Neutron and XRD Single-Crystal Diffraction Study and Vibrational Properties of Whitlockite, the Natural Counterpart of Synthetic Tricalcium Phosphate

: A crystal chemical investigation of a natural specimen of whitlockite, ideally Ca 9 Mg(PO 4 ) 6 [PO 3 (OH)], from Palermo Mine (USA), was achieved by means of a combination of electron microprobe analysis (EMPA) in WDS mode, single-crystal neutron diffraction probe (NDP) and single-crystal X-ray diffraction (XRD), and Fourier transform infrared (FTIR) spectroscopy. The crystal-chemical characterization resulted in the empirical formula (Ca 8.682 Na 0.274 Sr 0.045 ) Σ 9.000 (Ca 0.034 (cid:3) 0.996 ) Σ 1.000 (Mg 0.533 Fe 2+0.342 Mn 2+0.062 Al 0.046 ) Σ 0.983 (P 1.006 O 4 ) 6 [PO 3 (OH 0.968 F 0.032 ) Σ 1.000 ]. Crystal-structure reﬁnement, in the space group R 3 c , converged to R 1 = 7.12% using 3273 unique reﬂections from NDP data and to R 1 = 2.43% using 2687 unique reﬂections from XRD data. Unit cell parameters from NDP are a = 10.357(3) Å, c = 37.095(15) Å and V = 3446(2) Å 3 , and from XRD, the parameters are a = 10.3685(4) Å, c = 37.1444(13) Å and V = 3458.2(3) Å 3 . NDP results allowed a deeper deﬁnition of the hydrogen-bond system and its relation with the structural unit [PO 3 (OH)]. The FTIR spectrum is very similar to that of synthetic tricalcium phosphate Ca 3 (PO4) 2 and displays minor band shifts due to slightly different P-O bond lengths and to the presence of additional elements in the structure. A comparison between whitlockite, isotypic phases from the largest merrillite group, and its synthetic counterpart Ca 3 (PO 4 ) 2 is provided, based on the XRD/NDP and FTIR results.


Introduction
The study of calcium phosphates (CaP) is a topic of paramount interest for the scientific community, with these minerals being the natural counterparts of several biomaterials largely employed in biomedical applications such as cements, scaffolds and coatings of components of bone and teeth used in in orthopedics and dentistry [1]. These applications are mostly based on the similarity of the density of these compounds with that of human hard tissues [2]. The most abundant natural CaP belongs to the apatite series Ca 10 (PO 4 ) 6 (F,Cl,OH) 2 [3][4][5]; however, there is currently an arising interest for the mineral whitlockite, ideally Ca 9 Mg(PO 4 ) 6 [PO 3 (OH)], a rare species found as a secondary phase in some granite pegmatites [6]. The interest for whitlockite, is largely due to its relation with merrillite Ca 9 NaMg(PO 4 ) 7 and keplerite Ca 9 (Ca 0.5 0.5 )Mg(PO 4 ) 7 , two phosphate minerals found in meteorites, which represent the main reservoir of phosphate phosphorus in the Table 1. Whitlockite-group minerals approved by the IMA-CNMNC: ideal formula and cation site occupancy according to the structural formula [A(1) 3

Experimental
The whitlockite specimen from the Palermo Mine (USA) here examined was kindly made available by the "Museo Universitario di Scienze della Terra" (MUST), Sapienza University of Rome (Italy), catalogue number 27074/1.
Electron microprobe analysis was obtained by using a wavelength dispersive spectrometer (WDS mode) with a Cameca SX50 instrument, operating at 15 kV, sample current of 15  Single-crystal X-ray diffraction (XRD) data were collected with a Bruker KAPPA APEX-II single-crystal diffractometer (Sapienza University of Rome, Earth Sciences Department) equipped with a CCD area detector (6.2 × 6.2 cm 2 active detection area, 512 × 512 pixels) and a graphite crystal monochromator, using MoKα radiation from a fine focus sealed X-ray tube. The sample-to-detector distance was 4 cm. A set of 9473 reflections were integrated and corrected for Lorentz, polarization, background and absorption using the package of software Apex2 [21]. The systematic-absence analysis strongly suggested the choice of the trigonal space group R3c. The crystal structure was refined using SHELXL-2014 [22]. Final anisotropic refinement (by using 143 parameters) converged to R1 = 0.0243 for 2687 unique reflections with I > 2σ(I), and wR2 = 0.0528 for all data, confirming the original structural model of Gopal and Calvo (1972) [23]. Magnesium and Fe were unambiguously located at the M site. Sodium was preliminary assigned over the A(1), A(2), A(3) and X sites: among them, only the A(2) site scattering value suggested the presence of Na. Unit cell parameters are: a = 10.3685(4) Å, c = 37.1444(13) Å and V = 3458.2(3) Å 3 .
