research papers Pristine and hydrated fluoroapatite (0001) Xavier Torrelles,a* Immad M. Nadeem,b,c Anna Kupka,d Adrián Crespo-Villanueva,a ISSN 2052-5206 Sandrina Meis,d Hermann Giesd and Oier Bikondoae,f* a Institute of Materials Science of Barcelona (ICMAB-CSIC), Campus UAB, Bellaterra, Barcelona 08193, Spain, bLondon Centre for Nanotechnology and Department of Chemistry, University College London, 20 Gordon Street, London WC1H OAJ, UK, cHarwell Science and Innovation Campus, Diamond Light Source Ltd, Didcot, Oxfordshire OX11 0DE, Received 4 April 2019 UK, dFaculty of Geosciences, Department of Geology, Mineralogy and Geophysics, Ruhr-Universität Bochum, Accepted 22 July 2019 Universitätsstrasse 150, Bochum 44780, Germany, eDepartment of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK, and fXMaS, The UK-CRG Beamline, ESRF The European Synchrotron, CS40220, F-38043 Grenoble cedex 09, France. *Correspondence e-mail: torrelles@icmab.es, oier.bikondoa@esrf.fr Edited by M. de Boissieu, SIMaP, France The surface structure of fluoroapatite (0001) (FAp0001) under quasi-dry and Keywords: fluoroapatite (0001); water interface; humid conditions has been probed with surface X-ray diffraction (SXRD). surface structure; mineralogy; surface X-ray Lateral and perpendicular atomic relaxations corresponding to the FAp0001 diffraction. termination before and after H2O exposure and the location of the adsorbed CCDC references: 1942347; 1942348 water molecules have been determined from experimental analysis of the crystal truncation rod (CTR) intensities. The surface under dry conditions exhibits a Supporting information: this article has bulk termination with relaxations in the outermost atomic layers. The hydrated supporting information at journals.iucr.org/b surface is formed by a disordered partially occupied H2O layer containing one water molecule (33% surface coverage) adsorbed at each of the three surface Ca atoms, and is coupled with one OH group randomly bonded to each of the three topmost P atoms with a 33% surface coverage. 1. Introduction Apatites represent a group of phosphate minerals that are very common in nature. Their generic chemical formula is Ca5(PO4)3X, where X corresponds to a monovalent anion such as F, (OH) etc. Structurally, apatites crystallize in the hexagonal space group P63/m (No. 176) where the hexagonal axis is normal to a symmetry plane (Bragg et al., 1965). The apatite structure is built of unconnected [PO4] tetrahedra, with Ca2+ cations occupying the space between the tetrahedra, and the X anions compensating the extra charge of the Ca2+ cations and located along the c axis (Calderı́n et al., 2003). Fluoroapatite (calcium fluorophosphate, FAp) is a typical member of the apatite group with X = F. It contains 42 atoms per unit cell and has two formula units (Z = 2) per unit cell. FAp is often found as an accessory mineral in igneous rocks, in the form of elongated prismatic needle-shaped crystal inclusions (Haldar & Tišljar, 2014). The substitution of small amounts (4 to 7 wt%) of PO43 by CO32 leads to carbon- ated FAp, which is an important sink in the marine phos- phorus cycle (Ruttenberg & Berner, 1993). Apatites are also used as a source of phosphate for fertilizer production. Apatitic structures are also very relevant in biomineralization (Combes et al., 2016). Calcium hydroxyapatite is found in bones, and human enamel and dentine are composed of hy- droxyapatite (HAp, X = OH). FAp may also be found, in varying proportions, in human enamel that has been exposed to F ions, as FAp is chemically more stable than HAp. HAp and FAp are both used in regenerative medical techniques (Ben-Nissan, 2014). In some animal species (e.g. cartilaginous fish) instead of HAp enamel, the species have FAp enameloid, 830 https://doi.org/10.1107/S2052520619010412 Acta Cryst. (2019). B75, 830–838 research papers although the dentine is HAp (Lübke et al., 2015). Teeth with Table 1 FAp dentine have been found in the fossil record, but the The first line, for the dry case, indicates the weight evolution of each surface termination layer with (PO4) and without (PO3) the topmost O presence of FAp in the dentine is due to diagenesis and atom, and in the second line the weight of water and OH molecules in the exchange between the hydroxyl group and fluoride ions refinement process is indicated. (Renzi et al., 2016). The diagenetic transformation from HAp 1st layer, 1st layer, to FAp may depend on the microstructure of the original Dry O=0 O=1 2nd layer 3rd/4th layer tissue (Lübke et al., 2017). 