)
The chemical composition of the monazite samples was obtained using a JEOL JXA-8200WD-ED electron-probe microanalyzer (Akishima, Tokyo, Japan) using the same crystal that was used for Minerals 2020, 10, 1028 3 of 11 single-crystal data collection. The JEOL operating program on a Solaris platform was used for ZAF (atomic number; absorption, and flouresence) correction and data reduction. The wavelength dispersive (WD) analysis was conducted quantitatively using an accelerated voltage of 15 kV, a beam current of 2 × 10 −8 A, and a beam diameter of 5 µm. Peak overlapping problems in the elemental analysis of monazite are very common and were solved following the method previously described [18]. Various minerals and compounds were used as standards (CePO 4 for Ce and P, NdPO 4 for Nd, YPO 4 for Y, ThO 2 for Th, LaPO 4 for La, SmPO 4 for Sm, PrPO 4 for Pr, GdPO 4 for Gd, DyPO 4 for Dy, EuPO 4 for Eu, TbPO 4 for Tb, zircon for Si, Cr-augite for Ca, barite for S, pyromorphite for Pb, UO 2 for U, and hornblende for Fe). Qualitative energy-dispersive spectra (EDS) shows what elements are present in the sample and then quantitative analyses were obtained. Fourteen spots were analyzed for each sample. The oxide wt.% and the atom per formula unit (apfu), based on four O atoms, are given in Table 2.

Single-Crystal X-ray Diffraction (SCXRD)
Each monazite crystal was mounted on the tip of a glass fiber (diameter less than 0.1 mm) using an adhesive. The mounted crystal was placed on a goniometer head and centered in the X-ray beam. SCXRD data were collected with a Nonius Kappa CCD diffractometer using a Bruker Nonius FR591(Madison, WI, USA) Rotating Anode with graphite mono-chromated MoKα radiation (λ = 0.71073 Å). The generator setting was 50 kV and 36 mA, and the cryostat setting was set to 295 K (room temperature). The detector-crystal distance was fixed at 35 mm. A total of 10 frames were collected for unit-cell determination with scan settings of 1 • rotation per frame (total rotation = 10 • ) and 22 s exposure time per frame. After obtaining satisfactory unit-cell parameters and mosaicity values, complete datasets were collected using 2 • per frame rotation with exposure of 42 to 122 s per frame. The diffraction spots were measured in full, scaled with Scalepak, corrected for Lorentz-polarization, and integrated using the Nonius program suite DENZO-SMN (version 2000) [19]. The data were corrected for absorption using the analytical absorption correction method. The centrosymmetric space group P2 1 /n was obtained based on systematic absence of reflections and structure factor statistics. The experimental techniques used in this study are well established, e.g., in References [20][21][22][23][24][25][26].

Structure Refinements of SCXRD Data
Full-matrix least-squares refinements were carried out with the SHELXL-97 program using neutral atom scattering factors [27]. The WinGX program suite (version 2020.1) was used as the platform for the structure refinements [28]. Atom coordinates for monazite-Ce and SmPO 4 were used as the starting structural models [8]. The crystal structure of monazite was confirmed by direct methods followed by Fourier and difference Fourier maps. Anisotropic displacement parameters for all atoms were refined as well as the site occupancy factors (sofs) for the A and P sites, in terms of the dominant atom in these sites. Details of data collection, processing, and refinements are given in Table 3. The refined atom coordinates and displacement parameters are given in Table 4. Selected bond distances and angles are given in Table 5, which also includes bond-valence sum (BVS) values [29,30]. Table 3. Single-crystal structure refinement (single-crystal X-ray diffraction, SCXRD) data for the four monazite § samples used in this study.    (3)