Single-crystal neutron diffraction data were collected at room temperature on a 2 × 2 × 2 mm size crystal of whitlockite on the SXD instrument [24] at the ISIS Neutron and Muon Facility in Harwell (UK), using the time-of-flight (TOF) Laue diffraction method with polychromatic radiation in the range 0.3 to 8 Å. The sample was placed in a chamber evacuated to 10 −5 bar in order to avoid contamination of the diffraction pattern from the scattering of air. Data were collected in a series of five different angular orientations of the crystal with exposure time of about 4 h for each orientation. Unit cell parameters and Bragg intensities were extracted by using the line integral fitting procedure implemented in the SXD2001 software [25]. Data were corrected for Lorentz effects, but no absorption correction was applied. The starting model for the structure refinement was based on the atomic coordinates of the non-hydrogen atoms from the corresponding XRD analysis, while H was located from neutron Fourier difference maps. The structure Crystals 2021, 11, 225 4 of 18 was refined by full matrix least squares on F 2 using the SHELXL software [22]. A total of 6650 wavelength-dependent reflections were integrated to give 2024 unique reflections after merging for Fourier (R(σ) = 0.1225, 2θ max = 170.1 • ). Final statistical factors were: R1 merge = 0.0644, R1 = 0.0711, wR2 = 0.1693 with I > 2σ(I) and 156 refined parameters, goodness of fit GooF = 1.02. Hydrogen at the H(10) site was placed at the general position 18b with an occupancy value fixed to that of the O(10) site (= 0.857) because it is bonded to oxygen at O(10) as an (OH) group. Measured unit cell parameters are: a = 10.357(3) Å, c = 37.095 (15) Details of the selected whitlockite crystal, data collection and refinement are given in Table 2. Fractional atom coordinates and equivalent isotropic parameters are reported in Table 3; the crystallographic information files (CIF) can be obtained free of charge from the joint service Cambridge Structure Database (CSD) [26]-Inorganic Crystal Structure Database (ICSD) [27], quoting the depository number CSD2046688 (XRD refinement), and CSD2046635 (NDP refinement), via www.ccdc.cam.ac.uk/getstructures (accessed on 1 February 2021). The powder Fourier Transform Infrared (FTIR) spectrum of whitlockite sample was collected on a Nicolet iS50 FTIR spectrometer equipped with a DTGS detector and a KBr beam splitter; nominal resolution was 4 cm −1 and 64 scans were averaged for both sample and background. The sample was prepared as a KBr disk, mixing 1 mg of sample with 150 mg of KBr. A single crystal was oriented under a polarizing optical microscope by using a spindle stage, embedded in resin and doubly polished to the 100 µm thickness for polarized light FTIR experiments. The spectra were collected by using a Bruker Hyperion 3000 microscope attached to a Vertex V70 bench at INFN (Frascati, Rome, Italy). The system was equipped with a Globar IR source, a KBr beam splitter and an MCT detector. The polarizer was a gold wire grid; the beam diameter was set at 200 µm.

Microchemical Composition
Electron microprobe analysis of the present whitlockite detected the following elements (expressed as oxide wt%) in the WDS spectrum:

X-ray and Neutron Structural Studies
The unit cell parameters from neutron and X-ray diffraction measured for the present sample are in the range of those observed in other natural samples from whitlockite and merrillite subgroups from the literature ( Table 4). a,b whitlockite from this work (t.w.), respectively NDP ( a ) and XRD ( b ) data; EMP formula rounded to two decimal digits for the sake of clarity; c whitlockite 'heated' [23]; d [28]; e [29]; f [30]; g [31]; h [32]; i [33]; l,m [34]; n ideal chemical formula [35]; o [7].