2n 1.2 2.2 6.1 2.5/2.8 The mineral–water interface plays a fundamental role in the functions of apatite both in geochemistry and in medicine and H2O = 0, H2O = 0, H2O = 13, H2O = 13, biomineralization. Previously, we investigated the surface Humid OH = 0 OH = 13 OH = 0 OH = 13 structure of orthorhombic FAp (100) (FAp100) under dry and humid conditions [relative humidity (RH) 75%] using data 2n 1.5 1.4 1.3 1.16 from surface X-ray diffraction experiments (SXRD). The interface in a humid atmosphere shows a well organized and periodically ordered monolayer of water arranged laterally, structure is iteratively refined to find the best fit between the with atomic relaxations of the mineral surface structure experimental and theoretical structure factors. A modified smaller than those of the dry surface (Pareek et al., 2007). version of the ROD software – a modification that allows the Here we extend this study to the hexagonal FAp (0001) user to form blocks of molecules and rotate them around a (FAp0001) termination of a natural FAp single crystal under common origin – was used for this task (Vlieg, 2000; Torrelles dry conditions (in an He-saturated environment) followed by et al., 2004). The goodness-of-fit was evaluated in terms of two exposure to a water-saturated environment at ambient commonly used parameters, 2 (2n ) (Feidenhans’l, 1989) and temperatures. the R factor (Stout & Jensen, 1968):  th    1 X N Fi ðhklÞ  Fiexp ðhklÞ 2 2 2. Experimental and SXRD analysis details n ¼ 2 ; ð1Þ N  P i¼1 iexp A natural FAp single crystal from Durango, Mexico, with a Pn  th   exp     (0001) termination was rinsed with ultrapure water (resistivity i¼1 Fi ðhklÞ  Fi ðhklÞ 18.2 M cm), sonicated in ethanol (Sigma–Aldrich, purity R¼ Pn  exp   ; ð2Þ i¼1 Fi ðhklÞ >99.8%) and lastly mounted within a small Kapton tent in which He gas (Air Liquide, purity 5 N) was flowing continu- where N is the number of measured structure factors, P is the ously during the dry measurements. Next, water vapour was number of parameters optimized during the fitting procedure, introduced into the tent by bubbling helium through an and Fiexp ðhklÞ and Fith ðhklÞ are the experimental and theore- ultrapure water (resistivity 18.2 M cm) reservoir and an tically calculated structure factors, respectively. iexp ðhklÞ is the ultrapure-water-soaked paper tissue was placed in the tent. uncertainty associated with Fiexp and was estimated by aver- The SXRD experiments were carried out on beamline BM28 aging equivalent reflections. 2n behaves such that a value of 1 (XMaS) at the European Synchrotron Radiation Facility indicates good agreement between the experimental and (ESRF). All measurements were performed in a vertical four- theoretically calculated structure factors. The quoted precision circle geometry at a constant incidence angle of 0.5 and of each fitted parameter is determined by varying the para- photon energy of 15 keV (https://warwick.ac.uk/fac/cross_fac/ meter about its optimal values until 2n has increased by xmas/). To follow surface geometry changes qualitatively, the 1/(N  P) from its minimum value (Feidenhans’l, 1989). intensity of the (1, 1, 1.5) reflection was monitored. The The structure refinement of the pristine FAp0001 surface index of this reflection, and all others hereafter, is expressed under dry conditions was initiated from an ideal FAp0001 using Bravais–Miller indices (Hahn, 1996) and in terms of the termination. Relaxations were allowed layer by layer, gradu- reciprocal-lattice vectors h, k and l. These vectors are defined ally, starting from the surface and going into the bulk. The with reference to the real-space (1  1) unit cell of FAp0001 most favourable surface-layer termination was inspected by described by the lattice vectors a, b and c which are parallel to refining initially the experimental data set (CTRs) with each the ½2 1 1 0, ½1 2 1 0 and [0001] directions, respectively. The surface termination and their respective atomic occupancies magnitudes of these lattice vectors are a = b = 9.375 Å and c = (Table 1). Additional numbers of layers were considered, 6.8870 Å and the angles are  =  = 90 and  = 120 (Elliot, taking into account the progressive reduction with depth in 1994). the atomic distortions relative to their ideal positions. Fig. 1 A total of 581 and 704 reflections were measured under dry shows the evolution of 2n and R factor with the number of and humid conditions, respectively, which reduced to 535 [dry, layers in the model. From the fifth layer, the 2n value does not 14 crystal truncation rods (CTRs) + reflectivity] and 620 improve appreciably. (humid, 16 CTRs + reflectivity) non-equivalent reflections, The space group of FAp0001 is P63/m. Both the z mirror respectively. The structure of the surface was determined plane (m) and the symmetry translation along the z direction, adopting the usual approach: theoretical SXRD data are i.e. z + 12 (P63 subgroup), were checked. However, the two generated for a potential structure and then the model space groups were dropped during the refinement because Acta Cryst. (2019). B75, 830–838 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) 831 research papers Table 2 Atomic coordinates of the FAp0001 surface slab formed by two and a half bulk cells. The columns on the left show the ideal positions of the surface atoms in the bulk, (x, y, z)bulk. After refining the experimental data sets with dry and humid surfaces with their respective models, the atomic shifts with respect to the ideal positions are given as (x, y, z)dry and (x, y, z)humid, respectively. The error bars assigned to each shift are given by the corresponding subscript index (Torrelles et al., 2004). Atomic positions and shifts are given in crystallographic coordinates with respect to the hexagonal cell defined by the lattice parameters (9.375 Å, 9.375 Å, 6.887 Å, 90 , 90 , 120 ). By adding or subtracting (according to the sign indicated in the table) the corresponding shifts to/from the ideal atomic positions, the position of the fitted atom in the unit cell is obtained. Dashes (–) denote that the atom does not exist in the model, and asterisks (*) denote that the corresponding coordinate was kept fixed during the refinement procedure due to symmetry restrictions (atoms placed on a ternary axis). Atomic coordinates marked with an asterisk also indicate that the corresponding atom was placed on a ternary axis. Cai-j denotes Ca atom j in a layer i. Pi-(a!e) denotes a P atom in a layer i. The additional labels a to e help to identify the four O atoms bonded tetrahedrally to each P atom: Oa-t (oxygen a, top), Oa-1 and Oa-2 are oxygens placed on the same z level as the P atom and Oa-b (oxygen a, bottom). Surface atomic coordinates Atom label xbulk ybulk zbulk xdry ydry zdry xhumid yhumid zhumid O* 0.2419 0.9929 3.5292 – – – 0.052 0.032 0.031 F 0.0000 0.0000 3.2500 * * 0.0306 * * 0.0306 Ca1 0.2419 0.9929 3.2500 0.0072 0.0062 0.0042 0.0022 0.0072 0.0182 P1-a 0.3985 0.3690 3.2500 0.0055 0.0115 0.0083 0.0043 0.0112 0.0354 Oa-t 0.3411 0.2571 3.4292 – – – 0.032 0.042 0.051 Oa-1 0.3269 0.4844 3.2500 0.0075 0.0185 0.0045 0.0046 0.0265 0.0264 Oa-2 0.5876 0.4655 3.2500 0.0115 0.0325 0.0254 0.0025 0.0274 0.0075 Oa-b 0.3411 0.2571 3.0708 0.0185 0.0164 0.0173 0.0305 0.0024 0.0264 Ca2-1 0.3333 0.6667 3.0011 * * 0.0273 * * 0.0143 Ca2-2 0.6667 0.3333 2.9989 * * 0.0033 * * 0.0193 F 0.0000 0.0000 2.750 * * 0.0057 * * 0.0256 Ca3 0.7581 0.0071 2.750 0.0112 0.0022 0.0092 0.2 0.0092 0.0102 P2-b 0.6016 0.6310 2.750 0.0093 0.0073 0.0073 0.0153 0.0023 0.0074 Ob-t 0.6589 0.7429 2.9292 0.0145 0.0085 0.0374 0.0066 0.0175 0.0154 Ob-1 0.6731 0.4844 2.7500 0.0135 0.0145 0.0034 0.0186 0.0375 0.0134 Ob-2 0.4124 0.5345 2.7500 0.0205 0.0155 0.0034 0.0135 0.0214 0.0285 Ob-b 0.6589 0.7429 2.5708 0.0135 0.0115 0.0283 0.0085 0.0064 0.0244 Ca4-1 0.6667 0.3333 2.5011 * * 0.0162 * * 0.0052 Ca4-2 0.3333 0.6667 2.4989 * * 0.0102 * * 0.0012 F 0.0000 0.0000 2.2500 * * 0.0067 * * 0.0277 Ca5 0.2419 0.9929 2.2500 0.0062 0.0012 0.0002 0.0042 0.0072 0.0062 P3-c 0.3985 0.3690 2.2500 0.0063 0.0012 0.0123 0.0163 0.0012 0.0173 Oc-t 0.3411 0.2571 2.4292 0.0145 0.0034 0.0203 0.0175 0.0394 0.0084 Oc-1 0.3269 0.4844 2.2500 0.0065 0.0135 0.0313 0.0055 0.0035 0.0334 Oc-2 0.5876 0.4655 2.2500 0.0165 0.0075 0.0005 0.0005 0.0014 0.0125 Oc-b 0.3411 0.2571 2.0708 0.0055 0.0075 0.0044 0.0206 0.0215 0.0004 Ca6-1 0.3333 0.6667 2.0011 * * 0.0103 * * 0.0033 Ca6-2 0.6667 0.3333 1.9989 * * 0.0083 * * 0.0063 F 0.0000 0.0000 1.7500 * * 0.0047 * * 0.0306 Ca7 0.7581 0.0071 1.7500 0.0033 0.0043 0.0081 0.0062 0.0062 0.0072 P4-d 0.6016 0.6310 1.7500 0.0043 0.0012 0.0033 0.0052 0.0012 0.0152 Od-t 0.6589 0.7429 1.9292 0.0025 0.0205 0.0174 0.0096 0.0035 0.0145 Od-1 0.6731 0.4844 1.7500 0.0035 0.0085 0.0124 0.0165 0.0374 0.0104 Od-2 0.4124 0.5345 1.7500 0.0095 0.0065 0.0034 0.0085 0.0084 0.0154 Od-b 0.6589 0.7429 1.5708 0.0145 0.0144 0.0033 0.0035 0.0054 0.0014 Ca8-1 0.6667 0.3333 1.5011 * * 0.0072 * * 0.0052 Ca8-2 0.3333 0.6667 1.4989 * * 0.0032 * * 0.0122 F 0.0000 0.0000 1.2500 * * 0.0086 * * 0.0276 Ca9 0.2419 0.9929 1.2500 0.0022 0.0032 0.0021 0.0062 0.0072 0.0052 P5-e 0.3985 0.3690 1.2500 0.0043 0.0012 0.0073 0.0052 0.0022 0.0042 Oe-t 0.3411 0.2571 1.4292 0.0144 0.0064 0.0153 0.0134 0.0194 0.0104 Oe-1 0.3269 0.4844 1.2500 0.0115 0.0035 0.0154 0.0055 0.0034 0.0054 Oe-2 0.5876 0.4655 1.2500 0.0114 0.0085 0.0064 0.0094 0.0034 0.0134 Oe-b 0.3411 0.2571 1.0708 0.0105 0.0094 0.0013 0.0145 0.0174 0.0094 Ca10-1 0.3333 0.6667 1.0011 * * 0.0002 * * 0.0062 Ca10-2 0.6667 0.3333 0.9989 * * 0.0062 * * 0.0012 O 0.6589 0.7429 0.9294 0.0024 0.0104 0.0093 0.0015 0.0054 0.0034 models constructed with P63/m and P63 symmetries could not meters to define (x, y) coordinates (rotation angles and atomic adequately adjust the experimental data: their 2n goodness-of- shifts) plus 27 z parameters, a scale factor and a roughness fit factors were twice that of our best 2n . For this reason, the factor (total = 65 parameters). Models considering the phos- P3 symmetry of the 2D space group was selected to construct phate groups as rigid bodies can reduce the number of para- the final models used to adjust the data. The extra symmetry meters by a factor of five (Torrelles et al., 2004). Considering operations of P63/m and P63 [i.e. mirror plane or (z + 12) the P3 symmetry only, the structure of the surface retains a translation] reduce by almost a factor of two the number of (x, three-fold axis on the surface that provides different rotation y, z) parameters with respect to the P3 symmetry: 36 para- values for atoms that are not located on the same level (the 832 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) Acta Cryst. (2019). B75, 830–838 research papers atoms related to the three-fold axis have identical z coordi- nates). With this symmetry a total of 107 structural parameters for the dry surface were used, i.e. 60 (x, y) parameters, 45 (z) parameters, a scale factor and a roughness parameter. The humid surface model has six (x, y, z) parameters more than the dry model, plus two occupancy factors to determine the