Variations of Unit-Cell Parameters
The a, b, c, and β unit-cell parameters vary linearly with unit-cell volume, V, for the synthetic compounds SmPO 4 , PrPO 4 , CePO 4 , and LaPO 4 ( Figure 2) [8]. The a and b unit-cell parameters for our samples are close to the linear line drawn using the literature data in Reference [8] (Figure 2a,b). The a, b, and c unit-cell parameters for our samples vary linearly with V, but not the β angle (Figure 2d). Such linear relations were also observed in other minerals [32][33][34][35][36]. The red trend lines for our unit-cell parameters are different from those for the synthetic samples ( Figure 2). The largest a and b unit-cell parameters obtained for sample 1 differ by about 0.0263 and 0.0353 Å respectively, from the pure CePO 4 compound (Figure 2a,b), because the weighted average ionic radii for sample 1 (= 1.182 Å) differs slightly from CePO 4 (= 1.196 Å). The weighted average radii values were calculated based on the A site cations and their ionic radii [31].
The β unit-cell parameter decreases with increasing V, and our samples plot close to the linear line (Figure 2d). If the a, b, and c unit-cell parameters increase, then A and P cations come closer to each other and repulsion occurs, which may be the reason for the decrease in the β angle.

Site Occupancy Factor (sof) and Chemical Composition
The chemical compositions for our samples were discussed above. The sof for A site for our samples were refined using the dominant Ce or Sm atom and the values are 0.975(4), 0.999(7), 0.963(5), and 0.96(1) ( Table 4). These values indicate that the A site is 96% to 100% fully occupied by Ce or Sm atoms and may also contain a small amount of other heavier atoms to give an occupancy slightly < 1. The A site for samples 1, 2, and 3 contains 0.404, 0.330, and 0.367 apfu Ce, whereas sample 4 contains 0.193 apfu Sm ( Table 2). The number of electrons for Ln 3+ cations are very close to each other and the sofs obtained for the A site using either Ce or Sm atom are biased, as indicated by their chemical compositions. EPMA chemical data are commonly used to fix the A site occupancy. In this study, similar structural results were obtained either by fixing the A site occupancy or refining it.

Bond Distances and Chemical Compositions
The average <A-O> distances vary linearly with V, whereas the average <P-O> distance is nearly constant, as expected (Table 5, Figure 3). Data from the literature [8,9] are close to our linear lines. PO 4 is a rigid tetrahedron with a constant P-O distance of 1.528 Å, which is similar to that reported for apatite. Sample 2 has an average <A-O> distance of 2.532(5) Å compared to 2.559 Å [8], indicating the presence of cations that have smaller ionic radii at the A site. The weighted average ionic radii were calculated based on the A site cations and their ionic radii [31]. This ionic radius increases linearly with the average <A-O> distance (Figure 4). The main substituted cations at the A site are Y 3+ , Ca 2+ , Th 4+ , and U 4+ , and they have ionic radii smaller than Ln 3+ cations. The average <A-O> distances vary with substitutions between Ln 3+ and other cations.  The red dashed linear line is fitted to data from this study, whereas "a" is from Reference [8]. The ionic radii for A site cations control the average <A-O> distances in monazite.
The A-P cation-cation distance is shorter than the A-Pʹ distance ( Figure 5). The A-A distances vary from 4.0228(9) (sample 4) to 4.0628(3) Å (sample 1). The cation-cation distances vary linearly with the weighted average ionic radii of A site cations ( Figure 5). The two A-P distances for synthetic light rare earth phosphates vary linearly with the ionic radii of light Ln 3+ cations, but the degree of   The red dashed linear line is fitted to data from this study, whereas "a" is from Reference [8].
The ionic radii for A site cations control the average <A-O> distances in monazite.
The A-P cation-cation distance is shorter than the A-Pʹ distance ( Figure 5). The A-A distances vary from 4.0228(9) (sample 4) to 4.0628(3) Å (sample 1). The cation-cation distances vary linearly with the weighted average ionic radii of A site cations ( Figure 5). The two A-P distances for synthetic light rare earth phosphates vary linearly with the ionic radii of light Ln 3+ cations, but the degree of Figure 4. Average <A-O> distances vary linearly with the weighted average ionic radii of the A site cations. The red dashed linear line is fitted to data from this study, whereas "a" is from Reference [8]. The ionic radii for A site cations control the average <A-O> distances in monazite.
The A-P cation-cation distance is shorter than the A-P distance ( Figure 5). The A-A distances vary from 4.0228(9) (sample 4) to 4.0628(3) Å (sample 1). The cation-cation distances vary linearly with the weighted average ionic radii of A site cations ( Figure 5). The two A-P distances for synthetic light rare earth phosphates vary linearly with the ionic radii of light Ln 3+ cations, but the degree of variations differ [8]. This study shows that the degree of variations of the two A-P distances are not significant, whereas the A-A distances show significant variations ( Figure 5).
The bond valences (BV) for each of the 9 A-O and 4 P-O distances and their bond valance sum (BVS) in valence units (vu) were calculated [29,30] (Table 5). The BVS for the A site are 3.202, 3.330, 3.244, and 2.923 vu for samples 1 to 4, and 3.084 for monazite-Ce [8]. The ideal BVS for the A site is 3 vu. If A is coordinated to 8 instead of 9 O atoms, the BVS are 3.01, 3.145, and 3.063 vu for samples 1, 2, and 3, and these values are close to the ideal 3 vu (Table 5). Therefore, the longest A-O2ʺʹ distance may be excluded, so the A polyhedron is 8-coordinated in Ce-rich monazite, but 9 for sample 4.