For the description of the complex cationic sites within the whitlockite-type structure, we follow the above-reported notation introduced for the general structural formula as there is a self-consistence between the letters in the chemical and structural formula of the merrillite mineral group. Consequently, the following equivalences occur with the notation reported for the isotypic β-TCP phase (a = 10.4352(2) Å; c = 37.4029(5) Å; V = 3527.26 Å 3 ) by [36]: Thus, eight non-equivalent cationic sites are present in the whitlockite structure: A(1), A(2) and A(3) are located in the general Wyckoff positions 18b, whereas X and M are placed in the 6a special positions (Table 3). Two P atoms, occupying the T(2) and T(3) sites, and nine O atoms are located at general positions, whereas a third P, occupying the T(1) site, and one O atom, at the O(10) site, are in 6a special positions ( Table 3). The X site is only partially occupied; in the refinement of the β-TCP structure its occupancy is usually fixed at 50% for charge balance [12,36]; this is also the case of natural whitlockite and merrillite crystals, where the X site occupancy can be variable to compensate for constituents with different formal ionic charge from Ca 2+ such as Na + [32]. In some β-TCP structures, the X site may be vacant due to the occurrence of trivalent cations, e.g., for the Ca 9 RE(PO 4 ) 7 compound, trivalent rare earth cations substitute for Ca 2+ [10,37]. In the description of bond lengths and angles, we will discuss the NDP data only for clarity, with the XRD results being similar, as can be observed in Tables 5 and 6, where bond distances (Å) and bond valence parameters/sum are reported (BVP/BVS, expressed in valence units = v.u. [38]), respectively, from XRD (Table 5) and NDP refinement (Table 6). Table 5. Bond distances (Å) and bond valence/sum (BV/BVS, in valence units = v.u.) for the studied whitlockite (from XRD data). BV/BVS values for the A(2) and M sites calculated according to the single cationic occupancies (Table 3).

Bond
Distance Note: <X-O> distance not reported because of the interaction behavior of X-O(9) bond.  (Table 3). samples [4,[39][40][41]. The last tetrahedron, [ T(1) PO 3 (OH)], has P 5+ bonded to the O(10) (OH) group. The [ T(1) PO 3 (OH)] 2unit may flip 180 • along the c-axis keeping fixed the position of the O(9) oxygen atoms, but splitting the P-cation position in T(1) and T(1 ) about 0.76 Å apart with 85% and 15% occupancy, respectively (Table 3), as displayed in Figure 1. In detail, when T(1) is occupied, the tetrahedron points downward (-c) and the X site is vacant; it should be noted that the actually geometry of the [ T(1) PO 3 (OH)] polyhedron is that of a trigonal pyramid (site symmetry 3) having three O (9)   In some previous structural studies on whitlockite or synthetic TCP [36], the A(1)O 8 polyhedron is described as seven-fold coordinated by excluding the longest A(1)-O(3) distance (see, e.g., [12]). However, the A(1) Ca-O(3) O bond actually exists from a bond valence perspective. Table 6 shows that the bond-valence value for A(1) Ca 2+ -O(3) O 2− = 0.12 valence units (v.u.), is larger than 0.04× the cation valence [38]. As a result, it is reasonable to consider the A(1) Ca-O(3) O bond-distance in the coordination sphere of A(1). coordinated by excluding the longest A(1)-O(3) distance (see, e.g., [12]). However, the A(1) Ca-O(3) O bond actually exists from a bond valence perspective. Table 6 shows that the bond-valence value for A(1) Ca 2+ -O(3) O 2− = 0.12 valence units (v.u.), is larger than 0.04× the cation valence [38]. As a result, it is reasonable to consider the A(1) Ca-O(3) O bond-distance in the coordination sphere of A(1).   Table 4). Worth of note is the presence of Na at A(2), to date refined for the first time within whitlockite sub-group phases (Table 4). Sodium is a characteristic constituent of merrillite sub-group species, and in the closely related wopmayte Ca 6 Na 3 Mn 2+ (PO 4 ) 3 (PO 3 OH) 4 [31], it is up to 10 times more abundant than in the studied whitlockite. In wopmayite, Na is strongly ordered at A(3) [31], with as a result longer mean <A(3)-O> bond lengths. Our whitlockite also shows a longer <A(3)-O> and BVS values slightly lower than 2.00 consistent with the possible presence of a monovalent cation. However, refinement of Na at both A(3), A(1) and X gave negative site occupancy values, thus indicating the occurrence of Na at A(2) only.