position and surface coverage of the H2O and OH species present at the surface/interface. Although the number of parameters is large, we introduced bond-length restraints for [PO4] as a structurally invariant subunit with maximum tolerances up to 0.15 Å. These restraints allow us to compensate for the lower sensitivity of some O atoms of the model in phosphate groups located in layers 2-b, 3-a and 4-d with respect to the others bonded to the same group (the definition of these labels is given in Table 2). The use of bond- length restraints facilitates the convergence of the fit towards a real structure while maintaining the P—O bond distances within a physical range with a maximum–minimum bond tolerance of 10% (Watkin, 1994). Fig. 2 shows the two blocks of atoms forming the bulk unit cell. In previous work, the FAp–H2O interface has been probed by X-ray reflectivity (XRR) and CTR investigations (SXRD) with different sensitivities to the geometry of the surface structure (Pareek et al., 2007; Park et al., 2004). XRR measurements only yield a projection of the 2D structure onto 1D, with good information on layer distances but without information on the lateral structural periodicity. CTRs provide Figure 2 information on the mineral surface and on possible layers of The FAp0001 bulk unit cell, viewed (top) from the top and (bottom) adsorbates, provided these have the same lateral periodicity as laterally. The cell shows the two block layers forming the cell. The groups the mineral surface. XRR studies of the FAp–H2O interface of atoms belonging to each block are displayed separated by a plane. on a fully hydrated surface by Park et al. (2004) showed adsorption of two water layers at out-of-surface plane strated from a 3D analysis of the hydrated FAp100–water distances of 2.64 (9) and 4.17 (5) Å from the mineral surface. interface placed at distances from the relaxed surface of In our earlier SXRD study, specular and non-specular CTRs 1.6 (1) and 3.18 (10) Å (Pareek et al., 2008). These refined of the FAp(100) (FAp100)–H2O interface disclosed the surface models consider five surface blocks formed by ideal presence of one laterally ordered water layer in a humid F—Ca—[PO4] {block = F(1)—Ca(5)—[PO4](3); the numbers environment at an out-of-surface plane distance of 1.8 (1) Å in brackets indicate the number of elements of each type in a (Pareek et al., 2007), although specular X-ray reflectivity single block} as in the bulk. Each block contains two different showed the presence of two water layers when fully hydrated Ca layers at different heights, and each bulk unit cell contains (Park et al., 2004), giving a 1D representation of the surface two of these blocks. Hence, each unit cell contains four layers electronic density along the normal direction. In later work, with a spacing of one quarter of a unit cell (z = 0.25) the lateral ordering of these two water layers was demon- between them. See Fig. 2 for more details. 3. Results and discussion The starting model used to refine the data considers a surface slab with two and a half bulk unit cells. The initial positions of the atoms in the cell were the ideal bulk ones and the shifts from them follow P3 symmetry. The surface termination under dry conditions was deter- mined from a preliminary inspection of the evolution of 2n with each of the four possible termination layers (Table 1). The lowest values are obtained for F—Ca—[PO4] terminated Figure 1 The evolution of 2n and R factor with the number of layers considered in block layers, while those terminating in two Ca atoms show the model. higher 2 values. Acta Cryst. (2019). B75, 830–838 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) 833 research papers The best refined surface model includes five F—Ca—[PO4] unit cell, well localized along the surface normal at 2.23 (1) Å surface blocks (or ten atomic layers). Under dry conditions, above the topmost Ca layer. The red and blue curves in Fig. 3 the topmost layer is Ca—PO3 terminated where no O and/or (bottom) are obtained considering hydroxyl coverages of OH adsorption is observed to complete the typical octahedral 100% or 33%, respectively. The red curve considering full coordination of the Ca cation (presence of a phosphite PO3 coverage fits the experimental data slightly better. The anion). The influence of this O atom during the refinement is corresponding CTRs measured for this case only detect one also shown in Table 1 in terms of 2. water and one OH molecule per unit cell, thus with an atomic The surface resembles an ideal bulk termination with occupancy of 0.33. As each molecule can be bonded to only relaxations in the top surface layers. The surface roughness one of the three Ca and P atoms forming part of the surface, value obtained with ROD and using the approximate  model the model places one molecule of each specimen with an (Vlieg, 2000; Robinson, 1986, 1998 and references therein) was occupancy factor of 1/3 on top of them. To reconcile this small, implying that the FAp0001 surface is mostly flat ( = 0.04 apparent discrepancy between CTRs and reflectivity, we  0.01). The tilts of the [PO4] tetrahedron were fixed to the P3 performed an analysis of their corresponding temperature