Conclusions
Except for the β angle, the a, b, and c unit-cell parameters for monazite vary linearly with V because of the type of cations occupying the A site. The average <A-O> distances also vary linearly with V, whereas the average <P-O> distance is constant, so PO4 is a rigid tetrahedron. Bond-valence sums (BVS) around the A site indicate that it is coordinated to 8 O atoms in samples 1 to 3, but 9coordinated in sample 4. The A site can accommodate a wide range of cations that have similar ionic radii. This chemical flexibility at the A site permits the accommodation of Pu atoms. During nuclear power generation, 238 U in the fuel system absorbs a neutron and produces 239 Pu. The monazite structure is stable over a long geologic time, so it can be used for sequestration of Pu atoms over a million years.   The coordination number for the A 3+ cation to the O atoms is 9 [2,8,15]. However, this coordination number may be 8 [38]. The A 3+ -O bonds are not directional and the coordination may vary from 3 to 12 [39]. However, the most common coordination number for Ln 3+ is 8 or 9 [39].
The bond valences (BV) for each of the 9 A-O and 4 P-O distances and their bond valance sum (BVS) in valence units (vu) were calculated [29,30] (Table 5). The BVS for the A site are 3.202, 3.330, 3.244, and 2.923 vu for samples 1 to 4, and 3.084 for monazite-Ce [8]. The ideal BVS for the A site is 3 vu. If A is coordinated to 8 instead of 9 O atoms, the BVS are 3.01, 3.145, and 3.063 vu for samples 1, 2, and 3, and these values are close to the ideal 3 vu (Table 5). Therefore, the longest A-O2"' distance may be excluded, so the A polyhedron is 8-coordinated in Ce-rich monazite, but 9 for sample 4.

Conclusions
Except for the β angle, the a, b, and c unit-cell parameters for monazite vary linearly with V because of the type of cations occupying the A site. The average <A-O> distances also vary linearly with V, whereas the average <P-O> distance is constant, so PO 4 is a rigid tetrahedron. Bond-valence sums (BVS) around the A site indicate that it is coordinated to 8 O atoms in samples 1 to 3, but 9-coordinated in sample 4. The A site can accommodate a wide range of cations that have similar ionic radii. This chemical flexibility at the A site permits the accommodation of Pu atoms. During nuclear power generation, 238 U in the fuel system absorbs a neutron and produces 239 Pu. The monazite structure is stable over a long geologic time, so it can be used for sequestration of Pu atoms over a million years.