Of particular interest for most of the whitlockite structures is the coordination environment of the cation at the X site ( Figure 3). This cation is at 6a special position, being involved in a three-fold coordinated regular polyhedron with three equivalent X-O(1) bond distances at about 2.58(4) Å. Due to the disorder of the [ T(1) PO 3 (OH)] unit described above, it is very difficult to characterize the occupancy of the X site, which is located only~0.6 Å from O (10). Considering that the occupancy of the X site is constrained to compensate the charge balance, X-ray/neutron structure refinements were done at first with only the A(1), A(2) and A(3) sites occupied by Ca. The Fourier difference maps in both X-ray and neutron refinements showed a clear peak at the X-site position. In particular, in the X-rays map, this peak is at 0.65 Å from O(10) with electron density 1.53 e/Å 3 , while, in the neutrons map, it is at 0.57 Å from O(10) with a density of 1.64 fm/Å 3 . Adding this peak as X site occupied by Ca to the refinement, a strong correlation between the s.o.f. and the U iso of X occurred. This correlation was resolved by fixing U iso of X to 0.01 Å 2 (i.e., to the average value refined for the other Ca atoms in the structure) in X-ray/neutron refinements. The resulting s.o.f. is virtually the same in both refinements, 0.058(4) from X-rays and 0.06(2) from neutron, whereas the new refined X position resulted very close to O(10), X-O(10) = 0.51 Å and 0.57 Å in neutron and X-ray refinement, respectively. Its coordination polyhedron XO 6 ( Figure 3) comprises the three equivalents O(1) at 2.57-2.58 Å (NDP and XRD, respectively), and three equivalents O(9), belonging to the [ T(1) PO 3 (OH)] moiety, at 2.92-2.96 Å. In terms of bond valence, the contribution of X Ca 2+ can be considered as weak: about 0.20 v.u. and 0.08 v.u. for X-O(1) and X-O(9), respectively ( Table 6). The six-fold coordination of the X site is confirmed by the keplerite mineral [7], though this site is usually described as triangular in isotypic β-TCP compounds in that the three X-O(9) interactions tend to disappear being found over 2.96 Å [12].
age value refined for the other Ca atoms in the structure) in X-ray/neutron refin The resulting s.o.f. is virtually the same in both refinements, 0.058(4) from X-r 0.06(2) from neutron, whereas the new refined X position resulted very close to O O(10) = 0.51 Å and 0.57 Å in neutron and X-ray refinement, respectively. Its coord polyhedron XO6 (Figure 3) comprises the three equivalents O(1) at 2.57-2.58 Å (N XRD, respectively), and three equivalents O(9), belonging to the [ T(1) PO3(OH)] m 2.92-2.96 Å. In terms of bond valence, the contribution of X Ca 2+ can be considered a about 0.20 v.u. and 0.08 v.u. for X-O(1) and X-O(9), respectively ( Table 6). The coordination of the X site is confirmed by the keplerite mineral [7], though thi usually described as triangular in isotypic β-TCP compounds in that the three Xteractions tend to disappear being found over 2.96 Å [12].  [28][29][30]. Note that the M site is also ch  [28][29][30]. Note that the M site is also characterized by low values of isotropic thermal parameters ( Table 3). The M site population provided by EMP, (Mg 0.533 Fe 2+ 0.342 Mn 2+ 0.062 Al 0.046 ), is fully consistent with X-ray crystal-structure refinement: occupancy 56% of Mg (+ Al, which has X-ray scattering very similar to Mg) and 46% of Fe (+Mn, which has X-ray scattering very similar to Fe). This excellent agreement reflects the fact that same crystal used for XRD was analyzed with EMP. As for the neutron refinement, the M site occupancy, 80% of Mg and 20% of Fe, shows a slight deviation from what is provided by XRD. This deviation might be ascribed to a possible chemical inhomogeneity in the much bigger volume (about 8 mm 3 ) of the specimen used for the neutron diffraction. Bond

Three-dimensional Framework