symmetry given by the model. In ideal (bulk terminated) factors (Debye–Waller or DW, B = 82hu2i). The model was FAp0001, the Ca polyhedron can be considered as a CaO5F then refined using both data sets and considering a similar octahedron, but, in addition, a seventh weak bond to O exists, anisotropic dependence of the DW for H2O and OH mol- redefining the polyhedron as CaO5F(O) (Hughes et al., 1989). ecules (in-plane and out-of-plane DW components Bpar and For the ideal truncated surface, this coordination reduces to Bperp, respectively). The refinement process yields (Bpar, Bperp) four or five. Under dry conditions, the reduction in coordi- values of (15  4 Å2, 1.2  0.1 Å2) when considering occu- nation causes a non-uniform charge distribution of the pancies of 1 for water and OH molecules. The value of B topmost Ca atoms, which introduces significant distortions in becomes isotropic (Biso = 1.5  0.1 Å2) when the occupancies the atoms of the upper surface layers, as has already been of the molecules are 1/3. This analysis indicates that the H2O observed in FAp100 (Pareek et al., 2007). and OH molecules are well defined along the z direction but The exposure of FAp0001 to an H2O saturated atmosphere they show positional in-plane disorder. results in a relaxed surface where the atoms are displaced The refinements of the structure for the dry and humid data inwards, i.e. along the z direction, perpendicular to the surface. sets are shown in Figs. 4 and 5, respectively. The figures show The surface in a humid atmosphere is covered with a partially the experimental and calculated structure factors for both occupied H2O layer (three water molecules placed on top of each of the Ca atoms with an occupancy of 33%). In addition, three OH groups also appear on top of the P atoms with an occupancy of 33% each, thus completing the P coordination. The weight of the water and hydroxyl molecules in this surface was also tested in terms of 2, as indicated in Table 1. Considering the symmetry of the apatite crystal structure and the morphology of naturally occurring apatites, the basal plane (100) is rarely developed, perhaps because of its compara- tively fast growth kinetics. In order to keep the charge balanced and maintain the symmetry, a perfect cation or phosphate termination is not favoured and surface roughness is required to avoid charge separation. On the other hand, macroscopic adsorption experiments indicate that an equiva- lent of two monolayers of water are strongly adsorbed on microcrystalline apatite (Posner, 1985). The low water concentration detected at the (0001) surface is assigned to positional disorder, which could be the origin of this apparent small H2O/OH adsorption. To ensure both (i) the possible loss or not of one O atom bonded to the topmost phosphate unit in the dry surface and (ii) the percentage of the surface water and hydroxyl coverages (100% or 33%) on the hydrated surface, we have analysed the reflectivity curves measured for both cases. Both dry (top) and humid (bottom) curves are shown in Fig. 3. The dry reflectivity curve agrees with the results obtained from the Figure 3 analysis of the corresponding CTRs, confirming that one O Reflectivity curves for the dry and humid cases. The curves have been refined together with the CTRs and a model considering two and a half atom bonded to the topmost phosphate unit is lost, thus bulk unit cells. The red and blue curves were obtained considering surface forming a phosphite ion. The humid reflectivity curve indi- hydroxyl coverages of 100% or 33%, respectively. See text for more cates the presence of three water and three OH molecules per details. 834 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) Acta Cryst. (2019). B75, 830–838 research papers cases using the full data sets formed by CTRs and reflectivity Table 3 curves. Fig. 5 shows two curves obtained using two different Average rotation angles for each of the PO4/PO3 tetrahedral/phosphite (dry case) units at the surface versus depth for dry and humid cases. models. Red curves consider water and hydroxyl molecules at the surface with occupancy 13 and Biso = 1.5 Å2. In the second The signs + and  indicate the anticlockwise or clockwise rotation direction, respectively. The labels indicate the positions of the phosphate groups in the model (blue dashed curves) the occupancy factor of each H2O/ cell according to Table 2. The asterisk denotes the presence of a PO3 ion as OH molecule is 1 with (Bpar, Bperp) values of (15 Å2, 1.2 Å2). obtained from the analysis. Error bars are obtained from a 2n analysis As can be observed, the fit is slightly worse for reflections with (Feidenhans’l, 1989). high (h, k) values as a consequence of the absence of mole- PO4 (PO4)1-a/(PO3)1-a (PO4)2-b (PO4)3-c (PO4)4-d (PO4)5-e cular disorder along the z direction, as detected from the Dry ( 0.8 ) (+) 1.1* (+) 1.1 () 1.3 () 1.8 () 0.3 analysis of the reflectivity measurements. From our best model Humid ( 0.8 ) (+) 1.4 () 1.1 () 1.7 () 0.8 () 0.5 (red curves), the Ca—H2O bond distances are about 2.28 (5) Å (Pareek et al., 2007; Wolthers et al., 2012; Kerisit et al., 2003) and the OH—P bond lengths are 1.65 (5) Å (Gamoke et al., 2009) thus completing the P coordination. The The atomic relaxations of the surface layers in Table 2 single P—OH bond is slightly longer than P O (1.5 Å). The decrease when the depth increases. In the first two blocks, ideal atomic positions in fractional coordinates and the atomic relaxation is dominated by the rotations of the phosphates displacements obtained after the refining process (using the around the c axis, as indicated in Table 3, which gives the P3 symmetry) of the FAp0001 surface structure under dry and rotation angles for each of the five [PO4] groups considered in humid conditions are shown in Table 2. Top and lateral views our surface model for dry and water-saturated atmospheres. of the refined models are represented in Figs. 6 and 7. The The average atomic shifts for the dry and water-saturated evolution of 2n and R-factor figures of merit with the number atmospheres relative to the ideal bulk positions are easily of layers considered in the model during the refinement recognizable from the phosphorus tetrahedral rotation from procedure (five F—Ca—[PO4] surface blocks) is shown in the top (1) to the inner (5) surface layers (Table 3). The Fig. 1. average evolution of the angles of the [PO4] units with depth shows that the water-saturated surface is less distorted than the dry one (Table 4). This behaviour is similar to that detected for FAp100 under dry and humid (RH ’ 75%) Figure 4 A comparison between experimental (black symbols with error bars) and calculated (red continuous lines) structure factors for FAp0001 under dry Figure 5 conditions. A standard deviation error of 13% was estimated from A comparison between experimental (black symbols with error bars) and averaging between equivalent reflections. This value was also similar to calculated (red continuous lines) data for the humid FAp0001 surface using that obtained for the humid case. the water/humid model described in the main text. Acta Cryst. (2019). B75, 830–838 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) 835 research papers Table 4 the humid surface shows a smoother evolution towards the Evolution of the average bond angles ( ) and bond lengths (Å) for the bulk structure than that of the dry surface, as expected. three topmost surface phosphate units obtained from the atomic coordinates given in Table 2. A summary of these distortions is presented in Table 4, which shows the evolution of the average bond angle and The phosphate unit of the topmost surface layer (PO3)1-a of the dry surface is formed by three P—O bonds (marked with an asterisk). The angle is close to bond length with depth for the three topmost surface tetra- that expected for the phosphite ion, PO33 (120 ). For the humid case, the hedral [PO4] units. As observed, the average angles of the hydroxyl molecule has been considered to compute the average bond angle distorted tetrahedra are close to the bulk ones, except for the and bond length. The average bond angles and bond lengths of the bulk phosphate PO4 unit are 109.5 and 1.50 Å, respectively. Bond-angle and bond- topmost surface layer of the dry case, where the distortion is length errors were calculated from Carpenter (1979). rather large due to the absence of one P—O bond leading to a PO4 (PO4)1-a/(PO3)1-a (PO4)2-b (PO4)3-c [PO3] unit, with an average O—P—O angle of 112 (Table 4). On the humid surface, this situation is overcome by the partial Dry; angle, length 112.2, 1.48* 109.1, 1.46 109.1, 1.52 adsorption of one hydroxyl molecule that stabilizes the charge ( 0.5 ,  0.08 Å) Humid; angle, length 109.5, 1.50 109.1, 1.60 108.7, 1.46 distribution in the phosphate unit and reduces its distortion. ( 0.5 :  0.08 Å) The maximum/minimum bond-angle distortions for both cases are 123 and 94 (dry), and 121 and 100 (humid), which correspond to the topmost surface PO units. conditions (Pareek et al., 2007, 2008, 2009). From the analysis Earlier X-ray diffraction studies of the FAp100–H2O inter- of the data it looks as if the distortion of the top [PO4] is face on a fully hydrated surface show up to two layers of water relaxed as a function of surface depth to take up an almost molecules with (Park et al., 2004) and without (Pareek et al., regular tetrahedral shape again. Moreover, the dry surface 2007, 2008, 2009) lateral order. A direct comparison between shows oxygen-unsaturated phosphate units. The outermost the structural results obtained from these experiments and the surface P—O oxygen is lost, as determined from the structure results obtained in the present study cannot be made due to refinement. The resulting [PO3]3 ion unit (phosphite ion) the different structural surface terminations: orthorhombic for shows average O—P—O bond angles close to 120 , as would FAp100 and hexagonal for FAp0001. In our work, we obtain a be expected for this entity. The phosphite ion becomes a hexagonal dry surface free of O atoms on the topmost surface regular tetrahedron under a humid environment by partial layer. The topmost [PO4] tetrahedron is in fact a [PO3] unit adsorption of hydroxyl groups (one third of an OH group per where the apical O atom is missing. Average O—P—O bond PO3 unit = 33%). The experimental P—OH bond length is angles indicate that