The three-dimensional arrangement of whitlockite can be described by the repeat of two columnar arrays, indicated as 'I' and 'II' in Figure 4 16 ] pinwheel unit [32] (see inset (a) in Figure 4), which can be considered the building block of the whitlockite framework, as later illustrated. All cations in the I array, i.e., those at the X, M and T(1)/T(1 ), are in special position (x = y = 0, Table 3), and hence, they are constrained along the c axis. This constraint prevents any positional disorder except that along the z direction, as previously discussed for T(1) and O (10). Each I array is surrounded by six II arrays, whereas each II array is surrounded by two I and four II arrays ( Figure 5). The [M(TO4)6] pinwheel units assure the link between one I column and the six adjacent II columns, being the pinwheels flat in the c axis and held together by intralayer A(1) Ca cations, forming layers perpendicular to c axis ( Figure 6). These anionic units form a perfectly closest-packed planar arrangement [32]: these layers are linked by an interlayer of cations at A(2) and A(3) from II columns, making up the whitlockite three dimensional framework, further compacted by the interactions formed by the split T(1)O4 tetrahedron, which share O(9) with A(2)O8 and A(1)O8 from different II arrays, and the O(10′) vertex with the A(3)O8 polyhedron. This second joining mechanism among I and II arrays, formed by split T(1)O4 tetrahedron, is conditioned by the site symmetry of T(1) ( Table 3). In fact, as previously described, the T(1)O4 tetrahedron forms a triangular pyramid, whose three O(9) O base-vertices are shared at the same time both with one A(1)O8 polyhedron from an adjacent II array and with a A(2)O8 polyhedron belonging to another II array. Owing to the site symmetry, the joining mechanism is repeated three times, while the split along c of the tetrahedral unit causes the presence of O(10′) position, joined to three A(3)O8 polyhedra from adjacent II arrays. The framework is completed by the X-O bonds, considered as weak interactions owing to the low cation occupancy of the site, X (Ca0.034□0.996)Σ1.000.  (Table 3) and may, thus, cause disorder to give a denser arrangement. Two II arrays are joined together, thus making up a column, via A(1)-O-A(2) bonds, with A(1) and A(2) belonging to adjacent arrays (see the inset (b) in Figure 4).
Each I array is surrounded by six II arrays, whereas each II array is surrounded by two I and four II arrays ( Figure 5). The [M(TO 4 ) 6 ] pinwheel units assure the link between one I column and the six adjacent II columns, being the pinwheels flat in the c axis and held together by intralayer A(1) Ca cations, forming layers perpendicular to c axis ( Figure 6). These anionic units form a perfectly closest-packed planar arrangement [32]: these layers are linked by an interlayer of cations at A(2) and A(3) from II columns, making up the whitlockite three dimensional framework, further compacted by the interactions formed by the split T(1)O 4 tetrahedron, which share O(9) with A(2)O 8 and A(1)O 8 from different II arrays, and the O(10 ) vertex with the A(3)O 8 polyhedron. This second joining mechanism among I and II arrays, formed by split T(1)O 4 tetrahedron, is conditioned by the site symmetry of T(1) ( Table 3). In fact, as previously described, the T(1)O 4 tetrahedron forms a triangular pyramid, whose three O(9) O base-vertices are shared at the same time both with one A(1)O 8 polyhedron from an adjacent II array and with a A(2)O 8 polyhedron belonging to another II array. Owing to the site symmetry, the joining mechanism is repeated three times, while the split along c of the tetrahedral unit causes the presence of O(10 ) position, joined to three A(3)O 8 polyhedra from adjacent II arrays. The framework is completed by the X-O bonds, considered as weak interactions owing to the low cation occupancy of the site, X (Ca 0.034 0.996 ) Σ1.000 .  The whitlockite arrangement, as previously stated, is strictly related to that of typic β-TCP [32]. The occurrence of a trivalent RE-cation such as Cr 3+ [42], Fe 3+ [43] or m frequently REE 3+ [10] in the β-TCP structure leads to the formula Ca9RE 3+ (PO4)7, charac ized, compared to whitlockite, by a fully vacant X-site and by the presence of [ T(1) PO3(O)] unit according to the deprotonation-substitution mechanism RE 3+ + O 2-→ + (OH) - [11]. In the case of Cr 3+ and Fe 3+ , the mechanism of dopant distribution occ exclusively at the M site [42,43]. In the case of Ca9RE(PO4)7 β-TCP, the rare earth distri tion was discussed in [11] on the basis of the RE ionic radii. In detail, for 'low' RE (La to Gd), the dopant element is disordered over the A(1,2,3) sites, whereas the M site is fu occupied by Ca. As for the 'heavy' RE (from Tb to Lu) the dopant is disordered over A A (2) and M site, with A(3) being fully occupied by Ca [11].

Relations within Whitlockite Group Minerals
Phosphate phases from whitlockite subgroup are generally rare terrestrial miner  The whitlockite arrangement, as previously stated, is strictly related to that of typic β-TCP [32]. The occurrence of a trivalent RE-cation such as Cr 3+ [42], Fe 3+ [43] or m frequently REE 3+ [10] in the β-TCP structure leads to the formula Ca9RE 3+ (PO4)7, chara ized, compared to whitlockite, by a fully vacant X-site and by the presence of [ T(1) PO3(O)] unit according to the deprotonation-substitution mechanism RE 3+ + O 2-→ + (OH) - [11]. In the case of Cr 3+ and Fe 3+ , the mechanism of dopant distribution oc exclusively at the M site [42,43]. In the case of Ca9RE(PO4)7 β-TCP, the rare earth distr tion was discussed in [11] on the basis of the RE ionic radii. In detail, for 'low' RE (L to Gd), the dopant element is disordered over the A(1,2,3) sites, whereas the M site is f occupied by Ca. As for the 'heavy' RE (from Tb to Lu) the dopant is disordered over A A (2) and M site, with A(3) being fully occupied by Ca [11].

Relations within Whitlockite Group Minerals
Phosphate phases from whitlockite subgroup are generally rare terrestrial mine usually found as secondary phases in paragenesis with other minerals. Wopmayite, The whitlockite arrangement, as previously stated, is strictly related to that of isotypic β-TCP [32]. The occurrence of a trivalent RE-cation such as Cr 3+ [42], Fe 3+ [43] or more frequently REE 3+ [10] in the β-TCP structure leads to the formula Ca 9 RE 3+ (PO 4 ) 7 , characterized, compared to whitlockite, by a fully vacant X-site and by the presence of the [ T(1) PO 3 (O)] unit according to the deprotonation-substitution mechanism RE 3+ + O 2− → R 2+ + (OH) − [11]. In the case of Cr 3+ and Fe 3+ , the mechanism of dopant distribution occurs exclusively at the M site [42,43]. In the case of Ca 9 RE(PO 4 ) 7 β-TCP, the rare earth distribution was discussed in [11] on the basis of the RE ionic radii. In detail, for 'low' RE (La up to Gd), the dopant element is disordered over the A(1,2,3) sites, whereas the M site is fully occupied by Ca. As for the 'heavy' RE (from Tb to Lu) the dopant is disordered over A(1), A(2) and M site, with A(3) being fully occupied by Ca [11].

Relations within Whitlockite Group Minerals
Phosphate phases from whitlockite subgroup are generally rare terrestrial minerals, usually found as secondary phases in paragenesis with other minerals. Wopmayite, ideally Ca 6 Na 3 Mn(PO 4 ) 3 (PO 3 OH) 4 , is a secondary mineral from the Tanco mine, Bernic Lake, Manitoba (Canada); it crystallizes together with rhodochrosite, quartz, whitlockite, apatite, and other phases after dissolution of primary lithiophosphate by hydrothermal solutions. Wopmayite has a structural unit consisting of an [M 2+ (PO 4 ) 6 ] arrangement that is topologically the same as the structural units in the whitlockite and merrillite structures; it is related to whitlockite by the substitution Na + H → Ca + , whereby Na is incorporated primarily at the A(3) site and H attaches to the T(1)O 4 tetrahedron to produce an acid-phosphate group. Thus, merrillite contains no acid-phosphate group, whitlockite contains a single acid-phosphate group at T(3), and wopmayite contains acid-phosphate groups at both T(1) and T(3) [31].