this [PO3] unit could be similar to the 1.65 Å, compatible with a value reported elsewhere (Gamoke phosphite ion which has an average bond angle of 112 . et al., 2009). Moreover, the hydrated surface does not show a fully ordered The atomic displacements reduce strongly for layers (4) and layer of H2O or OH molecules on top of Ca and P, respectively, (5) in the same proportion as the rotation angles indicated in but rather partial occupancies. The adsorbed molecules show a Table 3. The evolution of [PO4] rotation angles with depth on rather large thermal vibration amplitude, as discussed Figure 6 Figure 7 The surface structure of dry FAp0001. (Left) Ball-and-stick representa- The surface structure of humid FAp0001. (Left) Ball-and-stick representa- tions of (top) top and (bottom) lateral views. (Right) The same views in a tions of (top) top and (bottom) lateral views. (Right) The same views in a polyhedral representation. Colours: P atoms are green, F violet, Ca blue polyhedral representation. Colours: P atoms are green, F violet, Ca blue, and O red. O red, H2O dark blue and OH light blue. 836 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) Acta Cryst. (2019). B75, 830–838 research papers previously, whose impact on the data is the attenuation of the from the topmost surface layer with a small DW value (Bperp = intensity profiles of the CTRs when their atomic weight 1.2 Å2). CTRs show similar positions for both molecules but increases. This intensity attenuation smoothes the profile of with lower occupancies that we interpret as in-plane positional the CTRs, reducing the amplitude of the oscillations or disorder. This positional disorder is compatible with a high features coming from the overlay. Since the atomic weight of molecular in-plane DW value (Bpar = 15 Å2) or a reduction of H2O/OH molecules is coupled with their corresponding DW their respective occupancy weight by a factor of three. values, the quantification of the water surface layer is difficult, In wet conditions the reaction of the hydroxyl OH ion with which is equivalent to supposing a disordered presence of the the phosphite [PO3] ion produces a phosphate [PO4] ion topmost water or hydroxyl molecules around the Ca and P termination. The sensitivity of the data to other water mole- specimens. cules adsorbed on the wet surface, i.e. a second layer of water In this case, the distance of the H2O monolayer from the molecules, would be smaller than those already adsorbed on relaxed surface is 2.23 Å, which is larger than that obtained by the topmost surface layer as a consequence of the high Pareek et al. (2007) (1.8 Å) but much shorter than that disorder already existing in this layer. obtained by Park et al. (2004) (2.64 Å) from reflectivity data. The significant difference between the structures of the The presence of a second H2O layer was not detected, prob- FAp100 and FAp0001 surfaces is the explicit presence of dis- ably due to the presence of large areas of the surface where ordered adsorbed water and hydroxyl molecules on the the molecules are mainly disordered. The effective ratio of outermost {0001} surface layer compared with the {1010} disordered H2O:OH molecules per unit cell is 1:1. Comparing surface of mineral specimens from the same locality. Also, the the differential heats of adsorption of water for FAp/ (0001) surface is very rare, whereas the (1010) prism face is a HAp(0001) and pristine (010) surfaces they are very similar common feature of the apatite morphology. The ratio of (Posner, 1985; Corno et al., 2009). For both surfaces, the heat surface area reflects the growth rate and is also related to the of vaporization for water (close to 10 kcal mol1; 1 kcal mol1 surface energy. Based on our results, the (0001) face with its = 4.184 kJ mol1) is reached when two water molecules per incomplete hydration obviously favours further growth. In unit cell are adsorbed. For our experimental FAp(0001) case, addition, fast growth of the {0001} face of apatite leads to a we only detect a 33% water occupancy per Ca atom at the pronounced development of the pyramidal faces {1011}. surface (and 13 OH molecule per [PO3] unit at the surface). Our results are also in agreement with the observation that Most likely, the apparent deficiency of water molecules bone apatite fibres grow preferentially along [0001] while the reflected by the CTR data set on our FAp(0001) surface is due {1010} faces are inhibited, because the perfect surface interacts to positional disorder. The FAp(100) cell definition (Pareek et with collagen or non-collagenous protein inhibiting further al., 2007), identical to the pristine (010) surface (Corno et al., growth, giving a means of controlling the size and morphology 2009), also shows two ordered water molecule layers at the of apatite nanocrystals in bone (Xie & Nancollas, 2010). In an surface, suggesting a value of heat of vaporization for water experimental study of glycine/H2O at face (1010) using similar to those of pristine (010) and FAp/HAp(0001) surfaces. grazing-incidence XRD structure analysis, charge matching of the amino acid with the Ca and phosphate ions has been shown to form a periodically ordered layer shielding the 4. Conclusions