Minor details are available for strontiowhitlockite, ideally Sr 9 Mg(PO 3 OH)(PO 4 ) 6 , the Sr-dominant analog of whitlockite, found in Kovdor deposit, Kola Pensinsula, Russia. The mineral, together to other phosphates such as carbonate fluoroapatite, occurs in a vein of dolomite carbonatite cutting host pyroxenites. At the time of its discovery, it was studied only with powder XRD technique, allowing no structure solution; its powder pattern was really close to that of whitlockite and of synthetic β-TCP [30]. Few details are available for hedegaardite, ideally (Ca,Na) 9 (Ca,Na)Mg(PO 3 OH)(PO 4 ) 6 , in the CMMNC Newsletter [20]. Lastly, the fluorine dominant whitlockite, ideally Ca 9 Mg(PO 4 ) 6 (PO 3 F), was approved in 2008 as a new mineral, with the name "bobdownsite" [44], but was later discredited being F-free and then indistinguishable from whitlockite [45].
The de-hydrogenated extra-terrestrial phases belong to the merrillite subgroup and are merrillite, ideally Ca 9 NaMg(PO 4 ) 7 , and keplerite, ideally Ca 9 (Ca 0.5 0.5 )Mg(PO 4 ) 7 (Table 1). Merrillite is typical of genetic environments of high temperature and pressure, having been found in Moon rocks and meteorites [29]: in this phase, Na + is refined at the X site, whereas Mg and Fe 2+ are refined at M, analogously to whitlockite [33]. Keplerite is a recent new mineral, typical of high-temperature environments characterized by extreme depletion of Na, such as pallasite and angrite meteorites and, on Earth, as pyrometamorphic rocks. It was recently interpreted as the Ca-dominant counterpart of merrillite, and both minerals are related by the heterovalent substitution at the X-site of the crystal structure: 2Na + (merrillite) ↔ Ca 2+ + (keplerite) [7].
Ferromerrillite, ideally Ca 9 NaFe 2+ (PO 4 ) 7 , occurs as a common accessory phase in several Martian meteorites, classified as basaltic and olivine-phyric shergottites. Besides the Fe 2+ presence at the M site, the samples were described as heavily deformed for the shock events during the entry in the atmosphere [34]. Minor details are available for mathyite, ideally Ca 9 (Ca 0.5 0.5 )Fe 2+ (PO 4 ) 7 , characterized by the absence of Na at the A(1,2,3) sites, and reported as the product of metasomatic process in the D'Orbigny angrite meteorite [35].

FTIR Spectroscopy
The powder FTIR spectrum of whitlockite in the 4000-400 cm −1 wavenumber region is compared in Figure 7 with that of pure β-TCP [11]. Both show a complex pattern in the P-O antisymmetric (1150-1000 cm −1 ) and symmetric (1000-900 cm −1 ) stretching regions, where bands assigned to the vibrational modes of distorted (PO 4 ) tetrahedra are observed [10,11].
Despite the significant interest for synthetic whitlockite that has emerged during the last years in biomaterial sciences [46], a complete FTIR study of natural whitlockite is missing in the literature. We can, thus, use for comparison the data known for the spectrum of the isotypical β-TCP, which has been widely investigated in terms of site-symmetry and factor group analysis [47,48], see also [39,40,49]. According to [47,48,50], the free phosphate ion (PO 4 ) 3− with ideal T d point symmetry displays four vibrational modes: (1) the antisymmetric stretching ν 3 at 1082 cm −1 ; (2) the symmetric stretching ν 1 at 980 cm −1 ; (3) the antisymmetric bending ν 4 at 567 cm −1 ; (4) the symmetric bending ν 2 at 420 cm −1 . In accordance with the selection rules, the triply degenerate antisymmetric stretching and bending modes (F 2 ) are both Raman and infrared active, whereas the non-degenerate symmetric stretching (A 1 ) and the doubly degenerate symmetric bending (E) are Raman active only. When the symmetry of the (PO 4 ) 3− ion is lowered from T d , band splitting, shifts of the absorption/scattering bands and appearance of non-active IR/Raman modes are observed [50].
Crystals 2021, 11, x FOR PEER REVIEW Figure 7. Powder FTIR spectra of whitlockite (blue) and TCP (red, sample from [11]): deta tetrahedral modes region (1600-400 cm −1 ).  The FTIR spectrum of whitlockite in the phosphate modes region (<1200 cm −1 , Figure 7) is similar to that of synthetic β-TCP, and shows the same band multiplicity, in agreement with their very similar phosphate framework; the only differences are observed in the wavenumber shift of some peaks, due to the slightly different P-O bond lengths (Figure 7, Table 7), and to the presence of additional minor constituents. The prominent features in the ν 4 antisymmetric bending region (500-700 cm −1 ) are also almost identical, in terms of both band multiplicity and position. The polarized spectra collected on the single-crystal (hk0) section are displayed in Figure 8. The section was prepared by orienting the crystal under the polarizing microscope using a spindle stage [51], which was then transferred onto the grain on a glass slide for cutting and the section was polished twice. Although the thickness was reduced (100 µm), the absorbance was below 1300 cm −1 due to the tetrahedral P-O modes, and is evidently out of scale; in the OH-stretching region, two broad bands are observed, centered at 2905 and 2415 cm −1 , respectively (Figure 8). Cooper et al. (2013) [31] presented a very similar pattern for the closely related wopmayite and assigned the former component to the (P)-OH stretching mode, while the latter, following the work of Moraes et al. (2006) [52] was assigned to an overtone of the P-O modes. This assignment is supported, although not conclusively, by the polarized spectra displayed in Figure 8     Despite the significant interest for synthetic whitlockite that has emerged durin last years in biomaterial sciences [46], a complete FTIR study of natural whitlock  [54] once we consider the strong incertitude in the curve for strong hydrogen-bonded systems.
The data of Figure 8 also show the appearance of an intense and relatively sharp peak at 1354 cm −1 for E//c. According to [31] this peak can be assigned to the (P)-O-H bending. An additional element supporting this inference comes from the NIR (near infrared) region from 6000-4000 cm −1 where absorptions due to the combination between the OH stretching and bending modes are observed [55]. Regarding the hypothesis of a stretching band at 2905 cm −1 and the (P)-O-H bending at 1354 cm −1 , a combination band around 4300 cm −1 is expected in the NIR spectrum; this component is in fact resolvable as a weak and broad band in Figure 9 (arrowed).  Despite the significant interest for synthetic whitlockite that has emerged during last years in biomaterial sciences [46], a complete FTIR study of natural whitlocki

Conclusions
In this work, we provide an in-depth crystal-chemical investigation of the rare natural calcium phosphate whitlockite, ideal formula Ca 9 Mg(PO 4 ) 6 [PO 3 (OH)]. EMP analysis highlighted the non-negligible presence of Na and Fe replacing Ca and Mg, respectively, in the formula. X-ray and neutron refinements showed the presence of a disordered [ T(1) PO 3 (OH)] 2− structural unit, split along the c-crystallographic axis. FTIR analysis showed that the powder MIR spectrum in the P-O framework mode region of whitlockite is very similar to that of synthetic β-TCP in terms of band multiplicity, in agreement with the essentially similar structural arrangement between the two compounds. The single-crystal FTIR data are consistent with the band assignment proposed for isotypic wopmayite [31] and show a single and very broad absorption due to an O-H group involved in a strong hydrogen bridge with the surrounding oxygen.
Author Contributions: All the authors conceived and designed the main ideas together, and wrote and supervised the whole work. F.B. provided the sample, the XRD data and the WDS analysis; F.C. contributed to XRD structural refinement; S.C.C. contributed to NDP structural refinement; G.D.V. and F.R. contributed to FTIR spectroscopy. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement:
The data contained in the crystallographic information files (CIF) are openly available at the joint service CSD-ICSD (www.ccdc.cam.ac.uk/getstructures (accessed on 1 February 2021)), quoting the depository number CSD2046688 (XRD refinement), and CSD2046635 (NDP refinement).