surface from the nutrient solution (Pareek et al., 2009). The surface/interface structure of FAp0001 under dry (He Obviously, the molecular disorder of light molecules such as environment) and humid (RH ’ 100%) conditions has been H2O and OH detected on the (0001)-surface is higher than probed with SXRD. The surface model built to simulate the that induced on the (1010) surface by heavier organic mole- dry and water exposed surfaces is formed by a slab of five cules. This lower ordering could be consequence of their blocks with the chemical formula Ca5(PO4)3F that forms a higher surface mobility under flowing vapor conditions as layered structure along the surface normal direction with a experimentally detected in the form of an anomalous increase length of 2.5 times the c-axis value for Fap(0001). Under dry of their in-plane Debye Waller. conditions, our findings indicate that the surface resembles an ideal bulk termination with relaxations in the top surface Acknowledgements layers. This surface is compatible with a [PO3] phosphite ion XMaS is a UK National Facility supported by the EPSRC. We termination where the P atom is neutral (one orbital is occu- are grateful to all the beamline team staff for their support. pied by two electrons and each of the other three is bonded to one O atom that is negatively charged). When the surface is exposed to wet conditions, the analysis of reflections with h or Funding information k values differing from zero shows Ca and P atoms bonded to Funding for the XMaS facility has been generously provided a partially occupied water or hydroxyl OH layer (33%), by the UK Engineering and Physical Sciences Council and respectively. Analysis of the reflectivity data for the humid latterly through UKRI. This work was supported by the case shows a surface fully covered with water and hydroxyl Engineering and Physical Sciences Research Council [grant molecules: three bonded to the Ca atoms (2.28 Å) and the numbers: NS/A000018/1 & EP/S020845/1], the European other three to the P atoms (1.65 Å), respectively. Reflectivity Union Fund for Regional Development POCTEFA through data show that the molecules are placed at well defined heights Project EFA194/16/TNSI, and by the Spanish Ministry of Acta Cryst. (2019). B75, 830–838 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) 837 research papers Education and Science (MEC) through a Severo Ochoa grant Lübke, A., Enax, J., Loza, K., Prymak, O., Gaengler, P., Fabritius, (No. SEV-2015-0496). H.-O., Raabe, D. & Epple, M. (2015). RSC Adv. 5, 61612– 61622. Lübke, A., Loza, K., Patnaik, R., Enax, J., Raabe, D., Prymak, O., Fabritius, H.-O., Gaengler, P. & Epple, M. (2017). RSC Adv. 7, 6215–6222. References Pareek, A., Torrelles, X., Angermund, K., Rius, J., Magdans, U. & Gies, H. (2008). Langmuir, 24, 2459–2464. Ben-Nissan, B. (2014). Editor. Advances in Calcium Phosphate Pareek, A., Torrelles, X., Angermund, K., Rius, J., Magdans, U. & Biomaterials. Heidelberg: Springer. Gies, H. (2009). Langmuir, 25, 1453–1458. Bragg, L., Claringbull, G. F. & Taylor, W. H. (1965). The Crystalline Pareek, A., Torrelles, X., Rius, J., Magdans, U. & Gies, H. (2007). State, Vol. IV, Crystal Structures of Minerals. Cornell University Phys. Rev. B, 75, 035418. Press. Park, C., Fenter, P., Zhang, Z., Cheng, L. & Sturchio, N. C. (2004). Calderı́n, L., Stott, M. J. & Rubio, A. (2003). Phys. Rev. B, 67, 134106. Am. Mineral. 89, 1647–1654. Carpenter, G. B. (1979). Acta Cryst. A35, 248–250. Posner, A. S. (1985). J. Biomed. Mater. Res. 19, 241–250. Combes, C., Cazalbou, S. & Rey, C. (2016). Minerals, 6, 34. Renzi, M. de, Manzanares, E., Marin-Monfort, M. D. & Botella, H. Corno, M., Busco, C., Bolis, V., Tosoni, S. & Ugliengo, P. (2009). (2016). RSC Adv. 6, 74384–74388. Langmuir, 25, 2188–2198. Robinson, I. K. (1986). Phys. Rev. B, 33, 3830–3836. Elliot, J. C. (1994). Structure and Chemistry of the Apatites and Other Robinson, I. K. (1998). Acta Cryst. A54, 772–778. Calcium Orthophosphates. Amsterdam: Elsevier Science. Ruttenberg, K. C. & Berner, R. A. (1993). Geochim. Cosmochim. Feidenhans’l, R. (1989). Surf. Sci. Rep. 10, 105–188. Acta, 57, 991–1007. Gamoke, B., Neff, D. & Simons, J. (2009). J. Phys. Chem. A, 113, Stout, G. H. & Jensen, L. H. (1968). X-ray Structure Determination. 5677–5684. New York: McMillan. Hahn, Th. (1996). Editor. International Tables for Crystallography, Torrelles, X., Barrena, E., Munuera, C., Rius, J., Ferrer, S. & Ocal, C. Vol. A, Space-group symmetry, 4th ed. Dordrecht: Kluwer. (2004). Langmuir, 20, 9396–9402. Haldar, S. K. & Tišljar, J. (2014). Introduction to Mineralogy and Vlieg, E. (2000). J. Appl. Cryst. 33, 401–405. Petrology, ch. 2, Basic Mineralogy. Amsterdam: Elsevier. Watkin, D. (1994). Acta Cryst. A50, 411–437. Hughes, J. M., Cameron, M. & Crowley, K. D. (1989). Am. Mineral. Wolthers, M., Di Tommaso, D., Du, Z. & de Leeuw, N. H. (2012). 74, 870–876. Phys. Chem. Chem. Phys. 14, 15145–15157. Kerisit, S., Parker, S. C. & Harding, H. C. (2003). J. Phys. Chem. B, Xie, B. & Nancollas, G. H. (2010). Proc. Natl Acad. Sci. USA, 107, 107, 7676–7682. 22369–22370. 838 Xavier Torrelles et al.  Pristine and hydrated fluoroapatite (0001) Acta Cryst. (2019). B75, 830–838